An exact method to solve a Bi-objective Resource Constraint Project Scheduling Problem

Abstract

The Resource Constraint Project Scheduling Problem (RCPSP) is one of the most challenging and interesting problems within the scheduling topic. It brings more and more attention to the researchers since the recent decades. In the RCPSP, we consider a project scheduling problem with a set of jobs submitted to precedence relationships as well as a set of resources with limited capacities. During each period, it is compulsory to guarantee enough resources since one resource could be required by several jobs in process. In this paper, we tackle a bi-objective RCPSP with minimization of the makespan and the total job tardiness. In order to find optimal Pareto fronts, we have introduced two bi-objective mathematical formulations and solved our problem with the two phase method (TPM). Our method is tested with instances randomly generated considering 10, 15, 20 jobs and 4 types of resources. In this paper, we report the experimental results within 1800s and more tests will be launched to explore the limits of the exact method.