Warehouse Location Under Continuous Economies of Scale

TLDR

Warehouse location is a nonconvex programming problem involving the geographic placement and sizing of intermediate facilities, with nonconvexities arising from economies of scale in facility costs. The paper aims to evaluate heuristics for solving warehouse location problems with continuous concave economies of scale. A heuristic program was developed and tested on practical problems, with computational experience discussed. Numerical examples suggest that the heuristic yields near‑optimal solutions and that facility sizing and location are highly sensitive to the shape of the cost functions.

Abstract

Warehouse Location is a nonconvex programming problem involving the geographic placing and sizing of intermediate facilities in distribution studies. The nonconvexities are caused by economies of scale associated with the cost of building and operating the facilities. A heuristic program has been developed for solving warehouse location problems when these economies are representable by continuous concave functions. The paper discusses the heuristics used and computational experience with the program on “practical” problems. On the basis of two numerical examples for which an optimal solution was obtained through a special purpose experimental mixed integer programming code, it is conjectured (1) that near optimal solutions can be achieved using the heuristic program and (2) that optimal sizing and locating of facilities are very sensitive to the shapes of the warehousing cost functions.