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Analysis of the single-vehicle cyclic inventory routing problem

Author

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  • El-Houssaine Aghezzaf
  • Yiqing Zhong
  • Birger Raa
  • Manel Mateo

Abstract

The single-vehicle cyclic inventory routing problem (SV-CIRP) consists of a repetitive distribution of a product from a single depot to a selected subset of customers. For each customer, selected for replenishments, the supplier collects a corresponding fixed reward. The objective is to determine the subset of customers to replenish, the quantity of the product to be delivered to each and to design the vehicle route so that the resulting profit (difference between the total reward and the total logistical cost) is maximised while preventing stockouts at each of the selected customers. This problem appears often as a sub-problem in many logistical problems. In this article, the SV-CIRP is formulated as a mixed-integer program with a nonlinear objective function. After a thorough analysis of the structure of the problem and its features, an exact algorithm for its solution is proposed. This exact algorithm requires only solutions of linear mixed-integer programs. Values of a savings-based heuristic for this problem are compared to the optimal values obtained for a set of some test problems. In general, the gap may get as large as 25%, which justifies the effort to continue exploring and developing exact and approximation algorithms for the SV-CIRP.

Suggested Citation

  • El-Houssaine Aghezzaf & Yiqing Zhong & Birger Raa & Manel Mateo, 2012. "Analysis of the single-vehicle cyclic inventory routing problem," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(11), pages 2040-2049.
    • Handle: RePEc:taf:tsysxx:v:43:y:2012:i:11:p:2040-2049
    DOI: 10.1080/00207721.2011.564321
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    Citations

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    Cited by:

    1. Pourya Pourhejazy & Oh Kyoung Kwon, 2016. "The New Generation of Operations Research Methods in Supply Chain Optimization: A Review," Sustainability, MDPI, vol. 8(10), pages 1-23, October.
    2. Verbeeck, C. & Vansteenwegen, P. & Aghezzaf, E.-H., 2016. "Solving the stochastic time-dependent orienteering problem with time windows," European Journal of Operational Research, Elsevier, vol. 255(3), pages 699-718.
    3. Diabat, Ali & Bianchessi, Nicola & Archetti, Claudia, 2024. "On the zero-inventory-ordering policy in the inventory routing problem," European Journal of Operational Research, Elsevier, vol. 312(3), pages 1024-1038.
    4. Vansteenwegen, Pieter & Mateo, Manuel, 2014. "An iterated local search algorithm for the single-vehicle cyclic inventory routing problem," European Journal of Operational Research, Elsevier, vol. 237(3), pages 802-813.
    5. Raa, Birger & Aouam, Tarik, 2021. "Multi-vehicle stochastic cyclic inventory routing with guaranteed replenishments," International Journal of Production Economics, Elsevier, vol. 234(C).
    6. Nadjib Brahimi & Tarik Aouam, 2016. "Multi-item production routing problem with backordering: a MILP approach," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1076-1093, February.
    7. Bertazzi, Luca & Chua, Geoffrey A. & Laganà, Demetrio & Paradiso, Rosario, 2022. "Analysis of effective sets of routes for the split-delivery periodic inventory routing problem," European Journal of Operational Research, Elsevier, vol. 298(2), pages 463-477.
    8. Mohd Kamarul Irwan Abdul Rahim & El-Houssaine Aghezzaf & Veronique Limère & Birger Raa, 2016. "Analysing the effectiveness of vendor-managed inventory in a single-warehouse, multiple-retailer system," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(8), pages 1953-1965, June.
    9. Agra, Agostinho & Christiansen, Marielle & Wolsey, Laurence, 2022. "Improved models for a single vehicle continuous-time inventory routing problem with pickups and deliveries," European Journal of Operational Research, Elsevier, vol. 297(1), pages 164-179.
    10. Cédric Verbeeck & Pieter Vansteenwegen & El-Houssaine Aghezzaf, 2017. "The time-dependent orienteering problem with time windows: a fast ant colony system," Annals of Operations Research, Springer, vol. 254(1), pages 481-505, July.
    11. Fokkema, Jan Eise & Land, Martin J. & Coelho, Leandro C. & Wortmann, Hans & Huitema, George B., 2020. "A continuous-time supply-driven inventory-constrained routing problem," Omega, Elsevier, vol. 92(C).
    12. Bertazzi, Luca & Coelho, Leandro C. & De Maio, Annarita & Laganà, Demetrio, 2019. "A matheuristic algorithm for the multi-depot inventory routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 524-544.
    13. Bertazzi, Luca & Laganà, Demetrio & Ohlmann, Jeffrey W. & Paradiso, Rosario, 2020. "An exact approach for cyclic inbound inventory routing in a level production system," European Journal of Operational Research, Elsevier, vol. 283(3), pages 915-928.
    14. Divsalar, Ali & Vansteenwegen, Pieter, 2016. "A two-phase algorithm for the cyclic inventory routing problemAuthor-Name: Chitsaz, Masoud," European Journal of Operational Research, Elsevier, vol. 254(2), pages 410-426.
    15. Raa, Birger, 2015. "Fleet optimization for cyclic inventory routing problems," International Journal of Production Economics, Elsevier, vol. 160(C), pages 172-181.
    16. Sonntag, Danja R. & Schrotenboer, Albert H. & Kiesmüller, Gudrun P., 2023. "Stochastic inventory routing with time-based shipment consolidation," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1186-1201.

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