Fuzzy stochastic EOQ inventory model for items with imperfect quality and shortages are backlogged

This article deals with an economic order quantity (EOQ) inventory model for items with imperfect quality in fuzzy stochastic environment, wherein shortages are allowed and completely backlogged. Fuzzy stochastic environment means linguistic ‘impreciseness’ and statistical ‘uncertainty’ both appear simultaneously. Due to uncertain demand trend, imperfect production process, natural disaster etc., the demand rate or imperfect quality items in the lot size can’t predict precisely or to fit the exact probability density function. In this context, we assume that demand rate as a fuzzy number and fraction of defective items as a fuzzy random variable. We formulate the model and derive the total profit which is a function of fuzzy random variable. The fuzzy random renewal reward theorem is used to find the fuzzy expected total profit per unit time. The fuzzy expected total profit function is defuzzified by using the signed distance method. The closed form solution of the model is derived and subsequently the concavity of the total profit function is proved. The solution procedure is illustrated with the help of numerical examples. Sensitivity of decision variables for change in different parameters is examined and discussed.