Chapter

Service Facility LocationLearn ing Otlie ctivesAfter completing this chapter, you should be able to:1, Explain the difference between competitive clustering and saturation marketing.2. Explain the impact of the lnternet on location decisions.3. Describe how a geographic information system is used in service location decisions.4. Ditferentiate between a Euclidian and metroporitan metric approach to measuring traver

distance.5. Locate a single facility using the cross-median approach.6, Use the Huff retail location model to estimate revenue and market share for a potential

site.7. Locate multiple facilities using the set covering model.From a marketing perspective service location focuses on attracting customers to a sitebecause of convenience (e.g., fast food restaurants located on a high traffic street) orphysical attributes (e.g., resort on a beautiful beach). However, location also affects theservice delivery design and has an impact on employees. Consider the experience of aninsurance firm in Los Angeles._

A study by David A. Lopez and Paul Gray illustrates how an insurance company inI os Angeles decentralized its operations by using telecommunications and stratigicallylocating its satellite offices.l An examination wai made of the benefits and costs to theinsurance firm when work was moved to the workers rather than when workers movedto their work. Insurance companies and other information-based industries are goodcandidates for employer decentralization, because members of their office staffperformroutine clerical tasks using the firm's computer databases. The proposed plan replacedth,e_ centralized operation in downtown Los Angeles with a netw;rkof regional satelliteoffices in the suburbs where the workers live.

The analysis also included a location study to determine the size, site, and number olsatellites that would minimize the variable costs associated with employee travel and thefixed costs of establishing the satellite offices. The decentralizatiorrplin yielded severalbenefits to the company: (l) reduced staff requirements, (2) reduced employee tumoverand training, (3) reduced salaries for clerical employees, (4) eliminatiorrof a lunch pro-gram, and (5) increased income from lease of the headquarters site. Employees whosetravel to work was reduced by at least 5% miles realized a net benefit over their reducedsalary and loss ofsubsidized lunch. This employee benefit is important in light ofincreas-ing energy expenses for transportation._

It w-as found that underwdting life insurance and servicing insurance policies couldbe performed at remote locations using online computers. phone communications usu_{ly were sufficient for personal contacts, and iew face-to-face meetings were needed.These findings substantiate those of other studies in Britain and Sweden indicating that

235

236 Paftfwo Designlng the Setvrce Enterprise

individuals require face{o-face contacts only for initial meetings and periodic refresh-ing; they do not require continual face-to-face contact to reach decisions and conductroutine business.

Traditionally, location decisions have been based on intuition and had a considerablerange of success. Although site selection often is based on oppofiunistic factors such assite-availability and favorable leasing, a quantitative analysis can be useful to avoid a seri-ous mistake. For example, regardless ofhow low the rent may be, being the only store ira deserted shopping mall offers no advantage.

This chapter begins with a discussion ofstrategic location considerations For example-the strategies ofcompetitive clustering or saturation malketing are used to attract custorn-ers to a service site. Other sewice delivery strategies, such as using marketing interme-diaries and the Intemet, remove the need for customer travel and, thus, a decision on sit;location can be based on other considerations, such as cost or availability ofskilled laborGeographic information systems (i.e., demand and its characteristics distributed across:ma.iet area; are a critical input to location models. The chapter concludes with a discus-sion of modeling considerations and a review of several facility location techniques fc;both single- and multiple-facility situations

5trat* ic l-oc*ti*n e*nsisJ*raticr'!sIn a study of La Quinta Motor Inns to leam why some inns were successful and othe:-'not, several strategic location dimensions were discovered including flexibility' comper:-tive posirioning, dlemand managernent, and focus.2

Flexibility of a location is a measure of the degree to which the service can react ::changing economic situations. Because location decisions are long-term commitmen'-:with capital-intensive aspects, it is essential to select locations that can be responsive ::future economic, demographic, cultural, and competitive changes. For example, loca:-ing sites in a number of states could reduce the overall risk of a financial crisis resultir-_:from regional economic downtums. This portfolio approach to multisite location cou-:be augmented by selecting individual sites near inelastic demand (e.g., locating a hot;'near a convention center).

Competitire positiot?lrg refers to methods by which the firm can establish itself rel:-tive to its competitors. Multiple locations can serve as a barrier to competition throug:building a firm's competitive position and establishing a market awareness. Acquirir.and holding prime locations before the market has developed can keep the competitic-from gaining access to these desirable locations and create an artificial barrier to enq'(analogous to a product patent).

Demand managemetl is the ability to control the quantity, quality, and timing c:demand. For example, hotels cannot manipulate capacity effectively because ofthe fixeinature ofthe facility; however, a hotel can control demand by locating near a diverse s-'-of market generators that supply a steady demand regardless of the economic conditiorthe day of the week. or the season.

Focus canbe developed by offering the same nanowly defined selvice at many loc3-tions. Many multisite service firms develop a standard (or formula) facility that can binfinite possibilities. Facilities may be located anywhere on the plane and are identifie;by an xy cartesian coordinate (or, in a global context, by latitudes and longitudes). a.shown in Figure 10.3. Distance between locations is measured at the extremes in one a:

Population Densityby Age Group li,rtdl

.: :|rL

Flll

'ils ,, I .F

Population Age Croups

t0-rl 55- s"fl

=cut[ 10.2Orssilication of Servicefrility Location Issues

:rcuRF 10.3G..graphic Structure

Chapter I0 Service Facilit! Location 143

two ways. One method is the euclidian metric, or yector, travel distance (remember thePythagorean theorem), which is defined as

tl, '",, l.$i - x t )12 't (_r, -- y , ).1)l

whered;; : distance between points i andl

x;,1 = coordinates ofthe ith pointxj, yj : cootdinales oftheTth pointFor example, if

thc origin x,, li :2,2 zurdthen

d,, == l{2 ^' q2 + (2 - 4)t1l .=. z.x:The other method is the metropolitan metric, or rectangttlar displacement, travel dis-

tance (i.e., north-south and east-west travel in urban areas), which is defined as

(2)

d,, : )x, - xi 't )y, '- !t1

Location on a Plan

llrc destinatiorr r-r, -y, = 4.4

Location on a Network

{3)

244 Patlfwo Designing the Serrice Enteryrise

Using the same example from above for the metropolitan metric:

d,, =., ;2 , 1l .+. 2 _ 4i,,,,, 4.0

Location on a network is characterized by a solution space that is restricted to thenodes of that network. For example, a highway system could be considered a network.with major highway intersections as nodes. The arcs of the network represent travel dis-tance (or time) between pairs of nodes, calculated using the shortest route.

