Dynamic order replenishment policy in Internet-based supply chains

We consider a problem of dynamic replenishment of parts in the supply chain consisting of single class of customers, company, and supplier. Customers request a service via the WEB-based ordering system and the company supports service using parts which are procured from the supplier. The replenishment process of parts possesses an Erlang distribution. With Poisson customer arrival process and exponential service times, the model is formulated as a Markov decision problem. The goal of this paper is to identify an order replenishment policy which minimizes the customer waiting, inventory holding, and order replenishment costs under both the discounted cost and average cost criteria. The main result is that the optimal ordering policy has a monotonic threshold structure. Computational results demonstrate that the replenishment model with Erlang lead times is more stable than that of exponential lead times in terms of the cost, and dynamic policies with a variable reorder point are more cost-effective than (Q, r) policy under the Erlang lead time model.