A Comment on Brimberg and ReVelle (2000): The maximum return-on-investment plant location problem
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Viewpoint A Comment on Brimberg and ReVelle (2000): The maximum return-on-investment plant location problem
Introduction The recent paper by Brimberg and ReVelle1 was stated to broaden the scope of applications, and the range of tools available to the decision-maker faced with real decisions, but the mathematical programming type method was only tested on a large number of random, arti®cial problems. A justi®cation for the work was largely based on the claim by ReVelle and Laporte2 that no reference to any investigation that seeks plant locations and market area delineation under an objective of maximum return on investment has yet been found. The Serck Services and Edmundsen Electrical studies The wish of ReVelle and Laporte2 to create new and more realistic decision tools for plant location is laudable but their statement reveals a lack of total familiarity with the literature. Studies predominantly carried out at Lancaster University in the late 1960s and early 1970s were published in Mercer et al.3 One was undertaken for Serck Services, which provided garages nationally with a small range of new and replacement vehicle components, and another was for Edmundsen Electrical, which was a wholesaler stocking ten thousand electrical items. In both cases, the unit sales and the prices able to be charged depended on the depot locations, so that the criteria had to be the measures of return on investment used by the managements of those companies. Branch locations and their trading areas were determined, with the alternatives of retaining or closing the existing branches, for progressively lower returns on investment, so that management could plan the strategic corporate expansion. Obviously, the number of vehicles assigned to each branch was also an output of the studies but the most important outcome was the insight into how the two companies should develop. Serck Services should have a large number of small depots, as opposed to the then-current policy of building large depots, and Edmundsen Electrical should expand in areas where the competition was weak, rather than where the market potential was high. Thus it is not surprising that both companies have progressed to become the market leaders in their ®elds! Locational additivity Using generalised forms of the relationships developed in the Lancaster studies, with real UK data and realistic
parameter values, Stoker4 ± 6 researched the depot location problem with the incorporation of marketing characteristics. Both demand and price were allowed to depend on the depot locations, which were determined by the numeric ± analytic method with location-allocation algorithms. Except for the transition from one to two depots, the locations in a real UK situation are additive in the sense that the optimal locations for (N 1) facilities include the optimal locations for N facilities, for both the maximum pro®t and maximum return on investment criteria. A special case of th
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