A fuzzy random periodic review mixture inventory model with backorder price discount

In this paper, a periodic review inventory model with a mixture of backorders and lost sales is developed under mixed fuzzy random environment. It is assumed that the supplier provides some price discount to control the backorder rate and gives an incentive to the customers to wait for the arrival of their orders rather than take their orders elsewhere. The annual customer demand is considered to be continuous fuzzy random variable following normal distribution. The model is analysed under three scenarios - no price discount, fixed price discount, and controllable price discount. An algorithm is presented to simultaneously determine the optimal values of the review period, the target inventory level, and the backorder price discount, so that the total annual cost is minimised. Numerical examples show that the case of controllable backorder price discount leads to the system incurring lowest operational costs.