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). 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.