The Sandwich algorithm for spatial equilibrium analysis

Abstract

Recent advances in mathematical programming techniques have made it possible to provide more realistic solutions to applied economic problems. Although mathematical programming techniques are widely used, the economic content of the solutions is often limited by the assumptions imposed by the algorithms available. This report is designed to demonstrate the increased flexibility which is currently available for the solution of a wide range of spatial economic problems. Transportation and transhipment models have been widely used in the analysis of the impact of policy changes on spatial activity, Borrell & Zwart [l]; Beck, Rathbun and Abbott [2]. One of the major shortcomings of such models has been an inability to model the impact of more flexible pricing policies on regional supply and demand, while maintaining the realistic non linearities which are associated with processing and transportation costs. In this paper a simplified version of the transhipment model developed by Borrell & Zwart [l] is modified to incorporate regional supply response while at the same time retaining complex processing and handling cost relationships. This report outlines the general form of the spatial equilibrium problem and some of the solution techniques available, in a format easily understood by readers not conversant with operational research techniques. Initially the problem is defined and solution methods used in the past are then briefly described. The advantages and disadvantages of these methods are outlined before showing how a relatively new solution technique may be able to improve both the scope and flexibility of the problems being solved.