Solution Methods for a Scheduling Problem with Incompatibility and Precedence Constraints

Consider a project which consists in a set of operations to be performed, assuming the processing time of each operation is at most one time period. In this project, precedence and incompatibility constraints between operations have to be satisfied. The goal is to assign a time period to each operation while minimizing the duration of the whole project and while taking into account all the constraints. Based on the mixed graph coloring model and on an efficient and quick tabu search algorithm for the usual graph coloring problem, we propose a tabu search algorithm as well as a variable neighborhood search heuristic for the considered scheduling problem. We formulate an integer linear program (useful for the CPLEX solver) as well as a greedy procedure for comparison considerations. Numerical results are reported on instances with up to 500 operations.ou