A mathematical programming approach towards optimized master production scheduling

The conventional material requirements planning (MRP) and master production scheduling (MPS) systems have gained wide acceptance among production management and control. In this paper, we consider further an aggregate optimization model for the usual MRP/MPS. That is, under a realistic assumption that the availability of material accumulates over time, we seek an optimal production schedule for most profitable operation subject to various capacity constraints. To this end, linear programming formulations are given for various levels of model complexity, ranging from a basic product-mix problem to a global aggregate production planning problem. We examine stage-wise decomposition from the point of view of practical computational feasibility and study the robustness of this decomposition. Finally, simplified numerical results are provided as illustrations.