A Methodological Note on Location-Allocation Models - NCBI

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A Methodological Note on Location-Allocation Models JOSEPH L. SCARPACI, MS Abstract: Three conditions render the use of standard methodologies inappropriate in solving location-allocation problems. This paper presents one alternative method for assigning an emergency aircraft to one of three hospitals in northern Chile when standard approaches are not suitable. Graph analyses and the demographic potential measures are used in the case presented. The main advantages of this alternative approach are its computational ease and the use of more than one method. (Am J Public Health 1984;

74:1155-1157.)

Introduction Location-allocation methodologies seek to locate one or more health facilities or services in the most desirable place with the use of heuristic or optimization techniques. Heuristic methods often reflect more of the real world constraints than optimization techniques by using a set of decision rules (algorithms) to find good solutions. Optimization techniques produce the best solution to the locational query based on stated constraints and objectives built into mathematical models. Integer programming, tree-searching methods, and linear programming are frequently used optimization techniques. ' Solutions to location-allocation problems have been allied, perhaps excessively so, to methods and models that require data and computer facilities that may be unavailable. Heuristic and optimization techniques cannot be used when: 1) problems are too complex and require expensive or excessive computer time; 2) techniques require inaccessible or expensive data; and 3) problems cannot be expressed as linear equations because of the complexity of the relationship.2 Problems of this sort were sounded out in a recent literature review that also called attention to the misguided use of certain methodologies in health and applied social science research. It was argued that simpler and alternative approaches to problem-solving should be considered.3

Problem A real world problem required the allocation of an emergency helicopter to one of three hospital service areas in sparsely populated rural northern Chile (Figure 1). A review of location-allocation models suggested that they were inappropriate in this case, according to points (1) and (2) stated above. Antecedents to the problem, as disclosed by local health officials,* were that population dispersion could be used as a surrogate measure for emergency medical care need, and only population size and density need be considered given the similar morbidity and socioeconomic

profiles of the three populations. Descriptive statistics from graph analyses and the use of a variant of the gravity model provided acceptable solutions. The methodology used reduces the dependence on a single method and provides ample room for important qualitative assessments. Method

Graph Analysis Two graphs showed the total and relative cumulative distribution of the rural populations surrounding the cities of Arica, Iquique, and Calama. Population size was calculated within 25 kilometer (15.5 mile) intervals based on cartographic,4 census,5 and public health office information,** as well as field work in July 1981 and February 1984. Relative population with regard to distance to regional hospitals is shown in Figure 2. Each of the three slopes portrays fairly dispersed populations, with 50 per cent residing within 77 and 87 kilometers of the hospitals. The Arican service area displays the least dispersed population within the 75 km mark. Residents in the Iquique hospital district are the most dispersed at the mid-way 75 km point, and 14 per cent of the population lives more than 150 kms from hospital care. Figure 3 depicts total cumulative distributions of the populations with respect to the regional hospitals. Arica and Calama are of similar size with only small differences at the 50 km mark. The Iquique hospital, however, must provide care to about 10,000 residents beyond the 75 km point-a population that is larger than the total population of Calama or Arica. Summing up, graph analyses show that Iquique is the most dispersed rural service area and would therefore profit most from the air ambulance. Demographic Potential Measure A measure which can readily summarize the aggregate effect of population dispersion was next included. This summary measure, the demographic potential, is a derivative of the gravity model designed by Stewart6 and measures proximity to a certain point (i.e., regional hospital) as well as aggregate accessibility.7 A modified version of the demo-

graphic potential becomes:

n

PDi= j E idO2 =

where

PDi is the population dispersion in the i region Pj is the population of subregion j djj2 is the distance between subregion j to hospital i

O 1984 American Journal of Public Health 0090-0036/84 $1.50

n equals the seven 25 km radii extending from hospital i Interpretation is straightforward: small summary measures indicate greater population dispersion than larger ones (Table 1). Strict interpretation of the summary measures suggests that Iquique deserves the emergency aircraft. However, such a decision should not ignore the small differences between Iquique (3.058) and Calama (3.353). Unlike confi-

*Interview with Dr. Hector R. Gutierrez, Director, Regional Hospital, Iquique; Dr. Sergio Urbina, Assistant Director, Regional Health District II, Antofagasta, July 1981.

**Interviews with National Health Service employees in Arica, Iquique, and Antofagasta, July 1981. Population estimates based on data gathered by medical personnel who periodically service those villages shown in Figure 1.

Address reprint requests to Joseph L. Scarpaci, MS, Doctoral Candidate, Department of Geography, University of Florida, Gainesville, FL 32611. This paper, submitted to the Journal June 2, 1983, was revised and accepted for publication April 19, 1984.

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0 H

0

O-a L 0

0 20 -

0

Kilometers from Regional Hospital FIGURE 2-Relative Distribution within Hospital Districts

FIGURE 1

dence levels used in statistical probabilities, there is no rejection level that can be set beforehand. In keeping with the approach of using more than one method, we return to the graph analyses and the descriptive statistics. It will be recalled from Figure 3 that the Iquique population beyond 75 km is larger than the populations of Arica and Calama. Even if the Calama summary measure was greater, to allocate the aircraft to Calama, based solely on the demographic potential, would ignore important aspects of population size and the possibility of providing emergency medical care to the largest population.

