A branch-price-and-cut algorithm for multi-mode resource leveling

We propose a new mixed integer programming formulation and solution algorithm for a multi-mode resource-constrained project scheduling problem with availability constraints (calendars) and the objective to minimize the resource availability cost. Our model exploits the problem structure and has an exponential number of variables, which necessitates a column generation approach. The linear programming relaxation is strengthened by adding valid inequalities that need to be carefully separated in order to show the desired effect. Integer optimal solutions are obtained by an exact state-of-the-art branch-price-and-cut algorithm.