Profit-oriented scheduling of resource-constrained projects with flexible capacity constraints

We consider a novel generalization of the resource-constrained project scheduling problem (RCPSP). Unlike many established approaches for the RCPSP that aim to minimize the makespan of the project for given static capacity constraints, we consider the important real-life aspect that capacity constraints can often be systematically modified by temporarily assigning costly additional production resources or using overtime. We furthermore assume that the revenue of the project decreases as its makespan increases and try to find a schedule with a profit-maximizing makespan. Like the RCPSP, the problem is $NP$-hard, but unlike the RCPSP it turns out that an optimal schedule does not have to be among the set of so-called active schedules. Scheduling such a project is a formidable task, both from a practical and a theoretical perspective. We develop, describe, and evaluate alternative solution encodings and schedule decoding mechanisms to solve this problem within a genetic algorithm framework and we compare them to both optimal reference values and the results of a commercial local search solver called LocalSolver.