Mathematical formulations for project scheduling problems with categorical and hierarchical skills

In this paper, we present six extensions to the multi-skilled resource-constrained project scheduling problem (MSRCPSP) by introducing hierarchical levels of skills. These hierarchical skills can impact the MSRCPSP in multiple different ways. This paper studies efficiency differences, cost differences, quality differences and more. For each of these problems we propose and analyse seven continuous and time-indexed (mixed-)integer linear programming formulations. A modular artificial dataset is generated that assembles instances of the presented problems as well as combinations of these problems. In the computational experiments, we solve these instances using the proposed mathematical formulations with the CPLEX solver. Finally, we compare the results of the different formulations for the resource-constrained project scheduling problems with hierarchical levels of skills in order to explain their inherent similarities and differences.

Automated summary

In this paper, six extensions to the multi-skilled resource-constrained project scheduling problem (MSRCPSP) are presented by introducing hierarchical levels of skills. The impacts of these hierarchical skills on the MSRCPSP are studied, including efficiency differences, cost differences, quality differences and more. Seven continuous and time-indexed (mixed-)integer linear programming formulations are proposed and analyzed for each of these problems. Computational experiments are conducted using a modular artificial dataset. The results of the different formulations for the resource-constrained project scheduling problems with hierarchical levels of skills are compared to explain their inherent similarities and differences.