Title: Robust vehicle routing under uncertainty via branch-price-and-cut

Journal Article · Sun Sep 12 00:00:00 EDT 2021 · Optimization and Engineering

DOI:https://doi.org/10.1007/s11081-021-09680-6· OSTI ID:1906188

Wang, Akang ^[1]; Subramanyam, Anirudh ^[2]; Gounaris, Chrysanthos E. ^[1]

Carnegie Mellon University, Pittsburgh, PA (United States)
Carnegie Mellon University, Pittsburgh, PA (United States); Argonne National Laboratory (ANL), Lemont, IL (United States)

Here, this paper contemplates how branch-price-and-cut solvers can be employed along with the robust optimization paradigm to address parametric uncertainty in the context of vehicle routing problems. In this setting, given postulated uncertainty sets for customer demands and vehicle travel times, one aims to identify a set of cost-effective routes for vehicles to traverse, such that the vehicle capacities and customer time window constraints are respected under any anticipated demand and travel time realization, respectively. To tackle such problems, we propose a novel approach that combines cutting-plane techniques with an advanced branch-price-and-cut algorithm. Specifically, we use deterministic pricing procedures to generate "partially robust" vehicle routes and then utilize robust versions of rounded capacity inequalities and infeasible path elimination constraints to guarantee complete robust feasibility of routing designs against demand and travel time uncertainty. In contrast to recent approaches that modify the pricing algorithm, our approach is both modular and versatile. It permits the use of advanced branch-price-and-cut technologies without significant modification, while it can admit a variety of uncertainty sets that are commonly used in robust optimization but could not be previously employed in a branch-price-and-cut setting.

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: Carnegie Mellon University; USDOE

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1906188

Journal Information:: Optimization and Engineering, Vol. 23, Issue 4; ISSN 1389-4420