Conclusions This methodological note has presented an alternative approach to allocating a health service or facility when standard optimization or heuristic techniques are inappropriate. Major advantages of the method presented are its computational ease and independence from a single technique. In the case presented, it was noted that there were small differences in the summary measures generated by the demographic potential. It was suggested that decisions based solely on the measure would be inappropriate and that the 1156

0 c 0 a

Ico

0

1-

Kilomete rs from Regional Hospital

FIGURE 3-Total Population Distribution within Hospital Districts

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PUBLIC HEALTH BRIEFS TABLE 1-Demographic Potentials for Iquique, Arica, and Calama Hospitals and Their Rural Service Areas

Anca dij

Calama

Iqique

(kms)

Pi

pi dQ2

25 50 75 100 125 150 175

3125 365 250 3110 1752 87 225

5.000 .146 .044 .311 .112 .004 .007

pi

pi

Pi j2di2

graphical constraints of those populations. In the case presented, response time would be too great for effective intervention in cardiac arrest cases, but would be acceptable for providing care to burn victims in the regional mining centers as well as victims of automobile accidents. REFERENCES

587 2580 1250 5367 3805 200 2311

5.624

.939 1.032 .222 .537 .244 .009 .075 3.058

1475 800 2600 1302 800 675 0

2.360 .320 .462 .130 .051 .030 .000 3.353

Chuquicamata is excluded because of the well developed medical system provided to residents by private and public mining corporations.

total size of the service areas should be taken into account before coming to a decision. The Chilean case presented reflects the limitations of data sources that might be evident in other regional settings. Applications of this method to other real world populations should reflect the emergency medical needs and geo-

1. Swain RW: Health Systems Analysis Columbus: Grid Publishing Company, 1981. 2. Dever GEA: Community Health Analysis. London: Aspen Systems, 1980. 3. McCracken KWJ: Dimensions of social well-being: implications of alternative spatial frames. Environ Plann A 1983; 15:579-592. 4. Organization of American States: Population Distribution Map of Chile. Scale, 1:1,000,000, 1960. 5. Servicio de Antofagasta: Memoria Anual. Antofagasta, Chile: Servicio Nacional de Salud, 1981. 6. Stewart JQ: Demographic gravitation: evidence and applications. Sociometry 1947; 11:31-58. 7. Isard W: Methods of Regional Analysis: An Introduction to Regional Science. London: MIT Press, 1966.

ACKNOWLEDGMENTS

An earlier version of this paper was presented at the annual meetings of the Southeastern Division of the Association of American Geographers, October 12, 1981, in Atlanta, Georgia. The author would like to thank the Fulbright Commission in Santiago, Chile for providing partial funding during the revision of this work. The author is also grateful for the helpful comments provided by three anonymous reviewers of a previous draft.

Insurance Incentives and Seat Belt Use LEON S. ROBERTSON, PHD result suggests that the economic incentive must be susAbstract: In 1983, Nationwide Insurance Company increased compensation payments for its clients injured or killed in a motor vehicle crash while using a seat belt. A survey of belt use was undertaken in the month after all those so insured had been informed of the change. Belt use by drivers insured by Nationwide was not significantly different from that of drivers insured by other companies. The incentive appears to have had no apparent effect on belt use. (Am J Public Health 1984; 74:1157-1158.)

Increasing the use of seat belts in motor vehicles is a major objective to reduce the severity of injury in motor vehicle crashes. One of the possible means that has been proposed to attain that objective is to use economic incentives for belt use. Several experiments, in which money or prizes were offered for belt use, have been reported. Drivers offered a chance to win a prize, if they were subsequently observed to use belts at a college campus parking lot, were found to increase use from 15 to 40 per cent during the period that the prizes were given. ' The effect of such incentives declines or is nonexistent when the prizes are no longer offered.2.3 This Address reprint requests to Leon S. Robertson, PhD, Department of Epidemiology and Public Health, Yale University, School of Medicine, 60 College Street, New Haven, CT 06510. This paper, submitted to the Journal March 23, 1984, was revised and accepted for publication May 7, 1984. © 1984 American Journal of Public Health 0090-0036/84$1.50

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tained for maximum effect. An industrial company has claimed 90 per cent belt use of employees offered rewards of items worth $12 to $15 wholesale for such use.4 In a follow-up period when the rewards were reduced to gifts costing the company $1 to $1.50, observations by independent observers found belt use ranging from 67 per cent of the incoming morning shift to 39 per cent of the outgoing night shift. These rates were substantially higher than the 10-15 per cent use of drivers at other locations in the community where the plant is located.5 Experimental-control comparisons of belt use by workers entering and leaving plants before and after being given fliers offering belt wearers a chance to win a prize found different effects depending on pre-experimental belt use and socioeconomic status. Those with the highest pre-experimental belt use (18 per cent) increased their use to 57 per cent in the afternoons, when fliers were distributed, and 28 per cent in the mornings. The increases were largely found among salaried workers. Hourly workers' belt use increased only 2 per cent in one plant and 7 per cent in another.6 Apparently belt use can be prompted by these lotterylike incentives among certain groups, but the effect does not appear to be sustained among substantial proportions of those affected when they are not in situations where the awards are potentially available. The question addressed in this communication is whether a potentially much larger but, in time and probability, more remote economic incentiveincreased compensation by insurance in a crash-has an effect on belt use. 1157