An HNP-MP Approach for the Capacitated Multi-Item Lot Sizing Problem With Setup Times

In this paper, we consider the capacitated multi-item lot sizing problem with setup times. The problem is to schedule different items over a horizon of periods with the objective to minimize the sum of setup cost and inventory holding cost. To achieve feasible high-quality solutions, we propose a new solution approach which hybrids Nested Partitions and Mathematical Programming (HNP-MP). Nested Partitions is a partitioning and sampling based heuristic method with a global perspective on the problem. In the proposed new method the Mathematical Programming method is implemented to calculate the promising index and to provide a good guidance on partitioning in the Nested Partitions framework. A time-oriented decomposition heuristic method, Relax-and-Fix, is also implemented to obtain good promising regions and speed up the computational process. Computational results based on benchmark test problems show that the approach is computationally tractable and is able to obtain good results. The approach outperforms other state-of-the-art approaches found in the literature. Note to Practitioners-The capacitated multi-item lot sizing problem with setup times considered in this paper is motivated by the attempt of effectively planning the production with lower setup cost and inventory holding cost under the constraints of limited capacities. An effective production planning on a lot sizing problem can provide a good guidance on the decision made by a Material Requirements Planning (MRP) system, and check for the conflicts with available capacities. Two areas of approaches are implemented to deal with the problem: the exact approach and the heuristic approach. The main drawback of the exact approach is the excessive computational time when the problem size becomes large. On the other hand, the main drawback of the heuristic approach is an inefficient objective solution. The goal of this paper is to propose a heuristic approach which outperforms other state-of-the-art approaches found in the literature. Practitioners can apply the proposed method into the extensions of lot sizing problems which consider backlogging, overtime, and shortage.