Downward compatible loading optimization with inter-set cost in automobile outbound logistics - Chen, Feng; Wang, Yu (European journal of operational research, 2020)
•A loading optimization problem in the outbound logistics of automobiles is studied.•The objective is to balance the service level of 3PL and the transportation cost.•An inter-set cost is defined to estimate the cost among destinations in an area.•A special downward compatible loading structure is considered.•An IP model and a column generation based heuristic algorithm are proposed.•Computational results and a case study show the performance of the algorithm. 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.