Integrated resource leveling and material procurement with variable execution intensities

Abstract

This paper addresses the concurrent planning of resource leveling and material ordering, aiming to minimize the completion time of the project and the total cost of project execution. The latter is comprised of material ordering, purchase and holding costs as well as the cost of fluctuations in resource utilization. All activities of the project are performed regarding variable execution intensities, which means that the effort spent to execute an activity is considered to vary over time. A bi-objective mixed-integer linear programming model is proposed to deal with the above-mentioned time-cost trade-off problem. The proposed model determines the start time of activities, the fraction of executing activities in each time period as well as the quantity and timing of orders for materials, while satisfying precedence relationships among activities. The problem belongs to the class of NP-hard problems. Hence, a genetic algorithm as well as two multi-objective meta-heuristic algorithms, namely non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective vibration damping optimization (MOVDO) algorithm, calibrated by Taguchi method, are utilized to solve 30 different sized test problems. Then, four performance metrics are used to assess the performance of both NSGA-II and MOVDO algorithms. Results show that MOVDO outperforms NSGA-II in the small-, medium- and large-sized test problems. Moreover, a sensitivity analysis on different-sized test problems, using MOVDO, shows that when the durations of activities are considered to be flexible, the Pareto front is significantly improved in terms of objective values, and the number of Pareto-optimal solutions (NPS) increases. This helps the project manager(s) make decisions on the schedule and the execution intensity of activities and material procurement in a more flexible manner.