Meta-Heuristic Procedures for the Multi-Resource Leveling Problem with Activity Splitting

Abstract

The proper utilization of resources is important to achieve project success. In project management, there are two types of resource scheduling problems. The first is resource allocation in which activities are scheduled depending on the availability of limited resources to ensure that resource limitations are not exceeded in any period. The second type is resource leveling which includes moving non-critical activities within their float to improve the resource profile while not extending the project's duration. Based on the review of related literature, resource leveling techniques can be grouped into three categories: heuristics, optimization and meta-heuristics. Most resource leveling techniques assume that activities cannot be split, meaning that once an activity starts, the work continues until the activity is completed. Activity splitting may be needed to improve resource utilization. Even with the few previous methods that incorporated activity splitting, resource leveling was accomplished using optimization techniques, which are not efficient for large size projects. A more computationally efficient approach to solve larger projects is to use meta-heuristic procedures such as Particle Swarm Optimization (PSO) and Simulated Annealing (SA). The proposed resource leveling technique is developed using Particle Swarm Optimization combined with Simulated Annealing, which assumes a time constrained project, with unlimited resources and allows for the splitting of non-critical activities. Since there are no benchmark problems available in the literature, a set of 180 test problems are created and used as a benchmark to test the proposed methods. An optimization model is then used to determine the exact solution for these benchmark problems. Next, six PSO heuristic procedures are developed and assessed using the 180 benchmark problems. The results of these procedures are then analyzed based on the percentage difference in cost and the computational time. From the analysis, it was observed that the heuristics are becoming trapped in local optimum and are unable to find optimal solutions. Hence, the six heuristic procedures are combined with Simulated Annealing, which searches for new solutions without being trapped in local optimum, and are assessed using the benchmark problems. PSO-SA Procedure 3, which is based on Quantum theory, generated the best results with an average of 4.23% cost difference between the generated and the optimal results. Moreover, 147 out of the 180 problems had a percentage cost deviation of less than or equal to 10%. As for the computation time, the heuristic procedures generated solutions with an average reduction of 7 times for the large size problems. Furthermore, the proposed heuristic is assessed for larger problems in which a near optimum solution is reached within 25 minutes, unlike the optimal procedure which takes longer than 24 hours. This research is an important additional step in the ongoing research on resource leveling. The proposed heuristic procedure offers several improvements over the current resource leveling techniques. The proposed procedure allows for activity splitting, which is more realistic and results in better resource profile. The new procedure takes advantage of combining Particle Swarm Optimization with Simulated Annealing to reach the optimum or near optimum solution in a short time period. The proposed procedure allows planners to consider the tradeoff between the cost of activity splitting and the cost of resource fluctuations resulting in minimum overall project cost.