THE INTERNATIONAL JOURNAL OF HEALTH PLANNING AND MANAGEMENT
Int J Health Plann Mgmt 2015; 30: 382–394. Published online 10 April 2014 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/hpm.2246
Optimal administrative scale for planning public services: a social cost model applied to Flemish hospital care Jos L.T. Blank1,2* and Bart van Hulst1 1 2
Delft University of Technology, Delft, The Netherlands Erasmus University Rotterdam, Rotterdam, The Netherlands
SUMMARY In choosing the scale of public services, such as hospitals, both economic and public administrative considerations play important roles. The scale and the corresponding spatial distribution of public institutions have consequences for social costs, defined as the institutions’ operating costs and the users’ travel costs (which include the money and time costs). Insight into the relationship between scale and spatial distribution and social costs provides a practical guide for the best possible administrative planning level. This article presents a purely economic model that is suitable for deriving the optimal scale for public services. The model also reveals the corresponding optimal administrative planning level from an economic perspective. We applied this model to hospital care in Flanders for three different types of care. For its application, we examined the social costs of hospital services at different levels of administrative planning. The outcomes show that the social costs of rehabilitation in Flanders with planning at the urban level (38 areas) are 11% higher than those at the provincial level (five provinces). At the regional level (18 areas), the social costs of rehabilitation are virtually equal to those at the provincial level. For radiotherapy, there is a difference of 88% in the social costs between the urban and the provincial level. For general care, there are hardly any cost differences between the three administrative levels. Thus, purely from the perspective of social costs, rehabilitation should preferably be planned at the regional level, general services at the urban level and radiotherapy at the provincial level. Copyright © 2014 John Wiley & Sons, Ltd. KEY WORDS:
healthcare; hospitals; network planning; optimization; social costs
INTRODUCTION When planning the level of administration for public services, considerations such as legitimacy, access, complementarities and externalities play important roles. The particular administrative level chosen for each service must ensure optimization in the exercise of democratic control, the safeguarding of public values, and reconciliation with other public services and other regions. One can also add to this list economic considerations, such as the minimization of social costs. Social costs are defined here *Correspondence to: Jos L.T. Blank, Centre for Innovations and Public Sector Efficiency Studies, Delft University of Technology P.O. Box 5015 2600 GA Delft, The Netherlands. E-mail: [email protected]
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as the operating costs of the public service (usually borne by the government) and the travel costs (usually borne by the individual citizen). Social costs are to a certain extent dependent on the scale and the spatial distribution of the public services. The issue of the scale and spatial distribution of public services therefore often appears on the political agenda. In the Netherlands, for example, various advisory bodies have extensively reported on this topic in recent years, for instance, in relation to the planning of services in education and healthcare (RVZ, 2008; Onderwijsraad, 2005). In this article, we address the issues of scale, geographical access and planning of public services from a purely economic perspective. There are two key questions: • What is the optimal spatial distribution of public services? • What is the optimal administrative level at which the planning of a public service should take place? We will answer the research questions by developing an economic model that makes a comparative assessment between the total operating costs of the public services and the travel costs of patients. The scale at which the public services are offered plays a crucial role in the model. At a small scale, it is possible to offer the service at a large number of locations and thereby keep the travel costs low; on the other hand, from a business economics point of view, a small scale can be disadvantageous because of the fixed costs per institution. With minor adjustments, the model can be applied to various public sectors. In this article, the model is illustrated using Flemish hospital care, in particular rehabilitation, general care and radiotherapy services (see, e.g., Blank et al., 2010). This illustration shows how the theoretical framework can be applied empirically. The model bears strong similarities to facility location models, for which there is a huge body of literature. In these models, public services are geographical locations that have been determined on the basis of a given, spatially distributed demand for services. The central question here is the locations at which public services should be located in order to minimize total travel time or travel costs (for examples of extensive overviews, see Daskin and Dean (2005). Some of these models are extended with a multi-objective function, in which case, the minimization problem also includes fixed costs or operating expenses (Current et al. (1990)). However, our model has three major differences from these models: • The objective function of our model is based on a social welfare perspective. It is generally acknowledged that decisions on hospital facility location affect both private (travel time and costs) and public interests (facility costs financed by public means). • Our model allows for non-linear forms of both private and public costs. In general, this type of model is based on somewhat rigid linear assumptions on costs and travel time, whereas in practice, these seem to be quite unrealistic. There is, for instance, a large body of literature showing that economies/diseconomies of scale prevail in hospitals. • Our model can be used not only to find an optimal solution for an economic problem but also to derive an optimal answer to the question which public administration level should be responsible for carrying out the planning procedure. The Copyright © 2014 John Wiley & Sons, Ltd.
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subsidiarity principle is used in combination with economic theory to provide a solution for the optimal planning level. This article is organized as follows. The Economic Theory section presents the various economic considerations, which in Economic Model section are translated into an economic model that can be applied empirically. The Empirical Application: Flemish Hospitals section describes the application of the model and the results. The conclusions are presented in the Results section. ECONOMIC THEORY Two factors play an important role in determining an optimal distribution of public services, the facility’s operating costs and the users’ travel costs (which include their vehicle and time costs). These “social” costs are determined by the spatial distribution of the public services. The question is according to what organizing principle is the distribution established, and what are the consequences for the social costs? The organizing principle refers to rules on pricing, permits and responsible authorities. The economic theory offers points of reference for defining an organizing principle, whereby social costs are minimized. The average costs of providing a service often depend on the size of the institution providing it. For a small institution, fixed costs contribute heavily to the average costs per service. As the size of the institution increases, the fixed costs have increasingly less impact on the average costs per service, as the fixed costs are shared by a larger number of services. If the size of an institution continues to increase, this advantage diminishes and the costs due to coordination increase: More management and more bureaucratic procedures are required (see, e.g., Blank and Valdmanis, 2013). According to this principle, the average cost curve has a U shape. A concentration of a specific facility initially leads to a decrease in the average costs per service. Starting from a specific size of an institution, the average costs per service increase again. Where public services are concentrated, the travel costs are high, because there are only a limited number of large-scale institutions and the average distance to these institutions is considerable. As the concentration decreases, the travel costs also rapidly decrease. From a certain point (expressed as the number of public services), adding more institutions barely affects average travel costs, as there is little further decrease in average distance. On a graph, the travel costs have a hyperbolic shape. Figure 1 shows the operating costs, travel costs and the sum of both (= social costs) as a function of a number of institutions. Note that when the number of institutions increases, the average institution size decreases. The social costs graph has a U shape and reaches a minimum at point NIopt. Figure 1 also reflects the point of minimum operating costs. At point NIsub, the total operating costs of all institutions are minimal. In an unregulated market with sufficient competition, there will be a tendency toward this suboptimum solution. Economic theory does not always provide a straight answer to the question of which public administration level is the optimal one at which to plan or govern public services. In the event that social cost differentials between different administration levels do not exist, the commonly accepted subsidiarity principle can be of Copyright © 2014 John Wiley & Sons, Ltd.
