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.

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.

Zusammenfassung
Thisbookresultsfrommyworkasaresearchassistant attheUniversitiesofFreiberg and Duisburg-Essen. Starting this research was very challenging due to the highly mathematically coined literature regarding game theoretical topics. The literature shows that cooperativegame theory is well studied from a theoretical point of view, but that ?elds of application are fairly limited up to now. Hence, the following researchquestion arose: What can be doneto make conceptsfrom cooperativegame theory more applicable to practical problems? The ?eld of supply chain management is predestined for many kinds of co- eration because companies will be more successful if they consider relationships to suppliers, customers, and/or competitors. Therefore, this work focuses on co- erations in supply networks (horizontal and vertical cooperation) concerning joint ordering and/or joint production. Problems of ordering and production for single decision makers are well studied in operations research and are used as a basis to develop cooperative models that display situations of cooperative decision making. Being one of the most essential problems in cooperations, the allocation of joint pro?ts or costs is the fundamental question in cooperativegame theory and will be the basic question answered by this work as well. Inbothplacesofmy doctorialstudies,FreibergandDuisburg,I hadvaluables- port without which this work would not have been possible. First of all, I thank Alf Kimms for providingme the chance to work on this topic, his guidance,challenging discussions, and the possibility to continue my work in Duisburg.

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.