service design - transtutors...cal utilities for customers. a cleaning service saves the customer...

IN ADDITION TO MAKING AND SELLINGCHOCOLATE products, Hershey’s has several

special retail outlets and theme parks that reinforce

the Hershey’s brand and create shared experiences for

Hershey’s customers. No visit to Times Square in New York City is

complete without a visit to Hershey’s with its 215-feet tall, 60-feet wide

storefront, the largest permanent fixture ever constructed in Times Square.

The store offers interactive activities as well as a wide selection of products

and personalized candies. Hershey’s Chicago provides a factory worker’s view

of chocolate making and sponsors field trips, birthday bashes, and scouting

events. Hershey’s Niagara Falls offers their own rendition of a chocolate

waterfall, and Hershey’s Shanghai surrounds the customer with the sights and

smells of every conceivable chocolate product.

These special stores display Hershey’s products and accessories and create

an atmosphere of fun and excitement. The theme park located in Hershey,

Pennsylvania, is a place for family fun, rides, costumed characters, shows,

concerts, a simulated factory tour, a chocolate spa, culinary events and, of

course, Hershey’s products. For the holiday season, special events include

Candylane, Holiday Sweet Lights, and the Holiday Cottage Traditional events.

Service Design

Chapter

5In this chapter, you will learn about . . .

The Service Economy

Characteristics of Services

The Service Design Process

Tools for Service Design

Waiting Line Analysis for ServiceImprovement

Web resources for

this chapter include

OM Tools Software

Internet Exercises

Online Practice Quizzes

Lecture Slides in

PowerPoint

Virtual Tours

Excel Exhibits

Company and Resource

Weblinks

Service Design AT HERSHEY’S

www.wiley.com/college/russell

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Copyright © 2011 John Wiley & Sons

190 Part 1 • Operations Management

Services are the predominant force in our society. In the United States, services account for 80%of the labor force, 94% of job growth, and 81% of GDP. Globally, services account for over 50%of the economics of Brazil, Russia, Japan, Germany, India, and China. The impact of supportingservices on product success has turned product-producing companies into service providers.Increased outsourcing of business services demands more in-depth understanding of the serviceproduct and standards for quality. Service computing has prompted a new level of understandingof customer requirements and design theory. Major societal problems, such as education, healthcare, disaster relief, and government services, depend on complex customer-focused processesand benefit significantly from an innovative and interdisciplinary approach to their study andanalysis. This unprecedented shift in customer, corporate, and societal demand for services and themanagement of corresponding resources has created a critical need for the study, analysis, anddesign of service systems.

The rise of the service sector is not just U.S. phenomenon, as shown in Figure 5.1. Services repre-sent the fastest growing sector of the global economy and account for two-thirds of global output,one-third of global employment, and nearly 20% of global trade.

Examining the latest U.S. figures on percent of employment by industry sector, we find thatmanufacturing accounts for a smaller percentage of employment than either education and health,professional services, government, or wholesale and retail trade. The United States has a positivebalance of trade in services, and a deficit in manufactured goods.

Figure 5.2 shows U.S. figures on percent of GDP by industry sector. Again, services account forthe largest percent, over 80%.

Clearly, the effective design and efficient operation of services are paramount to the health ofthe economy. In this chapter, we discuss the characteristics of services, the service design process,tools for service design, and waiting line theory for service improvement.

Careful design of these venues and activities helps to build the Hershey’s brand,

reward customers, and solidify Hershey values.

In this chapter, we’ll learn about the principles of service design and the

importance of a well-designed customer experience.

THE SERVICE ECONOMY

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US

UK

Sing

apor

e

Aus

tral

ia

Fran

ce

Ger

man

y

Japa

n

Kor

ea

Indi

a

Taiw

an

Mal

aysi

a

Chi

na

Phili

ppin

es

Indo

nesi

a

Thai

land

ServicesManufacturingAgriculture

100908070605040Pe

rcen

t

3020100

Figure 5.1

InternationalEmployment byIndustry Sector

Source: International Labour

Organization Yearbook of Labour

Statistics 2008, retrieved from

http://www.ilo.org

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Services are acts, deeds, performances or relationships that produce time, place, form or psychologi-cal utilities for customers. A cleaning service saves the customer time from doing the chores him-self. Department stores and grocery stores provide many commodities for sale in one convenientplace. An online broker puts together information in a form more usable for the investor. A nightout at a restaurant or movie provides psychological refreshment in the middle of a busy workweek.

Services can also be defined in contrast to goods. A good is a tangible object that can be createdand sold or used later. A service is intangible and perishable. It is created and consumed simultane-ously. Although these definitions may seem straightforward, the distinction between goods and ser-vices is not always clear-cut. For example, when we purchase a car, are we purchasing a good or theservice of transportation? A flat-screen TV is a manufactured good, but what use is it without the ser-vice of television broadcasting? When we go to a fast-food restaurant, are we buying the service ofhaving our food prepared for us, or are we buying goods that happen to be ready-to-eat food items?

In reality, almost all purchases of goods are accompanied by facilitating services, and almostevery service purchase is accompanied by facilitating goods. Thus, the key to understanding thedifference between goods and services lies in the realization that these items are not completelydistinct but rather are two poles on a continuum, as shown in Figure 5.3.

Chapter 5 • Service Design 191

81%

4%14%

1%

Manufacturing

Agriculture

Services

Other

Figure 5.2

Percent of GDP byIndustry Sectorfor United States

Source: Donald D. Kim, Brian M.

Lindberg, and Justin M. Monaldo,

“Advanced Statistics on GDP by

Industry for 2008,” Survey of

Current Business, U.S. Bureau of

Economic Analysis, 90(1), January

2010, retrieved from

http://www.bea.gov.

CHARACTERISTICS OF SERVICES

Services:

acts, deeds, or performances.

Goods:

tangible objects.

Automobile purchase

Auto repair

Restaurant meal

Hospital

Massage

Tax preparation

Lawn cutting

100% 75% 50% 25% 0 25% 50% 75% 100%

Rental car

Take-out food

Cell phone

Goods ServicesFigure 5.3

A Continuum fromGoods to Services

Source: Adapted from Earl W.

Sasser, R. P. Olsen, and D. Daryl

Wyckoff, Management of Service

Operations (Boston: Allyn Bacon,

1978), p. 11.

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Understanding the different characteristics of services can help us better design service activi-ties and the systems for their delivery.

Services can be distinguished from manufacturing by the following eight characteristics.Although not all services possess each of these characteristics, they do exhibit at least some ofthem to some degree.

1. Services are intangible. It is difficult to design something you cannot see, touch, store on ashelf, or try on for size. Services are experienced, and that experience may be different foreach individual customer. Designing a service involves describing what the customer is sup-posed to “experience,” which can be a difficult task. Designers begin by compiling informa-tion on the way people think, feel, and behave (called psychographics).

Because of its intangibility, consumers perceive a service to be more risky to purchasethan a product. Cues (such as physical surroundings, server’s demeanor, and service guaran-tees) need to be included in service design to help form or reinforce accurate perceptions ofthe service experience and reduce the consumer’s risk.

The quality of a service experience depends largely on the customer’s service expectations.Expectations can differ according to a customer’s knowledge, experience, and self-confidence.

Customers also have different expectations of different types of service providers. Youprobably expect more from a department store than from a discount store, or from a cardealer’s service center than from an independent repair shop. Understanding the customer andhis or her expectations is essential in designing good service.

2. Service output is variable. This is true because of the various service providers employed andthe variety of customers they serve, each with his or her own special needs. Even though cus-tomer demands vary, the service experience is expected to remain consistent. According to arecent survey, the most important measures of service quality to the customer are reliabilityand consistency. Service design, then, must strive for predictability or robustness. Examplesof services known for their consistency include McDonald’s, Holiday Inn, and ServiceMaster.Extensive employee training, set operating procedures, and standardized materials, equip-ment, and physical environments are used by these companies to increase consistency.

3. Services have higher customer contact. The service “encounter” between service providerand customer is the service in many cases. Making sure the encounter is a positive one is partof service design. This involves giving the service provider the skills and authority necessaryto complete a customer transaction successfully. Studies show a direct link between serviceprovider motivation and customer satisfaction. Moreover, service providers are not motivatedprimarily by compensation but rather by concurrence with the firm’s “service concept” andbeing able to perform their job competently.

High customer contact can interfere with the efficiency of a service and make it difficult tocontrol its quality (i.e., there is no opportunity for testing and rework). However, direct contactwith customers can also be an advantage for services. Observing customers experiencing a ser-vice generates new service ideas and facilitates feedback for improvements to existing services.

4. Services are perishable. Because services can’t be inventoried, the timing and location of delivery are important. Service design should define not only what is to be delivered but also where and when.

5. The service and the service delivery are inseparable. That means service design and processdesign must occur concurrently. (This is one area in which services have an advantage overmanufacturing—it has taken manufacturing a number of years to realize the benefits of con-current design.) In addition to deciding what, where, and when, service design also specifieshow the service should be provided. “How” decisions include the degree of customer partici-pation in the service process, which tasks should be done in the presence of the customer(called front-room activities) and which should be done out of the customer’s sight (back-room activities), the role and authority of the service provider in delivering the service, andthe balance of “touch” versus “tech” (i.e., how automated the service should be).

6. Services tend to be decentralized and geographically dispersed. Many service employees areon their own to make decisions. Although this can present problems, careful service designwill help employees deal successfully with contingencies. Multiple service outlets can be aplus in terms of rapid prototyping. New ideas can be field-tested with a minimum disturbanceto operations. McDonald’s considers each of its outlets a “laboratory” for new ideas.

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7. Services are consumed more often than products, so there are more opportunities to succeedor fail with the customer. Jan Carlzon, former president of SAS Airlines, calls these opportu-nities “moments of truth.” Services are confronted with thousands of moments of truth eachday. Careful design and redesign of the service encounter can help make each moment oftruth a positive experience. In a sense, the service environment lends itself more readily tocontinuous improvement than does the manufacturing environment.

8. Services can be easily emulated. Competitors can copy new or improved services quickly.New ideas are constantly needed to stay ahead of the competition. As a result, new service introductions and service improvements occur even more rapidly than new product introductions.


A L O N G T H E S U P P L Y C H A I N

Redbox Brings Self-Service to Movie Rentals

When is movie rental by mail less convenient? . . . when a redbox capitalizes on impulse rentals, low cost, and self-serviceat your local grocery store.

The now familiar Redbox kiosk appearing in supermar-kets throughout the United States was the brainchild ofMcDonald’s, who sought to bring fast-food prices and con-venience to the movie rental market. Today, Redbox operatesmore than 25,000 kiosks in supermarkets, drug stores, andbig box stores throughout the United States. Each kioskholds 700 to 800 DVDs and more than 200 movie titles.Customers rent a DVD from the machine for $1 a day usingtheir credit or debit cards, which can be charged an addi-tional day’s rental if the DVD is not returned within a 24-hourperiod. The kiosk resembles a retro London phone booth andallows customers to search movies by title, actor, genre, pop-ularity, and more. Customers can rent and return DVDs toany kiosk. A typical kiosk rents 140 DVDs per day and earnsmore than $50,000 annually in revenue.

McDonald’s eventually sold the company to Coinstar, acoin counting vending machine company that already had apresence and close relationship with the supermarket Industry.The location of the kiosks in grocery stores proved key to theservice concept, as the regular flow of traffic and subsequentreturn home encouraged rentals. Reliable and easy-to-usekiosks were also essential to its success. For those, Redboxcontracted with Flextronics, an electronics manufacturing

service (EMS) provider, with expertise in lean manufacturing,Six Sigma, and quick turnarounds. Flextronics expanded thecapacity of the original kiosks by 400%, reduced materialcosts by 25%, increased reliability to 99.75%, and introduced

THE SERVICE DESIGN PROCESS

Services that are allowed to just happen rarely meet customer needs. World-class services thatcome to mind—McDonald’s, Nordstrom, Federal Express, Disney World—are all characterizedby impeccable design. McDonald’s plans every action of its employees (including 49 steps tomaking perfect french fries); Nordstrom creates a pleasurable shopping environment with well-stocked shelves, live music, fresh flowers in the dressing rooms, and legendary salespersons; Fed-eral Express designs every stage of the delivery process for efficiency and speed; and DisneyWorld in Japan was so well designed that it impressed even the zero-defect Japanese.

