Maximising the weighted number of activity execution modes in project planning

In multimode resource-constrained project scheduling, activity modes are selected and activity start times are determined to minimise the project makespan subject to resource constraints. When disruptions occur during project execution delays to project activities may ensue. Therefore, the a priori selected modes restrict the options to adapt the project schedule given the deadline. During the project scheduling phase, information on the best execution mode to include in the baseline schedule for each activity is usually not available. Scheduling these projects requires decisions on the modes to incorporate in the solution to maximise the flexibility during project execution and to postpone the decision on how to implement the activity until more information is available. In this paper, we study a project scheduling problem with multiple execution alternatives. Our objective is to maximise the weighted number of alternative activity execution modes in the project solution under three different assumptions. The research is motivated by real-life project scheduling applications, where the activities to be planned are known in advance, but the execution of these activities is subject to uncertainty. We present a problem description and three mathematical formulations. Additionally, computational results on the efficiency of the formulations and the increased flexibility are reported.