Integrated Project Scheduling and Material Planning with Variable Activity Duration and Rewards

Integrating project scheduling and material ordering adds more realism to project scheduling and considers additional tradeoffs that could lead to reductions in the overall project costs. In this paper we review the evolution of the integrated problem, and investigate the impact of treating the activity duration as a decision variable on the activities schedule and materials plan. The effects of introducing rewards (penalties) for early (late) completion as well as materials quantity discounts on the project schedule and cost are also considered. These additions provide scheduling flexibility that might lead to further reduction in the projectʹs total cost or makespan. Considering the various project costs, we found that there exists an optimal schedule that either start as early as possible (at time zero) or completes as late as possible. We also show that if the project starts at time zero, then its duration cannot be longer than that for the case where the schedule ends as late as possible. It is also shown that the material ordering policy does not follow the Wagner and Whitin model when activity duration is variable or in the presence of quantity discounts. These results have led to modeling and solving the problem in a more efficient manner. Extensive computational work shows the validity of the model and the solution approach.