Locating social service centres using interactive graphics

OtlE(.;I The [nt Jl o ( M g m t S¢~ X,ol. II. No 2. pp 2Ol 205. 19:";3

03ql5-0483 ~3 0202!1l-O5S03000 Cop?right ~ 1943 P~rgamon Pre,,-; Lid

Printed in Great Britain -M[ rights re~,er,,ed

Locating Social Service Centres Using Interactive Graphics SC

BHATNAGAR

Indian Institute of Management. Ahmedabad. India (Receired Januar.v 1982; in recised ji~rrn September 1982) The paper explores the feasibility of using interactive graphic based solution procedures in location problems with discrete choices. It compares solutions generated through interactive graphics with those generated through optimization for a problem context where service centres had to be located in rural India. The comparison demonstrates the feasibility of generating near optimal solutions for problems with a certain dimensionality. Broad features of the graphic software are d e s c r i b e d . T h e p a p e r also highlights other advantages and limitations of the interactive graphic procedure.

I M P O R T A N C E OF L O C A T I O N PROBLEMS IN DEVELOPING countries like India a large part of the development expenditure is incurred on expanding the infrastructure for providing social services. In the annual planning, once the departmental budgets are known, an important and often time consuming process follows--the choice of locations for creating new facilities. The main actors involved in choosing locations are the District Development Officer (a government functionary), the Jilla Parishod Chief (elected leader of the local self government) and the local legislator. The elected representatives have a large say in the choice of locations. In the absence of any formal analysis and generation of alternatives, the final choice made on political consideration alone is often far from optimum. However, there is evidence that when alternatives are generated after formal analysis and placed before the decision makers, then they are considered [3]. At least some state governments are becoming aware of the short-comings of an unplanned location of facilities and have attempted to devise methodologies to locate facilities. For example, in Gujarat, maps have been developed at taluka level identifying the existing facilities, villages covered within 5 km of these facilities and villages out of their reach. 201

Efforts are then made to locate new facilities so ~ as to fully cover out of reach villages. The methodology was abandoned half way because of the effort involved.

O P T I M I Z I N G M O D E L S TO SOLVE L O C A T I O N P R O B L E M S Several papers report mathematical formulation for optimizing location problems, but very few of these are in the context of the developing world. One successful effort from the developing world was reported by Patel [4] on locating rural service centres optimally through the use of a linear integer programming formulation. His work related to the following problem. A budget for 1.4 million rupees was available to build service centres which were to be selected out of 45 potential locations in D h a r a m p u r taluka spreading over 237 villages and covering a total population of 193,000. The cost of a service centre differed between different potential locations because some locations already had part of the infrastructure built up. Some parts of this region are very backward and others relatively prosperous and therefore, to avoid locating service centres in populated prosperous areas, the objective stated was that of minimizing the maximum distance of any village

2~)2

Bhatna~ar--Locatin,~ Social Sert'ice Centves

from its nearest service centre, given the constraints of the budget. This was achieved by solving several problems in which the cost of locating service centres was minimized, given a specified service level. The service level was defined in terms of the maximum distance that a village could be from its nearest facility. Solutions were generated for service levels varying Dom 5 to 10km and the one within the budget of 1.4 million was chosen. This optimal solution involved I I service centres and achieved a service level of 6 km. Patel used an interactive computer programme with video display to sell his solution to the decision makers. He reports, "the interactive programme proved to be very valuable in convincing decision makers of the usefulness of the mathematical approach to the problem". Being an observer to the Dharampur exercise and having watched the pains of generating and selling a mathematically optimized solution, the author was led to explore interactive graphics as an alternative approach because of the promise that it has shown in other contexts [I]. A R A T I O N A L E FOR USING INTERACTIVE G R A P H I C S Analytical models of the type used in location problems demand enormous computing power and therefore need to be kept simple--a formulation involving multiple objectives can seldom be solved for any real problem without further simplifications [2]. In the Dharampur exercise formulation was kept simple by ignoring other possible criteria such as minimizing weighted distances or equality in the population served by the chosen centres. Nevertheless, it required considerable programming effort and computing power (an outside IBM 360/44 was used instead of the in-house HP2116B with 32KB of core which was found to be inadequate). Another important reason for simplicity is that decision makers are not comfortable implementing solutions whose underlying methodology is obscure to them, since they do not then feel sufficiently involved in the decision, and in fact may not be able to contribute their knowledge about each potential location. In the case of Dharampur, a tremendous selling effort was required, to such an extent that even the Chief Minister had to be involved in the exercise.

Interactive graphics incorporates the involvement of the decision maker, provided that he is willing to spend time at a graphic terminal. His preferences can be accommodated and several solutions explored, each being evaluated on many different criteria. Feasibility of generating solutions interactively depends on the ability of the averagely intelligent decision maker to comprehend the spatial dimensions of the problem, such as the number of facilities to be located in relation to the potential sites and the physical dispersion of villages to be covered. For most facilities the infrastructure is inadequately developed, as is the region within the infrastructure; the region within which the choice is to be made is either a taluka or a district, ensuring that potential locations are few in relation to the total villages that need to be covered.