The selection ofgeographic representation and distance metric often is dictated by theeconomics ofthe data collection effort and the problem environment. Networks can rep-resent more accurately the geographic uniqueness of an area (e.g., the travel restrictionscaused by a river with few bridges or by mountainous terrain). Unfortunately, the cost olgathering the travel tirres between nodes can be prohibitive. When locating is done on aplane that represents an urban area, the metropolitan metric often is used, because streetsfor some cities are arranged in an east-west and north-south pattern. Both the metro-politan and euclidian metrics require an estimate ofthe average speed to convert distancetraveled to time.

Number of FacilitiesThe location of a single facility generally can be treated mathematically with little dii-ficulty. Unfortunately, the methods used to site a single facility do not guarantee optimalresults when they are rrodified and applied to multisite location problems. Finding;unique set of sites is complicated by assigning demand nodes to sites (i.e., defining ser-vice areas for each site), and the problem is corrplicated further ifthe capacity at each sii;varies. In addition, for some services such as health care, a hierarchy of service exisL..Private physicians and clinics offer primary care, general hospitals provide primary careplus hospitalization, and health centers add special treahnent capabilities. Thus, the selec-tion of services provided also may be a variable in multisite location studies.

Optimization CriteriaPrivate and public sector location problems are similar in that they share the objectir':of maximizing sone measure of benefit. The location criteria that are chosen diffe:.however, because the "ownership" is different. Within the private sector, the locatio:-decision is governed by either minitrization ofcost (e.g., in the case ofdistribution ceni-ers) or maximization of profit (e.g., in the case of retail locations). In contrast, we lik:to think that public facility decisions are governed by the needs of society as a wholeThe objective for public decision making is to maximize a societal benefit that may bsdifficult to quantify.

Private Sector CriteriaTraditional private sector location analysis focuses on a trade-off between the cost c:building and operating facilities and the cost of transportation. Much of the literatur:has addressed this problem, which is appropriate for the distribution of products (i.e.the warehouse location problem). These models may find some applications in service-.-however, when the services are delivered to the customers (e.g., consulting, auditinr.janitorial, and lawn care services).

When the consumer travels to the facility, no direct cost is incurred by the provide:Instead, distance becomes a barrier restricting potential consumer demand and the co:-responding revenue generated. Facilities such as retail shopping centers therefore a--:located to attract the maximum number ofcustomers.

Public Sector CriteriaLocation decisions in the public sector are complicated by the lack of agreement c:goals and the difficulty of measuring benefits in dollars to make trade-offs with facili,.

Chapter 10 Set ce Faciliry Location 245

investment. Because the benefits of a public service are difficult to define or quantifydirectly, surrogate (or substitute) measures ofutility are used.

The average distance traveled by users to reach the facility is a popular sunogate. Thesmaller this quantity, the more accessible the system is to its users. Thus, the problembecomes one of minimizing the total average distance traveled, with a constraint on thenumber of facilities. The problem is additionally constrained by some maximum traveldistance for the user. Another possibility is the creation ofdemand. Here the user popula-tion is not considered fixed but is determined by the location, size, and number offacili-ties. The greater the demand created or drawn, the more efficient the system is in fillingthe needs of the region.

These utility surrogates are optimized with constraints on investment. Analysis ofcost-effectiveness usually is performed to examine trade-offs between investment andutility. The trade-offs for the surrogates are (l) the decrease in average distance traveledper additional thousand-dollar investment and (2) the increase in demand per additionalthousand-dollar investment.

Effecl of Optimization Criteria on LocationThe selection of optimization criteria influences service faciliry location. For example,William J. Abemathy and John C. Hershey studied the location of health centers for athree-city region.s As part of that study, they noted the effect of health-center locationswith respect to the following criteria:

I. Maximize utilizalion. Maximize the total number of visits to the centers.2. Minimize distance per capita. Minimize the average distance per capita to the closest

center.

3. Minimize distance per yisit. Minimize the average per-visit travel distance to the near-est center.

The problem was structured so that each city had a population with a different mixofhealth care consumption characteristics. These characteristics were measured alongtwo dimensions: (l) the effect of distance as a barrier to health care use and (2) theutilization rate at immediate proximity to a health care center. Figure 10.4 shows amap of the three cities and the location of a single health care center under each of thethree criteria. These criteria yield entirely different locations because of the differentbehavioral patterns of each city. For criterion I (maximize utilization), the center islocated at city C, because this city contains a large number of elderly individuals forwhom distance is a strong barrier. City B is selected under criterion 2 (minimize dis-tance per capita), because this city is centrally located between the two larger cities.City A is the largest population center and has the most mobile and frequent users ofhealth care; therefore, criterion 3 (minimize distance per visit) leads to this city beingselected-

c Center: auRE 10.4L.{ation ofOne HealthC.nter for Threeoiferent Criteriaff.: w. J. Abenathy and.l. C.+-E).'. A Spati.l-Allocatio.'i:ti.l for Regional Halth-SNicsraning. Rep.inted with pemis'6 arcn Op.tu b s R.seurchtr. N 3. l9?2, p.637, Operaiions+5.ah Society of Amsica. NoE3d.eproduciion pemined.tNl the c onsenr of rhe c opyrighr

Criterion govemingcenter loca(ions

L Utilizarion2. Distance pr capita3. Distance per visit

2J6 Pari Two Destg, ing the Setrice Enterprise

Facili N-oeatia:n Tec["]niAn understanding ofthe facility location problem can be gained from the results oflocat-ing a single facility on a line. For example, consider the problem of locating a beachmat concession along the beach front at Waikiki. Suppose you wish to find a locationthat would minimize the average walk to your concession from anywhere on the beachFurther, suppose you have data showing the density of bathers along the beachfront.which is related to the size and location of hotels. This distribution of bathers is shorvnschematically in Figure 10.5.