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Figure 1. Optimization of supply
help. This principle states that a public service should be executed or governed by the lowest public administration level that is capable of addressing that service effectively and efficiently. Thus, for different administration levels, varying from the municipality to the federal level, the aforementioned optimization problem can be solved. The corresponding social cost for each public administration level can then be calculated and compared with the other administration levels. The public administration level with the lowest social cost can then be indicated as the optimal level. If there are hardly any differences between levels, the subsidiarity principle demands that the lowest administrative level should be preferred. Note that in the economic discussion so far, the quality aspect has not been mentioned. For instance, quality restrictions, whereby a minimum scope of service provision is required, are easy to process into the planning model by incorporating in the model a lower limit of possible solutions. An example of this is the minimum required number of treatments of a specific type, for example, as formulated for radiotherapy. These rules are formulated as guidelines and are also a minimum requirement laid down by policymakers (see, for example, (Cionini et al., 2007; Health Council of the Netherlands, 2008; Quality Assurance Team for Radiation Oncology, 2007).
ECONOMIC MODEL Regarding the model specification, there are many alternatives to the U curve for the average costs per hospitalization. One is the semi-logarithmic curve (Figures 2, 3 and 4). The equation for a semi-logarithmic curve is as follows: lnðC Þ ¼ a þ by
(1)
C = costs of an institution y = quantity of services provided by an institution a, b = parameters of the model Copyright © 2014 John Wiley & Sons, Ltd.
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Figure 2. Average costs per bed versus scale, actual and estimated for rehabilitation
Figure 3. Average costs per bed and scale, actual and estimated for general care
Figure 4. Average costs per accelerator, estimated and radiotherapy
We assume that total services provided equals total demand: X
y¼ Y
(2)
In a region with a total demand Y for services and NI institutions, the following therefore applies for an average-sized institution: Y (3) lnðC Þ ¼ a þ b NI Copyright © 2014 John Wiley & Sons, Ltd.
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Note that we assume that Y is exogenous, namely, that total demand is not dependent on, for instance, travel distance. In densely populated areas with well-organized transport facilities, this assumption can be safely made. However, in other areas, for instance in developing countries, this might not be the case (see, e.g., Buor, 2003). The travel distance to a service is measured by the average distance in a region from the citizens’ houses to the nearest service. It is assumed that a region covering a certain number of square kilometers is divided into a number of sub-regions of equal size, with each sub-region having a single service. This service is located at the center of the sub-region. If we imagine this sub-region as a circle, then the average distance from each point inside the circle to the center of the circle equals 2/3R, with R = radius of the circle (see, e.g., Stone, 1991; Larson and Odoni, 1981). The radius of a circle can be calculated from the surface area (R = √(A/π). If we further assume that the crow-fly distance correction factor equals 1.5, then the average distance of each point in the circle to the center is equal to (Blank, 1993) rffiffiffiffiffiffiffiffiffiffiffi A=NI dist ¼ π
(4)
dist = average distance to the nearest institution A = number of square kilometers covered by the region NI = number of institutions Note that this is a rather rough measure. Geographic information systems can, of course, be used to compute average distances far more accurately (Wong et al., 2012). However, the central issue here is to establish the optimal number of public services and the optimal regional level, rather than the exact geographical locations. The total travel costs in a region for all citizens who rely on the service are equal to the average distance to the service multiplied by the kilometer price and the number of times the citizens have to travel to the service: TC ¼ distpnvY
(5)
TC = travel costs to the nearest institution dist = average distance to the nearest institution (Equation (4)) p = travel price per kilometer nv = annual number of trips per unit of service. The travel price per kilometer is defined as the average travel costs per kilometer for one service (e.g., bed or linear accelerator). Note that the use of one service may entail several trips. The travel price includes vehicle costs and time costs. The annual number of trips per unit of service includes patient and family visits. This visit frequency, as well as the intensity with which the capacity is used, affects the annual number of trips. For example, the number of trips linked to the use of an accelerator is much greater than for the use of a bed. Consequently, a linear (radiotherapy) accelerator is used by a larger number of patients annually than a hospital bed. The use of an accelerator is therefore associated with a larger number of trips Copyright © 2014 John Wiley & Sons, Ltd.
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between home and hospital. The number of trips per service on an annual basis is based on various plausible assumptions regarding visit frequency and intensity. Plausible parameters for the travel price per kilometer (based on the vehicle cost per kilometer, the hourly wage and the average speed) and the annual number of trips to a service can be substituted into Equation (5). As indicated, the total social costs are the sum of operating costs (Equation (3)) and travel costs (Equation (5)). Substituting Equation (4) in Equation (5) and then combining Equations (3) and (5) give the expression for the social costs: rffiffiffiffiffiffiffiffiffiffiffi Y A=NI NI þ pnvY SC ¼ exp a þ b* NI π
(6)
Where SC = social costs The minimization of Equation (6) with regard to the number of institutions gives the lowest social costs. We used a rather simple algorithm to establish the optimal number of institutions in a region. We start the algorithm by setting NI = 1 in a region. We then calculate the costs for NI and NI + 1. As the costs corresponding to NI + 1 are smaller than the costs corresponding to NI, we increase NI by 1 and recalculate the costs. The algorithm stops when the opposite is true. The NI and the corresponding costs are then the outcome of the algorithm. This procedure is repeated for each region.
EMPIRICAL APPLICATION: FLEMISH HOSPITALS Administrative context Planning services is an important policy tool of the Flemish healthcare service. The underlying principle is that services must be both sufficiently accessible and sufficiently available, and as high quality and cost-effective as possible. In 2001, at the request of the Flemish government, a study was made to develop a policy tool for controlling the programming, planning and setting up of public health and welfare services in Flanders (Hecke van, 2001). The objective was “to determine minimum geographic units for Flemish territory on the basis of socioeconomic factors (including schools, traffic and shops).” All sectors in the health and welfare policy area were included in order to arrive at a more effective inter-sector planning and network design. The result of the study was included in a Care Regions Decree. In order to optimize spatial distribution, an urban hierarchy was used in the decree. The more specialized the supply, the higher the position in the urban hierarchy. For this purpose, the geographical hierarchy in Flanders comprises several levels. In this paper, we use three levels, namely provincial, regional and urban. Flanders’ five provinces are divided into a total of 14 regions, which in turn are divided into a total of 38 urban areas. Copyright © 2014 John Wiley & Sons, Ltd.
