Two-stage robust project scheduling with material requirement planning

The primary objective of project scheduling is to provide a guideline for the successful completion of a project. Material requirement planning is also a crucial aspect because the cost of materials constitutes a significant proportion of the total project investment, and project activities cannot proceed without them. This paper aims to integrate these two components using a static two-stage robust optimisation model within a finite planning horizon, which incorporates material consumption uncertainty through a budget uncertainty set. In the first stage of the two-stage robust optimisation model, activity scheduling is determined before observing any uncertainty. In the second stage, the supply and holding decisions of materials are made based on the first-stage decisions and the uncertain parameter values. The model seeks to minimise the difference between the first-stage delay penalties and early completion rewards, as well as the worst-case acquisition and holding costs in the second stage. To obtain robust solutions, we formulate and prove an equivalent mixed-integer linear programming model based on the structure of the uncertainty set and the recourse function of the two-stage robust optimisation model. Finally, we compare the two-stage robust optimisation model with its deterministic and two-stage stochastic counterparts using the average and 90% percentile costs, and discuss the performance of an extended model that captures both the activity duration time and material consumption uncertainties.