The Destination-Loader-Door Assignment Problem for Automated Package Sorting Centers

This paper presents a new model and solution procedure for a problem that arises in configuring package sorting centers that perform multiple automated sorts per day. For a given set of loading bays, the first objective is to assign destinations to consecutive doors so that the number of changes of destination-to-door assignments from one sort to the next is minimized. The second and third objectives are to minimize the number of loaders who work the doors and to evenly distribute the volume of packages assigned to each loader. A variety of constraints vastly complicates these assignments and leads to a mixed-integer programming (MIP) model, which we significantly strengthened with structurally derived cuts. A novel feature of the formulation is the use of pattern variables to represent the door assignments. Taking a multiobjective programming approach, solutions are obtained by solving a series of MIPs, each addressing one of the three objectives. The effectiveness of our approach is demonstrated using data provided by a well-known package carrier for 24 work centers in four facilities. An additional contribution is a complexity analysis of the destination-to-door and the loader-to-door assignment subproblems. Both are shown to be strongly NP-hard. We also examine special cases of the loader subproblem and develop polynomial-time algorithms for them.