The objective isl,(s

-.r,) +')r.r',1,r; r)i_'

w, -

weight of demand (bathers) attached to the ith location on the beachxi : location ofthe lth dernand point on the beach in yards from the west end ofthe

beachs : site of the beach mat concessionThe total-distance function Z is differentiated with respect to s and set equal to zero

This yields

Minimize Z :

where

:,i-rl

This result suggests that the site should be located at the median with respect to th.density distribution ofbathers. That is, the site is located so that 50 percent of the poter-tial demand is to each side (i.e.,29 in Figure 10 5). We probably should have expecte:this, because the median has the property of minimizing the surr of the absolute devi:'tions from it.

The result for locating a site along a line can be generalized for locating a site on :plane if we use the metropolitan metric. Total travel distance will be minimized if th.coordinates of the site correspond to the intersection of the x and y medians for the-:respective density distributions. We will refer to this as the cross-nredian approach.

The selection of a solution technique is determined by the characteristics of the prof-lem, as outlined in Figure 10.2. Our discussion of location techniques is not exhaustir :but a few techriques will be discussed to illustrate various approaches to the probler'

J'' : \ ''.

T,'. : (r ur,lsa?

I 5 6 '7 8 9 l0ill 12\Yaikiki Beach Marked Off in Yards

s

s.,, : t" (s).a-|/)|

ncutt! 1 .5Location of BeachConcession +Iltt =

,,^,, = 29 4

Chapter 10 Serri.e Faciti\ Locotion j\?

The selected techniques also represent approaches that deal with the various problemcharacteristics: single-facility versus multiple-facility location, location on a plane or anetwork, and public versus private optimization criteria.

Cross Median Approach for a Single FacilityLocating a single facility on a plane to minimize the total travel distance Z by meansofthe metropolitan metric is straightforward using the cross-median approach. Theobjective is

w, : weight attached to the fth point (e.g., trips per month).r,,yi : coordinates ofthe ith demand point.r.,1" = coordinates ofthe service facility

n - number ofdemand points served

Note that the objective function may be restated as two independent terms.

Nlirirnize ./ frL:r t '

t,, ' '-a-L-,.i- | r-i

(r)

Recall from our beach mat example that the median of a discrete set of values is suchthat the sum ofabsolute deviations from it is a minimum. Thus, our optimum site will havecoordinates such that (1) x. is at the median value for w, ordered in the

"r direction and (2)1is at the median value for w, ordered in they direction. Because r.,.1,, or both may be uniqueor lie within a range, the optimal location may be at a point, on a line, or within an area.A copying service has decided to open an office in the central business district of a city. Themanager has identified four office buildings that will generate a major portion of its busi-ness, and Figure 10.6 shows the location of these demand points on an xy coordinate system.Weights are attached to each point and represent potential demand per month in hundredsof orders, The manager would like to determine a central location that will minimize the totaldistance per month that customers travel to the copying service.

\1ir irrrize

where

Z ,.,, lw,\)r, '- .r..: I r.1,, - r.. I

:, : rirJrle '10-'1-: u",inE servicr:

::!R[ 1 .6-'!cating a Copying:tnice Using Cross-Uedian Approach

'fz1.r=11

s zl (rra = 5)

24E Paftfwo Designing the Seflice Enteryrise

TABLE 10.4Mediah Value for

-r.

TA,&t[ 1S.5Median Value fory.

78

58

Because of the urban location, a metropolitan metric is appropriate. A site located by thecross-median approach will be used to solve this problem. First, the median is calculated usincequation (8):

Mcdian - i.+ {E)=2

From Figure 10.6, we find that the median hasavalueof (7 + 1 + 3 + 5)/2:8. To ider-tify the x-coordinate median for xe we sum the values of wi in the x direction both west t:east and east to west. The top half of Table 10.4 lists in descending order the demand poin'.:from west to east as they appear in Figure 10.6 (i.e., 1, 2, 3, 4). The weights attached to eac-demand point are summed in descending order until the median value of 8 is reached c'exceeded. The median value of 8 is reached when the weight of location 2 is added to th:weight of location l: thus, the first x median is established at the value of 2 miles (i.e., th:x coordinate of location 2 is circled).

This procedure is repeated with demand points ordered from east to west, as shown i-descending order in the bottom half of Table 10.4 (i.e., 4, 3, 2, 1). The second x median ,established at the value of 3 miles (i.e., the x coordinate of location 3 is circled).

Table 10.5 illustrates the same procedure for identifying the y-coordinate median for ys. Tt-:top half of Table 1 0.5 lists in descending order the demand points from south to north as the.appear in Figure I0.6 (i.e., 4, 1, 2, 3). ln this case, the median value of 8 is first exceeded i:location I when its weight is added to that of location 4 to yield a total of 12. The ymedian :established at the value of 2 miles (i.e., the y coordinate of location 1 is circled). At the botto-of Table 10.5, the demand points from north to south are listed in descending order as the,

2wi

.' 5q

t.

3

3

'l*1

=5+7:'12

+7:11

321

3

Q)4

Chapter l0 Ser|ice Focili^, Lo.:atiotl ?49

appear in Figure 10.6 (i.e., 3, 2, 1, 4). Again, the median value is first exceeded at location 1when its weight is added to those ol locations 3 and 2 to yield a total of 11. Thus, we are leftwith only one y median at 2 miles.

