Branch-and-Price for Personalized Multiactivity Tour Scheduling

This paper presents a branch-and-price approach to solve personalized tour-scheduling problems in a multiactivity context. Two formulations are considered. In the first, columns correspond to daily shifts that are modeled with context-free grammars, and tours are assembled in the master problem by means of extra constraints. In the second formulation, columns correspond to tours that are built in a two-phase procedure. The first phase involves the composition of daily shifts; the second assembles those shifts to generate tours using a shortest path problem with resource constraints. Both formulations are flexible enough to allow different start times, lengths, and days-off patterns, as well as multiple breaks and continuity and discontinuity in labor requirements. We present computational experiments on problems dealing with up to five work activities and a one-week planning horizon. The results show that the second formulation is stronger in terms of its lower bound and that it is able to find high-quality solutions for all instances with an optimality gap lower than 1%.