Sufficient working subsets for the tour scheduling problem

Mathematical programs to schedule service employees at minimum cost represent each feasible schedule, or tour, with an integer variable. In some service organizations, policies governing employee scheduling practices may permit millions of different tours. A common heuristic strategy is to reformulate the problem from a small working subset of the feasible tours. Solution quality depends on the number and types of schedules included in the model. This paper describes a working subset heuristic based on column generation. The method is general and can accommodate a mix of full- and part-time employees. Experiments revealed its formulations had objective values indistinguishable from those of models using all feasible tours, and significantly lower than those generated by alternative working subset procedures.