Abstract
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 mathcal {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 the solutions obtained to both optimal reference values and the results of a commercial local search solver called LocalSolver.
Highlights
Many models and procedures for resource-constrained project scheduling problems (RCPSPs) assume that the capacities of the renewable resources that are required to perform the project’s activities are exogenously given and that the objective is to find a schedule with a minimal project makespan or duration
Describe, and evaluate alternative solution encodings and schedule decoding mechanisms to solve this problem within a genetic algorithm framework and we compare the solutions obtained to both optimal reference values and the results of a commercial local search solver called LocalSolver
The remainder of this paper is organized as follows: in Sect. 2, we describe the assumptions of the resource-constrained project scheduling problem with makespan-specific revenues and option of overcapacity (RCPSP-ROC), give real-world examples, demonstrate basic problem and solution properties, and provide an overview of the related literature
Summary
Many models and procedures for resource-constrained project scheduling problems (RCPSPs) assume that the capacities of the renewable resources that are required to perform the project’s activities are exogenously given and that the objective is to find a (feasible) schedule with a minimal project makespan or duration. The revenue from a project typically decreases as its duration increases This immediately leads to the question how to use overtime and how to schedule such projects with flexible capacity constraints and makespan-dependent revenues in the most profitable way. The capacity Kr of resource r is often assumed to be exogenously given and constant over time, and one seeks a schedule that minimizes the project duration or makespan STJþ1 1⁄4 FTJ þ 1 We extend this well-known problem setting by adding the possibility to use overtime capacity zrt at resource r in period t, up to a limit zr , i.e., zrt zr in all periods, at a cost of jr monetary units per period and capacity unit of overtime.
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