The cross-median approach of determining the median from all four points of the compassensures that if a range of locations is appropriate, it will be identified readily. ln this case, anylocation on the line segment AB mlnimizes total travel distance (e.g., coordinates 2 = xs:3and % = 2).

Note from Table 10.6 that the total weighted travel distance calculated for point A andpoint B is equal to 35 m;les in both instances; thus, any location at either point A or point B oralong the line between them will be acceptable. As this example illustrates, a location solutioncan be a line (i.e., a city street), a point (i.e., an inter5ection), or an area (i.e., a city block).Thus, the cross-median approach can result in some site selection flexibility.

Huff Model for Retail OutletWhen locating a retail outlet such as a supermarket, the objective is to maximize profit.ln this case, a discrete number of alternative locations must be evaluated to find the mostprofitable site.

A gravity model is used to estimate consumer deniand. This model is based on thephysical analog that the gravitational attraction ol two bodies is directly proportionalto the product of their masses and inversely proportional to the square of the distancethat separates them. For a seryice, the attractiveness of a lacility may be expressed as

where

lii - attraction to facilityT for consumer I

,t : size ofthe facilityTZ,t : travel time from consumer r''s location to facilityl\ : parameter estimated empirically to reflect the effect of travel time on various

kinds of shopping trips (e.g., where a shopping mall may have a \ : 2, conven-ience stores would have a tr' : l0 or larger)

David L. Hulfdeveloped a retail location model using this gravity model to predict thebenefit that a customer would have for a particular store size and location.9 Krowing thatcustomers also would be attracted to other competing stores, he proposed the ratio P,r.

: -: -: 1 $.6 Total Weighted Distanc for Locations A and B

Location A (2,2)

j .1,/,ri ril

Cffice1

23

4

Distance1

1

43

Weight7

l3

5

Total142

XXXX

9i03i

25l Part Two Dsig,? itlg he Seryice Enterprise

For r stores, this ratio measures the probability ofa customer from a given statistical arear'traveling to a particular shopping facilityj.

4i,

s,

An estimate of Ejk,lhe total annual consumer expenditures for a product class k at aprospective shopping facilityT, then can be calculated as

F;i, ,= 2{Plic'iB,t)i=l

TA31 l t O.7Travel Distance in Miles(fr) (Using MetropolitanMetric)

where

Pu : probability of a consumer from a given statistical area i traveling to a shoppingfacilityT, calculated by means ofequation (10)

C, - number ofconsumers al area i.B;1 = average annual amount budgeted by consumer at area i for a product class trrt - nurnber ofslatislical areas

An estimate of Mrt, the market share captured by facilityl ofproduct class k sales, ca:be calculated as

8,,l/,:- " ''21L c',rs*,=1

An exhaustive procedure is used to calculate the expected annualprofit ofeach poter-tial site for various possible store sizes at the site. Net operating profit before taxes r:calculated as a percentage of sales adiusted for the size of the store. The result is a lis:ofpotential sites with the store size at each that maximizes profit. All that remains is r:negotiate a real estate deal for lhe site that comes closest to maximizing annual profit.

I21

33

4

42

3

TASLI 10,8Attraction (lr)

.t.

site (i)Proposed (51 : 2)xisting (52 = 1)Total attraction

Customer Location (i)1234

0.5 0.s 0.2222 0.50019 l! 9.99s i,' 9,tlL1.5 1.5 0.2847 0.61 l

Chapter 10 Set|icc Facility Locatiotl ?51.

' 'J "'-:,bability (P,r)

Site (/)ProposedExisting

Customer Location (i)1

.33

.67

2.33.67

3.74.22

4.82.18

L li,. til.! r othly Expendituresi r and Market Shar

i,.i , , rt

Customer Expenditures

Site (r)Proposed

ExistingTotals

I$2,3 334,667

23$ 333 $2,340667 660

Monthly Market4 Total Share o/o

$4,100 $9,106 0.s7900 6,894 0.43

r ' r',t1ri* !*.1: ..1 I'i**iral

. .ir'r

$7,000 $r,000 $3,000 $s,000 $r 6,000 1.00

Assume that the copying service in Example 10.1 has been established at (x = 2, y: 2), asshown by location A in Figure 10.6 (on p. 247) at the far left end of the optimal line. Further,assume that each customer order represents an expenditure of approximately $10. Becauseconvenience would be an important customer criterion, assume that tr : 2. lf we wish toopen a competing store at location (x: 3, y:2) (i.e., at location B on the far right end ofthe optimal line) but with trvice the capacity of the existing copy center, how much marketshare would we expect to capture? Using the travel distances in Table 10.7 as input to the Huffmodel, the calculations shown in Tables 10,8 to 1 0.'10 are obtained.

This example illustrates the result of an aggressive location strategy as used by well-financednational retail chains. For example, as the name might impl, Blockbuster Video has a reputa-tion of moving into a community with supersized stores and driving out small, locally oper-ated video-rental establishments.

Location Set Covering for Multiple FacilitiesThe difficulty of evaluating decisions regarding public facility location has resultedin a search for surrogate, or substitute, measures of the benefit of the facility location.One such measure is the distance that the most distant customer would have to travelto reach the facility. This is known as lhe maximql service distance. we want to findthe minimum number and location of facilities that will serve all demand points withinsome specified maximal service distance; this is known as lhe locqlion sel coNeringproblem.

A state department of health is concerned about the lack of medical care in rural areas, anda group of nine communities has been selected for a pilot program in which medical clinicswill be opened to serve primary health care needs. lt is hoped that every community will bewithin 30 miles of at least one clinic. The planners would like to determine the number ofclinics that are required and their locations. Any community can serve as a potential clinic siteexcept for community 6, because facilities are unavailable there. Figure 10.7 shows a network

: il ltt I l].1-:a!el Net\rork for ai irel Area

5

; r -

Part Two ,eslg, ing the Setri.e Enterprise

-IBLE 10.1 1Range of Sen ice forPotential Sites

'Conrmunrr\ 6 cannor serle as a

' S!bseri of porential slres.