Christopher Sadowski/Splash News/NewsCom

(continued)

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Service design is more comprehensive and occurs more often than product design. Theinherent variability of service processes requires that the service system be carefully designed.Figure 5.4 shows the service design process beginning with a service concept and ending withservice delivery.

The service concept defines the target customer and the desired customer experience. It also de-fines how our service is different from others and how it will compete in the marketplace. Some-times services are successful because their service concept fills a previously unoccupied niche ordiffers from the generally accepted mode of operation. For example, Citibank offers 15-minutemortgage approvals through online computer networks with real estate offices, credit bureaus, andbuilder’s offices, and an expert system loan-application advisor. Amazon excels at customer

a quick-load module for adding up to 75 new DVDs to stock.In addition, Flextronics created designs for both indoor andoutdoor kiosks, and integrated the hardware with server-sidesoftware to manage inventory from a central location. Re-markably, this was accomplished within an eighth-week timeperiod.

Forty percent of Redbox’s DVD rentals come from threemajor studios, Warner Brothers, Universal Studios, and 20thCentury Fox. It is this portion of the supply chain that givesRedbox headaches. Unhappy that new releases were offerednew for just $1, these studios put an embargo on Redbox for30 days after release, effectively blacklisting the company forrefusing to rent new releases at a premium price. Redbox cir-cumvented the studios by simply purchasing the new releases

at Walmart, creating their own box art, and adding them tostock on the day of release. Litigation is ongoing. New ser-vice design that challenges the status quo can be rocky.

What do you see as the future of movie rentals, given on-demand cable access, video streaming on the Web, andother new technologies? How does a company prepare itselfto adapt to these new environments?

Source: Adapted from Dawn Chmielewski, “Redbox’s $1 Vending-Machine Video Rentals Worry Studios,” Los Angeles Times,March 30, 2009; and “Flextronics and Redbox in Successful Partner-ship to Build DVD Rental Kiosks,” retrieved 01/02/2010 fromhttp://www.flextronics.com/webdocuments/redbox.pdf

Service Concept

Service Package

Performance Specifications

Design Specifications

Delivery Specifications

ServiceDelivery

Targetcustomer

Desiredserviceexperience

Physical items

Sensualbenefits

Psychological benefits

Customerexpectations

Customerrequirements

Activities FacilitiesProvider skills

Cost and time estimates

Schedule Deliverables Location

CustomerServiceProvider

Figure 5.4

The ServiceDesign Process

Service concept:

the purpose of a service; it defines

the target market and the customer

experience.

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service for online orders, and eBay’s worldwide reach creates more lively auctions with a hugecommunity of buyers and sellers. Shouldice Hospital performs only inguinal hernia operations,for which its doctors are very experienced and its facilities carefully designed. Local anesthesia isused; patients walk into and out of the operating room under their own power; and telephones,televisions, and dining facilities are located in a communal area some distance from patientrooms. As a result, patients quickly become ambulatory, are discharged within hours (compared tonormal week-long stays), and pay one-third less for their operations.

From the service concept, a service package is created to meet customer needs. The packageconsists of a mixture of physical items, sensual benefits, and psychological benefits. For a restau-rant the physical items consist of the facility, food, drinks, tableware, napkins, and other touchablecommodities. The sensual benefits include the taste and aroma of the food and the sights andsounds of the people. Psychological benefits are rest and relaxation, comfort, status, and a senseof well-being.

Effective service design recognizes and defines all the components of a service package. Find-ing the appropriate mix of physical items and sensual and psychological benefits and designingthem to be consistent with each other and the service concept is also important. A fast-foodrestaurant promises nourishment with speed. The customer is served quickly and is expected toconsume the food quickly. Thus, the tables, chairs, and booths are not designed to be comfortable,nor does their arrangement encourage lengthy or personal conversations. The service package isconsistent. This is not the case for an upscale restaurant located in a renovated train station. Thefood is excellent, but it is difficult to enjoy a full-course meal sitting on wooden benches in adrafty facility, where conversations echo and tables shake when the trains pass by. In the hospital-ity industry, Marriott Corporation is known for its careful design of specialty hotels. From itsCourtyard Marriott to Fairfield Inn to residential centers, each facility “fits” its clientele with awell-researched service package.

From the service package, service specifications are developed for performance, design, anddelivery. Performance specifications outline expectations and requirements for general and specificcustomers. Performance specifications are converted into design specifications and, finally, deliv-ery specifications (in lieu of manufacturing specifications).

Design specifications must describe the service in sufficient detail for the desired service experi-ence to be replicated for different individuals at numerous locations. The specifications typicallyconsist of activities to be performed, skill requirements and guidelines for service providers, andcost and time estimates. Facility size, location, and layout, as well as equipment needs, are alsoincluded. Delivery specifications outline the steps required in the work process, including the workschedule, deliverables, and the locations at which the work is to be performed.

THE SERVICE-PROCESS MATRIXNotice in Figure 5.4 that both customers and service providers may be involved in determiningperformance, design, and delivery specifications. Service processes can be classified according tothe degree of customization (involvement of the customer in service design and the delivery) andlabor intensity (involvement of the service provider in service design and delivery).

Figure 5.5 shows a service-process matrix based on these two service characteristics. Aprofessional service, such as accountant, lawyer, or doctor, is highly customized and verylabor intensive. A service shop, such as schools and hospitals, is less customized and labor in-tensive but still attentive to individual customers. A mass service, such as retailing and bank-ing, offers the same basic services to all customers and allows less interaction with the serviceprovider. Services with the least degree of customization and labor intensity, such as airlinesand trucking, are most like manufactured products and are thus best processed by a servicefactory.

The degree of contact between the customer and service provider has an impact on how indi-vidual services are designed and delivered. A large lecture class is taught differently than a senior-level seminar class. Charter airline flights entail more customer and provider participation than acommercial flight. Commissioning a work of art or custom building a home can involve thecustomer throughout the design and delivery process. Table 5.1 describes the design decisionsinvolved in high-contact versus low-contact services. Think about how these decisions affect theoperations and supply chain system.


Service package:

the mixture of physical items,

sensual benefits, and

psychological benefits.

Performance specifications:

outline expectations and

requirements.

Design specifications:

describe the service in enough

detail to be replicated.

Delivery specifications:

specify schedules, deliverables,

location.

• Virtual Tour

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Figure 5.5

The Service-Process Matrix

Source: Adapted from Roger

Schmenner, “How Can Service

Businesses Survive and Prosper?”

Sloan Management Review

27(3);29.

Table 5.1

Differences inDesign for High-Contact Services

Design Decision High-Contact Service Low-Contact Service

Facility location Convenient to customer Near labor or transportation

source

Facility layout Must look presentable, accommodate customer Designed for efficiency

needs, and facilitate interaction with customer

Quality control More variable since customer is involved Measured against established

in process; customer expectations and standards; testing and rework

perceptions of quality may differ, customer possible to correct defects

present when defects occur

Capacity Excess capacity required to handle peaks in Planned for average demand

demand

Worker skills Must be able to interact well with customers Technical skills

and use judgment in decision making

Scheduling Must accommodate customer schedule Customer concerned only with

completion date

Service process Mostly front-room activities; service may Mostly back-room activities;

change during delivery in response to customer planned and executed with

minimal interference

Service package Varies with customer; includes environment as Fixed, less extensive

well as actual service

Source: Adapted from R. Chase, N. Aquilano, and R. Jacobs, Operations Management for Compensative Advantage (New York:

McGraw-Hill, 2001), p. 210.

There are many different tools for designing services. Quality function deployment (QFD), dis-cussed in the previous chapter, has wide application in services. Other common tools are serviceblueprints, scripting, servicescapes, and waiting line analysis.

TOOLS FOR SERVICE DESIGN

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Alamy

John Coletti/Index Stock

Gary Conner/PhotoEdit

SuperStock, Inc.

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SERVICE BLUEPRINTINGService operations involve several different players (the customer, other customers in the sys-tem, the primary service provider, other service providers), both front and back room opera-tions, and different opportunities for interaction among the players during the service process.Service blueprinting is the process of recording in graphical form the activities and interactions ina service process. The term blueprinting is used to reinforce the idea that services need to be ascarefully designed as a physical product and documented with a blueprint of its own. Figure 5.6shows a service blueprint for an installment loan process. Notice the line visibility behindwhich “back office” operations are performed. Potential failure points and times estimatesare also included.

Figure 5.7 shows an expanded service blueprint of a coffee shop operation. Several more lineshave been added to the diagram. The line of influence shows activities designed to influence thecustomer to enter the service facility. The line of interaction is where the customer interacts withthe service provider and other customers. The line of visibility separates front office (or onstage)activities from back office (or backstage) activities. In this example, the barista prepares the coffeein front of the customer, but must go backstage to retrieve cups from the stockroom. The line ofsupport is where the service provider interacts with backstage support personnel to complete theirtasks. Moving these various lines on the service blueprint allows the designer to experiment withexpanding or decreasing the activities in each area. For example, the barista could disappear be-hind a curtain to prepare the coffee, or the customer could serve the coffee herself and interactwith the service provider only when paying.

F

Service blueprinting:

a specialized flow chart used for

service processes.

Figure 5.6

Service Blueprintfor an InstallmentLending Operation

Source: Lynn Shostack, “Service

Positioning through Structural

Change,” Journal of Marketing

51 (January, 1987), p 36. Reprinted

with permission by the American

Marketing Association.

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Barista asks forhelp upfront

Barista tells managerout of cups

Figure 5.7

Expanded ServiceBlueprint for aCoffee Shop

FRONT OFFICE AND BACK-OFFICE ACTIVITIESIn manufacturing firms, the focus of activities is on the back office (i.e., producing productsefficiently). Whereas, in service firms, the focus is on the front office, interacting with thecustomer. Every firm needs both a front and back office, but firms may structure these indifferent ways.

In the front office, the customer interface can be an individual, the service provider, or a self-service kiosk or machine. The interactions in the front office influence the customer’s perceptionof the service and thus are critical to a successful design. Typical front office goals are courtesy,transparency, responsiveness, usability, and fun.

The back office processes material or information to support the front office needs. Typicalgoals of the back office are efficiency, productivity, standardization, and scalability.

Obvious conflicts exist between front and back officers. Connecting the front and back officesin a meaningful way and encouraging the flow of information and support are two of the chal-lenges of service design. Designing the service with an eye to the entire system will help alleviatesome of the tensions. Mass customization is an example of a front/back compromise. Instead ofgiving customers the freedom to order anything they want, present a menu of options from whichthe customer may choose. This provides some stability to the back office, while also beingresponsive to the customer.

SERVICESCAPESIt is precisely because services are so intangible that physical cues to service quality are needed.Servicescapes design (1) the space and function where the service takes places; (2) the ambient con-ditions, such as music, temperature, décor, and noise; and (3) signs, symbols, and artifacts. It isimportant that the servicescape be consistent with the service concept, and that all the elements beconsistent with each other.

Servicescapes have proved to be extremely important to customer perception of service qualityand to their satisfaction with the service.

QUANTITATIVE TECHNIQUESThere are many quantitative techniques for improving the service process. One of the most com-mon and powerful is waiting line analysis, covered in the next several sections.

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Servicescapes:

the design of the physical

environment (including signs,

symbols, and artifacts) in which a

service takes place.

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Anyone who goes shopping, to the post office, or to a movie experiences the inconvenience ofwaiting in line. Not only do people spend time waiting in lines, but machinery waits in line to beserviced or repaired, trucks line up to be loaded or unloaded at a shipping terminal, and planeswait to take off and land. Waiting takes place in virtually every productive process or service.Since the time spent by people and things waiting in line is a valuable resource, the reduction ofwaiting time is an important aspect of operations management.

Companies are able to reduce waiting time and provide faster service by increasing their ser-vice capacity, which usually means adding more servers—that is, more tellers, more mechanics,or more checkout clerks. However, increasing service capacity has a monetary cost, and thereinlies the basis of waiting line, analysis; the trade-off between the cost of improved service and thecost of making customers wait.

Waiting lines are analyzed with a set of mathematical formulas which comprise a field ofstudy called queuing theory. Different queuing models and mathematical formulas exist to dealwith different types of waiting line systems. Although we discuss several of the most commontypes of queuing systems, we do not investigate the mathematical derivation of the queuing for-mulas. They are generally complex and not really pertinent to our understanding of the use ofwaiting line analysis to improve service.