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Model specification For the empirical application, a simplified division of hospital services was used, namely, rehabilitation care, general hospital care and radiotherapy. General hospital care does, of course, comprise a broad spectrum of services and could be more differentiated. Because the application primarily serves as an example, we have assumed that general hospital care is fairly homogenous and can be presented as one function. However, for practical policy purposes, the services would need to be more differentiated. The empirical application is performed by minimizing the annual costs. For the application of the model, we specified three sets of two equations representing the hospital costs and the travel costs of each distinct hospital service. We first determined the parameters of the cost curves (parameters “a” and “b” in Equation (1)). The parameters of the cost curves for rehabilitation and general hospital care were determined with multivariate regression. Data were provided by the Flemish ministry of healthcare and consist of the 2005 cost accountings of Flemish hospitals. Unfortunately, we were unable to find any reliable data to proceed in the same way for radiotherapy. Instead, we used information from the literature for the cost curves of radiotherapy (Ploquin and Dunscombe, 2008; van der Giessen et al., 2004; Dunscombe and Roberts, 2001); a detailed description is given in Blank et al. (2010). The parameters used are shown in Table 1. The established parameters of the cost functions can be visualized graphically. In Figures 2 and 3, the actual and estimated costs are shown and compared with the number of beds. Because there are no reliable data for the costs of radiotherapy, only the estimated costs related to the number of accelerators are shown in Figure 4. Figures 2 (rehabilitation) and 3 (general care) clearly show a U-shaped cost curve, with high average costs at small and large institutions and low average costs at medium-sized institutions. Figure 4 (radiotherapy) shows a strong decline in average costs at low numbers of accelerators. At a certain point, a further increase in accelerators barely affects the average costs. Next, we determine the travel price per kilometer and the number of trips per unit of service. As mentioned in the theoretical section, a number of plausible parameters for establishing the travel price and number of trips per unit of service need to be chosen. Blank et al. (2010) provide a detailed explanation and set of parameters. The outcomes are presented in Table 2. Bearing in mind the possible arbitrariness in the parameters, we also conducted sensitivity analyses to obtain an insight into the effects of the chosen parameters on the final outcomes.
Table 1. Parameters of cost curves for rehabilitation, basic hospital care and radiotherapy Facility
Constant (am)
Coefficient (bm)
15.1 17.0 15.20
0.010 0.003 0.167
Rehabilitation General care Radiotherapy Parameters relate to 2005 data Copyright © 2014 John Wiley & Sons, Ltd.
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Table 2. Travel price per kilometer, number of trips per unit of service Facility
Price
Number of trips
Rehabilitation (per bed) General care (per bed) Radiotherapy (per accelerator)
0.70 0.70 0.70
726 1560 20000
Finally, in order to be able to apply the model, data are needed on the size and composition of the demand (Y) for services per administrative level. These data were also provided by the Flemish ministry of healthcare and were extracted from two data sources, namely, Minimale Klinische Gegevens (registration of minimal clinical data) and Informatiestroom tussen de ziekenhuizen en de administratie gezondheidszorg (information flow between hospitals and the health administration). The first source consists of data on patients’ length of stay, diagnosis, age, gender and place of residence; the second includes data on medical activities, stays and inpatient days. The demand for care is expressed in physical units—namely, the demand for rehabilitation beds, for general hospital care beds and for linear accelerators—and on the basis of the current use of hospital care per capita of the population, subdivided according to age group. The use of beds is derived from a number of underlying parameters: hospitalization, average length of stay and degree of occupancy. For linear accelerators, use was made of incident data, utilization, repetition factor and severity of the treatments. Because the analysis focuses on the planning at different administrative levels, the demand for care is calculated at the lowest administrative level (urban level); the demand for care at a higher administrative level is then the aggregate of the underlying areas at urban level. The details of this calculation can be found in Blank et al. (2010). RESULTS The results are presented per region or administrative level (provincial, regional and urban; see Tables 3, 4 and 5). We then compare the results of the three administrative levels by comparing the social costs following from planning at a certain administrative level. • Table 3 shows that, if planned/provided at provincial level, the required number of hospitals providing rehabilitation, general hospital care and radiotherapy would be 30, 83 and 10, respectively. Table 3. Simulated number of hospitals, 2010, provincial level Province Antwerp Limburg East Flanders Flemish Brabant West Flanders Total
Rehabilitation
Basic
Radiotherapy
8 4 7 5 6 30
23 11 19 12 18 83
3 1 2 2 2 10
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Table 4. Simulated number of hospitals, 2010, regional level Region
Rehabilitation
Basic
Radiotherapy
2 4 2 3 1 4 3 2 2 2 1 2 1 2 31
4 13 4 6 3 12 8 5 6 5 3 6 3 5 83
1 1 1 1 1 1 1 1 1 1 1 1 1 1 14
Aalst Antwerp Bruges Brussels Genk Gent Hasselt Kortrijk Leuven Mechelen Oostend Roeselare Sint-Niklaas Turnhout Total
• Table 4 shows that at the regional level, the lowest social costs would be achieved by 31 hospitals providing rehabilitation, 83 providing general care and 14 providing radiotherapy. The number of hospitals providing rehabilitation is thus one less than at the regional level; for general hospital care, there is no difference between the regional and the provincial level; for radiotherapy, there is a difference of four hospitals. • Table 5 shows that, if provided at the urban level (38 areas), the required number of hospitals providing rehabilitation, general hospital care and radiotherapy would be 44, 38 and 84, respectively. Compared with the regional level, there is a marked increase for rehabilitation (+13) and radiotherapy (+24). For general hospital care, there is a difference of only one hospital. Optimal administrative level The social costs were calculated in order to determine the optimal administrative level. Table 6 shows the social costs of hospital care in an index with the province as reference point. The social costs at the provincial level were set at 100. An index of 110, for example, means that the costs are 10% higher than at the provincial level. Table 6 shows that the social costs can vary substantially between the administrative levels. • The social costs of rehabilitation at the urban level are 11% higher than at the provincial level. • At the regional level, the social costs of rehabilitation are somewhat higher than at the provincial level. • For radiotherapy, the social costs of providing the service at the urban level are 88% higher than at the provincial level. • For general hospital care, there are hardly any differences between the administrative levels. In that case, the subsidiarity principle prevails. Copyright © 2014 John Wiley & Sons, Ltd.
