A Benders decomposition algorithm for the multi-mode resource-constrained multi-project scheduling problem with uncertainty

In this research, we focus on the multi-mode resource-constrained multi-project scheduling problem from the perspective of consultants who attend design-bid-build contracts and put their efforts to optimize the client and contractors’ profits simultaneously. Each contractor may have a different level of knowledge and experience to perform a project. Therefore, the contractor selection to execute a project may affect the quality and satisfaction level of the project. This study aims to schedule activities of a certain number of projects with multiple execution modes and pre-specified relations. A multi-objective mixed-integer linear programming model is proposed to maximize satisfaction in contractor selection, minimize the total cost of projects and earliness and tardiness penalties, and minimize the total completion time of projects subject to resource constraints. It is assumed that activity durations are uncertain; thereby the globalized robust counterpart of the formulation is presented such that the normal range of the perturbation is the intersection of a box and a polyhedral. The proposed multi-objective model is solved by the multi-choice goal programming approach. This problem is computationally complex and the Benders decomposition (BD) method is utilized to solve it. Numerical experiments on different instances prove the quality of the proposed BD method and illustrate that the proposed model is capable of selecting a proper contractor and multi-project scheduling.