An inventory model involving back-order price discount when the amount received is uncertain

This paper presents and analyses the continuous review inventory model with order quantity, safety factor, back-order price discount, ordering cost and lead time as decision variables. Our work is based on the paper of Huang (2010 Huang, S.-P. (2010). Using simple and efficient algorithm involving ordering cost reduction and backorder price discount on inventory system under variable lead time. Information Technology Journal, 9(4), 804–810.Crossref] , Google Scholar]). We extend the model to incorporate the situation when the amount received is uncertain. The lead time demand is assumed follows a normal distribution. A solution procedure is developed to find the optimal solution. A numerical example is given to illustrate the model. A sensitivity analysis is also included to describe the effects of changes in the model parameters on the expected annual cost.