A fuzzy random continuous review inventory model with a mixture of backorders and lost sales under imprecise chance constraint

The article investigates a constrained continuous review inventory system with a mixture of backorders and lost sales. The proposed model is developed with the annual customer demand incorporated as a fuzzy random variable. The lead‐time is assumed to be constant while the lead‐time demand is assumed to be connected to the annual fuzzy random demand through the length of the lead‐time. A budget constraint is imposed on the model in the form of an 'imprecise' chance constraint to present a possible way of quantifying fuzzily defined uncertain information of the constraint. A methodology is proposed to determine the optimal order quantity and the reorder point such that the total cost incurred is minimised subject to the constraint. A numerical example is given to illustrate the proposed methodology.