Dynamic production planning model: a dynamic programming approach

Production planning is one of the most important issues in manufacturing. The nature of this problem is complex and therefore researchers have studied it under several and different assumptions. In this paper, applied production planning problem is studied in a general manner and it is assumed that there exists an optimal control problem that its production planning strategy is a digital controller and must be optimized. Since this is a random problem because of stochastic values of sales in future, it is modeled as a stochastic dynamic programming and then it is transformed to a linear programming model using successive approximations. Then, it is proved that these two models are equivalent. The main objective of the proposed model is achieving optimal decisions using forecasting sales which can be applied in master production schedule, manufacturing resource planning, capacity requirements planning, and job shop/shop floor scheduling.