The impact of fixed and variable costs in a multi-skill project scheduling problem: An empirical study

• A cost minimization multi-skill project scheduling problem is addressed.
• Fixed are variable costs are associated with the resources.
• We propose a “natural” non-linear mathematical formulation.
• Formulation is linearized at the expense of an extra set of continuous variables.
• An extensive computational experience is reported.

In this paper, we address a cost-oriented multi-skill project scheduling problem. The project consists on a set of activities such that, for some pairs, a start-to-start time dependency exists. The execution of each activity requires several skills. More than one resource of each skill may be required for processing an activity. A pull of multi-skilled resources is assumed. Costs are associated with resource usage and include fixed and variable costs. The former are incurred simply by using the resources; the latter depend on the final makespan of the project. For this problem, a mathematical programming modeling framework is proposed. The ‘natural’ model contains a non-linear objective function which, nonetheless, can be linearized at the expense of one additional set of continuous variables. The linearized model is enhanced using several sets of additional inequalities. The results of an extensive set of computational tests performed with the final model are reported. One major goal is to evaluate the possibility of using an off-the-shelf solver for tackling the problem. Another relevant goal is to understand the extent to which a cost-oriented objective influences the solutions obtained. Accordingly, we compare the solutions obtained using such objective with the solutions obtained using the traditional makespan minimization objective, often considered in project scheduling problems.