Constrained multi-project planning problems: A Lagrangean decomposition approach

This paper describes a Lagrangean decomposition technique for solving multi-project planning problems with resource constraints and alternative modes of performing each activity in the projects. The decomposition can be useful in several ways: from one side, it provides bounds on the optimum, so that the quality of approximate solutions can be evaluated. Furthermore, in the context of branch-and-bound algorithms, it can be used for more effective fathoming of the tree nodes. Finally, in the modelling perspective, the Lagrangean optimal multipliers can provide insights to project managers as prices for assigning the resources to different projects.