Bi-objective resource-constrained project scheduling problem with time-dependent resource costs

This work provides new insights on bi-criteria resource-constrained project scheduling problems. We define a realistic problem where the objectives to combine are the makespan and the total cost for resource usage. Timedependent costs are assumed for the resources, i.e., they depend on when a resource is used. An optimization model is presented and it is followed by the development of an algorithm aiming at finding the set of Pareto solutions. The intractability of the optimization models underlying the problem also justifies the development of a metaheuristic for approximating the same front. We design a bi-objective evolutionary algorithm that includes problem-specific knowledge and is based on the Non-dominated Sorting Genetic Algorithm (NSGA-II). The results of extensive computational experiments performed using instances built from those available in the literature are reported. The results demonstrate the efficiency of the metaheuristic proposed.