The total adjustment cost problem: Applications, models, and solution algorithms

Resource leveling problems arise whenever it is expedient to reduce the fluctuations in resource utilization over time, while maintaining a prescribed project completion deadline. Several resource leveling objective functions may be defined, consideration of which results in well-balanced resource profiles. In this paper, we concentrate on a special objective function that determines the costs arising from increasing or decreasing the resource utilizations. The resulting total adjustment cost problem occurs, for example, in the construction industry and can be formulated using mixed-integer linear programming models. Apart from a discrete time-based formulation, two polynomial formulations, namely an event-based model and a start-based model, which exploit structural properties of the problem are presented. In addition, a heuristic solution algorithm is proposed to generate start solutions for the problem. We use CPLEX 12.4 to solve medium-scale instances known from the literature. A computational performance analysis shows that the discrete time-based model and the start-based model are suitable for practical applications.