Scheduling Multiple Concurrent Projects Using Shared Resources with Allocation Costs and Technical Constraints

Resource constraint multiple project scheduling problem (RCMPSP), as a generalization of the resource constraint project scheduling problem (RCPSP), involves the scheduling of the activities of multiple separate projects, subject to precedence and shared resource constraints. RCMPSP is a NP-hard optimization problem having many applications in large scale construction, corporate wide logistics and manufacturing project management. The most common efficient heuristics in literature solve the problem using priority rules to allocate the activities and taking into account realistic assumptions to minimize the projects delays and the tardiness penalties. The single pass parallel heuristic approach presented in this paper introduces two cardinal restrictions related to renewable resources, pertain to non-negligible resource transfer overheads among the projects and the feasibility of such movements, due to technical constraints, during time periods. Using realistic assumptions for all the constituent elements of the RCMPSP finds the effect of the above constraints to the total project delay applying two well-known time-based single priority rules, dynamic earliest starting time (EST) and latest starting time (LST). Each independent project is formulated using a vertex and arc weighted directed acyclic graph. Depending on the usage of shareable resources activities belong to two mutually excluded types. The paper ends with a small detailed numerical example.