A Facility Sizing and Location in Spatial Price Equilibrium Model

Abstract

As reviewed in Chapter 4, within the framework of bilevel facility location models in spatial equilibrium, there are several different submodels that one can employ to describe economic competition amongst firms on the network. These economic models include the classic spatial price equilibrium (SPE) model, first introduced by Samuelson (1952) and enhanced for over three decades since then (e.g., Takayama and Judge, 1964) as well as models of oligopolistic competition (e.g., Cournot-Nash). In this chapter, we present a facility sizing and location in spatial price equilibrium model. We review the modifications required to the SPE submodel and to the facility location submodel which facilitate their linkage in an integrated model. Additionally, we consider how the sensitivity analysis results of Chapter 5 are used to generate a linear approximation of the implicit function relating changes in production and shipping levels to changes in market prices. This represents the “linking” component of the facility sizing and location in spatial price equilibrium model. This chapter also presents existence results for the integrated model, as well as a solution algorithm and numerical results.