The presented work combines two areas of research: cooperative game theory and lot size optimization. One of the most essential problems in cooperations is to allocate cooperative profits or costs among the partners. The core is a well known method from cooperative game theory that describes efficient and stable profit/cost allocations. A general algorithm based on the idea of constraint generation to compute core elements for cooperative optimization problems is provided. Beside its application for the classical core, an extensive discussion of core variants is presented and how they can be handled with the proposed algorithm. The second part of the thesis contains several cooperative lot sizing problems of different complexity that are analyzed regarding theoretical properties like monotonicity or concavity and solved with the proposed row generation algorithm to compute core elements; i.e. determining stable and fair cost allocations.

Provides a general solution method to compute cost allocations which is applicable to non-concave and non-monotone operations research games, too Includes a broad discussion of the core, its numerous known variants, extensions of the known variants, and new variants Discussion and solution of complex cooperative lot size optimization problems arising in supply networks Includes supplementary material: sn.pub/extras

Autorentext
Julia Drechsel worked as research assistant at the universities of Freiberg and Duisburg-Essen, Germany from 2005-2009. Since 2009 she is Senior Process Specialist for Supply Chain Optimization with Bayer Technology Services.

Inhalt
Selected Topics in Cooperative Game Theory.- Algorithmic Game Theory.- Cooperation in Supply Chains.- An Economic Lot Sizing Game.- A Lot Sizing Game with Uncertain Demand.- A Capacitated Lot Sizing Game with Transshipments, Scarce Capacities, and Player-Dependent Cost Coefficients.- A Multilevel Lot Sizing Game with Restricted Cooperation.- Conclusions and Future Research.