Multi-item Capacity Constrained Dynamic Lot-sizing and Sequencing with Setup Time

Production lot-sizing has a special significance in supply chain taking into account the fact that majority of the lot-sizing problems are associated with NP-hard scheduling and sequencing problems. The complexity increases exponentially when multi-item capacitated dynamic lot-sizing is considered. The basic economic production quantity (EPQ) model minimizes the sum of setup and holding cost under certain favorable assumptions. However, when assumptions are removed by introducing more complex constraints, the solution procedure becomes extremely difficult to solve. As a result NP-hardness arises which necessitates the use of heuristics. The objective of this paper is to minimize the sum of setup and inventory holding costs over a time horizon subject to constraints of capacity limitations and elimination of backlogging. As reports reveal, algorithm for an optimal solution exists in case of a single item production. But for multi-item problems, no algorithm exists which can provide global optimality. This paper develops a model for multi-item problem with setup time. Based on the model a program has been executed and feasible solutions have been obtained for the bench-mark data.