ELEMENTS OF WAITING LINE ANALYSISWaiting lines form because people or things arrive at the server faster than they can be served.This does not mean that the service operation is understaffed or does not have the capacity to han-dle the influx of customers. Most businesses and organizations have sufficient serving capacityavailable to handle its customers in the long run. Waiting lines result because customers do not ar-rive at a constant, evenly paced rate, nor are they all served in an equal amount of time. Customersarrive at random times, and the time required to serve each individual is not the same. A waitingline is continually increasing and decreasing in length (and is sometimes empty) but in the longrun approaches an average length and waiting time. For example, your local bank may haveenough tellers to serve an average of 100 customers in an hour, and in a particular hour only60 customers might arrive. However, at specific points in time during the hour, waiting lines mayform because more than an average number of customers arrive and they have transactions thatrequire more than the average amount of time.

Decisions about waiting lines and the management of waiting lines are based on these averagesfor customer arrivals and service times. They are used in queuing formulas or models to computeoperating characteristics such as the average number of customers waiting in line and the average timea customer must wait in line. Different sets of formulas are used, depending on the type of waitingline system being investigated. A bank drive-up teller window at which one bank clerk serves a sin-gle line of customers in cars is different from a single line of passengers at an airline ticket counterthat are served by three or four airline agents. In this section we present the elements that make upwaiting lines before looking at waiting line formulas.

Elements of a Waiting LineThe basic elements of a waiting line, are the calling population, arrivals, servers, and the waitingline or queue. The relationship between these elements is shown in Figure 5.8 for the simplest typeof waiting line system, a single server with a single queue. Following is a brief description of eachof these waiting line elements.

The Calling PopulationIn our discussions of waiting lines, a customer is a person or thing that wants service from an op-eration. The calling population is the source of the customers to the waiting line system, and it can beeither infinite or finite. An infinite calling population assumes such a large number of potentialcustomers that it is always possible for one more customer to arrive to be served. For example, forthe department store in Figure 5.8, we assume the calling population is infinite; to have, that is,the whole town or geographic area.

WAITING LINE ANALYSIS FOR SERVICE IMPROVEMENT

Providing quick service is an

important aspect of quality

customer service.

• Internet

Exercises

Operating characteristics:

average values for characteristics

that describe the performance

of a waiting line system.

Queue:

a single waiting line.

A waiting line system consists

of arrivals, servers, and

waiting line structure.

Calling population:

the source of customers; infinite

or finite.

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Figure 5.8

Elements of aWaiting LineSystem

A finite calling population has a specific, countable number of potential customers. Examplesof a finite calling population are a repair person in a shop who is responsible for a fixed number ofmachines to work on, a trucking terminal that services a fleet of ten trucks, or a nurse assigned toattend to only 12 patients.

The Arrival RateThe arrival rate is the rate at which customers arrive at the service facility during a specified period.This rate can be estimated from empirical data derived from studying the system or a similar sys-tem, or it can be an average of these empirical data. For example, if 100 customers arrive at a storecheckout counter during a 10-hour day, we could say the arrival rate averages 10 customers perhour. However, it might be that no customers would arrive during one hour and 20 customerswould arrive during another hour. Arrivals are assumed to be independent of each other and tovary randomly over time.

The variability of arrivals at a service facility often conform to a probability distribution. Arrivalscould be described by many distributions, but it has been determined (through years of research andthe practical experience of people in the field of queuing) that the number of arrivals per unit of timeat a service facility can frequently be described by a Poisson distribution. In queuing, the averagearrival rate, or how many customers arrive during a period of time, is signified by �.

For the models presented in this chapter, we assume there is no balking (refusing to join aline), reneging (leaving a line), or jockeying (changing lines) by customers in the waiting line sys-tem. We also assume that the arrival rate is less than the service rate (or else the line would growinfinitely long).

Arrival rate:

the frequency at which customers

arrive at a waiting line; most

frequently described by a Poisson

distribution.

Arrival rate is less than service

rate; � � �

E1C05.qxd 8/2/10 11:45 AM Page 201



Service TimesIn waiting line analysis arrivals are described in terms of a rate, and service in terms of time.Service times in a queuing process may also be any one of a large number of different probabilitydistributions. The distribution most commonly assumed for service times is the negative exponen-tial distribution. Although this probability distribution is for service times, service must beexpressed as a rate to be compatible with the arrival rate. The average service rate, or how manycustomers can be served in a period of time is expressed as �.

Empirical research has shown that the assumption of negative exponentially distributedservice times is not valid as often as is the assumption of Poisson-distributed arrivals. For actualapplications of queuing analysis, the assumptions for both arrival rate and service time distribu-tion would have to be verified.

Interestingly, if service times are exponentially distributed, then the service rate is Poisson dis-tributed. For example, if the average time to serve a customer is three minutes (and exponentiallydistributed), then the average service rate is 20 customers per hour (and Poisson distributed). Theconverse holds true for Poisson arrivals. If the arrival rate is Poisson distributed, then the timebetween arrivals is exponentially distributed.

Queue Discipline and LengthThe queue discipline is the order in which waiting customers are served. The most common type ofqueue discipline is first come, first served—the first person or item waiting in line is served first.Other disciplines are possible. For example, a machine operator might stack parts to be worked onbeside a machine so that the last part is on top of the stack and will be selected first. This queuediscipline is last in, first out. Or the machine operator might reach into a box full of parts and se-lect one at random. This queue discipline is random. Often customers are scheduled for serviceaccording to a predetermined appointment, such as patients at a dentist’s office or diners at arestaurant where reservations are required. These customers are taken according to a prearrangedschedule regardless of when they arrive at the facility. Another example of the many types ofqueue disciplines is when customers are processed alphabetically according to their last names,such as at school registration or at job interviews.

In manufacturing operations, sometimes jobs with the shortest expected processing times areselected first in order to get the most jobs processed in the shortest time period. In emergency ser-vices like emergency rooms at hospitals, the most critical problem is typically served first.

Queues can be of an infinite or finite size or length. An infinite queue can be of any size, with noupper limit, and is the most common queue structure. For example, it is assumed that the waitingline at a movie theater could stretch through the lobby and out the door if necessary. A finite queue

is limited in size. An example is the driveway at a bank teller window that can accommodate onlya limited number of cars, before it backs up to the street.

Basic Waiting Line StructuresWaiting line processes are generally categorized into four basic structures, according to the natureof the service facilities. In technical terminology they are called single-channel, single-phase; single-channel, multiple-phase; multiple-channel, single-phase; and multiple-channel, multiple-phase processes.

The number of channels in a queuing process is the number of parallel servers available. Thenumber of phases, on the other hand, denotes the number of sequential servers each customer mustgo through to complete service. An example of a single-channel, single-phase queuing operation isa post office with only one postal clerk waiting on a single line of customers. This is more com-monly called simply a single-server waiting line, and it is illustrated in Figure 5.9a. A post officewith several postal clerks waiting on a single line of customers is an example of a multiple-channel,single-phase process or simply a multiple-server waiting line. It is illustrated in Figure 5.9b. Theseare the two basic waiting line structures we will focus on in this chapter.

The other two waiting line structures we mentioned have multiple phases; that is, they have asequence of servers, one following another. For example, when patients go to a clinic for treatment orcheck into a hospital, they first wait in a reception room, then they may go to an office to fill out somepaperwork. When they get to the treatment room, the patients receive an initial checkup or treatmentfrom a nurse, followed by treatment from a doctor. This arrangement constitutes a single-channel,

Service time:

the time required to serve a

customers most frequently

described by the negative

exponential distribution.

Queue discipline:

the order in which customers are

served; most commonly first come,

first served.

Infinite queue:

can be of any length.

Finite queue:

the length is limited.

Channels:

the number of parallel servers for

servicing customers.

Phases:

the number of servers in sequence

a customer must go through.

E1C05.qxd 8/2/10 11:45 AM Page 202


multiple-phase queuing process. If there are several doctors and nurses, the process is a multiple-channel, multiple-phase process. Another example of a multiple-phase system is a manufacturingassembly line in which a product is worked on at several sequential machines or by several sequentialoperators at workstations. These are more complex structures and are beyond the scope of this text.

You may quickly visualize a familiar waiting situation that fits none of these categories ofwaiting line structures. The four waiting line structures we have described are simply the fourbasic general categories; but there are many variations, which often require very complex mathe-matical formulas to analyze. In some cases they can only be analyzed using simulation (the topicof Supplement 12). However, the basic fundamentals of waiting line analysis for the simplerqueuing models that we will discuss in this chapter are relevant to the analysis of all queuingproblems, regardless of their complexity.


United States Postal Servicewww.usps.com

(a) Single-server waiting line

United States Postal Servicewww.usps.com

(b) Multiple-server waiting line

Figure 5.9

Basic WaitingLine Structures

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OPERATING CHARACTERISTICSThe mathematics used in waiting line analysis do not provide an optimal, or “best,” solution. In-stead they generate measures referred to as operating characteristics that describe the perfor-mance of the waiting line system and that management uses to evaluate the system and makedecisions. It is assumed these operating characteristics will approach constant, average valuesafter the system has been in operation for a long time, which is referred to as a steady state. Thesebasic operating characteristics used in a waiting line analysis are defined in Table 5.2.

TRADITIONAL COST RELATIONSHIPS IN WAITING LINE ANALYSISThere is generally an inverse relationship between the cost of providing service and the cost ofmaking customers wait, as reflected in the cost curves in Figure 5.10. As the level of service, re-flected by the number of servers, goes up, the cost of service increases, whereas waiting cost de-creases. In the traditional view of waiting line analysis, the level of service should coincide withthe minimum point on the total cost curve.

The cost of providing the service is usually reflected in the cost of the servers, such as the costof the tellers at a bank, postal workers at a post office counter, or the repair crew in a plant or shop.As the number of servers is increased to reduce waiting time, service cost goes up. Service cost isnormally direct and easy to compute. The cost of waiting is not as easy to determine. The major de-terminant of waiting cost is the loss of business that might result because customers get tired ofwaiting or frustrated and leave. This business loss can be temporary (a single event) or permanent

A steady state is a constant,

average value for

performance characteristics

that the system will attain

after a long time.

Table 5.2

Queuing SystemOperatingCharacteristics

Notation Operating Characteristic

L Average number of customers in the system (waiting and being served)

Lq Average number of customers in the waiting line

W Average time a customer spends in the system (waiting and being served)

Wq Average time a customer spends waiting in line

Po Probability of no (i.e., zero) customers in the system

Pn Probability of n customer in the system

� Utilization rate; the proportion of the time the system is in use

As the level of service

improves, the cost of service

increases.

Total cost

Service cost

Waiting cost

Level of service

Expe

cted

cos

t

Figure 5.10

The CostRelationship inWaiting LineAnalysis

Better service typically

requires more servers.

E1C05.qxd 8/2/10 11:45 AM Page 204


(the customer never comes back). The cost due to a loss of business is especially difficult to deter-mine, since it is not part of normal accounting records, although some trade organizations for busi-nesses and industries occasionally provide such data. Other types of waiting costs include the lossof production time and salary for employees waiting to use machinery or load and unload vehicles.

Most companies and organizations that have waiting as an integral part of their service processusually establish a goal for customer waiting time that corresponds to a level of service they wantto achieve. For example, Taco Bell has determined that a three-minute average waiting time willresult in only 2.5% of customers leaving, which they consider to be an acceptable service goal.Bank of America has a similar waiting time goal for serving its bank customers. The U.S. PostalService has a goal of five minutes to serve its retail customers.

THE PSYCHOLOGY OF WAITINGIn some instances, it is not possible to reduce waiting times, or other important issues besides costmay be involved. When these situations occur, the problem of providing quality service often de-pends more on psychological solutions. In other words, the organization will try to make waitingmore palatable. For example, long lines are fairly common at Disney World, especially at certainpeak times during the day. Although it is unlikely that any company has analyzed the technicalaspects of waiting more than Disney, customers must still wait for long periods of time at certainshows, exhibits, and rides. Given the limited physical capacity of some attractions, the timerequired for a customer to complete them, and the large flow of customers, it is simply not possi-ble to make the lines shorter or the service quicker without letting fewer people into the park. Inthese cases Disney management attempts to improve service in other ways to reduce customerdissatisfaction. For example, they make use of costumed characters to entertain customers waitingin line and distract them from the long waits. Mobile vendors sell food, drinks, and souvenirs topeople in line. They provide accurate wait times, which are more tolerable than vague ones, andthey provide frequent updates. For customers who are particularly annoyed by long waits, they


Disney uses costumed

characters like Minnie Mouse

to entertain customers

waiting in line to distract

them from their long wait.

