Modelling stochastic lead times in a production-inventory system based on the Laplace transform method

Stochastic properties of a multi-period production-inventory system have been studied in several papers by applying the Laplace transform. However, the source of uncertainty has been limited to external demand and the production/replenishment lead time has been assumed to be constant. In this paper, we investigate the situation when the lead time is a random variable. Transform methods are again used to capture the stochastic properties of the system, such as stockout functions. With the objective of maximizing the net present value of the cash flow, we derive conditions for optimal production decisions in this system. The properties of cash outflow due to stockouts will also be discussed.