Comparison of exact and approximate methods of solving the uncapacitated plant location problem

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Abstract
This study was prompted by a recently published article in this journal on facility location by D. R. Sule. We show that the claim made by Sule of a novel and extremely simple algorithm yielding optimum solutions is not true. Otherwise, the algorithm would represent a breakthrough in decision‐making for which a number of notoriously hard problems could be efficiently recast as location problems and easily solved.In addition, several variants of common location problems addressed by Sule are reviewed. In the last twenty years, many methods of accurately solving these problems have been proposed. In spite of their increased sophistication and efficiency, none of them claims to be a panacea. Therefore, researchers have concurrently developed a battery of fast but approximate solution techniques. Sule's method was essentially proposed by Kuehn and Hamburger in 1963, and has been adapted many times since.We exhibit several examples (including the one employed by Sule) in which Sule's algorithms lead to nonoptimal solutions. We present computational results on problems of size even greater than those utilized by Sule, and show that a method devised by Erlenkotter is both faster and yields better results.In a cost‐benefit analysis of exact and approximate methods, we conclude that planning consists of generating an array of corporate scenarios, submitting them to the “optimizing black box,” and evaluating their respective merits. Therefore, much is to be gained by eliminating the vagaries of the black box—that is, by using an exact method—even if the data collection and the model representation introduce sizable inaccuracies. Ironically, large problems (those that typically require most attention) cannot be solved exactly in acceptable computational times. Pending the imminent design of a new generation of exact algorithms, the best heuristics are those that guarantee a certain degree of accuracy of their solutions.

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