Mixed-integer linear programming for resource leveling problems

• Published in: European journal of operational research Vol. 221; no. 1; pp. 27 - 37
• Main Authors: Rieck, Julia, Zimmermann, Jürgen, Gather, Thorsten
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.08.2012; Elsevier; Elsevier Sequoia S.A
• Subjects: Applied sciences; Cutting; Cutting planes; Exact sciences and technology; Integer programming; Inventory control, production control. Distribution; Leveling; Linear programming; Lower and upper bounds; Mathematical models; Mathematical problems; Mathematical programming; Minimum and maximum time lags; Operational research; Operational research and scientific management; Operational research. Management science; Optimization; Preprocessing; Project management; Project scheduling; Resource allocation; Resource leveling; Scheduling; Scheduling, sequencing; Studies; Temporal logic; Utilization; Minimum and maximum time lags; Project scheduling; Resource leveling; Cutting planes; Lower and upper bounds; Lower bound; Costs; Project management; Deadline; Mixed integer programming; Scheduling; Temporal constraint; Modeling; Cutting plane method; Linear model; Renewable resources; Time lag; Minimum time; Upper bound; Overload; Mixed model; Delay time; Planning; Resource management
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2012.03.003

► We model two resource leveling problems as mixed-integer linear programs. ► We present lower and upper bounds for resource requirements at particular points in time. ► Effective cutting planes are outlined. ► Instances with up to 50 activities and tight project deadlines are solved to optimality for the first time. We consider project scheduling problems subject to general temporal constraints, where the utilization of a set of renewable resources has to be smoothed over a prescribed planning horizon. In particular, we consider the classical resource leveling problem, where the variation in resource utilization during project execution is to be minimized, and the so-called “overload problem”, where costs are incurred if a given resource-utilization threshold is exceeded. For both problems, we present new mixed-integer linear model formulations and domain-reducing preprocessing techniques. In order to strengthen the models, lower and upper bounds for resource requirements at particular points in time, as well as effective cutting planes, are outlined. We use CPLEX 12.1 to solve medium-scale instances, as well as instances of the well-known test set devised by Kolisch et al. (1999). Instances with up to 50 activities and tight project deadlines are solved to optimality for the first time.