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Table 5. Simulated number of hospitals, 2010, urban level Region
Rehabilitation
Basic
Radiotherapy
1 3 1 1 1 2 1 1 1 1 1 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 44
2 9 2 2 1 4 1 1 2 1 1 9 1 2 4 1 2 4 4 2 1 1 2 2 1 2 1 4 2 3 1 1 1 2 1 2 1 1 84
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 38
Aalst Antwerpen Asse Boom Brasschaat Brugge Brussel Deinze Dendermonde Diest Genk Gent Geraardsbergen Halle Hasselt Herentals Ieper Kortrijk Leuven Lier Maaseik Maasmechelen Mechelen Mol Neerpelt Oostende Oudenaarde Roeselare Schilde Sint-Niklaas Sint-Truiden Tienen Tongeren Turnhout Veurne Vilvoorde Waregem Zottegem Total
Table 6. Estimated social costs according to administrative level, index province = 100 Region Province Regional Urban
Rehabilitation
Basic
Radiotherapy
Total
100 101 111
100 100 101
100 111 188
100 100 103
Copyright © 2014 John Wiley & Sons, Ltd.
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Thus, rehabilitation should be planned/governed at the urban level, general hospital care at the urban level, and radiotherapy at the provincial level. We used a sensitivity analysis to also examine the effect of the travel price on the outcomes. • Halving the travel price reduces the simulated number of hospitals providing different services by a minimum amount, general care (1) and radiotherapy (1). For rehabilitation, there is no change in the number of services. • Doubling the travel price does not increase the number of hospitals for any of the services. The effects are therefore very limited. The reason for this is that the hospital costs are substantially higher than the travel costs. It takes a substantial increase in the travel price (500%, for instance) for significant effects to appear. These parameters are not very plausible. CONCLUSIONS The administrative level of planning/governing public services is an issue that involves different perspectives. These perspectives are used to consider criteria on which to base the planning. In this article, we present an economic model that, on the basis of the premise of minimizing social costs, indicates the optimal administrative level. This model can be used to support administrative decision-making. Where there is an administrative tendency to shift responsibilities to the lowest possible administrative level, this model clearly shows that this can go hand in hand with a high degree of social cost inefficiency. The reverse can also be true. In the case of a centralized administrative approach, the model can also provide results indicating social inefficiencies. An empirical application of the model to various services in Flemish hospitals shows that a simple prototype of the model works and gives plausible results. The model provides not only insight into hospital costs related to the operational scale and into the travel costs for patients and their family members but also a reference for establishing the optimal administrative level. In this article, we demonstrated that the Flemish government has good reason to investigate the planning in hospital care in order to deal with social cost inefficiencies. In many Western countries, market reforms have led governments to simply drop strict care planning. However, we expect that market forces will generate social cost inefficiencies, causing the return of public services planning to the political agenda. In the case of hospital care, this will probably concern not general hospital care but low-volume and complex hospital services that require expensive infrastructure, such as radiotherapy. The model presented here has the potential to play an important role in healthcare service planning. It is also suitable for application in many other areas of public services, such as education.
ACKNOWLEDGEMENT The authors have no competing interests. Copyright © 2014 John Wiley & Sons, Ltd.
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REFERENCES Blank JLT. 1993. Kosten van kennis: een empirisch onderzoek naar de productiestructuur van het basisonderwijs in Nederland Sociale en Culturele Studie. SCP/VUGA: Rijswijk/Den Haag. Blank JLT, Valdmanis VG. 2013. Principles of Productivity Measurement: An Elementary Introduction to Quantative Research on the Productivity, Efficiency, Effectiveness and Quality of the Public Sector. Shaker Publishing B.V: Maastricht. Blank JLT, van Hulst BL, Wats MG. 2010. Verzorging verspreid: een economisch planningsmodel voor het zorgaanbod in Vlaamse ziekenhuizen IPSE Studies Research Reeks. IPSE Studies, TU Delft: Delft. Buor D. 2003. Analysing the primacy of distance in the utilization of health services in the Ahafo-Ano South district, Ghana. Int J Health Plann Manage 18(4): 293–311. Cionini L, Gardani G, Gabriele P, et al. 2007. Quality indicators in radiotherapy. Radiotherapy and Oncology 82(2): 191–200. Current J, Min H, Schilling D. 1990. Multiobjective analysis of facility location decisions. Eur J Oper Res (49): 295–307. Daskin MS, Dean LK. 2005. Location of health care facilities. In Handbook of OR/MS in Health Care: A Handbook of Methods and Applications, Sainfort F, Brandeau M, Pierskalla W (eds). Kluwer: Dordrecht, 43–76. Dunscombe P, Roberts G. 2001. Radiotherapy service delivery models for a dispersed patient population. Clin Oncol 13(1): 29–37.
Copyright © 2014 John Wiley & Sons, Ltd.
Health Council of the Netherlands. 2008. Searchlight on radiotherapy. A vision for 2015. (Vol. publication no. 2008/27). Health Council of the Netherlands: The Hague. Hecke van E. 2001. Ontwikkelen van een beleidsinstrument van programmatie, planning en inplanting van gezondheids- en welzijnsvoorzieningen. K.U. Leuven. Larson RC, Odoni AR. 1981. Urban Operations Research. Prentice-Hall, Englewood-Cliff: New York. Onderwijsraad. 2005. Variëteit in schaal. Drukkerij Artoos: Den Haag. Ploquin NP, Dunscombe PB. 2008. The cost of radiation therapy. Radiother Oncol 86(2): 217–223. Quality Assurance Team for Radiation Oncology. 2007. Comprehensive Audits of Radiotherapy Practices: A Tool for Quality Improvement. International Atomic Energy Agency: Vienna. RVZ. 2008. Schaal en Zorg. In RVZ (Ed.), Advies. Raad voor de Volksgezondheid en Zorg: Zoetermeer. Stone, RE. 1991. Technical note—some average distance results. Transp Sci 25(1): 83–90. van der Giessen, P-H, Alert J, Badri, C, et al. 2004. Multinational assessment of some operational costs of teletherapy. Radiother Oncol 71(3): 347–355. Wong LY, Heng BH, Cheah JTS, Tan CB. 2012. Using spatial accessibility to identify polyclinic service gaps and volume of under-served population in Singapore using Geographic Information System. Int J Health Plann Manage 27(3): e173–e185.
