A new discrete bargaining model on partitions of jobs between two manufacturers

In this dissertation we investigate a new cooperative game model, where two parties comprise an alliance to process a number of jobs offered by a customer and bargain about a reasonable processing profit distribution determined by a two-partition of these jobs.;In this model the non-negative integer-valued parameters of each job, which are the basic assumptions in traditional discrete scheduling models, are still adopted. We also assume each job is non-preemptive. Any party's utility function of the two-partition of these jobs does not possess any elegant continuous or concave property which is critical for the original Nash Bargaining Model (NBM), and furthermore we are only concerned with the integer-valued utility function. Consequently these assumptions result in a new discrete variation of the NBM. In this dissertation we highlight an important special case of our model, where after a two-partition of these jobs is given, each party's utility of processing the jobs assigned to him is related with an optimal schedule of these jobs which minimizes a cost (penalty) function.;This new model is motivated at least by the following real world phenomenon: after two manufacturers have jointly contracted with a customer for processing a number of jobs owing to their insufficient operation facilities, these two par ties need to negotiate a two-partition of these jobs to obtain a profit distribution acceptable for each one. In this dissertation we consider two situations of this model. In the first situation these two parties basically possess the same bargaining power. In the second situation one party possesses the greater bargaining power and can design some bargaining mechanisms more beneficial for himself attributed to his more operation techniques or facilities than the other's.;In order to solve the NBM Nash formulates an optimization problem. The unique solution of this problem is the famous Nash Bargaining Solution (NBS). We revise this optimization problem and supplement some new selection criteria of profit allocation to develop some bargaining mechanisms appropriate for the two situations of our model respectively. Each bargaining mechanism offers the alliance one, two, or several reasonable profit distribution(s) which can be selected by these two parties. Subsequently for any situation we propose some novel dynamic programming algorithms with respect to several specific utility function structures involving job schedules respectively to implement those relevant mechanisms in pseudo-polynomial time.