A hybrid pricing and cutting approach for the multi-shift full truckload vehicle routing problem

Ning Xue,Ruibin Bai,Rong Qu,Uwe Aickelin

doi:10.1016/j.ejor.2020.10.037

Abstract

Full truckload transportation (FTL) in the form of freight containers represents one of the most important transportation modes in international trade. Due to large volume and scale, in FTL, delivery time is often less critical but cost and service quality are crucial. Therefore, efficiently solving large scale multiple shift FTL problems is becoming more and more important and requires further research. In one of our earlier studies, a set covering model and a three-stage solution method were developed for a multi-shift FTL problem. This paper extends the previous work and presents a significantly more efficient approach by hybridising pricing and cutting strategies with metaheuristics (a variable neighbourhood search and a genetic algorithm). The metaheuristics were adopted to find promising columns (vehicle routes) guided by pricing and cuts are dynamically generated to eliminate infeasible flow assignments caused by incompatible commodities. Computational experiments on real-life and artificial benchmark FTL problems showed superior performance both in terms of computational time and solution quality, when compared with previous MIP based three-stage methods and two existing metaheuristics. The proposed cutting and heuristic pricing approach can efficiently solve large scale real-life FTL problems.

Highlights

In intermodal freight transportation, a large proportion of container transportation is carried out by barges, trains or ocean-going vessels (Braekers et al 2014)
The results indicate that good performance can be achieved compared with a reactive tabu search (RTS) method demonstrated in Ruiyou Zhang (2009)
Since there are many possible commodity assignments for a given route r, we evaluate them all and if the reduced cost of any given w ∈ W is found to be negative for route r, it is added to the Restricted Master Problem (RMP)

Summary

Introduction

A large proportion of container transportation is carried out by barges, trains or ocean-going vessels (Braekers et al 2014). Merits of this solution encoding One of the most helpful benefits of this solution encoding scheme is the transformation of a previous m-TSPTW based non-linear model (e.g. the model proposed by Chen (2016)) into a linear integer model, so it can be solved using various integer programming techniques This was done through hiding nonlinear time related constraints into the generation of the shift-independent feasible truck route set. For some applications (e.g. FTL with a small number of terminals), pre-computing all feasible routes is possible since the time related constraints in this problem are slightly different from those in the traditional pickup and delivery problem with time windows (PDPTW) In this multi-shift FTL problem, each commodity k has an operation time window (σ(k), τ (k)) defining its availability time and the delivery deadline. Let LPR be the relaxed model, and let LPR-(9-12) be the constraints corresponding to the constraints (9-12) of the master problem

Pricing methods We present three different route price estimation methods

Heuristic column generator for large R

Findings

Conclusions