A quick and effective metod for capacitated lot sizing with startup and reservation costs

The authors present a pure zero-one integer programming model for determining single-item production lot sizes in capacitated ‘long production run’ environments, where each production period is dedicated to a single product, and where production of a given item may extend over more than one production period. All costs, as well as capacity, are time-varying, and incude startup (changeover), reservation (opportunity), holding, and production costs. Holding and production costs may also vary within a period. The problem setting is effectively the single-item subproblem of the ‘multiple product cycling’ case. The present model is efficient primarily because of a structure which encourages integer solutions to the relaxed linear program, but also because of variable elimination strategies associated with capacity limitations. Although the formulation makes two simplifying assumptions versus previous research, these did not significantly hamper model performance. Experimentation on problems from the literature yielded a 93% optimality frequency, with less than 60 pivots required for 20 period problems, a tremendous efficiency improvement over previous models. As such, the model represents an excellent and practical first step toward efficiently solving multiple product problems on an industrial scale.