Branch and price for Preemptive Resource Constrained Project Scheduling Problem based on interval orders in precedence graphs

This paper describes an efficient exact algorithm to solve Preemptive Resource Constrained Project Scheduling Problem (Preemptive RCPSP). We propose a very original and efficient branch and bound procedure based upon minimal interval order enumeration, which involves column generation as well as constraint propagation and which is implemented with the help of the generic SCIP software. We perform tests on the famous PSPLIB instances which provide very satisfactory results. To the best of our knowledge it is the first algorithm able to solve at optimality all the set of j30 instances of PSPLIB in a preemptive way. Moreover, this algorithm allows us to update several best known lower bounds for the j60, j90 and j120 instances of PSPLIB.