Mode generation rules to define activity flexibility for the integrated project staffing problem with discrete time/resource trade-offs

In this paper, we study the project staffing problem with discrete time/resource trade-offs to minimise the personnel staffing budget. This staffing problem embeds activity scheduling flexibility by incorporating the project scheduling problem into the personnel staffing problem to improve the quality of the staffing plan. In addition, we introduce extra demand scheduling flexibility resulting from the design of alternative execution modes for the activities, modelled via discrete time/resource trade-offs. In this way, the project manager is able to decide on the team size and duration for every activity. We propose a two-stage methodology to first design specific alternative activity modes using heuristic rules-of-thumb and subsequently we assess the resulting quality, i.e. the staffing cost, via the integrated composition of the project schedule and associated staffing plan. The heuristic mode generation rules determine the selection of a limited set of relevant activities and modes. The computational results show that the impact of these heuristic generation rules on the staffing budget is dependent on the defined relation between different activity alternatives for a particular activity and on the estimated characteristics of the activity base modes. We show that by focusing on a particular well-chosen subset of activity alternatives or on a particular subset of activities, high-quality solutions realising most of the potential cost improvements resulting from the discrete time/resource trade-offs can be derived with a reduced effort.