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

A scenario decomposition algorithm for strategic time window assignment vehicle routing problems Subramanyam, Anirudh; Wang, Akang; Gounaris, Chrysanthos E. Transportation Research Part B: Methodological, Vol. 117 https://doi.org/10.1016/j.trb.2018.09.008	journal	November 2018
New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem Baldacci, Roberto; Mingozzi, Aristide; Roberti, Roberto Operations Research, Vol. 59, Issue 5 https://doi.org/10.1287/opre.1110.0975	journal	October 2011
Robust Optimization Ben-Tal, Aharon; El Ghaoui, Laurent; Nemirovski, Arkadi Princeton Series in Applied Mathematics https://doi.org/10.1515/9781400831050	book	December 2009
Robust vehicle routing problem with deadlines and travel time/demand uncertainty Lee, C.; Lee, K.; Park, S. Journal of the Operational Research Society, Vol. 63, Issue 9 https://doi.org/10.1057/jors.2011.136	journal	September 2012
Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows Jepsen, Mads; Petersen, Bjørn; Spoorendonk, Simon Operations Research, Vol. 56, Issue 2 https://doi.org/10.1287/opre.1070.0449	journal	April 2008
Solving the Asymmetric Travelling Salesman Problem with time windows by branch-and-cut Ascheuer, Norbert; Fischetti, Matteo; Grötschel, Martin Mathematical Programming, Vol. 90, Issue 3 https://doi.org/10.1007/PL00011432	journal	May 2001
Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints Solomon, Marius M. Operations Research, Vol. 35, Issue 2 https://doi.org/10.1287/opre.35.2.254	journal	April 1987
Dynamic ng-Path Relaxation for the Delivery Man Problem Roberti, Roberto; Mingozzi, Aristide Transportation Science, Vol. 48, Issue 3 https://doi.org/10.1287/trsc.2013.0474	journal	August 2014
A Bucket Graph–Based Labeling Algorithm with Application to Vehicle Routing Sadykov, Ruslan; Uchoa, Eduardo; Pessoa, Artur Transportation Science, Vol. 55, Issue 1 https://doi.org/10.1287/trsc.2020.0985	journal	January 2021
Local search based metaheuristics for the robust vehicle routing problem with discrete scenarios Solano-Charris, Elyn; Prins, Christian; Santos, Andréa Cynthia Applied Soft Computing, Vol. 32 https://doi.org/10.1016/j.asoc.2015.03.058	journal	July 2015
Primal Heuristics for Branch and Price: The Assets of Diving Methods Sadykov, Ruslan; Vanderbeck, François; Pessoa, Artur INFORMS Journal on Computing, Vol. 31, Issue 2 https://doi.org/10.1287/ijoc.2018.0822	journal	April 2019
A branch and bound algorithm for the capacitated vehicle routing problem Laporte, G.; Nobert, Y. Operations-Research-Spektrum, Vol. 5, Issue 2 https://doi.org/10.1007/BF01720015	journal	June 1983
A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty Sungur, Ilgaz; Ordóñez, Fernando; Dessouky, Maged IIE Transactions, Vol. 40, Issue 5 https://doi.org/10.1080/07408170701745378	journal	March 2008
Robust Optimization of a Broad Class of Heterogeneous Vehicle Routing Problems Under Demand Uncertainty Subramanyam, Anirudh; Repoussis, Panagiotis P.; Gounaris, Chrysanthos E. INFORMS Journal on Computing, Vol. 32, Issue 3 https://doi.org/10.1287/ijoc.2019.0923	journal	July 2020
Exact algorithms for the chance-constrained vehicle routing problem Dinh, Thai; Fukasawa, Ricardo; Luedtke, James Mathematical Programming, Vol. 172, Issue 1-2 https://doi.org/10.1007/s10107-017-1151-6	journal	May 2017
A generic exact solver for vehicle routing and related problems Pessoa, Artur; Sadykov, Ruslan; Uchoa, Eduardo Mathematical Programming, Vol. 183, Issue 1-2 https://doi.org/10.1007/s10107-020-01523-z	journal	June 2020
A Robust Approach to the Capacitated Vehicle Routing Problem with Uncertain Costs Eufinger, Lars; Kurtz, Jannis; Buchheim, Christoph INFORMS Journal on Optimization, Vol. 2, Issue 2 https://doi.org/10.1287/ijoo.2019.0021	journal	January 2020
An Adaptive Memory Programming Framework for the Robust Capacitated Vehicle Routing Problem Gounaris, Chrysanthos E.; Repoussis, Panagiotis P.; Tarantilis, Christos D. Transportation Science, Vol. 50, Issue 4 https://doi.org/10.1287/trsc.2014.0559	journal	November 2016
A survey of resource constrained shortest path problems: Exact solution approaches Pugliese, Luigi Di Puglia; Guerriero, Francesca Networks, Vol. 62, Issue 3 https://doi.org/10.1002/net.21511	journal	June 2013
Introduction to Stochastic Programming Birge, John R.; Louveaux, François Springer Series in Operations Research and Financial Engineering https://doi.org/10.1007/978-1-4614-0237-4	book	January 2011
Automation and Combination of Linear-Programming Based Stabilization Techniques in Column Generation Pessoa, A.; Sadykov, R.; Uchoa, E. INFORMS Journal on Computing, Vol. 30, Issue 2 https://doi.org/10.1287/ijoc.2017.0784	journal	May 2018
An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts Baldacci, Roberto; Christofides, Nicos; Mingozzi, Aristide Mathematical Programming, Vol. 115, Issue 2 https://doi.org/10.1007/s10107-007-0178-5	journal	August 2007
The robust vehicle routing problem with time windows Agra, Agostinho; Christiansen, Marielle; Figueiredo, Rosa Computers & Operations Research, Vol. 40, Issue 3 https://doi.org/10.1016/j.cor.2012.10.002	journal	March 2013
Robust Multiperiod Vehicle Routing Under Customer Order Uncertainty Subramanyam, Anirudh; Mufalli, Frank; Laínez-Aguirre, José M. Operations Research, Vol. 69, Issue 1 https://doi.org/10.1287/opre.2020.2009	journal	January 2021
