In this paper, a stochastic periodic review inventory model is developed. The backorder rate (backorder price discount), ordering cost (safety stock), lead time, and review period are treated as decision variables. The ordering cost and lead time can be controlled by using capital investment and crashing cost, respectively. It is assumed that shortages are allowed and partially backlogged. If an item is out of stock, the supplier may offer a negotiable price discount to the loyal, tolerant and obliged customers to pay off the inconvenience of backordering. Furthermore, it is assumed that the protection interval demand follows a normal distribution. Our objective is to develop an algorithm to determine the optimal decision variables, so that the total expected annual cost incurred has a minimum value. Finally, a numerical example is presented to illustrate the solution procedure, and sensitivity analysis is carried out to analyze the proposed model. The numerical results show that a significant amount of savings can be obtained by making decisions with capital investment in reducing ordering cost.
