Defect Production System Optimal Production Strategies

The typical economic production quantity (EPQ) model aims to provide the advices for the pratical production processes. In the typical EPQ model, the implicit assumption is that 100% of items in a produced lot are perfect. However, in a wide variety of real world situations, the production system may shift from the in-control state to the out-of-control state due to machine failures or other reasons, and since then produce a fixed percentage of defective items until the end of the production cycle. Therefore, there is a practical need to research the deteriorating production system to extend the EPQ model. The main focuses and innovations of this paper are summarized as follows.1) Taking into account the fuzzy random elapsed time, a fuzzy random EPQ model with deteriorating process without shortage is considered to extend the classical EPQ model. Based on the credibility theory, the expected total cost is derived by assuming that the elapsed time is characterized as a fuzzy random variable, and then the properties of the total cost function are revealed. The optimal production run length which can minimize the expected total cost is proved to exist and be unique, the upper and lower bounds of the optimal production run length are determined. Bisection method for the optimal production run length is designed. The degradations of the fuzzy random elapsed time into the random elapsed time and fuzzy elapsed time are considered, theory results show that the random EPQ model and fuzzy EPQ model are just the special cases degraded from the fuzzy random EPQ model. The effects of the rework cost and the percentage of the defective items on the optimal production policy are illustrated by numerical examples.2) Taking into account the fuzzy elapsed time, the EPQ model with fuzzy deteriorating production process and allowable shortage is investigated. Based on the credibility theory, the total cost per unit time function with shortage cost and fuzzy rework cost is derived. Some properties of the total cost function are revealed. The optimal production run length which can minimize the expected total cost per unit time is proved to exist and be unique. The upper and lower bounds of the optimal production run length are determined. Based on these properties, bisection method for the optimal production run length is designed. Finally, numerical examples are presented to illustrate the effects of the rework cost and the percentage of the defective items on the optimal production policy.3) Taking into account the random fuzzy elapsed time, an imperfect production system with random fuzzy deteriorating production process under allowable shortage is investigated. The EPQ model including fuzzy shortage cost and random fuzzy rework cost is established. Based on the credibility theory, the expected total cost per unit time is proved to be convex. The simultaneous perturbation stochastic approximation (SPSA) algorithm based on the random fuzzy simulation is provided to obtain the optimal production run length. Finally, numerical examples are presented to confirm the proposed model algorithm. This algorithm can help us get the optimal production run length under allowable shortage in random fuzzy environments.4) Taking into account the fuzzy random elapsed time, the EPQ model with fuzzy random deteriorating production process and allowable shortage is investigated. The EPQ model including shortage cost and fuzzy random rework cost is established. Based on the credibility theory, the expected total cost per unit time is derived, and then the properties of the cost function are revealed. The optimal production run length which can minimize the expected total cost is proved to exist and be unique, the upper and lower bounds of the optimal production run length are determined. Bisection method for the optimal production run length is designed. The degradations of the fuzzy random elapsed time are discussed to understand the proposed model in depth. The effects of the shortage cost, rework cost and the percentage of the defective items on the optimal production policy are illustrated by numerical examples.