A lower and upper bound guided nested partitions method for solving capacitated multi-level production planning problems

This paper considers the capacitated multi-level production planning problem with the consideration of backorders. Demand for each item is deterministic in each level and in each period with a given horizon of T periods. The objective is to minimize the total cost that includes setup, inventory holding, backlogging, and overtime cost. For each period, the demand must be satisfied without exceeding capacities. To achieve high quality solutions for this class of production planning problems, we develop a lower and upper bound guided nested partitions method. The optimization method effectively utilizes domain knowledge guided by both lower and upper bound solutions, and then provides an efficient partitioning and sampling strategy. Consequently, in the approach most of the search is kept around the most promising regions capable of leading to good solutions. Extensive computational tests show that our proposed heuristic approach provides good solution results based on benchmark problems.