A Branch-and-Cut-and-Price Algorithm for the Electric Vehicle Routing Problem with Multiple Technologies

AbstractWe provide an exact optimization algorithm for the electric vehicle routing problem with multiple recharge technologies. Our branch-and-cut-and-price algorithm relies upon a path-based formulation, where each column in the master problem represents a sequence of customer visits between two recharge stations instead of a whole route. This allows for massive decomposition, and parallel implementation of the pricing phase, exploiting the large number of independent pricing sub-problems. The algorithm could solve instances with up to thirty customers, nine recharge stations, five vehicles and three technologies to proven optimality. Near-optimal heuristic solutions were obtained with a general-purpose MIP solver from the columns generated at the root node.

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A branch-and-price algorithm for two-echelon electric vehicle routing problem

Complex & Intelligent Systems ◽

10.1007/s40747-021-00403-z ◽

2021 ◽

Author(s):

Zhiguo Wu ◽

Juliang Zhang

Keyword(s):

Vehicle Routing ◽

Electric Vehicle ◽

Vehicle Routing Problem ◽

Resource Constraints ◽

Master Problem ◽

Model Parameters ◽

Branch And Price ◽

Routing Problem ◽

Elementary Shortest Path ◽

Price Algorithm

AbstractMotivated by express and e-commerce companies’ distribution practices, we study a two-echelon electric vehicle routing problem. In this problem, fuel-powered vehicles are used to transport goods from a depot to intermediate facilities (satellites) in the first echelon, whereas electric vehicles, which have limited driving ranges and need to be recharged at recharging stations, are used to transfer goods from the satellites to customers in the second echelon. We model the problem as an arc flow model and decompose the model into a master problem and pricing subproblem. We propose a branch-and-price algorithm to solve it. We use column generation to solve the restricted master problem to provide lower bounds. By enumerating all the subsets of the satellites, we generate feasible columns by solving the elementary shortest path problem with resource constraints in the first echelon. Then, we design a bidirectional labeling algorithm to generate feasible routes in the second echelon. Comparing the performance of our proposed algorithm with that of CPLEX in solving a set of small-sized instances, we demonstrate the former’s effectiveness. We further assess our algorithm in solving two sets of larger scale instances. We also examine the impacts of some model parameters on the solution.

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Cover Inequalities for a Vehicle Routing Problem with Time Windows and Shifts

Transportation Science ◽

10.1287/trsc.2018.0885 ◽

2019 ◽

Vol 53 (5) ◽

pp. 1354-1371 ◽

Cited By ~ 1

Author(s):

Said Dabia ◽

Stefan Ropke ◽

Tom van Woensel

Keyword(s):

Vehicle Routing ◽

Vehicle Routing Problem ◽

Valid Inequalities ◽

Time Windows ◽

Branch And Cut ◽

Master Problem ◽

Loading Capacity ◽

Routing Problem ◽

Cover Inequalities ◽

And Shifts

This paper introduces the vehicle routing problem with time windows and shifts (VRPTWS). At the depot, several shifts with nonoverlapping operating periods are available to load the planned trucks. Each shift has a limited loading capacity. We solve the VRPTWS exactly by a branch-and-cut-and-price algorithm. The master problem is a set partitioning with an additional constraint for every shift. Each constraint requires the total quantity loaded in a shift to be less than its loading capacity. For every shift, a pricing subproblem is solved by a label-setting algorithm. Shift capacity constraints define knapsack inequalities; hence we use valid inequalities inspired from knapsack inequalities to strengthen the linear programming relaxation of the master problem when solved by column generation. In particular, we use a family of tailored robust cover inequalities and a family of new nonrobust cover inequalities. Numerical results show that nonrobust cover inequalities significantly improve the algorithm.

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