Graduate Thesis Or Dissertation
 

Determination of minimum operating cost for a multiple-item constrained inventory

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  • The objective of this study is to develop an ordering policy which will minimize the total cost associated with maintaining an inventory under active constraints. Previous work in this area has concentrated on the application of either the Lagrangian multiplier technique or the exchange curve which allows non-linear trades-offs between cost elements. However, if the constraint depends on the total inventory level such as warehouse space limitation or maximum investment in inventory, we can obtain the optimum level for operating the system at its minimum cost. The methodology presented herein is based on the composite probability density function representing the total inventory level. This function results from the additive combination of demand rates for individual items in the inventory. Demand is assumed to be compound Poisson for each item and thus the total inventory level may be adequately represented by the normal distribution as the number of items increases in the system. The optimum ordering policy and the distribution of the total inventory level for the system are obtained using simulation after considering Schaack and Silver's algorithm. In determining the optimum constraint level, the unit system cost, the penalty cost, and demand process are found to be important factors. The ratio of the unit system cost to the penalty cost determines the optimum constraint level for the given distribution of total inventory level. The distribution is also affected by the demand process. That is, the higher the demand the more variation which results. Thus increased savings result while stocking high-demand items. Development and implementation of this methodology is illustrated through the use of several example problems.
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