Developing project scheduling model with makespan and robustness objectives



The research on project scheduling has widely expanded over the last few decades. The vast majority of these research efforts focus on exact and suboptimal procedures for constructing a workable schedule, assuming complete information and a static deterministic problem environment. Project activities are scheduled subject to both technological precedence constraints and resource constraints, mostly under the objective of minimizing the project duration. The resulting schedule serves as the baseline for the execution of the project. During execution, however, the project is subject to considerable uncertainty, which may lead to numerous schedule disruptions. It is surprising to see that, given the large amount of projects that have finished late during the last decades, management still fails to quote accurate project due dates. This is problematic because virtually all organizations use their project plans not only as tools with which to manage the projects, but also as a foundation to make delivery commitments to clients. Therefore, a vitally important purpose of project plans and effective scheduling methods is to enable organizations to estimate completion dates of the corresponding projects. A project schedule also serves as a baseline for material procurement, contacts with subcontractors, coordination of internal resources and corrective actions the ultimate goal which is more akin to deterministic scheduling, is to make scheduling and resource allocation decisions that will allow quoting a due date that should be as low as possible. Such optimizations decisions need not only be taken before the project is actually started, but also scheduling and resource allocation should also be able during project execution in order protect promised dates from any sources of uncertainty that may occur. Additionally, if advance knowledge about the nature of the uncertainty in the project is available, it is desirable that the project schedule be robust to disruptions that may arise. One of the important approaches in this issue is constructing robust project schedule. Generally, this approach tries to construct robust project baseline schedule by considering uncertainty in such a way that any variations cannot make disruption in it as far as possible. In this article, we introduce the concept of schedule robustness and then we develop a bi-objective resource constrained project scheduling model. We consider the objectives of robustness maximization along with makespan minimization. Then, we present a tabu search algorithm that operates on surrogate functions. This algorithm is developed in order to generate an approximate set of efficient solutions. Many random project scheduling problems are generated, and then solved by the algorithm. Finally, the efficiency of the algorithm and the robustness surrogate functions are evaluated by simulation. Finally, the results show efficiency of the algorithm and developed surrogate function.