A survey of project scheduling problems since 1973 limited to work
done specifically in the project scheduling area (although several
techniques developed for assembly line balancing and job‐shop scheduling
can be applicable to project scheduling): the survey includes the work
done on fundamental problems such as the resource‐constrained project
scheduling problem (RCPSP); time/cost trade‐off problem (TCTP); and
payment scheduling problem (PSP). Also discusses some recent research
that integrates RCPSP with either TCTP or PSP, and PSP with TCTP. In
spite of their practical relevance, very little work has been done on
these combined problems to date. The future of the project scheduling
literature appears to be developing in the direction of combining the
fundamental problems and developing efficient exact and heuristic
methods for the resulting problems.
Management of projects is complicated by the scarcity of resources required to execute them. Limited resources usually extend the project completion times beyond those determined by CPM/PERT. Several solution procedures have been developed for solving the resource constrained project scheduling problem. One objective commonly used for these problems is to complete the project as early as possible (minimize makespan). The problem considered in this paper is a resource constrained project scheduling problem, with the added features that there are cash flows associated with the project activities, and the objective is to schedule the project activities in such a way that the net present value of cash flows is maximized. With these features the problem becomes financially motivated and more realistic. We introduce a branch and bound procedure to solve the resource constrained project scheduling problem with discounted cash flows. Our procedure exploits the known fact that potential resource violations can be eliminated by introducing additional precedence relations between certain project activities. Specifically, we use the "minimal delaying alternatives" concept to resolve resource conflicts. The bounds in the branch and bound procedure are computed by solving Payment Scheduling Problems, which can be formulated as linear programs and by that are well-solvable. We test our procedure computationally on a set of 90 test problems from the literature and compare it with the only other exact procedure we know of.project scheduling, resource constraints, net present value
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