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A vehicle routing problem with distribution uncertainty in deadlines

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journal contribution
posted on 2020-10-30, 11:14 authored by Dali Zhang, Dong Li, Hailin Sun, Liwen Hou
This article considers a stochastic vehicle routing problem with probability constraints. The probability that customers are served before their (uncertain) deadlines must be higher than a pre-specified target. It is unrealistic to expect that the perfect knowledge on the probability distributions of deadlines is always available. To this end, we propose a distributionally robust optimisation framework to study worst bounds of the problem, which exploits the moment information of the historical observations. This framework includes two steps. We first use Conditional Value-at-Risk (CVaR) as a risk approximation to the probability of missing customer deadlines. The resulting nonlinear model is then transformed into a semi-infinite mixed integer program, using the dual form of the CVaR approximation. A sample approximation approach is then used to address the computational challenges. As the standard CVaR approximation to probability constraints is rather conservative, we suggest a relaxation to the approximation and develop an iterative algorithm to find the right value of the parameter that is introduced to the relaxed CVaR constraints. The extensive numerical experiments show that the routing policies developed by the proposed solution framework are robust and able to achieve the required target, regardless of deadline distributions.

Funding

Shenzhen Fundamental Research Program (JCYJ 20190808164605481)

National Science Foundation of China (No. 71501127, 11871276)

History

School

  • Business and Economics

Department

  • Business

Published in

European Journal of Operational Research

Volume

292

Issue

1

Pages

311 - 326

Publisher

Elsevier BV

Version

  • AM (Accepted Manuscript)

Rights holder

© Elsevier

Publisher statement

This paper was accepted for publication in the journal European Journal of Operational Research and the definitive published version is available https://doi.org/10.1016/j.ejor.2020.10.026

Acceptance date

2020-10-21

Publication date

2020-10-27

Copyright date

2020

ISSN

0377-2217

Language

  • en

Depositor

Dr Dong Li . Deposit date: 28 October 2020

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