روش ترکیبی متاهیوریستیک برای مسئله تسطیح چند منبع با تقسیم فعالیت

In this paper, we consider the multi-resource leveling problem with the objective of minimizing the total costs resulting from the variation of the resource utilization and the cost of splitting non-critical activities. We propose hybrid meta-heuristic methods which combine particle swarm optimization (PSO) and simulated annealing (SA) search procedures to generate near-optimal project schedules in less computational time than the exact optimization procedure. The PSO algorithms are based on different update mechanisms for the particles' velocities and positions. The cost and computation time performances of the combined PSO/SA search procedures are evaluated using a set of benchmark problems. Based on the results of the computational experiments, we suggest one of the proposed heuristic procedures to be used for solving the multi-resource leveling problem with activity splitting.

Resource leveling is a resource management technique to minimize total deviations of resource requirements over a fixed project duration. Most resource leveling models proposed in the literature assume that activities may not be split, indicating that once an activity starts, it will continue until the work is finished. However, in practice, it may be cost effective to interrupt an activity to release its resources and assign them to other activities (Karaa and Nasr [7]). By allowing activities to be interrupted, the resulting resource leveling optimization model becomes mathematically complex as it introduces more decision variables and constraints (Hariga and El-Sayegh [4]). Furthermore, additional costs should be included in the objective function such as resource and activity dependent costs, which are incurred as a result of splitting activities. A resource-dependent cost involves the costs of acquiring or releasing the resource in a given period. On the other hand, activity-dependent costs are related to the stopping and restarting of the activity. Upon splitting an activity, the learning process of the resources is affected, and it will take some time for the resources to re-achieve the learning level just prior to splitting the activity. For more details about these two types of costs, interested readers can refer to Hariga and El-Sayegh [4]. Although extensive research works have been carried out on resource leveling without splitting, very little research is found on resource leveling with activity splitting. Hariga and El-Sayegh [4] developed a mathematical model having cost based objective function rather than the traditional utilization function for the multi-resource leveling problem with activity splitting. They formulated the problem as a mixed integer linear program model. Although their model is guaranteed to generate optimal project schedules, it requires a lot of computational effort for a large number of non-critical activities. Therefore, the purpose of this paper is to propose a cost and computational time efficient heuristic procedure for the resource leveling problem with activity splitting. The remainder of the paper is organized as follows. In Section 2, we review the literature relevant to the resource leveling problem with activity splitting. In Section 3, we discuss the proposed PSO–SA search procedures. In Section 4, we present the experimental framework and the computation results. Finally, in Section 5 we conclude the paper.

Resource leveling is a technique to smooth the resources' profiles by minimizing the fluctuations in their requirements over the project life. A recent research work proposed an exact method to level the costs of resources' usage while allowing activity splitting. Such optimization based method may not be time-efficient for large sized projects. Therefore, the contribution of this paper to the resource leveling literature is twofold. First, it proposes meta-heuristic methods capable of generating near-optimal and cost-leveled schedules for large sized projects. Second, it opens up new avenues for research on the development of other heuristic procedures for the problem addressed in this paper. We designed six hybrid PSO/SA search procedures; each having different mechanisms to update the particles' velocities and positions. The cost and time performances of the six heuristic procedures were assessed using 180 created benchmark problems. For each heuristic procedure, the minimum and maximum cost deviations from the optimal one are calculated along with the average cost deviation. PSO/SA procedure 3 has achieved the best results with an average cost difference of 4.23%. Furthermore, 81.67% of the tested problems have a percentage difference of less than or equal to 10%. As for the computation time, the heuristic procedures generated solutions in much less time as compared to the exact solution method. The improvement of the computation time of the hybrid PSO/SA is an interesting extension to the work in this paper. Indeed, future research may investigate the design of a new mechanism for particle positions' update to reduce the computational time of the meta-heuristics. Finally, one more topic for future research is to compare the proposed PSO/SA search procedures with other meta-heuristics such as genetic or Tabu search procedures.