D E S I G N OF G R A P H I C S O F T W A R E Interactive graphic software was developed to display a map of Dharampur indicating the location of different sized villages through a set of symbols. The 45 potential sites for service centres were displayed (see numbers marked on Fig. I). The user could interact with the data (characteristics of villages and village coordinates) to print out the details of a specific village (located through a hairline cursor) or could print out the distance between any two specified villages. The user would be required to choose potential sites (input the site numbers through the keyboard) and specify the desired service level. The software would evaluate the user's solution and redraw the map, erasing all villages covered by the chosen sites and displaying the chosen sites and 'out of reach' villages (i.e. beyond the specified service level). In addition a detailed evaluation on the following criteria would be printed out: (1) the total cost of the solution; (2) the weighted (on population of each village) distance that people from different villages will have to travel for each service centre, as well as a grand average; (3) the load of each centre, defined as the pop-

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Locations o f villages and potential sites.

ulation o f the villages to which this is the nearest facility; (4) a list of villages beyond the specified service level, their population and distance from the nearest service centre;

asked to arrive at solutions using the interactive software. The choice of locations was confined to the set of 45 potential villages which were considered in the optimization model. Several solutions were generated and it was found that the better ones compared well with the optimal solution reported by Patel.

(5) the maximum distance that any villager has to walk to reach the nearest facility.

INTERACTIVE SOLUTIONS

It was expected that a decision maker could interact with the graphic terminal, developing alternative solutions and evaluating them, to finally arrive at an acceptable solution. The opportunity to test this software with decision makers came at a training course in which a few district development officers were participating. The Dharampur problem was discussed as a case in the classroom and participants were

Table I presents evaluations of three solutions costing around 1.3 million rupees which were generated by the graphic software. The service level achieved by the three solutions ranges from 6.5 km to 7.09 km, placing about ten villages (out of 237) beyond 6 km from a service centre. These can be compared with the optimal solution reported by Patel (also presented in Table 1), a service level of 6 km at

Bhatna~ar--L~watin,4 Social Service Centre~

204

T~BLE [. A CI)MP-~,RISON ()F [%TERACTP, E ~,S ANALYTIC SOLUTIONS WITHIN AN OVERALL BUDGET OF 1.4 MILLION RUPEES

Solutions Optimal solution

Number of Total centres cost chosen tthousandrupees) 12

Average weighted distance {km)

Service Number of level Rangeof Mean villages Imaximum population population b e y o n d ,aa[king servedt served ~ 6km in km)

1385

2.92

8000-38300

16100

0

6.00

1 I1 1330 2 13 1290 3 13 1290 --mRound~'dto tlae~nearest hundred.

2.94 2.88 2.96

9200-31400 7100-35100 7200-25600

17600 14900 14900

9 7 10

6.50 6.46

Interactive solutions

7.09

The software development took 3 man months of effort and was written in F O R T R A N using callable PLOT 10 subroutines. A micro computer based graphic system (64KB memory, 13in. screen), with a 5 M B disk, a 2 pen. 10in. plotter and a 10in. digitizer tablet (several manufi~cturers offer such systems at around US$40,000) would have been more than adequate for the purpose.

a total cost of 1,385,000 rupees. It is interesting in this context to quote two solutions for a budget of one million which suggest that the interactive solution was in this case distinctly superior (see Table 2). It should be noted that participants who generated the above solutions spent about an hour on the terminal. The limited experiment clearly demonstrated the feasibility of generating acceptable solutions through interactive graphics.

CONCLUDING REMARKS HARDWARE AND SOFTWARE REQUIREMENTS

In Dharampur the optimum solution domain turned out to be fiat. It was therefore possible to generate good solutions using interactive graphics, even though the number of alternative solutions was extremely large. Dimensionality of the problem, discrete nature of location choices and the use of euclidean distances between villages enabled successful use of graphic procedures. More empirical evidence with larger problems is needed to confirm the promise of interactive graphics. Involvement of decision makers, ability to include additional qualitative information on potential choices and handling of multicriteria through iteratively improved solutions, are some of the advantages of a graphic solution procedure. Another advantage is that the kind of small computers that will be available to

The software for the case reported here was developed on a P D P - I 1/70 with a graphic terminal (Tetronix 4012 with a 10 in. screen) using PLOT 10 graphic software. The P D P - I 1/70 was configured with 256KB of main memory, 130 MB of on-line disk storage and was operating in a multiprogrammed time sharing environment," serving the computing needs of a management school. The graphic terminal was one of the 12 terminals (others were alphanumeric) hooked to the system. The absence of digitizing equipment was a definite handicap because digitizing maps manually was cumbersome. The computer system did not allow any single programme to be larger than 64 KB which was not found restrictive.

TABL[" 2. A COMPARISON OF AN INTERACTIVE VS AN ANALYTIC SOLUTION WITHIN AN OVERALL BUDGET OF ONE MILLION RUPEES

Optimal Interactive

Costs (thousand rupees) 985 1000

Average weighted distance (kin) 3.27 3.02

Rounded to the nearest hundred.

Maximum Rangeof distance population walked served ~ (km) 8500-61100 6.5 8600--47800 6.7

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Omega. Vol. I I. ,Vo. 2

district level planners are adequate for supporting graphic processing. The usefulness of optimizing models for providing b o u n d s for the interactive solutions should be recognized. In D h a r a m p u r good solutions could be developed without the knowledge of an o p t i m u m solution. In other cases b o u n d s may provide a necessary target.

ACKNOWLEDGEMENT The author is indebted to Ms Meena Bhaskar for her very able programming support.

REFERENCES [. ACHABALDD etal. (1976~ Designing and e~aluating a hearth care derisory system through the use of interactive computer graphics. Soc. Sci. Med. 12. 1-6. 2. BtTRA:,;GR (1980) Locating service offices: a multicriteria approach. Omega 8(2), 201-206. 3. Gt;PTA R e t a l . (1978) Rural development for rural poor, Dharampur project. Vol. Ill, Research Report. lIM/Ahmedabad. 4. PATELNR {19791 Locating rural social service centres in India. Mgrnt Sei. 25, 22-30.

Professor SC Bhatnagar, Computer and lnJbrmation ,~t'stems Group. Indian Institute af Management. ~tstrap,r, Ahmedahad 38001L India.

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