Joe Raedle/Getty Images

E1C05.qxd 8/2/10 11:45 AM Page 205



sell special passes for a fee that allows customers to go to the front of the line for some attractionsand to get into the park early before its normally scheduled opening.

Waiting rooms, such as at a doctor’s office, provide magazines and newspapers for customersto read while waiting. Televisions are occasionally available in auto repair waiting areas, in airportterminals, or in bars and lounges of restaurants where customers wait. Mirrors are purposelylocated near elevators to distract people while they wait. Supermarkets locate magazines and other“impulse-purchase” items at the checkout counter, not only as a diversion while waiting but aspotential purchases. All these tactics are designed to improve the quality of service that requireswaiting without actually incurring the cost of reducing waiting time.

Some service companies attempt to handle customer arrivals in a “smarter” way, by providingselective preferential treatment to certain types of customers in order to reduce their waiting time.For example, grocery stores have express lanes for customers with only a few purchases. Airlinesand car rental agencies issue special cards to frequent-use customers or customers who pay anadditional fee that allows them to join special waiting lines at their check-in counters. Telephoneretailers check the phone numbers of incoming calls, and based on a customer’s sales history,route the call to more experienced or specialized salespeople.

For some critical service providers, waiting times of any duration are simply not allowable.A police or fire department must provide sufficient service capacity so that calls for assistance canhave quick response. This often results in long periods of underutilization where police officers,or firefighters are not doing anything. In these cases, cost takes a back seat to service.

WAITING LINE MODELSThe simplest, most basic waiting line structure illustrated in Figure 5.9 is the single-server model.We run into this type of waiting line every day. When you buy a cup of coffee at your local Star-bucks, when you go to a professor’s office, when you use the copier in the library, and when youbuy a ticket to see a movie, you wait in line to be served by one server.

The Basic Single-Server ModelThere are several variations of the single-server waiting line system, however, in the basic single-server model we assume the following:

• Poisson arrival rate• Exponential service times• First-come, first-served queue discipline• Infinite queue length• Infinite calling population

The basic operating characteristics of this single-server model are computed using the followingformulas, where � � mean arrival rate, � � mean service rate, and n � the number of customers inthe waiting line system, including the customer being served (if any).

The probability that no customers are in the queuing system (either in the queue or beingserved) is

The probability of exactly n customers in the queuing system is

The average number of customers in the queuing system (i.e., the customers being serviced and inthe waiting line) is

L =

l

m - l

= ¢ lm≤n¢1 -

l

m≤Pn = ¢ l

m≤n

# P0

P0 = ¢1 - l

m≤

Assumptions of the basic

single-server model.

� � mean arrival rate;

� � mean service rate.

Basic single-server queuing

formulas.

E1C05.qxd 8/2/10 11:45 AM Page 206


The average number of customers in the waiting line is

The average time a customer spends in the queuing system (i.e., waiting and being served) is

The average time a customer spends waiting in line to be served is

The probability that the server is busy and a customer has to wait, known as the utilizationfactor, is

The probability that the server is idle and a customer can be served is

Remember that these operating characteristics are averages that result over a period of time; theyare not absolutes. In other words, customers who arrive at the bookstore checkout counter will notfind 3.2 customers in line. There could be no customers or 1, 2, 3, or 4 customers. The value 3.2 issimply an average over time, as are the other operating characteristics. Notice that there are fourcustomers in the system (L � 4) and 3.2 customers in line (Lq � 3.2). The difference is only 0.8customer being served because 20% of the time there is no customer being served (I � .20). Alsonote that the total time in the system of 10 minutes (W � 10) is exactly equal to the waiting timeof 8 minutes (Wq � 8) plus the service time of 2 minutes (i.e., 60/30).

Service Improvement AnalysisThe operating characteristics developed from the queuing formulas in Example 5.1 indicatethe quality of service at the Tech auxiliary bookstore. The average waiting time of eight

I = 1 - r = 1 -

l

m= P0

r =

l

m

Wq =

l

m(m - l)

W =

1

m - l=

L

l

Lq =

l2

m(m - l)


“Good” operating

characteristics for a waiting

line system, and hence good

service, are relative and

must have some basis for

comparison. For example,

the waiting time at this

McDonald’s in Pushkin

Square in Moscow averages

about 45 minutes. Americans

would not accept this level of

service. To Muscovites used

to waiting in lines that often

consume the better part of a

day, the waiting time at this

McDonald’s is amazingly

short. It represents good

service to them.

Roy/EXPLORER/Photo Researchers, Inc.

E1C05.qxd 8/2/10 11:45 AM Page 207



minutes is excessive and would likely cause customers to become frustrated and leave withoutmaking a purchase. Normally, a waiting time of two to three minutes is the most a customerwill comfortably tolerate at a store like this. Thus, the bookstore management could use theoperating characteristics to formulate new strategies to improve service and then test thesestrategies.

For example, the bookstore might consider adding an additional employee to assist the pre-sent operator. This would enable more customers to be served in less time, thus increasing theservice rate. If the service rate were increased from 30 customers per hour to 40 customers perhour, the waiting time would be reduced to only 2.25 minutes. Management would then have todecide whether the cost of the new employee is worth the reduction in waiting time. Alterna-tively, the bookstore could be redesigned to add an additional cash register as well as another

The auxiliary bookstore in the student center at Tech is a small facility that sells school sup-plies and snacks. It has one checkout counter where one employee operates the cash register.The cash register and operator represent the server in this waiting line system; the customerswho line up at the counter to pay for their selections form the waiting line.

Customers arrive at a rate of 24 per hour according to a Poisson distribution (� � 24), andservice times are exponentially distributed, with a mean rate of 30 customers per hour (� � 30).The bookstore manager wants to determine the operating characteristics for this waiting linesystem.

Solution

The operating characteristics are computed using the queuing formulas for the single-servermodel as follows:

= 0.20 probability that the server will be idle and a customer can be served

I = 1 - r = 1 - 0.80

= 0.80 probability that the server will be busy and the customer must wait

r =

l

m=

24

30

= 0.133 hour (8 minutes) average time in the waiting line per customer

Wq =

l

m(m - l)=

24

30(30 - 24)

= 0.167 hour (10 minutes) average time in the system per customer

W = 1

m - l=

1

30 - 24

= 3.2 customers on the average in the waiting line

Lq =

l2

m(m - l)=

(24)2

30(30 - 24)

= 4 customers on the average in the queuing system

L =

l

m - l=

24

30 - 24

= 0.20 probability of no customers in the system

P0 = £1 -

l

m≥ = £1 -

24

30≥

Example 5.1

A Single-ServerModel

E1C05.qxd 8/2/10 11:45 AM 8


employee to operate it. This would have the effect of reducing the arrival rate. If exiting cus-tomers split evenly between the two cash registers, then the arrival rate at each register would de-crease from 24 per hour to 12 per hour with a resulting customer waiting time of 1.33 minutes.Again, management would have to determine whether the reduction in waiting time is worth thecost of a new cash register and employee. This is the crux of waiting line analysis: determiningwhether the improvement in service is worth the cost to achieve it.

Solution of the Single-Server Model with ExcelExcel can be used to solve all of the queuing models in this chapter. The Excel solution screen for thesingle-server model for the auxiliary bookstore at Tech in Example 5.1 is shown in Exhibit 5.1. Excelfiles for this exhibit and all other exhibits in this chapter can be downloaded from the text Web site.

Advanced Single-Server ModelsThere are many variations of the single-server model as shown in Figure 5.11. The most commonare: constant service times, finite queue length, and finite calling populations.


D4/(D5–D4)

= (1/(D5–D4))*60

= (D4/D5*(D5–D4))*60

Exhibit 5.1

Single Server

• Excel File

(a) Single-Server,Constant Time

(b) Single-Server,Finite Queue

(c) Single-Server,Finite CallingPopulation

Figure 5.11

Advanced Single-ServerModels

E1C05.qxd 8/2/10 11:45 AM Page 209



Constant service times occur most often when automated equipment or machinery performsthe service. Examples are vending machines, car washes, and many manufacturing operations.

Finite queue lengths occur when there is a physical limitation to the length of the waiting line.For example, this can occur when cars waiting at a bank for an ATM machine are prohibited fromextending into the street.

A finite calling population refers to a situation when the number of “customers” that can arriveto a system is limited, such as invitation-only events, student advisees, or maintenance for a fleet ofrental cars.

The formulas for these models, included in the Summary of Key Formulas at the end of thechapter, can be quite involved. For that reason, all of these models, along with the single-servermodel and the multiple-server model discussed in the next section, can be solved with the Exceladd-in that accompanies this book, OM Tools. Exhibit 5.2 shows the OM Tools solution to a single-server finite queue problem.

MULTIPLE-SERVER MODELA large number of operational waiting line systems include multiple servers. These models can bevery complex, so in this section we present only the most basic multiple-server (or channel) wait-ing line structure. This system includes a single waiting line and a service facility with several in-dependent servers in parallel, as shown in Figure 5.9b. An example of a multiple-server system isan airline ticket and check-in counter, where passengers line up in a roped-off single line waitingfor one of several agents for service. The same waiting line structure is found at the post office,where customers in a single line wait for service from several postal clerks, or at a multiplex the-ater where customers typically line up in a single line to buy movie tickets from one of severalticket sellers.

The Basic Multiple-Server ModelThe formulas for determining the operating characteristics for the multiple-server model are basedon the same assumptions as the single-server model—Poisson arrival rate, exponential servicetimes, infinite calling population and queue length, and FIFO queue discipline. Also, recall that inthe single-server model, � � �; however, in the multiple-server model, s� � �, where s is thenumber of servers. The operating characteristics formulas are as follows.

Probability of zero customers

Exhibit 5.2

AdvancedSingle-ServerModels

• Excel File

With multiple-server models,

two or more independent

services in parallel serve a

single waiting line.

ss�� : The total number of

servers must be able to serve

customers faster than they

arrive.

E1C05.qxd 8/2/10 11:45 AM Page 210


The probability that there are no customers in the system (all servers are idle) is

The probability of n customers in the queuing system is

The probability that a customer arriving in the system must wait for service (i.e., the probabilitythat all the servers are busy) is

Utilization = r =

l

sm

Avg. time in queue = Wq = W -

1

m=

Lq

l

Avg. no. in queue = Lq = L -

l

m

Avg. time in system = W =

L

l

Avg. no. in system = L =

lm(l>m)s

(s - 1)!(sm - l)2P0 +

l

m

Pw =

1

s!¢ lm≤ s sm

sm - lP0

Pn = d1

s!sn- s ¢ lm≤n

P0, for n 7 s

1

n! ¢ lm≤n

P0, for n … s

P0 =

1

C an= s-1

n=0

1

n! £ lm≥

n

S +

1

s! £ lm≥

s

£ sm

sm - l≥


These passengers waiting in

line to purchase tickets or

check baggage and get a

boarding pass at LAX are part

of a waiting line system with

multiple servers. Passengers

are cordoned into a single

line to wait for one of several

airline agents to serve them.

The number of agents

scheduled for duty at the

check-in counter is

determined by waiting line

operating characteristics

based on different passenger

arrival rates during the day

and for different days.

David Young-Wolff/PhotoEdit

E1C05.qxd 8/2/10 11:45 AM Page 211



The student health service at Tech has a waiting room in which chairs are placed along a wall,forming a single waiting line. Some students have health problems that only require a nurse.The students are served by three nurses, each located in a separate room. Students are treatedon a first-come, first-served basis.

The health service administrator wants to analyze this queuing system because excessivewaiting times can make students angry and they complain. Students have a medical problemand thus are impatient anyway. Waiting increases their impatience.

A study of the health service for a six-month period shows that an average of 10 stu-dents arrive per hour (according to a Poisson distribution), and an average of four studentscan be served per hour by a nurse (Poisson distributed). Compare a three-server versusfour-server system.

Solution

a) Three-server system

Pw =

1

s!£ lm≥

s

sm

sm - lP0

= 0.35 hour or 21 minutes waiting in line

Wq =

Lq

l=

3.5

10

= 3.5 students waiting to be served

Lq = L -

l

m= 6 -

10

4

= 0.60 hour or 36 minutes in the health service

W =

L

l=

6

10

= 6 students in the health service

=

(10)(4)(10>4)3

(3 - 1)![3(4) - 10]2(0.045) +

10

4

L =

lm(l>m)s

(s - 1)!(sm - l)2P0 +

l

m

= 0.045 probability that no customers are in the health service.

