Final Report Summary - COOPSS (Cooperation in Service Systems and Service Supply Chains) In this project, we consider collaboration between multiple companies by sharing their resources to reduce cost due to economies of scale and scope. Before any such collaboration can be established, one basic question that needs to be answered is how the anticipated costs and benefits should be allocated among participating members such that it motivates them to cooperate.The purpose of this research is to answer the cost allocation question by studying the cooperative games of service systems and service supply. We especially aim to develop a mathematical framework and theoretical background that will help to characterize the cores of the associated cooperative games as much as possible. The project has three specific objectives: (i) investigation of the Cores of multi-attribute games and identification of the conditions that help to characterize the Cores of the multi-attribute games; (ii) development of a stochastic framework to study cooperation in stochastic systems and derivation of sufficiency conditions for Core non-emptiness of the cooperative games of stochastic systems (i.e. queueing systems); (iii) investigation of the Cores of the spare parts games The outcomes of this project towards each objective can be summarized as follows:(i) Investigation of the Cores of multi-attribute games: Multi-attribute games results from cooperation of several parties by pooling their resources of several types. The benefit of the cooperation is given by a multi-dimensional function of pooled resources. We study the properties of this function and the cores of the multi-attribute games embedded in this function. We derive the necessary and sufficient conditions on the function for all multi-attribute games embedded in this function to have non-empty cores. Moreover, we derive the necessary and sufficient conditions for all multi-attribute games embedded in this function to be convex. (ii) Development of a stochastic framework to study cooperation in stochastic systems (i.e. queueing systems): We consider a general setting for multi-class queueing systems and derive a set of sufficiency conditions such that if they are satisfied, the cores of the resulting cooperative games are non-empty. The new set of conditions requires an analysis of the queueing systems under perfectly correlated demand arrivals. We apply these conditions to show that the cores of the single class queueing games (lost and delay models) with general arrivals and deterministic service times are non-empty. (iii) Investigation of the Cores of the spare parts games: We study cooperation between a group of companies, who need spare parts to maintain their expensive equipment, by pooling their spare parts inventory. We derive several properties of the performance measures (i.e. expected number of inventory and backorders, and average number of backorders) of the spare parts system that play an important role in subsequent study of the cores of the corresponding games. We study three cooperation scenarios: (i) cooperation by inventory pooling, (ii) cooperation under optimal inventory investment, and (iii) cooperation under service level constraint. For many of these games, we show that the cores are non-empty by identifying a population monotonic allocation scheme (PMAS). For the games with empty cores, we present examples. This research contributes the theory of cooperative games with the results we established in objectives (i) and (ii). These results add on the limited number of theoretical and structural results derived on the operations management games and hopefully help the researchers to study cost allocation problem in advance collaborative service systems. In objective (iii), we illustrate an application of this theory in spare parts systems and show that PAMS’s exist for some common cooperation scenarios and under other scenarios stable cooperation might not be possible. On the practical side, the cooperative scenarios that we studied under objective (iii), help the practitioners to decide how to set up stable collaboration in spare parts setting and share the costs, and help them to understand under which arrangements stable collaboration is not possible from an economic point of view. The theoretical results we established here would help to identify these scenarios for other service systems.
