Optimal Scheduling of Vehicle Loading/Unloading Operations in Depots

Abstract

We deal with the problem of optimal scheduling of cargo loading or unloading for a fleet of vehicles in depots. We show that it can lead to fixed interval scheduling where starting and finishing times of jobs are prescribed and the goal is to assign them to a set of machines. However, in real applications the finishing times can be subject to uncertainty where the random delay can be caused by unpredictable complications. In our case this corresponds to problems during cargo loading/unloading or even delay on arrival. We propose a two-stage stochastic programming formulation and its robust coloring reformulation leading to a large mixed-integer programming problem. In the numerical study we solve several instances of the problem.