Working Paper
ON THE CHOICE OF MODELS FOR PUBLIC F A C I L I T Y LOCATION
Donald E r l e n k o t t e r A p r i l 1 9 8 0
WP-80-47
International Institute for Applied Systems Analysis
A-2361 Laxenburg, Austria
NOT F O R QUOTATION WITHOUT P E R M I S S I O N O F T H E AUTHOR
ON T H E C H O I C E O F MODELS F O R P U B L I C F A C I L I T Y L O C A T I O N
D o n a l d E r l e n k o t t e r A p r i l 1980
W P - 8 0 - 4 7
W o r k i n g Papers a r e i n t e r i m r e p o r t s on w o r k of t h e I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d S y s t e m s A n a l y s i s and have received o n l y l i m i t e d r e v i e w . V i e w s o r o p i n i o n s expressed h e r e i n do n o t n e c e s s a r i l y r e p r e -
s e n t t h o s e of t h e I n s t i t u t e o r of i t s N a t i o n a l M e m b e r O r g a n i z a t i o n s .
I N T E R N A T I O N A L I N S T I T U T E F O R A P P L I E D SYSTEMS A N A L Y S I S A - 2 3 6 1 L a x e n b u r g , A u s t r i a
FOREWORD
The public provision of urban facilities and services often takes the form of a few central supply points serving a large number of spatially dispersed demand points: for example, hospitals, schools, libraries, and emergency services such as fire and police. A fundamental characteristic of such systems is the spatial separation between suppliers and consumers. No market signals exist to identify efficient and inefficient geo- graphical arrangements, thus the location problem is one that arises in both East and West, in planned and in market economies.
This problem is being studied at IIASA by the Public Facil- ity Location Task (formerly the Normative Location Modeling Task) which started in 1979. The expected results of this Task are a comprehensive state-of-the-art survey of current theories and applications, an established network of international contacts among scholars and institutions in different countries, a frame- work for comparison, unification, and generalization of existing approaches, as well as the formulation of new problems and
approaches in the field of optimal location theory.
This paper is a result of collaboration between the Human Settlements and Services Area and the Resources and Environment Area which is hosting Professor Erlenkotter at IIASA. The author argues that for a large class of public sector location problems suitably modified private sector models perform better than
typical public sector models.
Oleg Vasiliev Chairman
Resources and Environment Area
Andrei Rogers Chairman
Human Settlements and Services Area
ABSTRACT
Public sector facility location models have been defined as those that minimize client costs for a given level of service subject to a public budget constraint, whereas private sector models are those that minimize the total costs for meeting fixed client demands. We snow that a slight reformulation of a typical public sector location model is both superior to the original model and equivalent to a typical private sector formulation.
Thus, for the class of problems considered, a standard model type is appropriate regardless of the institutional context.
CONTENTS
1. INTRODUCTION, 1
2. PUBLIC AND PRIVATE SECTOR MODELS, 2 3. THE CHOICE OF A MODEL, 5
4. AN ILLUSTRATIVE EXAMPLE, 7 5. CONCLUDING REMARKS, 9
REFERENCES, 1 1
ON THE CHOICE OF MODELS FOR PUBLIC FACILITY LOCATION D. Erlenkotter
1. INTRODUCTION
Traditionally a distinction has been drawn between public and private facility location models (ReVelle, Marks, and Liebman, 1970; Swain, 1974). According to this differentiation, public sector models typically have the objective of minimizing client costs for a given level of service subject to a public budget constraint, while private sector models seek to minimize the total costs for meeting specified fixed demands. The purpose of this note is to show for a large class of public sector location problems that so-called pablic sector models are economically and logically inferior to models of the private sector type.
The particular class of location problems that we address involves the public provision of what are essentially "private"
goods or services; we do not pretend to have models that address all the aspects of location of "public1' goods raised by Teitz
(1968), Schuler and Holahan (1977), and Lea (1979). However, as noted by Schuler and Holahan (1977), many public sector location problems and models involve provision of goods or services that are really "private" in nature in that a client travels to a
facility location to receive a well-defined "quantity" of a good or service. Thus this category of location problems seems worthy of attention.
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2. PUELIC AND PRIVATE SECTOR MODELS
A standard "public sector" facility location model is:
Minimize Z = C Pi C a . . x ieI j.eJ 11 i j
Xij E {0,11
subject to
where '
i is the population of clients at location i e I;
a is the travel cost per client from location i j
i E I to facility location j e J;
Xij is the fraction of the population of clients at i~ I that receive service at facility location j E J;
is 1 if a facility is opened at location j E J and 0 otherwise;
is the fixed cost for opening a facility at location j E J ;
is the variable capacity and service cost per client served at facility location j E J ; is the total budget for facility costs.
