IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v276y2019i3p1013-1033.html
   My bibliography  Save this article

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

Author

Listed:
  • Baller, Annelieke C.
  • Dabia, Said
  • Dullaert, Wout E.H.
  • Vigo, Daniele

Abstract

In a vendor-managed inventory setting, a supplier determines the timing and size of replenishments for its customers. In the Dynamic-Demand Joint Replenishment Problem (DJRP), one assumes that the supplier pays a fixed fee for replenishing a customer which often occurs if the supplier outsources transportation. Hence, there is no incentive for the supplier to schedule replenishments for nearby customers in the same period. This results in higher transportation costs for the carrier, decreased vehicle utilization and increased future fees for the supplier. To lower costs for both parties, this paper extends the traditional DJRP to the DJRP with Approximated Transportation Costs (DJRP-AT) by taking transportation considerations into account. Since routing problems are difficult to solve and it is not necessary to know the sequence of the deliveries to the customers as these are outsourced, the transportation costs for a given set of customers are approximated using classical schemes. A solution approach for the DJRP-AT based on Branch-and-Cut-and-Price is validated using test instances from the literature. Results show improvements of 4% on average and up to 14.4% for individual instances compared with the DJRP. Moreover, when the DJRP-AT is compared with the DJRP on instances derived from a real-life case, similar savings are obtained. Comparing the DJRP-AT to an equivalent problem with actual routing costs, the solution values of the DJRP-AT are on average only 0.77% higher showing the value of the approximation.

