Lot size dependent lead times in a Q,R inventory system

In a continuous-review or re-order level inventory control (Q,R) system, the safety stock is maintained to protect the system from the risk of stockouts during the replenishment lead time. Most inventory models assume that the lead time is ‘fixed’, and calculate the optimal level of safety stock on the basis of this assumption. We question this ’fixed lead time’ assumption. We recognize from the literature that manufacturing lead time is a function of lot size in many manufacturing environments, and explicitly consider the impact of lot size on the lead time and safety stock requirement. In so doing, we attempt to demonstrate that significant savings can occur if firms consider the interrelationships between the lot size and safety stock decisions. This paper begins with a discussion of the relationship between lot size and lead time. We then present an iterative algorithm that determines lot size and safety stock simultaneously, and compare it against a more conventional sequential approach. An example is provided to clarify the iteration proccedure, and a sensitivity analysis is used to test the performance of the proposed algorithm.