AN EXACT ALGORITHM FOR THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM-BASED ON A NEW MATHEMATICAL FORMULATION

In this paper we consider the Project Scheduling Problem with resource constraints, where the objective is to minimize the project makespan. We present a new 0-1 linear programming formulation of the problem th at requires an exponential number of variables, corresponding to all f easible subsets of activities that can be simultaneously executed with out violating resource or precedence constraints. Different relaxation s of the above formulation are used to derive new lower bounds, which dominate the value of the longest path on the precedence graph and are tighter than the bound proposed by Stinson et al. (1978). A tree sear ch algorithm, based on the above formulation, that uses new lower boun ds and dominance criteria is also presented. Computational results ind icate that the exact algorithm can solve hard instances that cannot be solved by the best algorithms reported in the literature.