Branch and Price for Preemptive and Non Preemptive RCPSP Based on Interval Orders on Precedence Graphs

International audienceThis paper first describes an efficient exact algorithm to solve Preemptive RCPSP and next discusses its extension to Non Preemptive RCPSP. In case of Preemptive RCPSP, we propose a very original and efficient branch and bound/price procedure based upon minimal interval order enumeration, 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. The two last sections are devoted to the description of some heuristics, which also involve the interval order framework and the basic antichain linear program and which aim at handling larger scale RCPSP preemptive instances, and to a discussion of the way our algorithm may be extended to Non Preemptive RCPSP