Knapsack polytopes: a survey Hojny, Christopher; Gally, Tristan; Habeck, Oliver Annals of Operations Research, Vol. 292, Issue 1 https://doi.org/10.1007/s10479-019-03380-2	journal	September 2019
The Distributionally Robust Chance-Constrained Vehicle Routing Problem Ghosal, Shubhechyya; Wiesemann, Wolfram Operations Research, Vol. 68, Issue 3 https://doi.org/10.1287/opre.2019.1924	journal	May 2020
Path-Reduced Costs for Eliminating Arcs in Routing and Scheduling Irnich, Stefan; Desaulniers, Guy; Desrosiers, Jacques INFORMS Journal on Computing, Vol. 22, Issue 2 https://doi.org/10.1287/ijoc.1090.0341	journal	May 2010
Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW Dror, Moshe Operations Research, Vol. 42, Issue 5 https://doi.org/10.1287/opre.42.5.977	journal	October 1994
A tutorial on column generation and branch-and-price for vehicle routing problems Feillet, Dominique 4OR, Vol. 8, Issue 4 https://doi.org/10.1007/s10288-010-0130-z	journal	June 2010
Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem Fukasawa, Ricardo; Longo, Humberto; Lysgaard, Jens Mathematical Programming, Vol. 106, Issue 3 https://doi.org/10.1007/s10107-005-0644-x	journal	October 2005
The Robust Vehicle Routing Problem with Time Windows: Compact Formulation and Branch-Price-and-Cut Method Munari, Pedro; Moreno, Alfredo; De La Vega, Jonathan Transportation Science, Vol. 53, Issue 4 https://doi.org/10.1287/trsc.2018.0886	journal	July 2019
Solving two-stage robust optimization problems using a column-and-constraint generation method Zeng, Bo; Zhao, Long Operations Research Letters, Vol. 41, Issue 5 https://doi.org/10.1016/j.orl.2013.05.003	journal	September 2013
The Robust Capacitated Vehicle Routing Problem Under Demand Uncertainty Gounaris, Chrysanthos E.; Wiesemann, Wolfram; Floudas, Christodoulos A. Operations Research, Vol. 61, Issue 3 https://doi.org/10.1287/opre.1120.1136	journal	June 2013
Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints Righini, Giovanni; Salani, Matteo Discrete Optimization, Vol. 3, Issue 3 https://doi.org/10.1016/j.disopt.2006.05.007	journal	September 2006
New Enhancements for the Exact Solution of the Vehicle Routing Problem with Time Windows Pecin, Diego; Contardo, Claudio; Desaulniers, Guy INFORMS Journal on Computing, Vol. 29, Issue 3 https://doi.org/10.1287/ijoc.2016.0744	journal	August 2017
Improved branch-cut-and-price for capacitated vehicle routing Pecin, Diego; Pessoa, Artur; Poggi, Marcus Mathematical Programming Computation, Vol. 9, Issue 1 https://doi.org/10.1007/s12532-016-0108-8	journal	June 2016
A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows Desrochers, Martin; Desrosiers, Jacques; Solomon, Marius Operations Research, Vol. 40, Issue 2 https://doi.org/10.1287/opre.40.2.342	journal	April 1992
Robust Optimization for a Maritime Inventory Routing Problem Agra, Agostinho; Christiansen, Marielle; Hvattum, Lars Magnus Transportation Science, Vol. 52, Issue 3 https://doi.org/10.1287/trsc.2017.0814	journal	June 2018
The robust vehicle routing problem with time windows: Solution by branch and price and cut Lu, Da; Gzara, Fatma European Journal of Operational Research, Vol. 275, Issue 3 https://doi.org/10.1016/j.ejor.2018.12.019	journal	June 2019
The Price of Robustness Bertsimas, Dimitris; Sim, Melvyn Operations Research, Vol. 52, Issue 1 https://doi.org/10.1287/opre.1030.0065	journal	February 2004
Robust constrained shortest path problems under budgeted uncertainty Alves Pessoa, Artur; Di Puglia Pugliese, Luigi; Guerriero, Francesca Networks, Vol. 66, Issue 2 https://doi.org/10.1002/net.21615	journal	May 2015
A new exact algorithm for the multi-depot vehicle routing problem under capacity and route length constraints Contardo, Claudio; Martinelli, Rafael Discrete Optimization, Vol. 12 https://doi.org/10.1016/j.disopt.2014.03.001	journal	May 2014
Selected Topics in Column Generation Lübbecke, Marco E.; Desrosiers, Jacques Operations Research, Vol. 53, Issue 6 https://doi.org/10.1287/opre.1050.0234	journal	December 2005
A short note on the robust combinatorial optimization problems with cardinality constrained uncertainty Lee, Taehan; Kwon, Changhyun 4OR, Vol. 12, Issue 4 https://doi.org/10.1007/s10288-014-0270-7	journal	August 2014
A Branch-Price-and-Cut Algorithm for the Inventory-Routing Problem Desaulniers, Guy; Rakke, Jørgen G.; Coelho, Leandro C. Transportation Science, Vol. 50, Issue 3 https://doi.org/10.1287/trsc.2015.0635	journal	August 2016
Branch-Cut-and-Price for the Robust Capacitated Vehicle Routing Problem with Knapsack Uncertainty Pessoa, Artur Alves; Poss, Michael; Sadykov, Ruslan Operations Research, Vol. 69, Issue 3 https://doi.org/10.1287/opre.2020.2035	journal	May 2021
Exact Branch-Price-and-Cut Algorithms for Vehicle Routing Costa, Luciano; Contardo, Claudio; Desaulniers, Guy Transportation Science, Vol. 53, Issue 4 https://doi.org/10.1287/trsc.2018.0878	journal	July 2019

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42 ENGINEERING
branch-price-and-cut
demand uncertainty
infeasible path elimination constraints
robust optimization
robust rounded capacity inequalities
travel time uncertainty
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Title: Robust vehicle routing under uncertainty via branch-price-and-cut

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