Mathematical models for the resource leveling problem


Today, many ventures in industry are carried out as projects. Such projects consist of a large number of individual activities impacted by time dependencies and priority. Within the framework of project planning, it is necessary to create a schedule and assign a start time to each activity. Resources such as employees or machines are usually required to execute an activity. Resources are required to execute projects. Thus, the objective of the resource leveling problem (RLP) is the most equal use of the resources used over the entire planning horizon.

The aim of the thesis is to first give an overview of alternative mathematical models for the RLP proposed in the literature. A selection of the models will then be implemented using an algebraic modeling language (e.g. GAMS) and subjected to performance analysis using test instances. Furthermore, the implemented models are to be extended so that practice-relevant problem aspects, such as sequence-dependent set-up times, shift times, parallel processing of orders or transport processes can be represented.

The thesis is aimed at students of economics and mathematics with an interest in mathematical modeling and optimization. Prerequisites are knowledge of the basics of operations research from the lectures on business research or project and resource management or similar. Programming or modeling experience is desired.


  • Rieck, J., Zimmermann, J., Gather, T. (2012): Mixed-integer linear programming for resource leveling problems, European Journal of Operational Research, 221(1), pp. 27-37.
  • Artigues C., Koné O., Lopez P., Mongeau M. (2015) Mixed-integer linear programming formulations. In: Schwindt C., Zimmermann J. (eds) Handbook on Project Management and Scheduling Vol.1. International Handbooks on Information Systems. Springer

For further information, please contact Max Reinke (