An extended optimization model for solving multi-product multi-period capacitated lot-sizing problems

This paper deals with a capacitated lot-sizing problem in deterministic, multi-product and multi-time period contexts. The problem has been formulated as a mixed-integer linear programming model, which minimizes total cost of production planning by considering the constraints of safety stock, multi-resource production resource, and storage capacity. Moreover, the proposed model aims to determine the capacity of resource production and warehousing in each period. This study applies an efficient parallel simulated annealing (PSA) algorithm for solving the real-sized problems in reasonable computational time to demonstrate the feasibility and applicability of the proposed model and solution procedure. Finally, the efficiency and usefulness of the proposed model and solution methodology are demonstrated through a set of randomly generated problems. Out of 20 samples, the mathematical model only solved 4 samples and in the largest instance, the horizontal time and number of type of products were 8 and 6 respectively. In two of the samples, PSA results in the optimum value. In other cases, the results were close to the optimum values.