=

1

C 1

0!£10

4≥

0

+

1

1!£10

4≥

1

+

1

2!£10

4≥

2

S +

1

3!£10

4≥

33(4)

3(4) - 10

P0 =

1

C an= s-1

n=0

1

n!£ lm≥

n

S +

1

s!£ lm≥

s

£ sm

sm - l≥

sm = (3)(4) = 12 ( 7 l = 10)

s = 3 service representatives

m = 4 students per hour per service representative

l = 10 students per hour

Example 5.2

A Multiple-Server WaitingLine System

E1C05.qxd 8/2/10 11:45 AM Page 212



The health service administrator has observed that students are frustrated by the waiting timeof 21 minutes and the 0.703 probability of waiting. To try to improve matters, the administratoris considering adding another nurse. The operating characteristics for this system must berecomputed with s � 4 nurses.

b) Four-server system

Substituting s � 4 along with � and � in the queuing formulas results in the followingoperating characteristics:

These results are significantly better; waiting time is reduced from 21 minutes to 3 minutes.This improvement in the quality of the service would have to be compared to the cost ofadding an extra nurse.

Pw = 0.31 probability that a student must wait for service

Wq = 0.05 hour, or 3 minutes, waiting in line

Lq = 0.5 students waiting to be served

W = 0.30 hour, or 18 minutes, in the health serviceL = 3.0 students in the health service

P0 = 0.073 probability that no students are in the health service

(i.e., that there are three or more students in the system)

= 0.703 probability that a student must wait for service

=

1

3!£10

4≥

33(4)

3(4) - (10)(0.045)

Exhibit 5.3

Multiple ServerWaiting Line in Excel

(Continued)

E1C05.qxd 8/2/10 11:45 AM Page 213



Explanation of Excel functions used in Exhibit 5.3

FACT (number)

A factorial is a count of the number of ways a group of items can be arranged (also called a per-mutation). The mathematical symbol for factorial is !. For example, 5! � 5 * 4 * 3 * 2 * 1 �120. In Excel, FACT (5) � 120.

VLOOKUP (lookup value, table array, column number that contains the value to be returned).

VLOOKUP searches for a value in the first column of a table array and returns a value in thesame row from another column in the table array. In this example, VLOOKUP(D6,G18:H36,2)looks up the number of servers, s, in the first column of the table and returns the value from thesecond column, which calculates the summation portion of the P0 formula.

SUMMARY

Services represent the fastest growing sector of the globaleconomy and account for two thirds of global output, onethird of global employment and nearly 20% of global trade.The world’s most industrialized nations are predominantlyservice economies.

Service design and operations present unique challenges dueto the intangible nature of services, the inherent variability inservice delivery, and the co-production of value by the customerand service provide. The design process involves developing a

service concept, defining the service package, and determiningperformance, design and delivery specifications. Design toolssuch as service blueprints, servicescapes, service scripts, andwaiting line analysis facilitate the design process.

Since waiting is an integral part of many service-relatedoperations, it is an important area of analysis. The mathemati-cal formulas presented in this chapter for modeling variouswaiting line structures provide the basis for designing and im-proving service systems.

• Practice

Quizzes

SUMMARY OF KEY TERMS

arrival rate the rate (�) at which customers arrive at a servicefacility during a specified period.

calling population the source of customers to a waiting line.channels the number of parallel servers.delivery specification specify schedules, deliverables, location.design specification describe the service in enough detail to be

replicate.goods tangible objects that can be created and sold at a later

date.infinite queue a waiting line that grows to any length.line of influence signs or activities that influences a customer to

seek a service.line of interaction point where a customer and service provider

interact.line of support point where a service provider interacts with

support personnel.line of visibility separates front office and back office activities.operating characteristics measures of waiting line performance

expressed as averages.performance specification outline expectations and requirements.

phases the number of sequential servers a customer must gothrough to receive service.

queue a single waiting line that forms in front of a servicefacility.

queue discipline the order in which customers are served.services acts, deeds or performances that provide value to the

customer.servicescapes the design of the physical environment (includ-

ing signs, symbols and, artifacts) in which a service takesplace.

service blueprinting a specialized flow chart used for serviceprocesses.

service concept the purpose of a service; it defines the targetmarket and the customer experience.

service package the mixture of physical items, sensual benefits,and psychological benefits provided to the customer.

service time the time required to serve a customer; the timeperiod divided by service time yields the service rate (�).

utilization factor (�) the probability the server is busy and thecustomer must wait.

E1C05.qxd 8/2/10 11:45 AM Page 214



SUMMARY OF KEY FORMULAS

Single-Server Model

where � � arrival rate� � service rate

Single-Server Model with Finite Calling Population

where N � population size

Single-Server Model with Finite Queue

where M � maximum number allowed in the system

Lq = L -

l(1 - PM)

m

L =

l>m

1 - l>m-

(M + 1)(l>m)M+1

1 - (l>m)M+1

P0 =

1 - l>m

1 - (l>m)M+1 W =

L

l(1 - PM)

Pn = (P0)(l>m)n, n … M Wq = W -

1

m

P0 =

1

aN

n=0

N!

(N - n)! al

mb

nWq =

Lq

(N - L)l

Lq = N - al + m

lb (1 - P0) W = Wq +

1

m

L = Lq + (1 - P0) Pn =

N!

(N - n)! al

mb

n

P0

I = 1 -

l

mLq =

l2

m(m - l)

r =

l

mL =

l

m - l

Wq =

l

m(m - l)Pn = ¢ l

m≤n¢1 -

l

m≤

W =

1

m - lP0 = 1 -

l

m

Single-Server Model with Constant Service Times

Multiple-Server Model

where s � number of servers

Wq = W -

1

m

Lq = L -

l

m

W =

L

l

L =

lm(l>m)s

(s - 1)!(sm - l)2P0 +

l

m

Pw =

1

s! al

mb

s sm

sm - lP0

Pn = d1

s!sn- s al

mb

n

P0, for n 7 s

1

n! al

mb

n

P0, for n … s

P0 =

1

c an= s-1

n=0 1

n! al

mb

n

d + 1

s! al

mb

s

asm

sm - lb

r =

l

mL = Lq +

l

m

W = Wq +

1

mLq =

l2

2m1m - l2

Wq =

Lq

lP0 = 1 -

l

m

SOLVED PROBLEMS

1. SINGLE-SERVER MODEL

The new-accounts officer at the Citizens Northern Savings Bankenrolls all new customers in checking accounts. During the three-week period in August encompassing the beginning of the newschool year at State University, the bank opens a lot of new ac-counts for students. The bank estimates that the arrival rate duringthis period will be Poisson distributed with an average of four

customers per hour. The service time is exponentially distributedwith an average of 12 minutes per customer to set up a new ac-count. The bank wants to determine the operating characteristicsfor this system to determine if the current person is sufficient tohandle the increased traffic.

• Animated Demo Problem

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SOLUTION

Determine operating characteristics for the single-server system:

� 0.80 probability that the new-accounts officer will bebusy and that a customer must wait

The average waiting time of 48 minutes and the average time inthe system are excessive, and the bank needs to add an extraemployee during the busy period.

2. MULTIPLE-SERVER MODEL

The Citizens Northern Bank wants to compute the operatingcharacteristics if an extra employee were added to assist withnew-accounts enrollments.

SOLUTION

Determine the operating characteristics for the multiple-serversystem:

s = 2 servers m = 5 customers per hour are served

l = 4 customers per hour arrive

Pw =

l

m=

4

5

= 0.80 hour (48 minutes) average time waiting

Wq = l

m(m - l)=

4

5(5 - 4)

= 1 hour average time in the system

W = 1

m - l=

1

5 - 4

= 3.2 customers on average waiting

Lq =

l2

m(m - l)=

42

5(5 - 4)

= 4 customers on average in the queuing system

L =

l

m - l=

4

5 - 4

= 0.20 probability of no customers in the system

P0 = a1 -

l

mb = a1 -

4

5b

m = 5 customers per hour are served l = 4 customers per hour arrive

The waiting time with the multiple-server model is 2.3 minutes,which is a significant improvement over the previous system;thus, the bank should add the second new-accounts officer.

= 0.229 probability that a customer must wait

= 1

2!£4

5≥

2(2)(5)

(2)(5) - 4(0.429)

Pw = 1

s!£ lm≥

s

sm

sm - l P0

in line = 0.038 hour (2.3 minutes) average time

Wq = Lq

l=

0.152

4

= 0.238 hour (14.3 minutes) average time in the system

W = L

l=

0.952

4

= 0.152 customer on average waiting to be served

Lq = L -

l

m= 0.952 -

4

5

= 0.952 customer on average in the system

= (4)(5)(4>5)2

1![(2)(5) - 4]2 (0.429) +

4

5

L = lm(l>m)s

(s - 1)!(sm - l)2 P0 +

l

m

= 0.429 probability that no customers are in the system

=

1

c1

0! a

4

5b

0

+

1

1! a

4

5b

1

d +

1

2! a

4

5b

2 (2)(5)

(2)(5) - 4

P0 =

1

C an= s-1

n=0 1

n!£ lm≥

n

S +

1

s!£ lm≥

s

£ sm

sm - l≥

QUESTIONS

5-1. How would you define a service?5-2. List eight characteristics of services and explain what

impact each characteristic has on the design process.5-3. Describe the service package for (a) a bank, (b) an airline,

and (c) a lawn service.5-4. Generate as many ideas as you can for additional services or

improvements in service delivery for (a) banking, (b) highereducation, and (c) health care.

5-5. Go to www.ibm.com and search for SSME. What is SSME?Why is it important to IBM?

5-6. Identify 10 real-life examples of queuing systems withwhich you are familiar.

5-7. Why must the utilization factor in a single-server model beless than one?

5-8. Give five examples of real-world queuing systems with finitecalling populations.

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5-9. List the elements that define a queuing system.5-10. How can the results of queuing analysis be used by a deci-

sion maker for making decisions?5-11. What is the mean effective service rate in a multiple-

server model, and what must be its relationship to thearrival rate?

5-12. For each of the following queuing systems, indicate if it isa single- or multiple-server model, the queue discipline,and if its calling population is infinite or finite:a. Hair salonb. Bankc. Laundromatd. Doctor’s officee. Adviser’s officef. Airport runwayg. Service stationh. Copy centeri. Team trainerj. Mainframe computer

5-13. For Example 5.1 in this chapter, discuss why the multiple-server model would or would not be appropriate as analternative to reduce waiting time.

5-14. Discuss briefly the relationship between waiting line analysisand quality improvement.

5-15. Define the four basic waiting line structures and give anexample of each.

5-16. Describe the traditional cost relationship in waiting lineanalysis.

5-17. a. Is the following statement true or false? The single-phase,single-channel model with Poisson arrivals and undefinedservice times will always have larger (i.e., greater) operat-ing characteristic values (i.e., W, Wq, L, Lq) than the samemodel with exponentially distributed service times. Explainyour answer.

b. Is the following statement true or false? The single-phase, single-channel model with Poisson arrivals andconstant service times will always have smaller (i.e.,lower) operating characteristic values (i.e., W, Wq, L,Lq) than the same model with exponentially distributedservice times. Explain your answer.

5-18. Under what conditions can the basic single-server andmultiple-server models be used to analyze a multiple-phase waiting line system?

5-19. Why do waiting lines form at a service facility even thoughthere may be more than enough service capacity to meetnormal demand in the long run?

5-20. Provide an example of when a first-in, first-out (FIFO) rulefor queue discipline would not be appropriate.

5-21. Under what conditions will the single-channel, single-phasequeuing model with Poisson arrivals and undefined servicetimes provide the same operating characteristics as the basicmodel with exponentially distributed service times?

5-22. What types of waiting line systems have constant servicetimes?

5-1. McBurger’s fast-food restaurant has a drive-through win-dow with a single server who takes orders from an intercomand also is the cashier. The window operator is assisted byother employees who prepare the orders. Customers arriveat the ordering station prior to the drive-through windowevery 3.6 minutes (exponentially distributed) and the ser-vice time is 2.4 minutes (exponentially distributed). Deter-mine the average length of the waiting line and the waitingtime. Discuss the quality implications of your results. If youdecide that the quality of the service could be improved, in-dicate what things you might do to improve quality.

