Workload-Balancing Constraints in a Continuous-Time Integer Programming Formulation for the Resource-Constrained Project Scheduling Problem

In project management, the resource allocation problem consists of determining a schedule for the set of project activities that are related to each other by prescribed precedence relations and that require some time and some scarce resources to complete. In general, the goal is to minimize the project duration or time-to-market. In many cases, each resource represents a team of people with specific skills, such as engineering or marketing specialists. To promote team productivity and cohesion, it is often desirable to balance the workload within the team, i.e. among the resource units. We analyze two alternative approaches to formulate appropriate workload-balancing constraints in a mixed-binary linear optimization problem. In the first approach, the maximum deviation of each unit’s workload from the average workload is bounded, and in the second approach, the maximum workload difference between any pair of units is bounded. Our computational results for a standard test set from the literature show that balanced workloads can generally be achieved without increasing project duration; moreover, the second approach provides more flexibility, resulting in fewer instances for which no feasible solution exists.