A column generation-based diving heuristic to solve the multi-project personnel staffing problem with calendar constraints and resource sharing

Project managers are often responsible for the management of multiple projects and associated personnel budgeting decisions. In order to determine the workforce size and mix accurately, we integrate the multi project scheduling problem and personnel staffing problem. We construct a baseline personnel roster that takes the personnel scheduling constraints into account and model the workload stemming from the project activities as an endogenous variable in the model. In order to decrease the overall staffing budget, we consider the sharing of resources, i.e. personnel resources can be transferred between projects. In the problem under study, we consider unproductive resource transfer times and different restrictions related to the sharing of resources imposed on the schedule of individual workers, which is often neglected in the literature. We propose a multi-stage solution procedure that exploits the optimal linear programming solution, obtained via column generation, to find a high-quality integer solution based on a diving heuristic. In order to improve the computational performance, different speed-up mechanisms are included relying on a state space reduction. Detailed computational experiments are presented to evaluate and benchmark different alternative optimisation strategies. Managerial insights are provided which give insight in the benefits of resource sharing. ? 2020 Elsevier Ltd. All rights reserved.