Modelling a type-2 fuzzy inventory system considering items with imperfect quality and shortage backlogging

In this paper, an inventory model considering items with imperfect quality is developed in fuzzy environment, wherein shortages are allowed and are backlogged. In order to detect the items with imperfect quality, all items are screened before they are sent for consumption, and all imperfect quality items are sold at discounted price, called salvage value. In view of the fact that demand may not be predicted precisely, because it depends upon many uncertain and perturbing market activities, it is assumed to be a type-2 fuzzy variable. Quantity of imperfect quality items in the received lot may not be predicted precisely; hence percentage of imperfect quality items is also considered as a type-2 fuzzy variable. In this regard, this study developed a de-fuzzification method of type-2 fuzzy variable pertaining to interval approximation. The mathematical model is analysed to find closed form formulae of order quantity and backlogging quantity. Finally, the proposed methodology and model are testified on numerical examples, and sensitivity of decision variables is examined and discussed to underline the managerial insights as well as to establish the robustness of the mathematical model.