Approaches to Solving RCPSP Using Relaxed Problem with Consumable Resources

In the work a resource-constrained project scheduling problem (RCPSP) is considered. This classical NP-hard problem evokes interest from both theoretical and applied points of view. Thus we can divide effective (i.e. polynomial) approximation algorithms in two groups: fast heuristic algorithms for the whole problem and generalizations and algorithms with performance guarantee for particular cases. In first section we consider the statement of the problem and some generalizations. Along with renewable resources we consider consumable resources which can be stored to be used at any moment after the moment of allocation. A polynomial optimal algorithm for solving the problem with consumable resources only was suggested by Gimadi, Sevastianov and Zalyubovsky [2]. So we can consider polynomially solved relaxation of RCPSP. In this relaxation instead of each renewable resource we have consumable resource which is allocated at each moment of time in one and the same amount. Then we can use information about the solution of this relaxation for approximate solving the original problem in polynomial time (for example, the order of starting times can be used as a heuristic for serial scheduling scheme). Furthermore, the optimal value of relaxation gives the lower bound for the optimal value of the original problem.