skip to main content
research-article

The Heterogeneous Flexible Periodic Vehicle Routing Problem: : Mathematical formulations and solution algorithms

Published: 01 May 2022 Publication History

Abstract

The aim of this paper is to introduce the Flexible Periodic Vehicle Routing Problem with Heterogeneous Fleet, a variant of the Periodic Vehicle Routing Problem. Flexibility is introduced in service schedules and delivered quantities, heterogeneity comes from different vehicles capacities and speeds. Three Mixed-Integer Linear Programming formulations and a matheuristic, based on Kernel Search, are proposed. Computational tests are made to evaluate the performance of the three formulations and to assess the quality of the solutions provided by the matheuristic.

Highlights

The Heterogeneous Flexible Periodic Vehicle Routing Problem (HFPVRP) is introduced.
In the HFPVRP, speeds and capacities of vehicles may differ.
Three different mathematical formulations are proposed to represent the HFPVRP.
A Kernel Search matheuristic, denoted as KSHFP, is developed to solve the HFPVRP.
Computational experiments were carried out to evaluate its performance.
Computational results show the quality of solutions found by the KSHFP.

References

[1]
Abreu R.C., Arroyo J.E.C., An application of ILS heuristic to periodic vehicle routing problem with heterogeneous fleet and fixed costs, in: 2015 Latin American Computing Conference (CLEI), IEEE, 2015, pp. 1–9.
[2]
Angelelli E., Mansini R., Speranza M.G., Kernel search: A general heuristic for the multi-dimensional knapsack problem, Comput. Oper. Res. 37 (11) (2010) 2017–2026.
[3]
Angelelli E., Mansini R., Speranza M.G., Kernel Search: A new heuristic framework for portfolio selection, Comput. Optim. Appl. 51 (1) (2012) 345–361.
[4]
Angelelli E., Speranza M., The application of a vehicle routing model to a waste collection problem: Two case studies, in: Klose A., Speranza M., Van Wassenhove L.N. (Eds.), Quantitative Approaches to Distribution Logistics and Supply Chain Management, in: Lecture Notes in Economics and Mathematical Systems, vol. 519, Springer, Berlin, Heildeberg, 2002, pp. 269–286.
[5]
Archetti C., Bertazzi L., Laporte G., Speranza M.G., A branch-and-cut algorithm for a vendor-managed inventory-routing problem, Transp. Sci. 41 (3) (2007) 382–391.
[6]
Archetti C., Fernández E., Huerta-Muñoz D.L., The flexible periodic vehicle routing problem, Comput. Oper. Res. 85 (2017) 58–70.
[7]
Archetti C., Fernández E., Huerta-Muñoz D.L., A two-phase solution algorithm for the flexible periodic vehicle routing problem, Comput. Oper. Res. 99 (2018) 27–37.
[8]
Archetti C., Guastaroba G., Huerta-Muñoz D.L., Speranza M.G., A Kernel Search for the multivehicle inventory routing problem, Int. Trans. Oper. Res. 1 (1) (2021) 1.
[9]
Archetti C., Savelsbergh M.W., Speranza M.G., To split or not to split: That is the question, Transp. Res. E 44 (1) (2008) 114–123.
[10]
Archetti C., Speranza M., Vehicle routing problems with split deliveries, Int. Trans. Oper. Res. 30 (2012) 3–22.
[11]
Archetti C., Speranza M.G., The inventory routing problem: the value of integration, Int. Trans. Oper. Res. 23 (3) (2016) 393–407.
[12]
Baptista S., Oliveira R.C., Zúquete E., A period vehicle routing case study, European J. Oper. Res. 139 (2) (2002) 220–229.
[13]
Beltrami E.J., Bodin L.D., Networks and vehicle routing for municipal waste collection, Networks 4 (1) (1974) 65–94.
[14]
Campbell A.M., Wilson J.H., Forty years of periodic vehicle routing, Networks 63 (1) (2014) 2–15.
[15]
Carvalho D.M., Nascimento M.C., A kernel search to the multi-plant capacitated lot sizing problem with setup carry-over, Comput. Oper. Res. 100 (2018) 43–53.
[16]
Christofides N., Beasley J.E., The period routing problem, Networks 14 (2) (1984) 237–256.
[17]
Filippi C., Guastaroba G., Speranza M.G., A heuristic framework for the bi-objective enhanced index tracking problem, Omega 65 (2016) 122–137.
[18]
Francis P., Smilowitz K., Modeling techniques for periodic vehicle routing problems, Transp. Res. B 40 (10) (2006) 872–884.
[19]
Francis P., Smilowitz K., Tzur M., The period vehicle routing problem with service choice, Transp. Sci. 40 (4) (2006) 439–454.
[20]
Francis P., Smilowitz K.R., Tzur M., Flexibility and complexity in periodic distribution problems, Nav. Res. Logist. 2 (54) (2007) 136–150.
[21]
Francis P., Smilowitz K.R., Tzur M., The period vehicle routing problem and its extensions, in: The Vehicle Routing Problem: Latest Advances and New Challenges, Vol. 43, Springer, Oxford, 2008, pp. 73–102.
[22]
Guastaroba G., Speranza M.G., A heuristic for BILP problems: The single source capacitated facility location problem, European J. Oper. Res. 238 (2) (2014) 438–450.
[23]
Koç C., Bektaş T., Jabali O., Laporte G., Thirty years of heterogeneous vehicle routing, European J. Oper. Res. 249 (1) (2016) 1–21.
[24]
Lin S., Kernighan B., An effective heuristic algorithm for the Traveling Salesman Problem, Oper. Res. 21 (1973) 498–516.
[25]
Miller C., Zemlin R., Tucker A., Integer programming formulation of traveling salesman problems, J. ACM 7 (4) (1960) 326–329.
[26]
Russell R., Igo W., An assignment routing problem, Networks 9 (1) (1979) 1–17.

Cited By

View all

Index Terms

  1. The Heterogeneous Flexible Periodic Vehicle Routing Problem: Mathematical formulations and solution algorithms
          Index terms have been assigned to the content through auto-classification.

          Recommendations

          Comments

          Information & Contributors

          Information

          Published In

          cover image Computers and Operations Research
          Computers and Operations Research  Volume 141, Issue C
          May 2022
          335 pages

          Publisher

          Elsevier Science Ltd.

          United Kingdom

          Publication History

          Published: 01 May 2022

          Author Tags

          1. Kernel Search
          2. Matheuristics
          3. Vehicle Routing
          4. Heterogeneous fleet

          Qualifiers

          • Research-article

          Contributors

          Other Metrics

          Bibliometrics & Citations

          Bibliometrics

          Article Metrics

          • Downloads (Last 12 months)0
          • Downloads (Last 6 weeks)0
          Reflects downloads up to 16 Jan 2025

          Other Metrics

          Citations

          Cited By

          View all

          View Options

          View options

          Media

          Figures

          Other

          Tables

          Share

          Share

          Share this Publication link

          Share on social media