Int J Health Plann Mgmt 2015; 30: 382–394. DOI: 10.1002/hpm
Int J Health Plann Mgmt 2015; 30: 382–394. Published online 10 April 2014 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/hpm.2246
Optimal administrative scale for planning public services: a social cost model applied to Flemish hospital care Jos L.T. Blank1,2* and Bart van Hulst1 1 2
Delft University of Technology, Delft, The Netherlands Erasmus University Rotterdam, Rotterdam, The Netherlands
SUMMARY In choosing the scale of public services, such as hospitals, both economic and public administrative considerations play important roles. The scale and the corresponding spatial distribution of public institutions have consequences for social costs, defined as the institutions’ operating costs and the users’ travel costs (which include the money and time costs). Insight into the relationship between scale and spatial distribution and social costs provides a practical guide for the best possible administrative planning level. This article presents a purely economic model that is suitable for deriving the optimal scale for public services. The model also reveals the corresponding optimal administrative planning level from an economic perspective. We applied this model to hospital care in Flanders for three different types of care. For its application, we examined the social costs of hospital services at different levels of administrative planning. The outcomes show that the social costs of rehabilitation in Flanders with planning at the urban level (38 areas) are 11% higher than those at the provincial level (five provinces). At the regional level (18 areas), the social costs of rehabilitation are virtually equal to those at the provincial level. For radiotherapy, there is a difference of 88% in the social costs between the urban and the provincial level. For general care, there are hardly any cost differences between the three administrative levels. Thus, purely from the perspective of social costs, rehabilitation should preferably be planned at the regional level, general services at the urban level and radiotherapy at the provincial level. Copyright © 2014 John Wiley & Sons, Ltd. KEY WORDS:
healthcare; hospitals; network planning; optimization; social costs
INTRODUCTION When planning the level of administration for public services, considerations such as legitimacy, access, complementarities and externalities play important roles. The particular administrative level chosen for each service must ensure optimization in the exercise of democratic control, the safeguarding of public values, and reconciliation with other public services and other regions. One can also add to this list economic considerations, such as the minimization of social costs. Social costs are defined here *Correspondence to: Jos L.T. Blank, Centre for Innovations and Public Sector Efficiency Studies, Delft University of Technology P.O. Box 5015 2600 GA Delft, The Netherlands. E-mail: [email protected]
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as the operating costs of the public service (usually borne by the government) and the travel costs (usually borne by the individual citizen). Social costs are to a certain extent dependent on the scale and the spatial distribution of the public services. The issue of the scale and spatial distribution of public services therefore often appears on the political agenda. In the Netherlands, for example, various advisory bodies have extensively reported on this topic in recent years, for instance, in relation to the planning of services in education and healthcare (RVZ, 2008; Onderwijsraad, 2005). In this article, we address the issues of scale, geographical access and planning of public services from a purely economic perspective. There are two key questions: • What is the optimal spatial distribution of public services? • What is the optimal administrative level at which the planning of a public service should take place? We will answer the research questions by developing an economic model that makes a comparative assessment between the total operating costs of the public services and the travel costs of patients. The scale at which the public services are offered plays a crucial role in the model. At a small scale, it is possible to offer the service at a large number of locations and thereby keep the travel costs low; on the other hand, from a business economics point of view, a small scale can be disadvantageous because of the fixed costs per institution. With minor adjustments, the model can be applied to various public sectors. In this article, the model is illustrated using Flemish hospital care, in particular rehabilitation, general care and radiotherapy services (see, e.g., Blank et al., 2010). This illustration shows how the theoretical framework can be applied empirically. The model bears strong similarities to facility location models, for which there is a huge body of literature. In these models, public services are geographical locations that have been determined on the basis of a given, spatially distributed demand for services. The central question here is the locations at which public services should be located in order to minimize total travel time or travel costs (for examples of extensive overviews, see Daskin and Dean (2005). Some of these models are extended with a multi-objective function, in which case, the minimization problem also includes fixed costs or operating expenses (Current et al. (1990)). However, our model has three major differences from these models: • The objective function of our model is based on a social welfare perspective. It is generally acknowledged that decisions on hospital facility location affect both private (travel time and costs) and public interests (facility costs financed by public means). • Our model allows for non-linear forms of both private and public costs. In general, this type of model is based on somewhat rigid linear assumptions on costs and travel time, whereas in practice, these seem to be quite unrealistic. There is, for instance, a large body of literature showing that economies/diseconomies of scale prevail in hospitals. • Our model can be used not only to find an optimal solution for an economic problem but also to derive an optimal answer to the question which public administration level should be responsible for carrying out the planning procedure. The Copyright © 2014 John Wiley & Sons, Ltd.
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subsidiarity principle is used in combination with economic theory to provide a solution for the optimal planning level. This article is organized as follows. The Economic Theory section presents the various economic considerations, which in Economic Model section are translated into an economic model that can be applied empirically. The Empirical Application: Flemish Hospitals section describes the application of the model and the results. The conclusions are presented in the Results section. ECONOMIC THEORY Two factors play an important role in determining an optimal distribution of public services, the facility’s operating costs and the users’ travel costs (which include their vehicle and time costs). These “social” costs are determined by the spatial distribution of the public services. The question is according to what organizing principle is the distribution established, and what are the consequences for the social costs? The organizing principle refers to rules on pricing, permits and responsible authorities. The economic theory offers points of reference for defining an organizing principle, whereby social costs are minimized. The average costs of providing a service often depend on the size of the institution providing it. For a small institution, fixed costs contribute heavily to the average costs per service. As the size of the institution increases, the fixed costs have increasingly less impact on the average costs per service, as the fixed costs are shared by a larger number of services. If the size of an institution continues to increase, this advantage diminishes and the costs due to coordination increase: More management and more bureaucratic procedures are required (see, e.g., Blank and Valdmanis, 2013). According to this principle, the average cost curve has a U shape. A concentration of a specific facility initially leads to a decrease in the average costs per service. Starting from a specific size of an institution, the average costs per service increase again. Where public services are concentrated, the travel costs are high, because there are only a limited number of large-scale institutions and the average distance to these institutions is considerable. As the concentration decreases, the travel costs also rapidly decrease. From a certain point (expressed as the number of public services), adding more institutions barely affects average travel costs, as there is little further decrease in average distance. On a graph, the travel costs have a hyperbolic shape. Figure 1 shows the operating costs, travel costs and the sum of both (= social costs) as a function of a number of institutions. Note that when the number of institutions increases, the average institution size decreases. The social costs graph has a U shape and reaches a minimum at point NIopt. Figure 1 also reflects the point of minimum operating costs. At point NIsub, the total operating costs of all institutions are minimal. In an unregulated market with sufficient competition, there will be a tendency toward this suboptimum solution. Economic theory does not always provide a straight answer to the question of which public administration level is the optimal one at which to plan or govern public services. In the event that social cost differentials between different administration levels do not exist, the commonly accepted subsidiarity principle can be of Copyright © 2014 John Wiley & Sons, Ltd.
