Robust Optimization of Resource-constrained Multi-Project Scheduling Problem with Uncertain Activities Duration

Abstract

Multi-project scheduling problem is one of the most important problems in the project scheduling applications, which has attracted considerable attention in the past decades. Due to the importance of resources in the multi-project scheduling problem, the resource sharing policy is used in this research. In addition, in each project, the activities durations are subject to the considerable uncertainty. Due to the rapid changing of the environment and also the uniqueness of the projects, one cannot estimate the probability distribution for the activity uncertain durations with certainty. In addition, the problem in multi-project scale needs a more conservative approach when facing with uncertainty. Therefore, the robust optimization approach is employed in this paper. So that the maximum total weighted tardiness of the projects should become minimum. The robust resource-constrained multi-project scheduling problem (RRCMPSP) is investigated in this paper as a two-stage model. A scenario relaxation algorithm is applied resulting optimal solutions for the RRCMPSP, which is tested on the examples produced by the RanGen. So, in this paper, an overall optimal structure containing all of the projects for the multi-project problem is obtained in a way that the maximum differences between the finish time of projects and their due date would become minimum.