On the Quasi-Concavity of Equipment Sharing Games with Perishable Raw Materials

Abstract

We study the equipment sharing problem where a group of food & beverage companies share the same equipment of a contractor and wish to have their processing tasks coordinated such that the total cost is minimized. The raw materials to be processed are perishable, which incur a decay cost as time goes. One key issue of this equipment sharing problem is how to allocate the total cost among the participants. We apply cooperative game theory to tackle this issue and formulate the problem as an equipment sharing game. First, we study the 1-equipment sharing game in which all participants share one equipment. We show that the 1-equipment sharing game is quasi-concave when the fixed operation cost is larger than a certain value. We then discuss the special case where the processing time for all participants is equal. For this case, we further investigate the properties of the 1-equipment sharing game and the multi-equipment sharing game. We identify the conditions under which the Shapely value and the τ-value can be easily calculated for the 1-equipment and multi-equipment sharing games.

Keywords

Equipment sharing / quasi-concave games / perishable raw materials / decay loss

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