Generation schemes for the resource-constrained project scheduling problem with partially renewable resources and generalized precedence constraints

Abstract

In recent years, new resource types have been established in project scheduling. These include so-called partially renewable resources, whose total capacity applies only to a subset of periods in the planning horizon. In this paper, we consider the extension of the resource-constrained project scheduling problem with those partially renewable resources as well as generalized precedence constraints with the objective of minimizing the project duration (RCPSP/max-π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi $$\\end{document}). For this problem it is known that already the determination of a feasible solution is NP-hard in the strong sense. Hence, we present two different generation schemes that are able to find good feasible solutions in short time for most tested instances. The first one is a construction-based heuristic wherein the activities of the project are scheduled iteratively time- and resource-feasibly. The second one is a relaxation-based generation scheme, in which—starting from the schedule consisting of the earliest start times—resource conflicts are identified and resolved by inserting additional resource constraints.