MINIMAX INVENTORY AND QUEUEING MODELS.
STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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The paper studies inventory and queueing models. It frequently focuses on a situation in which the relevant distribution functions are unknown. Instead, known are the classes from which these distribution functions can be chosen by nature. If one knows the relevant distribution functions one can seek decision policies that minimize the expected cost. Otherwise one seeks decision policies that minimize the maximum expected cost to be incurred, this maximum being taken over all possible distribution functions. This second criterion is referred to as the minimax criterion. In Chapter II the report proves minimax analogs to Scarfs and Veinotts well-known results on the optimality of s,S ordering policies for inventory models. In addition slightly weakened are the ordering they impose on the fixed charges. In Section 4 of Chapter II the report assumes that the sequences of demands for an inventory model are chosen by nature from a compact set so that as demands become known, the class of future possible sequences of demands is restricted. The object is to utilize this information in determining an optimal policy. Thus one has a non-Bayesian learning procedure. Author
- Operations Research