An algorithm with three variations for the approximate solution of fixed charge problems. Computational experience shows it is extremely fast and yields very good solutions. The basic approach in all three variants of the algorithm is (1) 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, search for a better extreme point by jumping over adjacent extreme points to resume iterating two or three extreme points away. Problems in which economies of scale give rise to separable piecewise-linear concave objective functions are easily formulated as fixed charge problems. The algorithm is being used by the U.S. Environmental Protection Agency's Office of Solid Waste Management Programs to solve a problem of regional solid waste planning: the selection of disposal sites to be developed and the determination of how the wastes of each municipality in a region should be distributed among the sites. 21 pp. Ref.