WEEK-16

WAITING LINE MANAGEMENT

Waiting lines abound in all sorts of service systems. And they are non-value-

added occurrences. For customers, having to wait for service can range from being acceptable (usually short waits), to being annoying (longer waits), to being a matter of life and death(e,g., in emergencies). k?,- businesses, the costs of waiting comes from lower productivity and competitive

disadvantage) For society, the costs are wasted resources (e.g.., fuel consumption of cars stuck in traffic) and reduced quality of life. Hence, it is important for system designers and managers of existing service systems to fully appreciate the impact of waiting lines.

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i() 527 hecorne.,s temporarily overloaded, giving. rise to Waiting lines; at other times,

4 the system is idle because there are no customers: It follows that in systems where variability is minimal or nonexistent ,waiting lines do not ordinarily

form. Managerial Implications of Waiting Lines Managers have a number of very good reasons to be concerned with waiting

tines. Chief among those reasons are the following;

1. The cost to provide waiting space.

2. A possible loss of business should customers leave the line before

being served or refuse to wait at all.

3. A possible loss of goodwill.

4. A possible reduction in customer satisfaction.

5. The resulting congestion that may disrupt other business operatiosn

and/or customers.

Goal of waiting-line Analysis: '

The goal of queuing is essentially to minimize -total costs. 'i here are two

basic categories of cost in queuing situation: those associated with customers waiting for service and those associated with capacity. Capacity costs are the

costs of maintaining the ability .to provide service. Examples include the number of b-ayktrat a car wash, the number of checkouts at a supeunarket, the n__..----- . . ).-)'S number of repair people to handle equipment breakdowns, and the number

of lanes on a highway. en a service _ e ca acity is lost since it

C) cannot be stored The customer waiting include the salaries paid to

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employees while they waitfor service (mechanics waiting for tools, the drivers of trucks waiting to unload), the cost of the space for waiting ( size of doctor's waiting room, length of driveway at a car wash, fuel consumed

by planes waiting to land), and any loss of business due to customers refusing to wait and possibly going elsewhere in the future.

A practical difficulty frequently encountered is pinning down the cost of

' ,_customer waiting time, especially since major portions of that cost are not a part of.accouniing data. One approach often used is to treat waiting times or the line lengths as a policy variable: A manager simply specifies an acceptable level of waiting and directs that capacity be'established to

Lachieve that level.

Characteristics of waitin: Lines

There are numerous m ear from which an analyst can choose. Naturally, much of the success of the anal is will depend on choosing an appropriate model. Model choice is affected by the characteristics of the system under investigation. The main characteristics are

1. Population source 2. Number of servers (channels) 3. Arrival and service patterns 4. Queue discipline (order of service)

Population Source "),4

" The approach to use in analyzing a queuing problem depends on whether

the potential number of customers is limited. There are two possibilities: infinite-source and finite-source populations. In an infinite-source

situation, the potential number of customers greatly exceeds system

capacity. Infinite-source situations exist whenever service is tinrestricld.

Examples are supennarlcets, drugstores, banks, restaurants, theatres, amusement centers, and toll bridges. Theoretically, large numbers of

customers from the "calling population" can request service at any time.

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When the poter.tial number.of customers is limited, .d finite-source.

situation exists. An examples is the repairman responsible for a certain number of machines in a company. The potential number of machines

that might need repairs at any one time cannot .exceed the number of

machines assigned to the repairer.

Number of Servers (Channels) 1 The capacity of queuing systems is a function of the'Capacity of each

t\_/ server and the number of servers being used. The terms server and

\,_,. channel are synonymous, and it is generally assumed that each channel

v can handle one customer at a time. Systems can be either single- or i-` ,,cf multiple-channel. Example of single-channel systems are small grocery

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stores with one checkout counter, some theatres, single-bty car washes, and chive-in banks with one teller. Multiple-channel systems (those with more than one server) are commonly found in banks, at airline ticket counters, at auto service centers, and at gas stations.

A related distinction is the number of stepS or phases in a queuing system:For example, at theme parks, people go from one attraction to

c.. ;) another. Each attraction constitutes a separate phase where queues can form. Arrival and Service Patterns Waiting lines area direct result of arrival and service variability. They

) ,, occur because random, highly variable arrival and service patterns cause systems to be temporarily overloaded. .1_14,1=fratry--___imst-ainces-tla.:abilities-

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- ,_-: Queue Discipline (`" Queue discipline refers to the order in which customers are processed.

A11.1 but one of the models to be described shortly assume that service is \-___

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Examples of systems that do not serve on a first-comc-- basi- d e .., rn (----)

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processing of jobs. In these and similar situations, customers do not all - --

represents the same waiting costs-;--those_with the hig.hest C.O.StS4, e.g., the

most seriously ill) are_processed first, even tlIol(),_ther_customers may have arrived earlier.

Measures of waiting Line Performance

The Operations manager typically looks t five measures when evaluating existing or proposed service systems: 1. The average number of customers waiting, either in line or in the

system.

2. The average time customers wait, either in line or inthe system. 3. System utilization

-which refers to the percentage of capacity utilized. 4. The implied cost of a given level of capacity and its related waiting

line. 5. The probability that an arrival will have to wait for service.

Of these measures, system utilization bears some elaboration. It reflects the extent to which the servers are busy rather than idle. On the surface, it

might seem that the operations manager would want to seek 100 percent

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