Optimizing Systems When Components Have Discontinuous Cost Functions

A special type of problem can be solved by linear programming even though some of the cost functions are discontinuous at zero due to fixed charges. A group of systems is represented on a flow chart, a network of directed links. Any single path through the network represents a complete system. The minimum-cost single path is the desired solution. Associated with each link are certain machines and known operating costs which apply if that link is in the system. A certain machine may be specified in several links, and a given system may use such a “multiple-use” machine once, several times, or not at all. This fact prohibits the use of a link cost that is constant regardless of the rest of the system. The types of restriction equations are limited, and the simplex algorithm normally yields a solution of the form x_ı = 0 or 1. The use of integer-solution methods allows further restrictions to be added Problems of determining optimum production levels and the materials handling system for this production can be solved.