A Local Search Approach to the Resource Constrained Project Scheduling Problem to Minimize Convex Costs

As the resource constrained project scheduling problem (RCPSP) has a wide range of applications, its models, extensions and algorithms have been intensively studied [2]. As for objective functions, makespan minimization has commonly been used, while the importance of non-regular ones such as earliness-tardiness are also recognized. In this paper, we introduce a time-lag cost, which is charged according to the difference of start times of the two activities specified, and consider the RCPSP to minimize convex time-lag costs (RCPSP-CTL). This cost includes the earliness-tardiness cost as a special case. If there is no resource constraint, RCPSP-CTL can be formulated as a convex cost flow problem, and thus can be solved in polynomial time. In this paper, we propose a local search method exploiting this property. In our algorithm, based on the observation that resource constraints can be removed by introducing additional precedence constraints between activities that consume a common scarce resource, we try to find such additional precedence constraints by local search so that the objective value is minimized under resource constraints.