Community1

23456789

Set of Communitiesserved from Site

1 ,2,3,41,2,3

1,2,3,4,51,3,4,5,6,7

3,4,5,64,5,6,7,8

4,6,7 ,86,7,8,9

8'9

Potential Sites That CouldServe the Community*

1,2,f,4(1,2))1

1,2,3,4,51,3,4,5,7(3,4,rr4,5,7 ,8(4,7,qr

7,4,9(8,e)t

identifying the cities as numbered circles; lines drawn between the sites show the travel di5-tances in miles.

The problem is approached by first ldentifying for each community the other commun 'ties that can be reached from it within the 30-mile travel limit. Beginning with community Iwe see in Figure 10./ that communities 2, 3, and 4 can be reached within the 30-ml :distance limit. The results ol similar inspections for each community are reported in th:second column of Table 10.1 I as the set of communities served from each site. An equlva'lent statement could be made that this set, less any communities that could not serve z:a site, represents the set oI sites that could cover the community in question for servic.within 30 miles. Thus, for community 5, a clinic located at site 3,4, or 5 meets the maxim-travel limit.

The third column of Table 10.11 represents the set of potential sites that could cover.given community. Several of these sets have been placed in parentheses, however, becaus:they represent subsets of other potential locations. For example, because community 2 ce-only be served by sites 1, 2, and 3, one of these sites must be selected for a clinic loc:-tion. ldentifying these subsets reduces the problem size while ensuring that restrictions a-.satisfied.

Note that because of our desire to minimize the number of clinics to cover all the comn'r-nities, any site common to two or more of these subsets is an excellent candidate for selectio-ln this case, sites 3, 4, and 8 are candidates. From inspection, we see that if sites 3 and 8 a'.selected, all subsets are accounted for; thus, all communities can be covered with iust thei:two clinics. We also have identified the service reqion for each clinic; the clinic located at cor-munity 3 will serve communities 1 through 5, and the clinic located at community 8 will se..:communities 6 through 9.

The location set covering problem often can yield more than one solution. ln this examp :if the maximal travel distance were set at 40 miles, the followinq five pairs of clinic site loc:tions would provide coveraqe: (3, 8), (3, 9), (4, 7), (4, 8), and (4, 9).

Summary Facility location plays an important role in the strategy ofa service firm through its int.l--ence on the competitive dimensions of flexibility, competitive positioning, demand ma..-agement, and focus. Strategies such as competitive clustering are corrunon for shoppii:goods, and saturation n.rarketing has been successful for some small retail outlets.addition, use of rrarketing intermediaries can decouple the provider from the consrnt;:lf the requirement for face-to-face interaction between server and custolner is not nece.sary, as illustrated by Internet service providers, the substitution of electronic commur -cation for physical transportation becomes possible.

HERE A BUN, THERE A BUN, EVERYWHERE A BUN.EUNThe idea of clustering or saturation marketing has come of age and been embtaced enthusi-astically by many companies such as Au Bon Pain, Eenetton, and Starbucks, At first blush, thenotion of locating several shops from one company in a small geographical area, sometimeswithin one block of each other, seems risky. For Au Bon Pain, a chain known for its specialsandwiches and baked goods, the advantages have outweighed the disadvantages.

Saturation marketing decreases the need for advertising-why advertise when prospectivecustomers can't walk one bloc( or sometimes even just one tloor in a department store, with-out passing a Benetton clothing shop or a Starbucks coffee shop? Au Bon Pain has also foundthat it i5 easier to supervise the shops when they are located close together. Saturation market-ing is most successful in high-density, urban locations, particularly for businesses like Starbucksand Au 8on Pain, which are not destination shops. Customers usually stop at these places ontheir way to other destinations.

Clustering seems to work betterwith company-owned outlets rather than with independently-owned franchises. lf one company-owned outlet does siphon off a little business from anotherone, it does not affect the company's bottom line. lf one independently-owned franchise siphonsbusiness from another one, however, it is of concern to an independent owner who comes outon the shortr end-

The discussion of facility location techniques began with the single-facility problem.The cross-median approach identified an optimal location for minimizing the totaldistance traveled by customers. The location ofa single retail outlet to maxin.rize profit isan impoftant decision that has been studied by David Hulfusing a gravity model to predictcustomer attractiveness to a store based on its size and location. For the multiple-facilitylocation problen.r, the concept of location set covering is central to understanding themany approaches to identifring n]ultiple-site locations.

Competitive clusteringthe grouping ofcom-petitors (e.9., automobiledealerships) in close prox-imity for convenience incomparative shopping bycustomers. p. 2J ZCross-median an approachto the location ofa singlefacility using the metro-politan metric to minimizethe total weighted distancetlaveled. p. 246E-distance a barrier foundin Web site design createdby internal and extemalnavigatton. p. 239Huff model a retail loca-tion model that is basedon an analogy to celestialgravity to measure the

attraction of a customer fora facility . p. 249Location set coveringal approach to findingthe mini:num numberand location of facilitiesthat will serve all demandpoints within a specifiedmaximum travel distance.p. 251Marketing intermediar-ies a business entity in thechannel of distributionbetween the final customerand the service provider(e.g., a bank extendingcredit to a retailer througha credit card). p. 2J8Metropolitan metrica measure ofdistancetraveled assuming rectan-

gular displacement (e.9.north-south and east-westtravel in urban areas).p.243Saturation marketing thelocation of a firm's individ-ual outlets (e.g., ice creamvendors) in close proximityto create a significant pres-ence that attracts cuslomerattention. p. 237

) , ': PartIwo Designing the Senice EnteryAse

T,, t-.::. t ilr-:r:..-...,: ..-...-'.,: i.l!11:.ii I

l*t*r;:eiiv*l-xei t !5t'

/\ Y@\@

$*llv*ciFr*bierns

l. Pick a particular service, and identify shortcomings in its site selection.2. How would you proceed to estimate empirically the parameter }, in the Huff retail

location model for a branch bank?3. What are the characteristics of a service that would make communication a gooci

substitute for transportation?4. What are the benefits ofusing intermediaries in the service distribution channel?5. Go to http://www.mapinfo.com/ and find the definition of "location intelligence."

