Cost/Value Allocations in Supply Chain Operations

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Cooperation among manufacturers has the potential to create a robust network of financially successful manufacturing firms that is essential for the resurgence of manufacturing in the US. These firms stay nimble by maintaining independent ownerships and keeping their sizes small. But they can also benefit from economy of scale enjoyed by large enterprises by joining forces with other members of their supply chain. Quantity discount in procurement, risk pooling in inventory control, and cost efficiency in environment regulation compliance are just a few examples of advantages that can be achieved by cooperation. Because firms are motivated to pursue their own interests, value sharing and/or cost allocation schemes are of vital importance for the formation of stable cooperative relationships. Cooperative game theory lays out a general framework for identifying and analyzing these schemes. Nevertheless, combining the general theory with supply chain specifics to develop implementable solutions and algorithms is a major challenge, which will be tackled in this project. This research will provide analytical tools to determine whether a mutually profitable cooperation is possible for a given set of manufacturers, and if so, identify allocation schemes to sustain the relationship. This research will analyze cooperative games in supply chain systems, such as the Newsvendor model and the Economic Lot Sizing model. The analysis will be also extended to more general versions of these systems that feature multi-period decision-making, price-demand relationships, concave inventory costs, and finite demand windows. The aim is to develop general conditions under which non-empty cores exist and identifying possible monotone allocation schemes. The underlying optimization problems that characterize individual participants' behavior and determine the outcome of the games, are difficult and will be addressed by new optimization techniques developed during this research. Moreover, the project will consider not only the effect of allocation schemes on incentive to cooperate, which is a verifiable action, but also participants' effort levels, which are not directly observable. Therefore, in addition to willingness to participate, the design of the value sharing/cost allocation scheme also needs to take into account incentive to contribute, and the development of such schemes in this project will add a new dimension to the existing models in the supply chain literature.