Scheduling cleaning activities on trains by minimizing idle times

We consider a workforce scheduling problem which consists of determining optimal working shifts for cleaning personnel at a rail station. Trains arrive and depart according to a specified schedule and require a given amount of cleaning time from the personnel before their departure from the station. Working shifts must specify a sequence of trains to be cleaned by a worker together with corresponding cleaning times and are subject to contract regulations which impose both a minimum and a maximum duration of the shift. We model the problem as a mixed-integer program with a pseudo-polynomial number of variables and propose an exponentially sized reformulation obtained through Dantzig–Wolfe reformulation. The reformulation is strengthened by valid inequalities and used to compute lower bounds on the optimal cost. A heuristic algorithm based on column generation and variable fixing is then proposed and computationally evaluated on both a set of instances derived from real data and a larger set of randomly generated ones. The reported computational results show that the algorithm provides solutions very close to the optimal ones within 1 h of computing time.