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

This paper studies the multi-project scheduling problem that involves multiple projects with di erent importance weights, prede ned assigned due dates, activities with uncertain durations, and renewable constrained resources. the resource sharing policy is applied to share 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 con dence. 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 nd an optimal structure that contains all of the projects such that it transfers the resources between the activities based on the resource sharing policy, while the maximum weighted di erences between the projects' nish times and their assigned due dates will be minimum.