Lot sizing

We have a huge civic project, includes several sub-projects, which are divided into activities. This project is a project to rehabilitate 550,000 hectares of agricultural land in the provinces of Khuzestan and Ilam. The project has been divided according to the plots of land. The Jehad in Tehran is managing the projects. They need project scheduling as well as resource levelling and "lot-sizing". Levelling and lot sizing are the most important issues in utilizing the limited resources. For determining the scope and the size of those sub-projects as well as their parallel activities, so far, many models have been proposed. However, the models are weak either in higher resource utilization or in solving numerically the problems. In this paper, our effort has been concentrated on developing scheduling, resource levelling, and lot sizing model, based on balancing utilization of resources, so that the real size civil project could be solved within an acceptable duration time. This paper proposes a goal programming linear model for simultaneous project scheduling and resource levelling. This model determines the best schedule of sub-activities (optimal "lot size" of each sub-activity) to reach the minimum amount of diversion of resources consumed from the number of resources available for the entire periods of the planning horizon. In fact, if the best "lot sizes" have been taken, then minimum fluctuation of the active resources is reached. The proposed model has been used to schedule a project with 87 activities. This project has been scheduled and, accordingly, the optimal volume (the "lot size") of sub-activities have been determined for each activity at any period of time. In this way, only 4 resources out of a total of 32 resources are in shortage. In contrast, the scheduling of this project, using the CPM, results in a shortage of 13 resources.