A Redesigned Benders Decomposition Approach for Large-Scale In-Transit Freight Consolidation Operations

The growth in online shopping and third party logistics has caused a revival of interest in finding optimal solutions to the large scale in-transit freight consolidation problem. Given the shipment date, size, origin, destination, and due dates of multiple shipments distributed over space and time, the problem requires determining when to consolidate some of these shipments into one shipment at an intermediate consolidation point so as to minimize shipping costs while satisfying the due date constraints. In this paper, we develop a mixed-integer programming formulation for a multi-period freight consolidation problem that involves multiple products, suppliers, and potential consolidation points. Benders decomposition is then used to replace a large number of integer freight-consolidation variables by a small number of continuous variables that reduces the size of the problem without impacting optimality. Our results show that Benders decomposition provides a significant scale-up in the performance of the solver. We demonstrate our approach using a large-scale case with more than 27.5 million variables and 9.2 million constraints

Freight consolidation with divisible shipments, delivery time windows, and piecewise transportation costs

•We propose an optimization model for a transportation problem with freight consolidation.•The model incorporates piecewise costs, and delivery time windows.•A three-phase exact solution method is proposed to solve real-life size problems.•The computational performance is demonstrated via a real-life based case problem. This paper studies the freight consolidation problem for a third party logistics (3PL) provider that transships products from multiple suppliers to a single business customer over a contracted multi-period horizon. Under a two-echelon setting, shipments from geographically dispersed sources that are en route to the customer are first transported to intermediary facilities for possible consolidation into full-container loads. Each shipment has a preset pickup date at the source and a delivery time window at the destination. Further, each shipment can be partitioned into multiple shipments that can be routed to different intermediary facilities. Shipments reaching the intermediary facilities are consolidated and forwarded to the final destination in the second echelon. A mixed integer programming model is developed for this problem, which employs piecewise cost functions to capture the economies of scales that are common in transportation. To speed up obtaining solutions, an exact solution methodology is proposed. The proposed solution method lends itself to container load relaxation, temporal decomposition, and valid cut generation. The effectiveness of the proposed algorithm is demonstrated via a real-life problem faced by a large 3PL provider. A computation study is carried out to investigate the proposed method's sensitivity to key factors such as the demand structure, delivery time windows, number of gateways and the consolidation cost breakpoints

In-transit freight consolidation of indivisible shipments

This paper studies the multi-period freight consolidation problem for a third-party logistics (3PL) provider that transships multiple products from multiple suppliers to a single end customer. The shipments are first transported to select consolidation terminals where the 3PL provider aims to consolidate the inbound shipments so as to reduce costs. This imposes a complex decision problem to the 3PL provider since consolidation may require that the inbound shipments spend more time at the terminals, whereas all shipments have prespecified pickup dates and delivery deadlines. Moreover, the shipments picked up from the suppliers are indivisible, that is, a shipment cannot be split into multiple lots and assigned to separate routes. This paper presents a mixed-integer linear programming model and proposes a heuristic for solving the resulting problem. The proposed heuristic partitions the multi-period problem into multiple subproblems by splitting the planning horizon into smaller mutually exclusive units which makes the planning problem relatively insensitive to the length of the planning horizon and hence scalable. The effectiveness of the proposed heuristic is demonstrated via a real-life problem: a close-to-optimal solution for a 360-day planning problem that could not be solved using commercial solvers due to its size is obtained within two hours