The Total Adjustment Cost Problem with Variable Activity Durations and Intensities

Resource levelling is a crucial problem in project management since excessive peaks of resource usage in a schedule may cause additional costs, e.g., related to the need of relying on external resources. For this reason, this problem has been widely studied in the literature and much attention has been devoted in understanding the effect of using different cost functions. In this paper, we study the resource levelling problem with the so called total adjustment cost objective which has been more considered recently in the literature than others. For this problem, we propose a mixed-integer program in which, besides standard ingredients, variable durations and variable execution intensities of the activities are allowed to further smooth the shape of the resource profile function over time. To the best of our knowledge, there is no similar model for this problem with this objective function since the total adjustment cost problem is typically tacked with in the literature with fixed activity durations and fixed execution intensities. A computational experimentation on known benchmarks has been conducted. Moreover, a comparison with a competing and highly performing model present in the literature for the same problem with fixed durations and fixed execution intensities of the activities is presented, properly adapting our model to work with the same setting.