A Stochastic Allocation Problem

Haim Mendelson, Joseph S. Pliskin and Uri Yechiali
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Haim Mendelson: Tel Aviv University, Tel Aviv, Israel
Joseph S. Pliskin: Tel Aviv University, Tel Aviv, Israel
Uri Yechiali: Tel Aviv University, Tel Aviv, Israel

Operations Research, 1980, vol. 28, issue 3-part-ii, 687-693

Abstract: A given quantity of a resource is to be allocated to several activities. The amount of the resource allocated to each activity is used to supply stochastic demands occurring randomly. The system operates as long as all the demands can be met. Whenever the demand of any one activity exceeds its allotment the system fails. The problem is to find the allocation which maximizes the expected time until failure. It is shown that when the available quantity of the resource is large, the optimal allocation is proportionate to the expected demand rate of each activity. An application to a multi-installation inventory problem is presented.

Date: 1980
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