مدل مقدار تولید اقتصادی با موضوع عملکرد تصادفی برای فرآیند تراکم پذیری

This paper develops a new model for determining economic production quantity in an imperfect production system that generates defective items randomly. The production system utilizes an inspection subsystem to identify defective items (including reworkable and non-reworkable items) from non-defectives. Among defective items, reworkable items could be reworked once, and again an inspection is carried out. Furthermore, the inspection is error-prone that can result in returned items from customers. The proposed model considers realistic conditions in order to provide an optimal production plan. For example, rates of main and rework processes, batch size and back-order are considered as decision variables simultaneously such that rates of main and rework processes are not the same and take different values due to amount of the money that producer invests in each process (contributed as process compressibility). The objective function consists of different cost terms including shortage, regular production, setup of regular production, inventory holding, rework, inspection, disposal of scarped items and returned items from customer. The model is proved to be a convex nonlinear program. As it is difficult to obtain exact closed-form relations for the optimal solution, a problem-specific algorithm is designed. Under certain conditions, the algorithm can achieve the global optimum within a single iteration; otherwise it can be achieved in a polynomial time. Finally computational experiences are reported.

Considering different decision factors, real world production planning is a complicated issue for production managers. The basic economic production quantity (EPQ) is introduced to determine production quantity and backlog while minimizing total costs. This basic problem is developed further by considering different concepts and constraints in the literature. Most of the times, imperfect items are inevitable in the production system which could be detected by inspection procedures. Also, the inspection is imperfect in most cases. Furthermore, machines could also operate in different settings and production rates, which is contributed as process compressibility. These conditions increase the complexity of batch sizing. Different models are proposed in the literature that each of them considered different working conditions. This section provides a brief review of the progress in the literature and then detailed assumptions of the problem are provided in the next section.

This paper studied an imperfect production system with a set of new working assumptions such as process compressibility, reworking and inspection simultaneously. Also regular production process and rework process can be carried out with different process rates in their corresponding upper and lower bounds by paying their related costs and different stochastic percent of defectives. Next an integrated model is presented which simultaneously determines production lot size, backlog, rate of regular production and rate of rework with the objective of minimizing the total costs. While the model is nonlinear and could not be easily solved within a closed form solution, a simple algorithm is developed to obtain optimal solution. There are several possible extensions of the current study that could constitute future research endeavors in this field. One immediate extension can be to investigate the problem when there are multi products and/or multi stages. Besides, the model can be extended to deal with other types of uncertainties such as by applying the fuzzy set theory in measuring the demand rate and the percentage of defective products. Also this research can be extended in the following directions in order to be of more reality: