Downward compatible loading optimization with inter-set cost in automobile outbound logistics

This paper addresses an essential loading optimization problem arising in the outbound logistics of automobiles. The problem is to assign a set of orders of finished cars to a set of heterogeneous auto-carriers and to deliver these finished cars from a depot to multiple destinations. The involved destinations are located within a relatively small distance to the depot. A value corresponding to each order represents its urgency level, and an inter-set cost is defined among destinations to estimate the related transportation cost. The objective of the problem is to maximize the weighted total value of the assigned orders minus the total inter-set cost subject to a full-load constraint and a downward compatible loading structure. An integer programming model and a column generation based algorithm are proposed. The proposed algorithm is implemented based on serial and parallel programming, respectively. Computational results based on randomly generated instances and a case study with real data show that the proposed algorithm can generate near-optimality solutions efficiently, and outperforms solving the integer programming model by an IP solver and a rule-based method applied in practice. (C) 2020 Elsevier B.V. All rights reserved.