A production–inventory model with remanufacturing for defective and usable items in fuzzy-environment

This paper investigates a production–remanufacturing system for a single product over a known-finite time horizon. Here the production system produces some defective units which are continuously transferred to the remanufacturing unit and the constant demand is satisfied by the perfect items from production and remanufactured units. Remanufacturing unit uses the defective items from production unit and the collected used-products from the customers and later items are remanufactured for reuse as fresh items. Some of the used items in the remanufacturing unit are disposed off which are not repairable. The remanufactured units are treated as perfect items. Normally, rate of defectiveness varies in a production system and may be approximated by a constant or fuzzy parameter. Hence, two models are formulated separately with constant and fuzzy defective productions. When defective rate is imprecise, optimistic and pessimistic equivalent of fuzzy objective function is obtained by using credibility measure of fuzzy event by taking fuzzy expectation. Here, it is assumed that remanufacturing system starts from the second production cycle and after that both production and remanufacturing units continue simultaneously. The models are formulated for maximum total profit out of the whole system. Here the decision variables are the total number of cycles in the time horizon, the duration for which the defective items are collected and the cycle length after the first cycle. Genetic Algorithm is developed with Roulette wheel selection, Arithmetic crossover, Random mutation and applied to evaluate the maximum total profit and the corresponding optimum decision variables. The models are illustrated with some numerical data. Results of some particular cases are also presented.