Exploring the Cooperative Game Nature of a Two-agent Scheduling Problem

The multi-party (multi-agent) scheduling problems have received increasing attention for about ten years. Most of the research only focuses on the scheduling aspect while a distinct cooperative game model is originally constructed for a two-party setting in this literature. This game model is established to highlight the reasonable (cooperative) profit sharing, although the current multi-agent scheduling research interest lies in the balancing cost allocation. The two parties, each having his own set of jobs, cooperatively reserve a processing time slot offered from a single (third-party) processing resource and perform their own jobs together on that resource. All the jobs of these two parties have a common processing time. Each of those jobs is uninterruptable and available at the beginning of the time slot. One cooperation profit function is proposed for each party to evaluate various profit sharing schemes. The function consists of three terms and is defined as the first term minus the other two. Term one is the gross profit relying on the number of the party’s jobs, term two is the total completion time of his jobs determined by the (processing) sequence of both parties’ jobs, i.e., global sequence, and term three is his opportunity cost. It means the function still and only depends on the global sequence after each party’s job number is given. Two approaches based on cooperative games are designed to yield the final profit sharing scheme (solution) accepted to each party, the related algorithms are developed, and the analysis of computational complexity is presented. Besides the abovementioned contributions, the literature also mentions a situation accruing non-cooperation, where two successive time slots are independently and serially reserved by two parties.