# Simple and optimal rationing policies for an inventory model with several demand classes

By Philip Melchiors
Working Papers
No. 02, June 1999
Abstract:
In this paper we analyze an $(s,Q)$ inventory model with unit Poisson demand, several demand classes and lost sales. When dealing with different demand classes, the usual approach is to control the inventory by critical levels at which stock is reserved for demand of high priority. We present two different rationing policies, a simple critical level policy where the critical levels are constant, and an optimal policy where the critical levels are allowed to depend on the time since the actual outstanding order (if any) was issued. As the simple policy is much easier to implement in practice, we investigate the cost difference of using the simple policy instead of the optimal policy in a numerical study. We also compare the two rationing policies with the best non-rationing policy.
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