Project scheduling with inventory constraints

Inventory constraints refer to so-called cumulative resources, which can store a single or several different products and have a prescribed minimum and maximum inventory, where the inventory is depleted and replenished over time. Some additional applications of cumulative resources, e.g. investment projects, are also discussed in this paper. We study some properties of the feasible region of the project scheduling problem with inventory constraints and general temporal constraints and especially show how to resolve so-called resource conflicts. The feasible region represents the intersection of a union of polyhedral cones with the polyhedron of time-feasible solutions. These results can be exploited for constructing an efficient branch-and-bound algorithm which enumerates alternatives to avoid stock shortage and surplus by introducing precedence constraints between disjoint sets of events. Finally, we sketch how the procedure can be truncated to a filtered beam search heuristic. An experimental performance analysis shows that problem instances with 100 events and five cumulative resources can be solved in less than one minute.