A Heuristic Adjacent Extreme Point Algorithm for the Fixed Charge Problem

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Abstract
An algorithm with three variations is presented for the approximate solution of fixed charge problems. Computational experience shows it to be extremely fast and to yield very good solutions. The basic approach is (1) to obtain a local optimum by using the simplex method with a modification of the rule for selection of the variable to enter the basic solution, and (2) once at a local optimum, to search for a better extreme point by jumping over adjacent extreme points to resume iterating two or three extreme points away. This basic approach is the same as that used by Steinberg [Steinberg, D. I. 1970. The fixed charge problem. Naval Res. Log. Quart. 17 217-236.], Cooper [Cooper, L. 1975. The fixed charge problem--I: A new heuristic method. Comp. & Maths, with Appls. 1 89-95.], and Denzler [Denzler, D. R. 1969. An approximate algorithm for the fixed charge problem. Naval Res. Log. Quart. 16 411-416.] in their algorithms, but is an extension and improvement of all three. The algorithm is being used by the U.S Environmental Protection Agency's Office of Solid Waste Management Programs to decide on the number, type, size, and location of the disposal facilities to operate in a region, and how to allocate the region's wastes to these facilities.

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