What use can be made ofgeographic infonnation?

The class discusses the business opportunities ofusing Google Earth.

1. Cross-Median Location ProblemProblem StatementA health clinic is being planned to serve a rural area in west Texas. The service areaconsists of four cornmunities at the following xy coordinate locations in miles: A (6, 2 r.B (8, 6), C (5,9), D (3,4), with populations of2,000, 1,000, 3,000, and 2,000, respec-tively. Recommend a "cross-median" location for the health clinic minimizing the totalweighted metropolitan distance traveled.SolutionFirst, calculate the median value in thousands:

Mediar ,,,, (2 ; I | 3 I 2) i2 .,,, ,4.Second, plot the four communities on a grid with population in thousands as sub-

scripts:

Third, draw the -r-median dotted line (i.e., vertical line) on the plot by moving fromleft to right, adding the weights until the sum is equal to or exceeds the median (i.e..D2 + C3 : 5)- The result is one vertical line at.r = 5. Moving frorn right to left, add ri.:weights until the sum is equal to or exceeds the median (i.e., B1 + 42 + C3

- 6). The

result is the same venical line at r = 5.

Chapter l0 Serric? Facility Location )a),;

Fourth, draw the.1,-median dotted line (i.e., horizontal line) on the plot by movingfrom top to bottom, adding the weights until the sum is equal to or exceeds the median(i.e., Ca + B1 : 4). The result is a horizontal line at1, : 6. Moving from bottom to top,add the weights until the sum is equal to or exceeds the median (i.e., A.2 + D2 - 4). Theresult is another horizontal line at J, = 4. The reconmended location results in a linesegment shown as a dark line in the plot with x1, cseldinates of (5,4 to 5,6).2. Retail Location Using the Huff ModelProblem StatementThe west Texas area in the plot above is served by a grocery store in community D. Aproposed store with three times the floor space is being considered for location in com-munity C. Assume that monthly expenditures per custorner average about $100. Then,using the metropolitan metric for travel and \ = 2, use the Huffmodel to estimate theimpact on monthly expenditures and market share for the existing store in community Dif the proposed store in community C is constructed.SolutionFirst, determine the travel distances using the metropolitan metric:

Travel Distance in Miles (ft) (Using Metropolitan Metric)Community (i)

Site (/ )Proposed C (5, 9)Existing D (3, 4)

A (6, 2)8

5

B (8, 6)67

c (5, 9)07

D (3, 4)7

0

Second, using equation (14), calculate the attraction matrix with l, : 2. For example,the attraction of communif)' A to the proposed location at C (with .9 : 3 to account forthe larger floor space) would be calculated as

0.04(r9

Note that the attraction is given a value of- where the store is located in the samecommunity (4; : 0 in the denominator).

Attraction (,4t)

Community Location (i)Site (r)Proposed 5r : 3Existing 5, : 1Total attraction

.r :'s : L: r:._l_-I,i Ir xr b+

o.o4690.0400

B0.083 30.02040.1037

c D

0.0869

Third. using equation (15), calculate the probability using the total athaction as thedenominator. For example, the probability ofresidents in community A traveling to theproposed grocery store location at C would be calculated as

.1. 1,.'.^-_-T,r

i-l

0 0169-

: 0 il0.0469 r t).01

Pa:|f\\o Desisrling the Serrice Enlerpise

Probability (Pr)

Community Location (i )site (/)ProposedExisting

B.80.20

.54

.46

c1.00

D01.0

Fourth, using equation (16), the montlrly expenditures are calculated, and using equa-tion (17), the market shares are determined. For example, expenditures from residents o:community A at the proposed grocery store location at C would be calculated as

i . L\t'(,8 | ltt.8. r.i-lrlr,4{r,r l0{)r {lrrR.nrr0/1

Monthly E\pendilures (E;a) and Markel Share (Mlr)

Community Expenditures

Site U)ProposedExistingTotals

AB$108,000 $ 80,000

e2P00 ?9,-099$200,000 $100,000

CD$300,000 $ 0

200,000

Monthly MarketTotal Share 9',;

$488,000 0.61

$300,000 $200,000 $800,000312,000 0.39

1.00

10.1. Revisit the copying service in Example 10.1 and assume that over the years. ti:monthly demand from the four customers has increased to the following weigh::w1 :7, w2: 9, w: : 5, wa: 7. If we previously located the copying service

-

point A in Figure 10.6, should we now consider a relocation?10.2. A temporary-help agency wants to open an office in a suburban section of a 1ar5:

ciry It has identified five large corporate offices as potential customers. The loc:-tions ofthese offices in miles on an 11, coordinate grid lor the area are c1 = (4. :c2

- @, 11), ca -- (l,2), ca = (ll, 11), and c5 = (14,7). The expected dema::for temporary help from these cuslomers is weighted as w, = 3, w2 = 2, w3 - -)r1 : 4, and ra/s : 1. The agency reimburses employees for travel expenses incun;:by their assignments; therefore, recomn.rend a location (i-e., ry coordinates) for i::agency that will minimize the total weighted metropolitan distance forjob-relat::travel.

10.3. Four hospitals located in one county are cooperating to establish a centralized bloc-bank facility to serve them all. On an ry coordinate grid of the county, the hosF:-tals are found at the following locations: l{ : (5, l0), H2: 0, 6), $ - (.4. Iand Ha: (16. 3). The expected number of deliveries per month from the blo.-:bank to each hospital is estimated at 450, I ,200, 300, and 1,500, respectively. Usi::the cross-median approach, recorrmend a location for the blood bank that will m::-imize the total distance traveled.