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Figure 1. Optimization of supply
help. This principle states that a public service should be executed or governed by the lowest public administration level that is capable of addressing that service effectively and efficiently. Thus, for different administration levels, varying from the municipality to the federal level, the aforementioned optimization problem can be solved. The corresponding social cost for each public administration level can then be calculated and compared with the other administration levels. The public administration level with the lowest social cost can then be indicated as the optimal level. If there are hardly any differences between levels, the subsidiarity principle demands that the lowest administrative level should be preferred. Note that in the economic discussion so far, the quality aspect has not been mentioned. For instance, quality restrictions, whereby a minimum scope of service provision is required, are easy to process into the planning model by incorporating in the model a lower limit of possible solutions. An example of this is the minimum required number of treatments of a specific type, for example, as formulated for radiotherapy. These rules are formulated as guidelines and are also a minimum requirement laid down by policymakers (see, for example, (Cionini et al., 2007; Health Council of the Netherlands, 2008; Quality Assurance Team for Radiation Oncology, 2007).
ECONOMIC MODEL Regarding the model specification, there are many alternatives to the U curve for the average costs per hospitalization. One is the semi-logarithmic curve (Figures 2, 3 and 4). The equation for a semi-logarithmic curve is as follows: lnðC Þ ¼ a þ by
(1)
C = costs of an institution y = quantity of services provided by an institution a, b = parameters of the model Copyright © 2014 John Wiley & Sons, Ltd.
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Figure 2. Average costs per bed versus scale, actual and estimated for rehabilitation
Figure 3. Average costs per bed and scale, actual and estimated for general care
Figure 4. Average costs per accelerator, estimated and radiotherapy
We assume that total services provided equals total demand: X
y¼ Y
(2)
In a region with a total demand Y for services and NI institutions, the following therefore applies for an average-sized institution: Y (3) lnðC Þ ¼ a þ b NI Copyright © 2014 John Wiley & Sons, Ltd.
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Note that we assume that Y is exogenous, namely, that total demand is not dependent on, for instance, travel distance. In densely populated areas with well-organized transport facilities, this assumption can be safely made. However, in other areas, for instance in developing countries, this might not be the case (see, e.g., Buor, 2003). The travel distance to a service is measured by the average distance in a region from the citizens’ houses to the nearest service. It is assumed that a region covering a certain number of square kilometers is divided into a number of sub-regions of equal size, with each sub-region having a single service. This service is located at the center of the sub-region. If we imagine this sub-region as a circle, then the average distance from each point inside the circle to the center of the circle equals 2/3R, with R = radius of the circle (see, e.g., Stone, 1991; Larson and Odoni, 1981). The radius of a circle can be calculated from the surface area (R = √(A/π). If we further assume that the crow-fly distance correction factor equals 1.5, then the average distance of each point in the circle to the center is equal to (Blank, 1993) rffiffiffiffiffiffiffiffiffiffiffi A=NI dist ¼ π
(4)
dist = average distance to the nearest institution A = number of square kilometers covered by the region NI = number of institutions Note that this is a rather rough measure. Geographic information systems can, of course, be used to compute average distances far more accurately (Wong et al., 2012). However, the central issue here is to establish the optimal number of public services and the optimal regional level, rather than the exact geographical locations. The total travel costs in a region for all citizens who rely on the service are equal to the average distance to the service multiplied by the kilometer price and the number of times the citizens have to travel to the service: TC ¼ distpnvY
(5)
TC = travel costs to the nearest institution dist = average distance to the nearest institution (Equation (4)) p = travel price per kilometer nv = annual number of trips per unit of service. The travel price per kilometer is defined as the average travel costs per kilometer for one service (e.g., bed or linear accelerator). Note that the use of one service may entail several trips. The travel price includes vehicle costs and time costs. The annual number of trips per unit of service includes patient and family visits. This visit frequency, as well as the intensity with which the capacity is used, affects the annual number of trips. For example, the number of trips linked to the use of an accelerator is much greater than for the use of a bed. Consequently, a linear (radiotherapy) accelerator is used by a larger number of patients annually than a hospital bed. The use of an accelerator is therefore associated with a larger number of trips Copyright © 2014 John Wiley & Sons, Ltd.
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between home and hospital. The number of trips per service on an annual basis is based on various plausible assumptions regarding visit frequency and intensity. Plausible parameters for the travel price per kilometer (based on the vehicle cost per kilometer, the hourly wage and the average speed) and the annual number of trips to a service can be substituted into Equation (5). As indicated, the total social costs are the sum of operating costs (Equation (3)) and travel costs (Equation (5)). Substituting Equation (4) in Equation (5) and then combining Equations (3) and (5) give the expression for the social costs: rffiffiffiffiffiffiffiffiffiffiffi Y A=NI NI þ pnvY SC ¼ exp a þ b* NI π
(6)
Where SC = social costs The minimization of Equation (6) with regard to the number of institutions gives the lowest social costs. We used a rather simple algorithm to establish the optimal number of institutions in a region. We start the algorithm by setting NI = 1 in a region. We then calculate the costs for NI and NI + 1. As the costs corresponding to NI + 1 are smaller than the costs corresponding to NI, we increase NI by 1 and recalculate the costs. The algorithm stops when the opposite is true. The NI and the corresponding costs are then the outcome of the algorithm. This procedure is repeated for each region.
EMPIRICAL APPLICATION: FLEMISH HOSPITALS Administrative context Planning services is an important policy tool of the Flemish healthcare service. The underlying principle is that services must be both sufficiently accessible and sufficiently available, and as high quality and cost-effective as possible. In 2001, at the request of the Flemish government, a study was made to develop a policy tool for controlling the programming, planning and setting up of public health and welfare services in Flanders (Hecke van, 2001). The objective was “to determine minimum geographic units for Flemish territory on the basis of socioeconomic factors (including schools, traffic and shops).” All sectors in the health and welfare policy area were included in order to arrive at a more effective inter-sector planning and network design. The result of the study was included in a Care Regions Decree. In order to optimize spatial distribution, an urban hierarchy was used in the decree. The more specialized the supply, the higher the position in the urban hierarchy. For this purpose, the geographical hierarchy in Flanders comprises several levels. In this paper, we use three levels, namely provincial, regional and urban. Flanders’ five provinces are divided into a total of 14 regions, which in turn are divided into a total of 38 urban areas. Copyright © 2014 John Wiley & Sons, Ltd.
