A Modeling and Hybridized Decomposition Approach for the Multi-level Capacitated Lot-Sizing Problem with Setup Carryover, Backlogging, and Emission Control

The goal of the production planning problem is to determine the optimum quantity to produce in order to satisfy demand over a predetermined planning horizon with the least amount of money spent. Making the appropriate choices in production planning will impact a manufacturing company’s performance and productivity, which is crucial to remain competitive in the market. Therefore, developing and enhancing techniques for solving production planning problems is very significant. This paper proposes a mixed-integer linear programming model for this extension of the dynamic multi-level capacitated lot-sizing under study, where setup carryover, backlogging, and emission control are considered. An item Dantzig-Wolfe decomposition-based heuristic procedure is developed, and a dynamic programming and column generation approach is used to solve the problem. We also propose a multi-step iterative capacity allocation heuristic procedure to handle any infeasibilities that arise when solving the problem. We evaluate the performance of the developed solution approach using a test data set available in the literature. Computational results show that the proposed optimization framework provides competitive solutions within a reasonable timeframe.