Chapter I 0 Service Fdci[iDJ Lacalio aaT

10.4. A pizza delivery service has decided to open a branch near off-campus studenthousing. The project manager has identified five student apartment complexesin the northwst area ofthe city, the locations of u.hich, on an.ry coordinate grid inmiles, are Cl = (1, 2), C2 - Q,6), Cr - (3, 3), Ca = @,1), and C5 = (5, 4). Theexpected demand is weighted as w1 : 5, w, : 4, w3 : 3, w4: l, and w5 = 5.Using the cross-median approach, recommend a location for the pizza branch thatwill minimize the total distance traveled.

10.5. A small city airport is served by four airlines. The terminal is rather spread out,with boarding areas located on an xy coordinate grid at A = (1, 4), B = (5, 5),C: (8, 3), and D

- (8, l). The number of flights per day, of approximately

equal capacity, is A = 28, B :22, C = 36. and D: 18. A new central baggageclaim area is under construction. Using the cross-median approach, recommenda location for the new baggage claim area that will minimize the total weighteddistance from the boarding areas.

10.6. You have been asked to help locate a catering service in the central businessdistrict ol a city. The locations of potential customers on an ry coordinate gridare P1 = g, 4'), P2 - (12, 4), P3 - Q, 7), P4 : (l l, I l), and P5 : Q, 14).The expected demand is weighted as w1 = 4, w2: 3, w3 : 2, wa : 4, andw5 : l. Using the cross-median approach, recommend a location lor the cater-ing service that will minimize the total weighted distance traveled to serve thecustomers.

10.7. Revisit the copying sewice Huff analysis in Example 10.2. Recalculate themonthly customer expenditures and the market share for the proposed copyingcenter at location B if the new store will be three times the capacity ofthe exist-ing store at location A and the new demand weights from Exercise l0.l above areused.

10.8. A locally owned department store samples two customers in each of five geo-graphic areas to estimate consumer spending in its home appliances department.Il is estimated that these customers are a good sample ofthe 10,000 customers thestore serves. The number of customers in each area is C, : 1,599, Cz = 2,500,C: = 1,000, Cl = 3,000, and C5 = 2,000. It is found that the two consumershave the following budgets in dollars for home appliances per year: 811

- 100,

Brz = 150; 821 -75,822:100;811= 125, Bn:125l' -Bal = 100, Baz= 120;and 851 : l20,Bsz= 125.a. Using the Huffretail location model, estimate annual home appliance sales for

the store-b. Bull's-Eye, a chain department store, opens a branch in a shopping complex

near by. The BullS-Eye branch is three times larger than the locally owned store.The travel times in minutes from the five areas to the two stores (/ = I for thelocally owned store,l = 2 for Bull's-Eye) are Zll = 20, Tp= 15:, Ty = 35,722 : 20' 231 = 30, Ttz = 25l' Ta1 : 20, Ta2: 25l. and 251 = 25, Tt = 25'Use the Huff retail location model to estimate the annual consumer expendi-tures in the home appliance section ofeach store assuming that \ = L

10.9. A community is crmently being served by a single self-serve gas station withsix pumps. A competitor is opening a new facility with 12 pumps across towr.Table 10- 12 shows the travel times in minutes from the four different areas in thecommunity to the sites and the number of customers in each area.a. Using the Huff retail location model and assuming that \ : 2, calculate the

probability ofa customer traveling from each area to each site.b. Estimate the proportion ofthe existing market lost to the ne!\' competitor

Patlf\No Designi g lhe fkrvice Enlerytise

Travel Times toGas Stations

fi{: r.3ttr{. 1*.8Service Area Network

AreaOld stationNew competitorNumber of customers

1

520

100

2

1

8150

3

91280

4l56

50

10.10. Recall the rural medical clinics in Example 10.3 and suppose that each conmu-nity were required to be 25 miles at most from the nearest clinic. How many clin-ics would be needed, and what would their locations be? Give all possible locationsolutions.

l0.l l. A bank is plaming to serve the rural cornmunities shown in Figure 10.8 withautomated teller machines (ATMs). The travel time in minutes between colnmu-nities in the service area is shown on the network in Figure 10.8. The bank isinterested in detennining the number ar.rd location of ATMs necessary to sen ethe communities so that a machine will be within 20 minutes' travel time of anrcommunity.

10.12. The volunteer fire department serving the communities in Figure 10.8 has jus:purchased two used fire engines auctioned offby a nearby city.a. Select all possible pairs of communities in which the fire engines could be

located to ensure that all corrmunities can be reached in 30 minutes or less.b. What additional consideration could be used to make the final site selectior

from the community pairs found in part a?

Joan Taylor, the administrator of Life-Time lnsurance Company,which is based in Buffalo, New York, was cha.qed with estab-lishing a health maintenance organization (HMO) satelliteclinic in Austin, Texas. The HMO concept would offer Austinresidents an alternative to the traditional fee-Jor-service medi-cal care. lndividuals could enroll in the HMO voluntarily and,for a lixed fee, be eligible for health services. The fee would bepaid in advance.

Ms. Taylor care{ully planned the preliniina.y work thatwould be required to establish the ne\"r' c lnic n Austin, and

when she arrived, mo5t of the arrangements had been cor.pleted. The location of the ambulatory health center (clinichowever, had not been selected. Preliminary data on the es'.,mated number of potential enrollees in the HMO had bee-determined by census tract, and these data are presented i-Table 10,13. Using the cross-median approach and the ce.-sus-tract map in Figure l0.9, recommend a location for tl-iclinic.

