International Journal of Industrial Engineering & Production Research

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In the fundamental production inventory model, in order to solve the economic production quantity (EPQ) we always fix both the demand quantity and the production quantity per day. But, in the real situation, both of them probably will have little disturbances every day. Therefore, we should fuzzify both of them to solve the economic production quantity (q*) per cycle. Using α-cut for defuzzification the total variable cost per unit time is derived. Therefore the problem is reduced to crisp annual costs. The multi-objective model is solved by Global Criteria Method with the help of GRG (Generalized Reduced Gradient) Technique. In this model shortages are permitted and fully backordered. The purpose of this paper is to investigate a computing schema for the EPQ in the fuzzy sense. We find that, after defuzzification, the total cost in fuzzy model is less than in the crisp model. So it permits better use of the EPQ model in the fuzzy sense arising with little disturbances in the production, and demand.

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One of the basic assumptions of classical production-inventory models is that all products are of perfect quality. However, in real manufacturing situations, the production of defective items is inevitable, and a fraction of the items produced may be naturally imperfect. In fact, items may be damaged due to production and/or transportation conditions in the manufacturing process. On the other hand, some reworkable items exist among imperfect items that can be made perfect by additional processing. In addition, the classical production-inventory models assume that there is only one product in the system and that there is an unlimited amount of resources. However, in many practical situations, several products are produced and there are some constraints related to various factors such as machine capacity, storage space, available budget, number of allowable setups, etc. Therefore, we propose new constrained production-inventory models for multiple products where the manufacturing process is defective and produces a fraction of imperfect items. A percentage of defective items can be reworked, and these products go through the rework process to become perfect and return to the consumption cycle. The goal is to determine economic production quantities to minimize the total cost of the system. The analytical solutions are each derived separately by Lagrangian relaxation method, and a numerical example is presented to illustrate and discuss the procedure. A sensitivity analysis is performed to investigate how the variation in the inputs of the models affects the total cost of the inventory system. Finally, some research directions for future works are discussed.