A Stochastic Dynamic Programming Model for Production Systems Planning with the Possibility of Producing Defective Products in a Finite Planning Horizon

Productivity of production systems depends on proper planning in various fields such as production, maintenance and repairs, inventory control, etc. Considering the major and direct impact of the production plan on other fields, it is necessary to prepare this plan with a suitable approach so that the production systems can be properly managed and costs can be reduced as much as possible. Limitations such as the need to supply a certain amount of demand in a certain period of time, the possibility of producing defective products, and the imposition of costs due to frequent system setup, make managers a challenge in providing an accurate plan. In this research, an attempt is made to plan the production process in a multi-period single product system by taking advantage of the Markov decision process and taking into account the above-mentioned constraints. In the following problem, using the stochastic dynamic programming technique, the best possible action will be selected and in other words, the best production volume will be determined for each period. The goal is to determine the volume of production in each period and for different states, in such a way that at the end of the permitted periods of production, the entire demand can be covered with the lowest cost. The effectiveness of the model is examined by solving a numerical example and analysis of the effects of changing parameters on the results of the problem has been presented. The results show that there is a direct relationship between the average cost rate and the costs related to setting up the system and producing each product unit, and the relationship between the said rate and the probability of producing healthy products and the production capacity is inverse. Increasing the production capacity after a certain threshold will not affect the average cost rate.