5-2. The ticket booth on the Tech campus is operated by oneperson, who is selling tickets for the annual Tech versusState football game on Saturday. The ticket seller can servean average of 12 customers per hour (Poisson distributed);on average, 8 customers arrive to purchase tickets eachhour (Poisson distributed). Determine the average time aticket buyer must wait and the portion of time the ticketseller is busy.

5-3. The Minute Stop Market has one pump for gasoline,which can service 10 customers per hour (Poisson distrib-uted). Cars arrive at the pump at a rate of 5 per hour(Poisson distributed).

a. Determine the average queue length, the average time acar is in the system, and the average time a car must wait.

b. If, during the period from 4:00 P.M. to 5:00 P.M., the arrival rate increases to 12 cars per hour, what will bethe effect on the average queue length?

5-4. The Universal Manufacturing Company produces a par-ticular product in an assembly-line operation. One of themachines on the line is a drill press that has a single as-sembly line feeding into it. A partially completed unit ar-rives at the press to be worked on every 8 minutes, onaverage, according to an exponential distribution. Themachine operator can process an average of 10 parts perhour (Poisson distributed). Determine the average numberof parts waiting to be worked on, the percentage of timethe operator is working, and the percentage of time themachine is idle.

5-5. The management of Universal Manufacturing Company(Problem 5-4) likes to have its operators working 90% of thetime. What must the assembly line arrival rate be in order forthe operators to be as busy as management would like?

5-6. The Peachtree Airport in Atlanta serves light aircraft. It hasa single runway and one air traffic controller to landplanes. It takes an airplane 8 minutes to land and clear the

PROBLEMS• GO Tutorial

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weigh station. If they see four or more trucks in line, theywill pass by the station and risk being caught and ticketed.What is the probability that a truck will pass by the station?

5-11. In Problem 5-8, the head of the Management Department atTech is considering the addition of a second advisor in thecollege advising office to serve students waiting to have theirschedules approved. This new advisor could serve the samenumber of students per hour as the present advisor. Deter-mine L, Lq, W, and Wq for this altered advising system. As astudent, would you recommend adding the advisor?

5-12. Annie Campbell is a nurse on the evening shift from 10:00 P.M. to 6:00 A.M. at Community Hospital. She isresponsible for 15 patients in her area. She averages twocalls from each of her patients every evening (Poisson dis-tributed), and she must spend an average of 10 minutes(negative exponential distribution) with each patient whocalls. Nurse Smith has indicated to her shift supervisor thatalthough she has not kept records she believes her patientsmust wait about 10 minutes on average for her to respondand she has requested that her supervisor assign a secondnurse to her area. The supervisor believes 10 minutes is toolong to wait, but she does not want her nurses to be idlemore than 40% of the time. Determine what the supervisorshould do.

5-13. Wallace Publishers has a large number of employees who usethe company’s single fax machine. Employees arrive ran-domly to use the fax machine at an average rate of 20 perhour. This arrival process is approximated by a Poisson distri-bution. Employees spend an average of two minutes usingthe fax machine, either transmitting or receiving items. Thetime spent using the machine is distributed according to anegative exponential distribution. Employees line up in singlefile to use the machine, and they obtain access to it on a first-come, first-served basis. There is no defined limit to thenumber who can line up to use the machine.

Management has determined that by assigning an oper-ator to the fax machine rather than allowing the employeesto operate the machine themselves, it can reduce the aver-age service time from the current 2 minutes to 1.5 minutes.However, the fax operator’s salary is $8 per hour, whichmust be paid 8 hours per day even if there are no employ-ees wishing to use the fax machine part of the time. Man-agement has estimated the cost of employee time spentwaiting in line and at the fax machine during service to be17¢ per minute (based on an average salary of $10.20 perhour per employee). Should the firm assign an operator tothe fax machine?

5-14. The Universal Manufacturing Company has a single assem-bly line that feeds two drill presses in parallel. As partiallycompleted products come off the line, they are lined up tobe worked on as drill presses become available. The unitsarrive at the workstation (containing both presses) at therate of 90 per hour (Poisson distributed). Each press opera-tor can process an average of 60 units per hour (Poissondistributed). Compute L, Lq, W, and Wq.

5-15. The Escargot is a small French restaurant with 6 waiters andwaitresses. The average service time at the restaurant for a

runway (exponentially distributed). Planes arrive at theairport at the rate of 5 per hour (Poisson distributed).a. Determine the average number of planes that will stack

up waiting to land.b. Find the average time a plane must wait in line before it

can land.c. Calculate the average time it takes a plane to clear the

runway once it has notified the airport that it is in thevicinity and wants to land.

d. The FAA has a rule that an air traffic controller can, onthe average, land planes a maximum of 45 minutes outof every hour. There must be 15 minutes of idle timeavailable to relieve the tension. Will this airport have tohire an extra air traffic controller?

5-7. The National Bank of Union City currently has one outsidedrive-up teller. It takes the teller an average of three min-utes (exponentially distributed) to serve a bank customer.Customers arrive at the drive-up window at the rate of12 per hour (Poisson distributed). The bank operations offi-cer is currently analyzing the possibility of adding a sec-ond drive-up window at an annual cost of $20,000. It isassumed that arriving cars would be equally divided be-tween both windows. The operations officer estimates thateach minute’s reduction in customer waiting time wouldincrease the bank’s revenue by $2000 annually. Should thesecond drive-up window be installed? What other factorsshould be considered in the decision besides cost?

5-8. During registration at Tech every quarter, students in theDepartment of Management must have their coursesapproved by the departmental advisor. It takes the advisoran average of five minutes (exponentially distributed) toapprove each schedule, and students arrive at the adviser’soffice at the rate of 10 per hour (Poisson distributed). Com-pute L, Lq, W, Wq, and �. What do you think about thissystem? How would you change it?

5-9. All trucks traveling on Interstate 40 between Albuquerqueand Amarillo are required to stop at a weigh station. Trucksarrive at the weigh station at a rate of 120 per eight-hourday (Poisson distributed), and the station can weigh, on theaverage, 140 trucks per day (Poisson distributed).a. Determine the average number of trucks waiting, the aver-

age time spent at the weigh station by each truck, and theaverage waiting time before being weighed for each truck.

b. If the truck drivers find out they must remain at theweigh station longer than 15 minutes on the average,they will start taking a different route or traveling atnight, thus depriving the state of taxes. The state ofNew Mexico estimates it loses $10,000 in taxes peryear for each extra minute (over 15) that trucks mustremain at the weigh station. A new set of scales wouldhave the same service capacity as the present set ofscales, and it is assumed that arriving trucks would lineup equally behind the two sets of scales. It would cost$50,000 per year to operate the new scales. Should thestate install the new set of scales?

5-10. In Problem 5-9(a), suppose arriving truck drivers look tosee how many trucks are waiting to be weighed at the

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table (of any size) is 80 minutes (exponentially distributed).The restaurant does not take reservations and parties arrivefor dinner (and stay and wait) every 16 minutes (Poisson dis-tributed). The restaurant is concerned that a lengthy waitingtime might hurt its business in the long run. What is thecurrent waiting time and queue length for the restaurant?Discuss the quality implications of the current waiting timeand any actions the restaurant might take.

5-16. Cakes baked by the Freshfood Bakery are transported fromthe ovens to be packaged by one of three wrappers. Eachwrapper can wrap an average of 120 cakes per hour (Poissondistributed). The cakes are brought to the wrappers at therate of 300 per hour (Poisson distributed). If a cake sitslonger than 5 minutes before being wrapped, it will not befresh enough to meet the bakery’s quality control standards.Does the bakery need to hire another wrapper?

5-17. The Draper Clinic has two general practitioners who seepatients daily. An average of 6.5 patients arrive at the clinicper hour (Poisson distributed). Each doctor spends an aver-age of 15 minutes (exponentially distributed) with a patient.The patients wait in a waiting area until one of the two doc-tors is able to see them. However, since patients typically donot feel well when they come to the clinic, the doctors do notbelieve it is good practice to have a patient wait longer thanan average of 20 minutes. Should this clinic add a thirddoctor, and, if so, will this alleviate the waiting problem?

5-18. The Wearever Shoe Company is going to open a new branchat a mall, and company managers are attempting to determinehow many salespeople to hire. Based on an analysis of malltraffic, the company estimates that customers will arrive atthe store at the rate of 9 per hour (Poisson distributed), andfrom past experience at its other branches, the companyknows that salespeople can serve an average of 6 customersper hour (Poisson distributed). How many salespeople shouldthe company hire in order to maintain a company policy thaton average a customer should have to wait for service nomore than 30% of the time?

5-19. When customers arrive at Gilley’s Ice Cream Shop, theytake a number and wait to be called to purchase ice creamfrom one of the counter servers. From experience in pastsummers, the store’s staff knows that customers arrive atthe rate of 35 per hour (Poisson distributed) on summerdays between 3:00 P.M. and 10:00 P.M. and a server canserve 15 customers per hour on average (Poisson distrib-uted). Gilley’s wants to make sure that customers wait nolonger than 5 minutes for service. Gilley’s is contemplatingkeeping three servers behind the ice cream counter duringthe peak summer hours. Will this number be adequate tomeet the waiting time policy?

5-20. Huang’s television-repair service receives an average offour TV sets per 8-hour day to be repaired. The servicemanager would like to be able to tell customers that theycan expect their TV back in 3 days. What average repairtime per set will the repair shop have to achieve to pro-vide 3-day service on the average? (Assume that thearrival rate is Poisson distributed and repair times areexponentially distributed.)


5-21. Partially completed products arrive at a workstation in amanufacturing operation at a mean rate of 40 per hour(Poisson distributed). The processing time at the worksta-tion averages 1.2 minutes per unit (exponentially distrib-uted). The manufacturing company estimates that each unitof in-process inventory at the workstation costs $31 perday (on the average). However, the company can add extraemployees and reduce the processing time to 0.90 minuteper unit at a cost of $52 per day. Determine whether thecompany should continue the present operation or addextra employees.

5-22. The Seaboard Shipping Company has a warehouse terminalin Spartanburg, South Carolina. The capacity of each termi-nal dock is three trucks. As trucks enter the terminal, the dri-vers receive numbers, and when one of the three dock spacesbecomes available, the truck with the lowest number entersthe vacant dock. Truck arrivals are Poisson distributed, andthe unloading and loading times (service times) are expo-nentially distributed. The average arrival rate at the terminalis five trucks per hour, and the average service rate per dockis two trucks per hour (30 minutes per truck).a. Compute L, Lq, W, and Wq.b. The management of the shipping company is consider-

ing adding extra employees and equipment to improvethe average service time per terminal dock to 25 min-utes per truck. It would cost the company $18,000 peryear to achieve this improved service. Management estimates that it will increase its profit by $750 per yearfor each minute it is able to reduce a truck’s waitingtime. Determine whether management should make the investment.

c. Now suppose that the managers of the shipping com-pany have decided that truck waiting time is excessiveand they want to reduce the waiting time. They have determined that there are two alternatives available forreducing the waiting time. They can add a fourth dock,or they can add extra employees and equipment at theexisting docks, which will reduce the average servicetime per location from the original 30 minutes per truckto 23 minutes per truck. The costs of these alternativesare approximately equal. Management desires to imple-ment the alternative that reduces waiting time by thegreatest amount. Which alternative should be selected?

5-23. Drivers who come to get their licenses at the department ofmotor vehicles have their photograph taken by an automatedmachine that develops the photograph onto the license cardand laminates the complete license. The machine requires aconstant time of 4.5 minutes to develop a completed license.If drivers arrive at the machine at the mean rate of 11 perhour (Poisson distributed), determine the average length ofthe waiting line and the average waiting time.

5-24. A vending machine at Municipal Airport dispenses hotcoffee, hot chocolate, or hot tea in a constant service timeof 30 seconds. Customers arrive at the vending machine ata mean rate of 50 per hour, Poisson distributed. Determinethe average length of the waiting line and the average timea customer must wait.

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according to an exponential distribution. The average time tocomplete a trip is 20 minutes (exponentially distributed).Determine the average number of customers waiting for ser-vice and the average time a customer must wait for a cab.

