Mathematical Methods of Operations Research vol. 60, no. 3, pp. 497 - 521
This paper addresses an optimal inventory control in a supply chain in which customers arrive at a facility according to a Poisson process and the facility provides service which takes exponential amounts of time, using items supplied by an outside supplier with exponential lead time process. Formulating our model as a Markov decision problem, we identify a replenishment policy which maximizes the facility's profit subject to the costs of service delay, inventory holding, and replenishment setup and analytically examine how the changes in system parameters affect the optimal profit and the optimal replenishment policy. We show that these results can be extended to Erlang lead time process. We present numerical study for the optimal performance evaluation and comparison of the optimal replenishment policy with (Q, r) policy.