A p-Step Formulation for the Capacitated Vehicle Routing Problem

Published Online:https://doi.org/10.1287/trsc.2024.0936

References

  • Alyasiry AM, Forbes M, Bulmer M (2019) An exact algorithm for the pickup and delivery problem with time windows and last-in-first-out loading. Transportation Sci. 53(6):1695–1705.LinkGoogle Scholar
  • Augerat P (1995) Approche polyèdrale du problème de tournées de véhicules. PhD thesis, Institut Nationale Polytechnique de Grenoble, Grenoble, France.Google Scholar
  • Baldacci R, Hadjiconstantinou E, Mingozzi A (2004) An exact algorithm for the capacitated vehicle routing problem based on a two-commodity network flow formulation. Oper. Res. 52(5):723–738.LinkGoogle Scholar
  • Baldacci R, Mingozzi A, Roberti R (2011) New route relaxation and pricing strategies for the vehicle routing problem. Oper. Res. 59(5):1269–1283.LinkGoogle Scholar
  • Christofides N, Eilon S (1969) An algorithm for the vehicle dispatching problem. J. Oper. Res. Soc. 20(3):309–318.CrossrefGoogle Scholar
  • Costa L, Contardo C, Desaulniers G (2019) Exact branch-price-and-cut algorithms for vehicle routing. Transportation Sci. 53(4):946–985.LinkGoogle Scholar
  • Desaulniers G, Desrosiers J, Solomon MM (2006) Column Generation, vol. 5 (Springer Science & Business Media, Boston).Google Scholar
  • Desrochers M, Laporte G (1991) Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints. Oper. Res. Lett. 10(1):27–36.CrossrefGoogle Scholar
  • Dollevoet TAB, Munari P, Spliet R (2020) A p-step formulation for the capacitated vehicle routing problem. Accessed November 17, 2025, https://repub.eur.nl/pub/123411/EI-2020-01.pdf.Google Scholar
  • Feillet D, Dejax P, Gendreau M, Gueguen C (2004) An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems. Networks 40(3):216–229.CrossrefGoogle Scholar
  • Gavish B (1984) The delivery problem: New cutting plane procedures. Proc. TIMS XXVI Conf. (Copenhagen, Denmark).Google Scholar
  • Godinho M, Gouveia L, Magnanti T (2008) Combined route capacity and route length models for unit demand vehicle routing problems. Discrete Optim. 5(2):350–372.CrossrefGoogle Scholar
  • Jepsen M, Petersen B (2009) Partial path column generation for the vehicle routing problem Internat. Network Optim. Conf. (INOC) (Pisa, Italy), 1–6.Google Scholar
  • Karp R (1972) Reducibility among combinatorial problems. Miller R, Thatcher J, eds. Complexity of Computer Computations (Springer, Boston), 85–103.CrossrefGoogle Scholar
  • Laporte G, Nobert Y (1987) Exact algorithms for the vehicle routing problem. North-Holland Math. Stud. 132:147–184. CrossrefGoogle Scholar
  • Leggieri V, Haouari M (2017) Lifted polynomial size formulations for the homogenous and heterogeneous vehicle routing problems. Eur. J. Oper. Res. 263(3):755–767.CrossrefGoogle Scholar
  • Letchford A, Salazar-González J (2015) Stronger multi-commodity flow formulations of the capacitated vehicle routing problem. Eur. J. Oper. Res. 244(3):730–738.CrossrefGoogle Scholar
  • Lysgaard J, Letchford A, Eglese R (2004) A new branch-and-cut algorithm for the capacitated vehicle routing problem. Math. Programming 100(2):423–445.CrossrefGoogle Scholar
  • Martinelli R, Pecin D, Poggi M (2014) Efficient elementary and restricted non-elementary route pricing. Eur. J. Oper. Res. 239(1):102–111.CrossrefGoogle Scholar
  • Pecin D, Pessoa A, Poggi M, Uchoa E (2017) Improved branch-cut-and-price for capacitated vehicle routing. Math. Programming Comput. 9(1):61–101.CrossrefGoogle Scholar
  • Righini G, Salani M (2006) Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints. Discrete Optim. 3(3):255–273.CrossrefGoogle Scholar
  • Righini G, Salani M (2008) New dynamic programming algorithms for the resource constrained elementary shortest path problem. Networks 51(3):155–170.CrossrefGoogle Scholar
  • Rist Y, Forbes M (2021) A new formulation for the dial-a-ride problem. Transportation Sci. 55(5):1113–1135.LinkGoogle Scholar
  • Rist Y, Forbes M (2022) A column generation and combinatorial benders decomposition algorithm for the selective dial-a-ride-problem. Comput. Oper. Res. 140:105649.CrossrefGoogle Scholar
  • Spliet R (2023) The complexity of the pricing problem of the set partitioning formulation of vehicle routing problems. Oper. Res. 71(5):1454–1457.LinkGoogle Scholar
  • Toth P, Vigo D (2014) Vehicle Routing, Problems, Methods, and Applications, 2nd ed. (Society for Industrial and Applied Mathematics, Philadelphia).Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.