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

•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.