Chapter 10 Senice Facility Localion t59

gridated Nlmber ofl*!Etia! Enrollees perCllJus Tract

Census Tract'1

2

4567

89

10't1

12'13.01

Enrollees, in Thousands Census Tract13.O21415.0',]15.O215.0316.0116.0218.032021 .0121.O223.O'l

45

6453252434

Enrollees, in Thousands5

4

1

21

4'|

2422)

C.rsueTract MepJ {ustin, Texas

tarcl Furniture, lnc. (AFl), is a growing regional chain oI dis"::unt furniture and large-appliance stores. Management has:a-Eted the small city of Bluff Lake as the next location fo. a-{ail outlet. Although the total population is cunently 21,000,guff Lake is expected to grow during the next decade because:f increased mining in the surroundinq hill5.

AFI'S marketing department did a general analy5is of thepotential of market expansion into Bluff Lake, but the task oflocating the best site for a store has been given to Mr. CarlosCutierrez. AfteI obtaining the market data on Bluff Lake, MrGutierrez decides it would be very appropriate to utilize theHuff location model in developing a recommendation for the

Pailwo Designing lhe Senice E teryrise

companyrs management, This is because there are existingcompetitors and several potential sites under consideration.

Figure 10.10 is a map of Bluff Lake showing maior streetsand highways, the railway (AFl will ship its merchandise intothe city by rail {rom a regional warehouse 800 miles away),Crystal Rivet Bluff Lake, and the census block groups (num-bered 1 through 12). Table 10.14 gives the number of house-holds, average annual income per household, and averageannual furniture/large-appliance expenditure per householdfor each census block group.

ln Figure l0.10, the letters A and B show the locations ofAFI'S existing competitors, and Table 'i0.15 indicates the sizesof these existing stores to the nearest 5,000 square feet of salesarea. The letters X, Y and Z in Figure 1 0.10 show the possiblesites that Mr. cutierrez feels AFI could use for a retail store. Themaximum size limit (i.e., sales area) of each potential locationis qiven in Table 10.16.

On the basis of average speeds for the main streets andhighways obtained from the city's planning departmenl Mr.Cutierrez has developed a matrix of travel times between thex;sting and potential retail sites and the center oI each censusblock group. These travel times can be found in Table '10.1 7.

From experience with other AFI locations, Mr. Gutierre2has developed a fairly accurate portrayal of the relation-ship between store size (i.e., sales area) and margin on sales.expenses, and net operating profit before taxes. This informa-tion is shown in Table 10.18.Questions1. Utilizing a spreadsheet version of the Huff location mod

(with }. = 1.0), recommend a store size and location fc'AFl, Assuming that AFI does not wish to consider a storithat is smaller than 10,000 square feel assess the store sizj(based on 5,000-square-foot increments) up to the max-mum allowable sales area for each potential site.

i:r{;t,ltf l*_toBluffLake

State Park

}'|-t+ Railroad

-

Freeway_ Major streel_ _ Park boufldary

..'\ River4 Census block groop

Existing relail oodetsPotential sires

;AE{-t I *.'li.,j Markt Data

qul:\--

Census BlockG roup

Number ofHouseholds

7301,1 301,035

635'l 60105125470305

1,755900290

7,64A

Avg. Annuallncome

65,000,70,00045,000-50,00080,000-85,000

150,000-over25,000-30,00020,000-25,00020,000-25,00040,000-45,00030,000-3s,00085,000-90,00075,000,80,000

150,000-over

Avg. AnnualFurniture/Large-Appliance

Expenditures per Household1

2

456789

101112

$1801252803s0

755060

11s90

265215370

"',}jat is the expected annual net operating profit before=xes

and expected market share for the outlet you have-:

.

- Part Two Derjr.ring the Seni.e tnt?rfise

Min, H. "Location Planning of Airport Facilities Using the Analytic Hierarchy Process."Logistics and Transpoftation Reyiew 30, no. I (March 1995), pp.79-94.Price. W. L.. and M. Turcorre. "Locaring a Blood Bank." Inrerlaces 1 6, no. 5 ( 1986).w. l'116.Schmenner, Roger W. "The Location Decisions ofNew Services." In New ServiceDevelopment, eds. J. A. Fitzsimmons and M. J. Fitzsimmons. Thousand Oaks, Calif.:Sage Publications, 2000, pp. 216-38.Swersey, Arthur J., and Lakshman S. Thakur. "An Integer Programming Model forLocating Vehicle Emissions Testing Starions." Management Science 4l,no. 3 (March1995), pp. 496-s12.

fintjnE:l*S l- D. A. Lopez and P. Gray, "The Substitution ofCommunication for Transportation: A Case Study''-'Managenzent Science 23, no. I I (July 1977), pp. I149 60.

2. S. E. Kimes and J. A. Fitzsimmons, "selecting Profitable Hotel Sites at La Quinta Motor lnns.'.Interfaces 20,no.2(March 1990), pp. 12-20.

l. Suzanne Alexander, "Saturating Cities with Stores Can Pay," The Wall Sneet Journdl Septembe:I, 1989, p. 81.

4. James H, Donnelly, "Marketing lntermediaries in Channels of Disftibution for Se ices," Jounr,j.of Marketing 40, January 1976, pp. 55,70.

5. Julie E. Kendall, "E-distance and th Theatres of South .tersey," Decisiot Line, March 2001.pp. 13 15.

6, S. E. Kimes and J. A. Fitzsimmons, "selecting Profitable Hotel Sites at La Quinta Motor Inns.-Interfaces 20, no. 2 (March 1990), pp. 12-20-

7. Christian Harder, ArcView GIS Means B,sr)ress, Redlands, Calic: Environmental Researc:Systems,lnc., (1997), pp. 125.

8. W. J. Abemathy and J. C. Hershey, "A Spatial-Allocation Model for Regional Health Senici.Pla\ring," Operations Research 20, no. 3 (May-Iwe 1972), pp. 62942.

9. David L. Huff, "A Programmed Solution for Approximating an Optimum Retail Location," adr":Econonics, August 1966, pp. 293-303.

10. This case was prepared by James H. Vance under the supervision of Professor James -:-

Fitzsirnmons.