An Exact Method for the Daily Package Shipment Problem with Outsourcing

TL;DR

This paper introduces an exact, efficient method for solving a large-scale daily package shipment problem with outsourcing, significantly reducing costs and computational time in a real-world Chinese logistics context.

Contribution

The paper proposes a novel two-layer localized model and a column generation algorithm to efficiently solve a complex, NP-hard package shipment problem with outsourcing options.

Findings

Cost savings of up to 1 million CNY daily.

Faster solution times than CPLEX for large instances.

Effective handling of large-scale, real-world shipment data.

Abstract

The package shipment problem requires to optimally co-design paths for both packages and a heterogeneous fleet in a transit center network (TCN). Instances arising from the package delivery industry in China usually involve more than ten thousand origin-destination (OD) pairs and have to be solved daily within an hour. Motivated by the fact that there is no interaction among different origin centers due to their competitive relationship, we propose a novel two-layer localized package shipment on a TCN (LPS-TCN) model that exploits outsourcing for cost saving. Consequently, the original problem breaks into a set of much smaller shipment problems, each of which has hundreds of OD pairs and is subsequently modelled as a mixed integer program (MIP). Since the LPS-TCN model is proved to be Strongly NP-hard and contains tens of thousands of feasible paths, an off-the-shelf MIP solver cannot produce a reliable solution in a practically acceptable amount of time. We develop a column generation based algorithm that iteratively adds "profitable" paths and further enhance it by problem-specific cutting planes and variable bound tightening techniques. Computational experiments on realistic instances from a major Chinese package express company demonstrate that the LPS-TCN model can yield solutions that bring daily economic cost reduction up to 1 million CNY for the whole TCN. In addition, our proposed algorithm solves the LPS-TCN model substantially faster than CPLEX, one of the state-of-the-art commercial MIP solvers.