Three Game Theoretic Models in Operations Management.

摘要

This thesis investigates three problems in operations management, by using different concepts and techniques in Game Theory. The first problem is a two-echelon supply chain problem involving wholesaling, transporting and retailing of certain kind of perishable product. A key characteristic of the problem is that the upstream supplier adopts a. Group Buying Scheme (GBS) as his pricing mechanism and the downstream retailers, taking into consideration of the supplier's pricing mechanism, their respective market demands and other retailers' likely reactions, compete with each other to maximize their profit respectively. We model this problem as a. Stackberg game where supplier is the leader and retailers are the followers. Furthermore, the retailers' optimal ordering problem is solved by applying the solution concepts in Competition Game Theory and we prove that the Nash equilibrium always exists. Moreover, the equilibrium is the only Pareto optimal Nash equilibrium and a strong equilibrium as well. Finally we show that the GBS pricing mechanism, as compared with the traditional Flat Price scheme, can bring the supplier and retailers to a win-win situation.;The second is a project management problem with task subcontracting. The project owner (P0) outsources the tasks in his project to different subcontractors (SCs), with contracts to govern the completions of the tasks and the associated costs and bonus. We model the subcontractors' task processing problem as a Cooperative Game so that subcontractors can benefit by resource sharing and execution time rescheduling. We prove that our cooperative game is balanced and propose a core allocation vector constructed from the optimal dual solution. Meanwhile, the project owner's optimal strategy to design the contracts is also obtained by implicit optimization skills.;The third problem we consider concerns about manufacturing outsourcing, where multiple manufacturers outsource their jobs to a third-party firm. The manufacturers book time windows from the third-party to process their jobs whose processing times are stochastic. Due to the capacity limitation of the third-party and the uncertainty in their processing times, it may be beneficial for the manufacturers to cooperate, provided that a proper cooperative mechanism can be devised. We model this problem as a Cooperative Game. However, it is more than a Sequencing Game commonly studied in the literature, because we consider the optimal booking decisions and the random processing times, which make it possible for the manufacturers to achieve a risk pooling effect by collaborating and booking together. We prove that the outsourcing game is balanced in the situation where the unit booking cost for each time window is unique. We also construct a core allocation based on the core vector derived form a Permutation Game. A main breakthrough is that the connective admissible rearrangement assumption is removed for the stochastic sequencing/booking game, following Slikker's technique.