Stationary Analysis and Optimality Conditions for (o, S) Policies in Multi-Commodity Inventory Control Problems
FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING
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An m-commodity m or 1 inventory control model with periodic review is formulated and studied when a dyadic stationary ordering Sigma, S policy in E sup m is used. It is assumed that 1 the ordering decision at the beginning of each of a sequence of periods of time is affected by a single set up cost, a linear variable ordering cost and holding and shortage costs 2 the demands for the items in each period are identically and independently distributed continuous random variables 3 the delivery of orders is immediate and 4 complete backlogging of unfilled demands is allowed. Next the model is analyzed by minimizing the expression for the stationary total expected cost per period. The set of simultaneous equations used to determine the optimal policy parameters are restated in terms of a real valued function in E sup m. Finally, the optimization analysis is restricted to the special case of a two-commodity inventory control problem where the demands for the items obey the exponential distribution, and the holding and shortage costs are linear.
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