Multi Project Scheduling and Material Planning Using Lagrangian Relaxation Algorithm

Resource-constrained project scheduling is one of the well-known problems in project management. There are many cases where the appropriate schedule was determined first and material ordering plan was decided considering the given schedule. This approach ignores the interactions between these decisions. The integration of project scheduling, material procurement, and production planning of non-renewable resources leads to the coordination of project implementation and supplying resources. This coordination reduces total costs, including operating activities, production, ordering, holding, and penalty costs for late project completion. In addition to, there are many organizations that implement the multi project at the same time and decisions are made in a multi project environment. In this paper, a mixed integer programming model is presented for the resource-constrained multi-project scheduling problem and material ordering and production planning. Due to the application of Lagrangian relaxation algorithm in solving complex problems, this algorithm has been used to solve the proposed mathematical model. To evaluate the performance of the proposed model and solution method, a set of sample examples is solved and the numerical results are given. The findings of this paper show the good performance of the model and the solution method and can provide managerial insights for project managers and resource suppliers.