Revenue sharing for resource transfer among projects

Abstract We study a problem in which independent project managers cooperate to generate additional revenue by reallocating their resources. This additional revenue equals the increase in the direct return of a project minus the resource transfer cost. For each project, its direct return is closely related to its duration, which is mainly determined by the amount of resources available. In practice, the relationship between direct return and resources can be very complex. We study the situation that all projects use one same type of continuously divisible renewable resource and require some other types of discrete renewable resources. The activity processing rate of a project depends on its continuous resource and can be linear, strictly concave, or convex. The direct return of a project is linear over time. Based on results reported in the literature, we first show that it is not uncommon for the direct return of a project to be concave in relation to the amount of resources. Then, we formulate the resource transfer problem (RTP) as a convex programming problem and derive interesting properties. Furthermore, we design a revenue sharing scheme, which is in the core of a corresponding cooperative game. Finally, we conduct numerical experiments to show the value of cooperation, examine the efficiency of the proposed additional revenue sharing scheme, and evaluate the effects of the transfer cost, the unit time reward/penalty, and the amount of initial resource.