(An) algorithm for capacity-constrained dynamic production planning with no-backlogging over a fixed time horizon

Abstract

A single-product dynamic production planning problem over a fixed time horizon, T, is considered under the assumption that demands over the T-period horizon are known, no backloggings are allowed and both unit production and holding costs are constant, but set-up costs are time-variant. Each production is also constrained in period wise capacity limit. The mechanism of the optimal solution verification for the problem is known, while various computational methodologies of either dynamic programming approach or branch-and-bound technique for finding the optimal solution have turned out inefficient for large problems. Thereupon, this study shows that certain periods can be identified as production points(periods). Those identified production points are verified to be included in a set of optimal production points. Each of those production points is applied for their directly-preceding preiods to be determined as optimal regeneration points, upon which the time horizon,T, is decomposed. The identifications of those production points and regeneration points are shown to lead to the reduction of computational requirements in branch-and-bound approach.