Optimizing railway crew schedules with fairness preferences

Railway crew scheduling deals with generating duties for train drivers to cover all train movements of a given timetable while taking into account a set of work regulations. The objective is to minimize the overall costs associated with a crew schedule, which includes workforce costs and hotel costs. A cost minimal schedule often contains duties that are unpopular to train drivers, and these unpopular duties are often unevenly distributed among crew depots. At the company that motivated our research, for example, train drivers dislike duties that start in the early morning hours. Currently, some crew depots operate large numbers of these unpopular duties, while others do not have any unpopular duties at all. The train drivers perceive this situation as unfair. They prefer schedules with fewer and more evenly distributed unpopular duties across crew depots. In this paper, we define and measure unpopularity and (un)fairness in a railway crew scheduling context. We integrate fairness conditions into a column generation-based solution algorithm and analyze the effect of increased fairness on cost. We also show how increased fairness affects the unpopularity of a schedule. Our method has been applied to test instances at a large European railway freight carrier. Compared to a standard approach that penalizes only the number of unpopular duties in a schedule, we were able to significantly improve schedule fairness with only marginal increases in schedule cost.