A Multi-objective optimization model for project scheduling with time-varying resource requirements and capacities

Proper and realistic scheduling is an important factor of success for every project. In reality, project scheduling often involves several objectives that must be realized simultaneously, and faces numerous uncertainties that may undermine the integrity of the devised schedule. Thus, the manner of dealing with such uncertainties is of particular importance for effective planning. A realistic schedule must also take account of the time-based variations in the capacity of renewable resources and the amount of resources needed to undertake the activities and the overall effect of such variations on the schedule. In this study, we propose a multi-objective project scheduling optimization model with time-varying resource requirements and capacities.This model, with the objectives of minimizing the project makespan, maximizing the schedule robustness, and maximizing the net present value, considers the interests of both project owner and contractor simultaneously. Two multi-objective solution algorithms, NSGA-II and MOPSO, are modified and adjusted with Taguchi method to be used for determination of the set of Pareto optimal solutions for the proposed problem. The proposed solution methods are evaluated by the use of fifteen problems of different sizes derived from Project Scheduling Problem Library (PSPLIB). Finally, solutions of the algorithms are evaluated in terms of five evaluation criteria. The comparisons show that NSGA-II yields better results than MOPSO algorithm. Also, we show that ignoring the time-based variations in consumption and availability of resources may lead to underestimation of project makespan and significant deviation from the optimal activity sequence.