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Model specification For the empirical application, a simplified division of hospital services was used, namely, rehabilitation care, general hospital care and radiotherapy. General hospital care does, of course, comprise a broad spectrum of services and could be more differentiated. Because the application primarily serves as an example, we have assumed that general hospital care is fairly homogenous and can be presented as one function. However, for practical policy purposes, the services would need to be more differentiated. The empirical application is performed by minimizing the annual costs. For the application of the model, we specified three sets of two equations representing the hospital costs and the travel costs of each distinct hospital service. We first determined the parameters of the cost curves (parameters “a” and “b” in Equation (1)). The parameters of the cost curves for rehabilitation and general hospital care were determined with multivariate regression. Data were provided by the Flemish ministry of healthcare and consist of the 2005 cost accountings of Flemish hospitals. Unfortunately, we were unable to find any reliable data to proceed in the same way for radiotherapy. Instead, we used information from the literature for the cost curves of radiotherapy (Ploquin and Dunscombe, 2008; van der Giessen et al., 2004; Dunscombe and Roberts, 2001); a detailed description is given in Blank et al. (2010). The parameters used are shown in Table 1. The established parameters of the cost functions can be visualized graphically. In Figures 2 and 3, the actual and estimated costs are shown and compared with the number of beds. Because there are no reliable data for the costs of radiotherapy, only the estimated costs related to the number of accelerators are shown in Figure 4. Figures 2 (rehabilitation) and 3 (general care) clearly show a U-shaped cost curve, with high average costs at small and large institutions and low average costs at medium-sized institutions. Figure 4 (radiotherapy) shows a strong decline in average costs at low numbers of accelerators. At a certain point, a further increase in accelerators barely affects the average costs. Next, we determine the travel price per kilometer and the number of trips per unit of service. As mentioned in the theoretical section, a number of plausible parameters for establishing the travel price and number of trips per unit of service need to be chosen. Blank et al. (2010) provide a detailed explanation and set of parameters. The outcomes are presented in Table 2. Bearing in mind the possible arbitrariness in the parameters, we also conducted sensitivity analyses to obtain an insight into the effects of the chosen parameters on the final outcomes.
Table 1. Parameters of cost curves for rehabilitation, basic hospital care and radiotherapy Facility
Constant (am)
Coefficient (bm)
15.1 17.0 15.20
0.010 0.003 0.167
Rehabilitation General care Radiotherapy Parameters relate to 2005 data Copyright © 2014 John Wiley & Sons, Ltd.
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Table 2. Travel price per kilometer, number of trips per unit of service Facility
Price
Number of trips
Rehabilitation (per bed) General care (per bed) Radiotherapy (per accelerator)
0.70 0.70 0.70
726 1560 20000
Finally, in order to be able to apply the model, data are needed on the size and composition of the demand (Y) for services per administrative level. These data were also provided by the Flemish ministry of healthcare and were extracted from two data sources, namely, Minimale Klinische Gegevens (registration of minimal clinical data) and Informatiestroom tussen de ziekenhuizen en de administratie gezondheidszorg (information flow between hospitals and the health administration). The first source consists of data on patients’ length of stay, diagnosis, age, gender and place of residence; the second includes data on medical activities, stays and inpatient days. The demand for care is expressed in physical units—namely, the demand for rehabilitation beds, for general hospital care beds and for linear accelerators—and on the basis of the current use of hospital care per capita of the population, subdivided according to age group. The use of beds is derived from a number of underlying parameters: hospitalization, average length of stay and degree of occupancy. For linear accelerators, use was made of incident data, utilization, repetition factor and severity of the treatments. Because the analysis focuses on the planning at different administrative levels, the demand for care is calculated at the lowest administrative level (urban level); the demand for care at a higher administrative level is then the aggregate of the underlying areas at urban level. The details of this calculation can be found in Blank et al. (2010). RESULTS The results are presented per region or administrative level (provincial, regional and urban; see Tables 3, 4 and 5). We then compare the results of the three administrative levels by comparing the social costs following from planning at a certain administrative level. • Table 3 shows that, if planned/provided at provincial level, the required number of hospitals providing rehabilitation, general hospital care and radiotherapy would be 30, 83 and 10, respectively. Table 3. Simulated number of hospitals, 2010, provincial level Province Antwerp Limburg East Flanders Flemish Brabant West Flanders Total
Rehabilitation
Basic
Radiotherapy
8 4 7 5 6 30
23 11 19 12 18 83
3 1 2 2 2 10
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Table 4. Simulated number of hospitals, 2010, regional level Region
Rehabilitation
Basic
Radiotherapy
2 4 2 3 1 4 3 2 2 2 1 2 1 2 31
4 13 4 6 3 12 8 5 6 5 3 6 3 5 83
1 1 1 1 1 1 1 1 1 1 1 1 1 1 14
Aalst Antwerp Bruges Brussels Genk Gent Hasselt Kortrijk Leuven Mechelen Oostend Roeselare Sint-Niklaas Turnhout Total
• Table 4 shows that at the regional level, the lowest social costs would be achieved by 31 hospitals providing rehabilitation, 83 providing general care and 14 providing radiotherapy. The number of hospitals providing rehabilitation is thus one less than at the regional level; for general hospital care, there is no difference between the regional and the provincial level; for radiotherapy, there is a difference of four hospitals. • Table 5 shows that, if provided at the urban level (38 areas), the required number of hospitals providing rehabilitation, general hospital care and radiotherapy would be 44, 38 and 84, respectively. Compared with the regional level, there is a marked increase for rehabilitation (+13) and radiotherapy (+24). For general hospital care, there is a difference of only one hospital. Optimal administrative level The social costs were calculated in order to determine the optimal administrative level. Table 6 shows the social costs of hospital care in an index with the province as reference point. The social costs at the provincial level were set at 100. An index of 110, for example, means that the costs are 10% higher than at the provincial level. Table 6 shows that the social costs can vary substantially between the administrative levels. • The social costs of rehabilitation at the urban level are 11% higher than at the provincial level. • At the regional level, the social costs of rehabilitation are somewhat higher than at the provincial level. • For radiotherapy, the social costs of providing the service at the urban level are 88% higher than at the provincial level. • For general hospital care, there are hardly any differences between the administrative levels. In that case, the subsidiarity principle prevails. Copyright © 2014 John Wiley & Sons, Ltd.
