Stochastic models for inventory management at service facilities
University of Toronto, Dec 2012 (based on this paper)
A service facility which provides service to customers using items of inventory is considered. It is assumed that customers arrive according to a Poisson random process and service times are exponential random variables independent of each other and of arrival times. In such a system, queues might form or we may run out of inventory. The questions are when and by how much we must place an inventory refill order so as to minimize the total cost of waiting customers, inventory and ordering cost. A Markov decision processes is exploited to describe the stochastic control problem at service facility. Heuristic algorithms that approximate the optimal solutions are suggested and numerical results are obtained.