Dominant Strategies Implementation of the Critical Path Allocation in the Project Planning Problem

In this paper we propose to analyze the economic problem of allocating tasks on time in order to finish a complex project when information about tasks' duration and predating sequences of tasks is privately owned by the agents that undertake each task. In order to achieve the efficient allocation of tasks -using the well-known Critical path method in the Operations Research literature-, the planner must design the appropriate incentives and compensations to the agents based on the reported information. We show the existence of mechanisms that implement in dominant strategies the efficient allocation of tasks on time. When we further add new desirable properties like individual rationality, an impossibility result emerges.