Continuous review inventory model with controllable lead time, lost sales rate and order processing cost when the received quantity is uncertain

• A continuous review single-stage inventory replenishment model is design for a single product with uncertain received quantity.
• The lost sales and ordering cost are functions of capital expenditure and an exponential crashing cost function is considered to reduce lead time.
• A mathematical model and an iterative algorithm were used to derive the optimal replenishment policy of the system.
• The aim is to minimize the total relevant cost of the system by optimizing order quantity, lost sales rate, ordering cost and lead time simultaneously.

In practice the quantity received may not match the quantity ordered due to worker's strike, rejection during inspection, damage during transportation, human errors in counting, etc. Accordingly, the managers often must make decisions under uncertain quantity received circumstances. In this study, we investigate the continuous review inventory model with shortages include the case where the quantity received is uncertain, in which the lead time, lost sales rate and order processing cost are decision variables. Here, we consider the lead time crashing cost is an exponential function of lead time, and the order processing cost and lost sales rate are logarithmic functions of capital investment. The objective of this study is to minimize the total relevant cost by simultaneously optimizing the order quantity, lost sales rate and order processing cost. In addition, an efficient algorithm is developed to determine the optimal policy, and our approach is illustrated through a numerical example. From the results of numerical example, it can be shown that, the significant savings can be achieved through the reductions of order processing cost and lost sales rate.