A Warehouse-Location Problem

This paper describes a method for determining a more profitable geographic location pattern for the warehouses that are employed by a firm in delivering known quantities of its finished product to its customers, where the number of warehouses is also permitted to vary. It is shown that this can normally be expected to be a concave minimization problem. Unfortunately, there are usually no practical computational methods for determining the values of the variables that correspond to the absolute minimum of a concave cost function. However, a local optimum can be determined by a method described in the article. The method involves a sequence of transportation computations that are shown to converge to the solution. An illustrative small scale computation is included. An appendix explains in intuitive terms the nature of the computational difficulties that arise in a concave-programming problem.