The General Optimal Market Area Model

Abstract

for their helpful comments. AbstractMarket area models determine the optimal size of market for a facility. These models are grounded in classical location theory, and express the fundamental tradeoff between economies-of-scale from larger facilities and the higher costs of transport to more distant markets. The simpler market area models have been discovered and rediscovered, and applied and reapplied, in a number of different settings. We review the development and use of market area models, and formulate a General Optimal Market Area model that accommodates both economies-of-scale in facilities costs and economies-of-distance in transport costs as well as different market shapes and distance norms. Simple expressions are derived for both optimal market size and optimal average cost, and also the sensitivity of average cost to a non-optimal choice of size. The market area model is used to explore the implications of some recently proposed distance measures and to approximate a large discrete location model, and an extension to price-sensitive demands is provided. i ' 1 "Accession Fo, NTIS GRA&I DTIC TAB

Evaluation of Plant Focus Strategies: A Continuous Approximation Framework

“…Similar results are obtained by Newell (1973), Geoffrion (1979), and Erlenkotter (1989) when the demand density and cost parameters are constant over the market area. Naturally, A * turns out to be constant in these earlier papers, whereas it is a surface defined over the two-dimensional plane in this paper.…”

“…Naturally, A * turns out to be constant in these earlier papers, whereas it is a surface defined over the two-dimensional plane in this paper. The optimal cost TC(A * ) is insensitive to small errors in A * or model parameters as also observed by Erlenkotter (1989). This robustness property is important because it is an indication that the geometry of service regions are not crucial for the model.…”

“…That paper extends and unifies the optimal market area models of Newell (1973), Geoffrion (1979) and Erlenkotter (1989). These classical models focus on the issue of facility size and service region under simplifying assumptions about topology and demand density, leaving determination of the precise plant locations to a subsequent analysis.…”

“…Erlenkotter (1989) points out that K is relatively robust to the distance metric and the shape of the service region and provides sample values for K .…”

Location-allocation for distribution to a uniform demand with transshipments

“…From Eqs. (16), (19), and (21), D4(K, C) and D3(K, C) are at least K times as large as D2(K, C). These results suggest that optimally allocating destinations is more important than optimally locating terminals.…”