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Table 5. Simulated number of hospitals, 2010, urban level Region
Rehabilitation
Basic
Radiotherapy
1 3 1 1 1 2 1 1 1 1 1 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 44
2 9 2 2 1 4 1 1 2 1 1 9 1 2 4 1 2 4 4 2 1 1 2 2 1 2 1 4 2 3 1 1 1 2 1 2 1 1 84
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 38
Aalst Antwerpen Asse Boom Brasschaat Brugge Brussel Deinze Dendermonde Diest Genk Gent Geraardsbergen Halle Hasselt Herentals Ieper Kortrijk Leuven Lier Maaseik Maasmechelen Mechelen Mol Neerpelt Oostende Oudenaarde Roeselare Schilde Sint-Niklaas Sint-Truiden Tienen Tongeren Turnhout Veurne Vilvoorde Waregem Zottegem Total
Table 6. Estimated social costs according to administrative level, index province = 100 Region Province Regional Urban
Rehabilitation
Basic
Radiotherapy
Total
100 101 111
100 100 101
100 111 188
100 100 103
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Thus, rehabilitation should be planned/governed at the urban level, general hospital care at the urban level, and radiotherapy at the provincial level. We used a sensitivity analysis to also examine the effect of the travel price on the outcomes. • Halving the travel price reduces the simulated number of hospitals providing different services by a minimum amount, general care (1) and radiotherapy (1). For rehabilitation, there is no change in the number of services. • Doubling the travel price does not increase the number of hospitals for any of the services. The effects are therefore very limited. The reason for this is that the hospital costs are substantially higher than the travel costs. It takes a substantial increase in the travel price (500%, for instance) for significant effects to appear. These parameters are not very plausible. CONCLUSIONS The administrative level of planning/governing public services is an issue that involves different perspectives. These perspectives are used to consider criteria on which to base the planning. In this article, we present an economic model that, on the basis of the premise of minimizing social costs, indicates the optimal administrative level. This model can be used to support administrative decision-making. Where there is an administrative tendency to shift responsibilities to the lowest possible administrative level, this model clearly shows that this can go hand in hand with a high degree of social cost inefficiency. The reverse can also be true. In the case of a centralized administrative approach, the model can also provide results indicating social inefficiencies. An empirical application of the model to various services in Flemish hospitals shows that a simple prototype of the model works and gives plausible results. The model provides not only insight into hospital costs related to the operational scale and into the travel costs for patients and their family members but also a reference for establishing the optimal administrative level. In this article, we demonstrated that the Flemish government has good reason to investigate the planning in hospital care in order to deal with social cost inefficiencies. In many Western countries, market reforms have led governments to simply drop strict care planning. However, we expect that market forces will generate social cost inefficiencies, causing the return of public services planning to the political agenda. In the case of hospital care, this will probably concern not general hospital care but low-volume and complex hospital services that require expensive infrastructure, such as radiotherapy. The model presented here has the potential to play an important role in healthcare service planning. It is also suitable for application in many other areas of public services, such as education.
ACKNOWLEDGEMENT The authors have no competing interests. Copyright © 2014 John Wiley & Sons, Ltd.
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REFERENCES Blank JLT. 1993. Kosten van kennis: een empirisch onderzoek naar de productiestructuur van het basisonderwijs in Nederland Sociale en Culturele Studie. SCP/VUGA: Rijswijk/Den Haag. Blank JLT, Valdmanis VG. 2013. Principles of Productivity Measurement: An Elementary Introduction to Quantative Research on the Productivity, Efficiency, Effectiveness and Quality of the Public Sector. Shaker Publishing B.V: Maastricht. Blank JLT, van Hulst BL, Wats MG. 2010. Verzorging verspreid: een economisch planningsmodel voor het zorgaanbod in Vlaamse ziekenhuizen IPSE Studies Research Reeks. IPSE Studies, TU Delft: Delft. Buor D. 2003. Analysing the primacy of distance in the utilization of health services in the Ahafo-Ano South district, Ghana. Int J Health Plann Manage 18(4): 293–311. Cionini L, Gardani G, Gabriele P, et al. 2007. Quality indicators in radiotherapy. Radiotherapy and Oncology 82(2): 191–200. Current J, Min H, Schilling D. 1990. Multiobjective analysis of facility location decisions. Eur J Oper Res (49): 295–307. Daskin MS, Dean LK. 2005. Location of health care facilities. In Handbook of OR/MS in Health Care: A Handbook of Methods and Applications, Sainfort F, Brandeau M, Pierskalla W (eds). Kluwer: Dordrecht, 43–76. Dunscombe P, Roberts G. 2001. Radiotherapy service delivery models for a dispersed patient population. Clin Oncol 13(1): 29–37.
Copyright © 2014 John Wiley & Sons, Ltd.
Health Council of the Netherlands. 2008. Searchlight on radiotherapy. A vision for 2015. (Vol. publication no. 2008/27). Health Council of the Netherlands: The Hague. Hecke van E. 2001. Ontwikkelen van een beleidsinstrument van programmatie, planning en inplanting van gezondheids- en welzijnsvoorzieningen. K.U. Leuven. Larson RC, Odoni AR. 1981. Urban Operations Research. Prentice-Hall, Englewood-Cliff: New York. Onderwijsraad. 2005. Variëteit in schaal. Drukkerij Artoos: Den Haag. Ploquin NP, Dunscombe PB. 2008. The cost of radiation therapy. Radiother Oncol 86(2): 217–223. Quality Assurance Team for Radiation Oncology. 2007. Comprehensive Audits of Radiotherapy Practices: A Tool for Quality Improvement. International Atomic Energy Agency: Vienna. RVZ. 2008. Schaal en Zorg. In RVZ (Ed.), Advies. Raad voor de Volksgezondheid en Zorg: Zoetermeer. Stone, RE. 1991. Technical note—some average distance results. Transp Sci 25(1): 83–90. van der Giessen, P-H, Alert J, Badri, C, et al. 2004. Multinational assessment of some operational costs of teletherapy. Radiother Oncol 71(3): 347–355. Wong LY, Heng BH, Cheah JTS, Tan CB. 2012. Using spatial accessibility to identify polyclinic service gaps and volume of under-served population in Singapore using Geographic Information System. Int J Health Plann Manage 27(3): e173–e185.
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