5-31. A retail catalogue operation employs a bank of six telephoneoperators who process orders using computer terminals.When a terminal breaks down, it must be disconnected andtaken to a nearby electronics repair shop, where it is repaired.The mean time between terminal breakdowns is six workingdays, and the mean time required to repair a terminal is twoworking days (both exponentially distributed). As a result oflost sales, it costs the mail-order operation an estimated $50per day in lost profits each day a terminal is out for repair.The company pays the electronics repair shop $3000 per yearon a service agreement to repair the terminals. The companyis considering the possibility of signing a new service agree-ment with another electronics repair shop that will providesubstitute terminals while the broken ones are at the repairshop. However, the new service agreement would cost themail-order operation $15,000 per year. Assuming that thereare 250 working days in a year, determine what the mail-order operation should do.

5-32. The Baytown Post Office has four stations for service. Cus-tomers line up in single file for service on an FIFO basis. Themean arrival rate is 40 per hour, Poisson distributed, and themean service time per server is five minutes, exponentiallydistributed. Compute the operating characteristics for this op-eration. Does the operation appear to be satisfactory in termsof: (a) postal workers’ (servers’) idle time; (b) customer wait-ing time and/or the number waiting for service; and (c) thepercentage of the time a customer can walk in and get servedwithout waiting at all?

5-33. Andromeda Books is a small independent publisher of fictionand nonfiction books. Each week the publisher receives anaverage of eight unsolicited manuscripts to review (Poissondistributed). The publisher has 12 freelance reviewers in thearea who read and evaluate manuscripts. It takes a revieweran average of 10 days (exponentially distributed) to read amanuscript and write a brief synopsis. (Reviewers work ontheir own, seven days a week.) Determine how long the pub-lisher must wait on average to receive a reviewer’s manu-script evaluation, how many manuscripts are waiting to bereviewed, and how busy the reviewers are.

5-34. Amanda Fall is starting up a new house painting business,Fall Colors. She has been advertising in the local newspa-per for several months, and based on inquiries and infor-mal surveys of the local housing market she anticipatesthat she will get painting jobs at the rate of four per week(Poisson distributed). Amanda has also determined that itwill take a four-person team of painters an average of 0.7week (exponentially distributed) for a typical painting job.a. Determine the number of teams of painters Amanda

needs to hire so that customers will have to wait nolonger than two weeks to get their houses painted.

b. If the average price for a painting job is $1700 andAmanda pays a team of painters $500 per week, willshe make any money?

5-25. In Problem 5-20 suppose that Huang’s television-repairservice cannot accommodate more than 10 TV sets at atime (under repair and waiting for service). What is theprobability that the number of TV sets on hand will exceedthe shop capacity?

5-26. Norfolk, Virginia, a major seaport on the East Coast, has aship coal-loading facility. Currently, coal trucks filled withcoal arrive at the port facility at the mean rate of 149 perday (Poisson distributed). The facility operates 24 hours aday. The coal trucks are unloaded one at a time on a first-come, first-served basis by automated mechanical equip-ment that empties the trucks in a constant time of eightminutes per truck, regardless of truck size. The port author-ity is negotiating with a coal company for an additional30 trucks per day. However, the coal company will not usethis port facility unless the port authority can assure themthat their coal trucks will not have to wait to be unloaded atthe port facility for more than 12 hours per truck on theaverage. Can the port authority provide this assurance?

5-27. The Waterfall Buffet in the lower level of the National ArtGallery serves food cafeteria-style daily to visitors andemployees. The buffet is self-service. From 7:00 A.M. to9:00 A.M. customers arrive at the buffet at a rate of eight perminute; from 9:00 A.M. to noon, at four per minute; fromnoon to 2:00, at 14 per minute; and from 2:00 P.M. to clos-ing at 5:00 P.M., at eight per minute (Poisson distributed).All the customers take about the same amount of time toserve themselves and proceed to the buffet. Once a cus-tomer goes through the buffet, it takes an average of0.4 minute (exponentially distributed) to pay the cashier.The gallery does not want a customer to have to wait longerthan four minutes to pay. How many cashiers should beworking at each of the four times during the day?

5-28. The Hair Port is a hair-styling salon at Riverside Mall. Fourstylists are always available to serve customers on a first-come, first-served basis. Customers arrive at an average rateof four per hour (Poisson distributed), and the stylists spendan average of 45 minutes (exponentially distributed) oneach customer.a. Determine the average number of customers in the

salon, the average time a customer must wait, and theaverage number waiting to be served.

b. The salon manager is considering adding a fifth stylist.Would this have a significant impact on waiting time?

5-29. The Riverton Police Department has eight patrol cars thatare on constant call 24 hours per day. A patrol car requiresrepairs every 30 days, on average, according to an exponen-tial distribution. When a patrol car is in need of repair it isdriven into the motor pool, which has a repairperson onduty at all times. The average time required to repair a pa-trol car is 12 hours (exponentially distributed). Determinethe average time a patrol car is not available for use and theaverage number of patrol cars out of service at any onetime, and indicate if the repair service seems adequate.

5-30. The Crosstown Cab Company has four cabs on duty duringnormal business hours. The cab company dispatcher re-ceives requests for service every seven minutes, on average,

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5-35. The Associate Dean in the College of Business at Tech isattempting to determine which of two copiers he shouldlease for the college’s administrative suite. A regular copierleases for $8 per hour and it takes an employee an averageof six minutes (exponentially distributed) to complete acopying job. A deluxe, high-speed copier leases for $16 perhour, and it requires an average of three minutes to com-plete a copying job. Employees arrive at the copying ma-chine at the rate of seven per hour (Poisson distributed) andan employee’s time is valued at $10 per hour. Determinewhich copier the college should lease.

5-36. The Corner Cleaners 24-hour laundromat has 16 wash-ing machines. A machine breaks down every 20 days(exponentially distributed). The repair service the laun-dromat contracts takes an average of one day to repair amachine (exponentially distributed). A washing machineaverages $5 per hour in revenue. The laundromat is con-sidering a new repair service that guarantees repairs in0.50 day, but they charge $10 more per hour than thecurrent repair service. Should the laundromat switch tothe new repair service?

5-37. The Ritz Hotel has enough space for six taxicabs to loadpassengers, line up, and wait for guests at its entrance.Cabs arrive at the hotel every 10 minutes and if a taxi dri-ves by the hotel and the line is full it must drive on. Hotelguests require taxis every five minutes on average andthen it takes a cab driver an average of 3.5 minutes toload passengers and luggage and leave the hotel (expo-nentially distributed).a. What is the average time a cab must wait for a fare?b. What is the probability that the line will be full when a

cab drives by and it must drive on?5-38. The local Quick Burger fast food restaurant has a drive-

through window. Customers in cars arrive at the window atthe rate of 10 per hour (Poisson distributed). It requires anaverage of four minutes (exponentially distributed) to takeand fill an order. The restaurant chain has a service goal ofan average waiting time of three minutes.a. Will the current system meet the restaurant’s service goal?b. If the restaurant is not meeting its service goal, it can add

a second drive-in window that will reduce the servicetime per customer to 2.5 minutes. Will the additionalwindow enable the restaurant to meet its service goal?

c. During the two-hour lunch period the arrival rate ofdrive-in customers increases to 20 per hour. Will thetwo-window system be able to achieve the restaurant’sservice goal during the rush period?

5-39. From 3:00 P.M. to 8:00 P.M. the local Big-W Supermarket hasa steady arrival of customers. Customers finish shopping andarrive at the checkout area at the rate of 80 per hour (Poissondistributed). It is assumed that when customers arrive at thecash registers they will divide themselves relatively evenly sothat all the checkout lines are even. The average checkouttime at a register is seven minutes (exponentially distributed).The store manager’s service goal is for customers to be out ofthe store within 12 minutes (on average) after they completetheir shopping and arrive at the cash register. How many cash


registers must the store have open in order to achieve themanager’s service goal?

5-40. Customers arrive at the lobby of the exclusive and expen-sive Ritz Hotel at the rate of 40 per hour (Poisson distrib-uted) to check in. The hotel normally has three clerksavailable at the desk to check guests in. The average timefor a clerk to check in a guest is four minutes (exponen-tially distributed). Clerks at the Regency are paid $12 perhour and the hotel assigns a goodwill cost of $2 per minutefor the time a guest must wait in line. Determine if the pre-sent check-in system is cost effective; if it is not, recom-mend what hotel management should do.

5-41. The Delacroix Inn in Alexandria is a small exclusive hotelwith 20 rooms. Guests can call housekeeping from 8:00 A.M.to midnight for any of their service needs. Housekeepingkeeps one person on duty during this time to respond toguest calls. Each room averages 0.7 call per day to house-keeping (Poisson distributed), and a guest request requiresan average response time of 30 minutes (exponentially dis-tributed) from the staff person. Determine the portion oftime the staff person is busy and how long a guest mustwait for his or her request to be addressed. Does the house-keeping system seem adequate?

5-42. Jim Carter builds custom furniture, primarily cabinets,bookcases, small tables, and chairs. He only works on onepiece of furniture for a customer at a time. It takes him anaverage of five weeks (exponentially distributed) to build apiece of furniture. An average of 14 customers approachJim to order pieces of furniture each year (Poisson distrib-uted): however, Jim will only take a maximum of eightadvance orders. Determine the average time a customermust wait to receive a furniture order once it is placed andhow busy Jim is. What is the probability that a customerwill be able to place an order with Jim?

5-43. Judith Lewis is a doctoral student at State University, andshe also works full time as an academic tutor for 10 schol-arship student athletes. She took the job hoping it wouldleave her free time between tutoring to devote to her ownstudies. An athlete visits her for tutoring an average ofevery 16 hours (exponentially distributed), and she spendsan average 1.5 hours (exponentially distributed) with theathlete. She is able to tutor only one athlete at a time, andathletes study while they are waiting.a. Determine how long a player must wait to see

her and the percentage of time Judith is busy. Does the job seem to meet Judith’s expectations,and does the system seem adequate to meet the athlete’s needs?

b. If the results in part (a) indicate that the tutoringarrangement is ineffective, suggest an adjustment thatcould make it better for both the athletes and Judith.

5-44. Agents at the security gate at the Hurtsfield County RegionalAirport are able to check passengers and process themthrough the security gate at the rate of 52 per hour (Poissondistributed). Passengers arrive at the gate throughout the dayat the rate of 45 per hour (Poisson distributed).a. Determine the average waiting time and waiting line.

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nine per hour. It takes 25 minutes (exponentially distrib-uted) for a crane to unload a container from a truck, placeit on a flatbed railcar, and secure it. Suggest a waiting linesystem that will effectively handle this level of containertraffic at the inland port.

5-46. The Dominion Landing theme park has a new water ride,the Raging Rapids. The ride holds 36 people in boat-carsand it takes 4.1 minutes to complete the ride circuit. It alsotakes the ride attendants another 3.5 minutes (with virtu-ally no variation) to load and unload passengers. Passen-gers arrive at the ride during peak park hours at the rate of4.4 per minute (Poisson distributed). Determine the lengthof the waiting line for the ride.

b. The passenger traffic arriving at the airport securitygate varies significantly during the day and flight takeoffs tend to cluster making the passenger trafficvery heavy at specific times while at other times thereis little or no passenger traffic through the security gate.At the times leading up to flight takeoffs passengers arrive at a rate of 125 per hour (Poisson distributed).Develop and solve a waiting line system that can accommodate this increased level of passenger traffic.

5-45. The inland port at Pittsburgh is a transportation hub thattransfers shipping containers from trucks coming fromeastern seaports to rail cars for shipment to inland destina-tions. Containers arrive at the inland ports at the rate of

CASE PROBLEM 5.1

Streamlining the Refinancing Process

First National Bank has been swamped with refinancing

requests this year. To handle the increased volume, it

divided the process into five distinct stages and created

departments for each stage.

The process begins with a customer completing a loan

application for a loan agent. The loan agent discusses the

refinancing options with the customer and performs

quick calculations based on customer-reported data to

see if the customer qualifies for loan approval. If the

numbers work, the customer signs a few papers to allow

a credit check and goes home to wait for notification of

the loan’s approval.

The customer’s file is then passed on to a loan proces-

sor, who requests a credit check, verification of loans or

mortgages from other financial institutions, an appraisal

of the property, and employment verification. If any prob-

lems are encountered, the loan processor goes to the

loan agent for advice. If items appear on the credit report

that are not on the application or if other agencies have

requested the credit report, the customer is required to

explain the discrepancies in writing. If the explanation is

acceptable, the letter is placed in the customer’s file and

the file is sent to the loan agent (and sometimes the

bank’s board) for final approval.

