Robust optimization for the resource-constrained multi-project scheduling problem with uncertain activity durations

This paper studies the multi-project scheduling problem which involves multiple projects with different importance weight; with predefined assigned due dates; with activities that have uncertain durations; and with renewable resources that are constrained. The resource sharing policy is applied to share the resources among projects. Due to the environmental rapid changes and also the uniqueness of projects, the probability distribution function of uncertain durations cannot be estimated with confidence. Besides, the multi-project scheduling problem with its large scale investment dictates a conservative approach to deal with the existing uncertainty. Therefore, the Robust Resource-Constrained Multi-Project Scheduling Problem (RRCMPSP) is studied in this paper while the maximum total weighted tardiness of the projects should be minimized. A scenario-relaxation algorithm is implemented which results in optimal solutions for the RRCMPSP. The aim is to find an optimal structure containing all the projects in such a way that it transfers the resources between the activities based on the resource sharing policy while the maximum weighted differences between the projects finish times and their assigned due dates will be minimum.