The customer receives a letter of loan approval and is

asked to call the closing agent to schedule a closing date

and to lock in a loan rate if the customer has not already

done so.

The closing agent requests the name of the customer’s

attorney to forward the loan packet. The attorney is respon-

sible for arranging a termite inspection, a survey, a title

search, and insurance and for preparing the closing papers.

The attorney and the closing agent correspond back and

forth to verify fees, payment schedules, and payoff amounts.

The loan-servicing specialist makes sure the previous

loan is paid off and the new loan is set up properly. After

the closing takes place, the bank’s loan-payment specialist

takes care of issuing payment books or setting up the

automatic drafting of mortgage fees and calculating the

exact monthly payments, including escrow amounts.

The loan-payment specialist also monitors late payment

of mortgages.

It is difficult to evaluate the success or failure of the

process, since the volume of refinancing requests is so

much greater than it has ever been before. However, cus-

tomer comments solicited by the loan-servicing specialist

have been disturbing to management.

Customer Comments:

• I refinanced with the same bank that held my

original loan, thinking erroneously that I could save

time and money. You took two months longer

processing my loan than the other bank would have,

and the money I saved on closing costs was more

than eaten up by the extra month’s higher mortgage

payments.

• I just got a call from someone at your bank claiming

my mortgage payment was overdue. How can it be

overdue when you draft it automatically from my

checking account?

• How come you do everything in writing and through

the mail? If you would just call and ask me these

questions instead of sending forms for me to fill out,

things would go much more quickly.

• If I haven’t made any additions to my house or prop-

erty in the past year, you appraised it last year, and

you have access to my tax assessment, why bother

with another appraisal? You guys just like to pass

around the business.

(Continued)

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CASE PROBLEM 5.2

Herding the Patient

Bayside General Hospital is trying to streamline its op-

erations. A problem-solving group consisting of a nurse,

a technician, a doctor, an administrator, and a patient is

examining outpatient procedures in an effort to speed

up the process and make it more cost-effective. Listed

here are the steps that a typical patient follows for diag-

nostic imaging:

• Patient enters main hospital entrance.

• Patient takes a number and waits to be called to reg-

istration desk.

• Patient registers.

• Patient is taken to diagnostic imaging department.

• Patient registers at diagnostic imaging reception.

• Patient sits in department waiting area until dressing

area clears.

• Patient changes in dressing area.

• Patient waits in dressing area.

• Patient is taken to exam room.

• Exam is performed.

• Patient is taken to dressing area.

• Patient dresses.

• Patient leaves.

1. Create a service blueprint of the procedure and

identify opportunities for improvement.

2. Describe what elements of a servicescape would

make this service more palatable to the customer and

efficient for the hospital staff.

CASE PROBLEM 5.3

The College of Business Copy Center

The copy center in the College of Business at State Uni-

versity has become an increasingly contentious item

among the college administrators. The department heads

have complained to the associate dean about the long

lines and waiting times for their secretaries at the copy

center. They claim that it is a waste of scarce resources

for the secretaries to wait in line talking when they could

be doing more productive work in the office. Hanford

Burris, the associate dean, says the limited operating bud-

get will not allow the college to purchase a new copier or

copiers to relieve the problem. This standoff has been

going on for several years.

To make her case for improved copying facilities, Lau-

ren Moore, a teacher in Operations Management, as-

signed students in her class to gather some information

about the copy center as a class project. The students

were to record the arrivals at the center and the length of

• I never know who to call for what. You have so many

people working on my file. I know I’ve repeated the

same thing to a dozen different people.

• It took so long to get my loan approved that my credit

report, appraisal report, and termite inspection ran

out. You should pay for the new reports, not me.

• I drove down to your office in person today to deliver

the attorney’s papers, and I hoped to return them with

your signature and whatever else you add to the clos-

ing packet. The loan specialist said that the closing

agent wouldn’t get to my file until the morning of the

scheduled closing and that if she hit a snag, the clos-

ing could be postponed! I’m taking off half a day from

work to attend the closing and “rescheduling” is not

convenient. I know you have lots of business, but I

don’t like being treated this way.

• I received a letter from one of your loan-payment

specialists today, along with a stack of forms to com-

plete specifying how I want to set up my mortgage

payments. I signed all these at closing—don’t you

read your own work? I’m worried that if I fill them

out again you’ll withdraw the payment twice from

my account!

1. Create a service blueprint of the refinancing process.

Why do you think the bank organized its process this

way? What problems have ensued?

2. Examine the process carefully. Look at customer/

provider interactions. Which steps create value for

the customer? Which steps can be eliminated?

Construct a new blueprint showing how the overall

process can be improved.

(Continued)

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time it took to do a copy job once the secretary actually

reached a copy machine. In addition, the students were to

describe how the copy center system worked.

When the students completed the project, they turned

in a report to Professor Moore. The report described the

copy center as containing two machines. When secre-

taries arrive for a copy job, they join a queue, which

looked more like milling around to the students, but they

acknowledged that each secretary knew when it was his

or her turn, and, in effect, the secretaries formed a single

queue for the first available copy machine. Also, since

copy jobs are assigned tasks, secretaries always stayed

to do the job no matter how long the line was or how long

they had to wait. They never left the queue.

From the data the students gathered, Professor Moore

was able to determine that secretaries arrived every

eight minutes for a copy job and that the arrival rate was

Poisson distributed. Furthermore, she was able to deter-

mine that the average time it takes to complete a job was

12 minutes, and this is exponentially distributed.

Using her department’s personnel records and data

from the university personnel office, Dr. Moore deter-

mined that a secretary’s average salary is $8.50 per hour.

From her academic calendar she added up the actual

days in the year when the college and departmental of-

fices were open and found there were 247. However, as

she added up working days, it occurred to her that during

the summer months the workload is much less, and the

copy center would probably get less traffic. The summer

included about 70 days, during which she expected the

copy center traffic would be about half of what it is during

the normal year, but she speculated that the average

time of a copying job would remain about the same.

Professor Moore next called a local office supply firm

to check the prices on copiers. A new copier of the type in

the copy center now would cost $36,000. It would also re-

quire $8000 per year for maintenance and would have a

normal useful life of 6 years.

Do you think Dr. Moore will be able to convince the asso-

ciate dean that a new copy machine will be cost effective?

CASE PROBLEM 5.4

Northwoods Backpackers

Bob and Carol Packer operate a successful outdoor wear

store in Vermont called Northwoods Backpackers. They

stock mostly cold-weather outdoor items such as hiking

and backpacking clothes, gear, and accessories. They

established an excellent reputation throughout New

England for quality products and service. Eventually, Bob

and Carol noticed that more and more of their sales were

from customers who did not live in the immediate vicinity

but were calling in orders on the telephone. As a result,

the Packers decided to distribute a catalog and establish a

phone-order service. The order department consisted of

five operators working eight hours per day from 10:00 A.M.

to 6:00 P.M., Monday through Friday. For a few years the

mail-order service was only moderately successful; the

Packers just about broke even on their investment. How-

ever, during the holiday season of the third year of

the catalog order service, they were overwhelmed with

phone orders. Although they made a substantial profit,

they were concerned about the large number of lost sales

they estimated they incurred. Based on information pro-

vided by the telephone company regarding call volume

and complaints from customers, the Packers estimated

they lost sales of approximately $100,000. Also they felt

they had lost a substantial number of old and potentially

new customers because of the poor service of the catalog

order department.

Prior to the next holiday season, the Packers explored

several alternatives for improving the catalog order ser-

vice. The current system includes the five original opera-

tors with computer terminals who work eight-hour days,

five days per week. The Packers have hired a consultant

to study this system, and she reported that the time for

an operator to take a customer order is exponentially

distributed with a mean of 3.6 minutes. Calls are

expected to arrive at the telephone center during the six-

week holiday season according to a Poisson distribution

with a mean rate of 175 calls per hour. When all opera-

tors are busy, callers are put on hold, listening to music

until an operator can answer. Waiting calls are answered

on a first-in, first-out basis. Based on her experience

with other catalog telephone order operations and data

from Northwoods Backpackers, the consultant has deter-

mined that if Northwoods Backpackers can reduce cus-

tomer call waiting time to approximately one-half minute

or less, the company will save $135,000 in lost sales dur-

ing the coming holiday season.

Therefore, the Packers have adopted this level of call

service as their goal. However, in addition to simply

avoiding lost sales, the Packers believe it is important to

reduce waiting time to maintain their reputation for good

customer service. Thus, they would like about 70% of

their callers to receive immediate service.

(Continued)

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The Packers can maintain the same number of work-

stations/computer terminals they currently have and

increase their service to 16 hours per day with two opera-

tor shifts running from 8:00 A.M. to midnight. The Packers

believe when customers become aware of their extended

hours the calls will spread out uniformly, resulting in a

new call average arrival rate of 87.5 calls per hour (still

Poisson distributed). This schedule change would cost

Northwoods Backpackers approximately $11,500 for the

six-week holiday season.

Another alternative for reducing customer waiting

times is to offer weekend service. However, the Packers

believe that if they do offer weekend service, it must coin-

cide with whatever service they offer during the week. In

other words, if they have phone order service eight hours

per day during the week, they must have the same ser-

vice during the weekend; the same is true with 16-hours-

per-day service. They feel that if weekend hours differ

from weekday hours it will confuse customers. If eight-

hour service is offered seven days per week, the new call

arrival rate will be reduced to 125 calls per hour at a cost

of $3600. If Northwoods offers 16-hour service, the mean

call arrival rate will be reduced to 62.5 calls per hour, at

a cost of $7300.

Still another possibility is to add more operator sta-

tions. Each station includes a desk, an operator, a phone,

and a computer terminal. An additional station that is in

operation five days per week, eight hours per day, will cost

$2900 for the holiday season. For a 16-hour day the cost

per new station is $4700. For seven-day service, the cost of

an additional station for eight-hour per-day service is

$3800; for 16-hour-per-day service the cost is $6300.

The facility Northwoods Backpackers uses to house its

operators can accommodate a maximum of 10 stations.

Additional operators in excess of 10 would require the

Packers to lease, remodel, and wire a new facility, which

is a capital expenditure they do not want to undertake

this holiday season. Alternatively, the Packers do not

want to reduce their current number of operator stations.

Determine what order service configuration the

Packers should use to achieve their goals, and explain

your recommendation.

REFERENCES

Chase, R., F. R. Jacobs, and N. Aquilano. Operations Manage-ment for Competitive Advantage. New York: McGraw-Hill/Irwin, 2005.

Cooper, R. B. Introduction to Queuing Theory, 2nd ed. New York:North Holland, 1981.

Davis, M., and J. Heineke. Operations Management. New York:McGraw-Hill/Irwin, 2004.

Fitzsimmons, J., and M. Fitzsimmons. Service Management.New York: McGraw-Hill/Irwin, 2004.

Gross, D., and C. Harris. Fundamentals of Queuing Theory, 2nd ed.New York: Wiley, 1985.

Hillier, F. S., and O. S. Yu. Queuing Tables and Graphics. NewYork: North Holland, 1981.

Kleinrock, L. Queuing Systems, vols. 1 and 2. New York: Wiley,1975.

Lee, A. Applied Queuing Theory. New York: St. Martin’s Press,1966.

Lovelock, C. H. Managing Services: Marketing, Operations, andHuman Resources. Englewood Cliffs, NJ. Prentice Hall, 1992.

Morse, P. M. Queues, Inventories, and Maintenance. New York:Wiley, 1958.

Prahalad, C. K., and Venkat Ramaswamy. The future of Competi-tion: Co-creating Unique Value with Customers. Boston:Harvard Business School Press, 2004.

Saaty, T. L. Elements of Queuing Theory with Applications. NewYork: Dover, 1983.

Sampson, S. E. Understanding Service Businesses. Salt LakeCity, UT: Brigham Young University, 1999.

Shostack, G. L. “Designing Services That Deliver.” HarvardBusiness Review (January–February 1984), pp. 133–139.

Solomon, S. L. Simulation of Waiting Line Systems. Upper SaddleRiver, NJ: Prentice Hall, 1983.

White, J. A., J. W. Schmidt, and G. K. Bennett. Analysis ofQueuing Systems. New York: Academic Press, 1975.

Zeithaml, V. Service Quality. Cambridge, MA: Marketing ScienceInstitute 2004.

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