Suggested Citation

  • Baller, Annelieke C. & Dabia, Said & Dullaert, Wout E.H. & Vigo, Daniele, 2019. "The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1013-1033.
    • Handle: RePEc:eee:ejores:v:276:y:2019:i:3:p:1013-1033
    DOI: 10.1016/j.ejor.2019.01.070
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719301055
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.01.070?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jesus Cunha & Rafael Melo, 2016. "On reformulations for the one-warehouse multi-retailer problem," Annals of Operations Research, Springer, vol. 238(1), pages 99-122, March.
    2. Robinson, Powell & Narayanan, Arunachalam & Sahin, Funda, 2009. "Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms," Omega, Elsevier, vol. 37(1), pages 3-15, February.
    3. Wang, Lin & He, Jing & Wu, Desheng & Zeng, Yu-Rong, 2012. "A novel differential evolution algorithm for joint replenishment problem under interdependence and its application," International Journal of Production Economics, Elsevier, vol. 135(1), pages 190-198.
    4. Khouja, Moutaz & Goyal, Suresh, 2008. "A review of the joint replenishment problem literature: 1989-2005," European Journal of Operational Research, Elsevier, vol. 186(1), pages 1-16, April.
    5. He-Yau Kang & Amy H.I. Lee & Chien-Wei Wu & Cheng-Han Lee, 2017. "An efficient method for dynamic-demand joint replenishment problem with multiple suppliers and multiple vehicles," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 1065-1084, February.
    6. Awi Federgruen & Joern Meissner & Michal Tzur, 2007. "Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 55(3), pages 490-502, June.
    7. M. Haimovich & A. H. G. Rinnooy Kan, 1985. "Bounds and Heuristics for Capacitated Routing Problems," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 527-542, November.
    8. N. Absi & C. Archetti & S. Dauzère-Pérès & D. Feillet, 2015. "A Two-Phase Iterative Heuristic Approach for the Production Routing Problem," Transportation Science, INFORMS, vol. 49(4), pages 784-795, November.
    9. Langevin, André & Soumis, François, 1989. "Design of multiple-vehicle delivery tours satisfying time constraints," Transportation Research Part B: Methodological, Elsevier, vol. 23(2), pages 123-138, April.
    10. A Hindle & D Worthington, 2004. "Models to estimate average route lengths in different geographical environments," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(6), pages 662-666, June.
    11. Roel G. van Anholt & Leandro C. Coelho & Gilbert Laporte & Iris F. A. Vis, 2016. "An Inventory-Routing Problem with Pickups and Deliveries Arising in the Replenishment of Automated Teller Machines," Transportation Science, INFORMS, vol. 50(3), pages 1077-1091, August.
    12. Çavdar, Bahar & Sokol, Joel, 2015. "A distribution-free TSP tour length estimation model for random graphs," European Journal of Operational Research, Elsevier, vol. 243(2), pages 588-598.
    13. Larsen, Christian & Turkensteen, Marcel, 2014. "A vendor managed inventory model using continuous approximations for route length estimates and Markov chain modeling for cost estimates," International Journal of Production Economics, Elsevier, vol. 157(C), pages 120-132.
    14. Ventura, José A. & Valdebenito, Victor A. & Golany, Boaz, 2013. "A dynamic inventory model with supplier selection in a serial supply chain structure," European Journal of Operational Research, Elsevier, vol. 230(2), pages 258-271.
    15. Jesus O. Cunha & Rafael A. Melo, 2016. "On reformulations for the one-warehouse multi-retailer problem," Annals of Operations Research, Springer, vol. 238(1), pages 99-122, March.
    16. Shoshana Anily & Michal Tzur, 2005. "Shipping Multiple Items by Capacitated Vehicles: An Optimal Dynamic Programming Approach," Transportation Science, INFORMS, vol. 39(2), pages 233-248, May.
    17. Claudia Archetti & Luca Bertazzi & Gilbert Laporte & Maria Grazia Speranza, 2007. "A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem," Transportation Science, INFORMS, vol. 41(3), pages 382-391, August.
    18. Ian R. Webb & Bruce R. Buzby & Gerard M. Campbell, 1997. "Cyclical schedules for the joint replenishment problem with dynamic demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(6), pages 577-589, September.
    19. Jabali, Ola & Gendreau, Michel & Laporte, Gilbert, 2012. "A continuous approximation model for the fleet composition problem," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1591-1606.
    20. Turkensteen, Marcel & Klose, Andreas, 2012. "Demand dispersion and logistics costs in one-to-many distribution systems," European Journal of Operational Research, Elsevier, vol. 223(2), pages 499-507.
    21. Max Shen, Zuo-Jun & Qi, Lian, 2007. "Incorporating inventory and routing costs in strategic location models," European Journal of Operational Research, Elsevier, vol. 179(2), pages 372-389, June.
    22. Hoque, M.A., 2006. "An optimal solution technique for the joint replenishment problem with storage and transport capacities and budget constraints," European Journal of Operational Research, Elsevier, vol. 175(2), pages 1033-1042, December.
    23. Anna Franceschetti & Ola Jabali & Gilbert Laporte, 2017. "Rejoinder on: Continuous approximation models in freight distribution management," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 443-444, October.
    24. Daganzo, Carlos F., 1984. "The length of tours in zones of different shapes," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 135-145, April.
    25. Anna Franceschetti & Ola Jabali & Gilbert Laporte, 2017. "Continuous approximation models in freight distribution management," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 413-433, October.
    26. Olsen, Anne L., 2008. "Inventory replenishment with interdependent ordering costs: An evolutionary algorithm solution," International Journal of Production Economics, Elsevier, vol. 113(1), pages 359-369, May.
    27. Narayanan, Arunachalam & Robinson, Powell, 2010. "Efficient and effective heuristics for the coordinated capacitated lot-size problem," European Journal of Operational Research, Elsevier, vol. 203(3), pages 583-592, June.
    28. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    29. E P Robinson & A Narayanan & L-L Gao, 2007. "Effective heuristics for the dynamic demand joint replenishment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 808-815, June.
    30. Dasci, Abdullah & Verter, Vedat, 2001. "A continuous model for production-distribution system design," European Journal of Operational Research, Elsevier, vol. 129(2), pages 287-298, March.
    31. Mohammed A. Darwish & Osama M. Odah & Suresh Kumar Goyal, 2013. "Vendor-managed inventory models for items with imperfect quality," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 18(4), pages 401-433.
    32. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.
    33. Carlos F. Daganzo, 1984. "The Distance Traveled to Visit N Points with a Maximum of C Stops per Vehicle: An Analytic Model and an Application," Transportation Science, INFORMS, vol. 18(4), pages 331-350, November.
    34. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vidal, Thibaut & Laporte, Gilbert & Matl, Piotr, 2020. "A concise guide to existing and emerging vehicle routing problem variants," European Journal of Operational Research, Elsevier, vol. 286(2), pages 401-416.
    2. Boliang Lin & Fan Yang & Shuting Zuo & Chang Liu & Yinan Zhao & Mu Yang, 2019. "An Optimization Approach to the Low-Frequency Entire Train Formation at the Loading Area," Sustainability, MDPI, vol. 11(19), pages 1-15, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Anna Franceschetti & Ola Jabali & Gilbert Laporte, 2017. "Continuous approximation models in freight distribution management," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 413-433, October.
    2. Vidal, Thibaut & Laporte, Gilbert & Matl, Piotr, 2020. "A concise guide to existing and emerging vehicle routing problem variants," European Journal of Operational Research, Elsevier, vol. 286(2), pages 401-416.
    3. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
    4. Wang, Lin & He, Jing & Wu, Desheng & Zeng, Yu-Rong, 2012. "A novel differential evolution algorithm for joint replenishment problem under interdependence and its application," International Journal of Production Economics, Elsevier, vol. 135(1), pages 190-198.
    5. Ellegood, William A. & Campbell, James F. & North, Jeremy, 2015. "Continuous approximation models for mixed load school bus routing," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 182-198.
    6. Saravanan Venkatachalam & Arunachalam Narayanan, 2016. "Efficient formulation and heuristics for multi-item single source ordering problem with transportation cost," International Journal of Production Research, Taylor & Francis Journals, vol. 54(14), pages 4087-4103, July.
    7. Geunes, Joseph & Shen, Zuo-Jun Max & Emir, Akin, 2007. "Planning and approximation models for delivery route based services with price-sensitive demands," European Journal of Operational Research, Elsevier, vol. 183(1), pages 460-471, November.
    8. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    9. Fontaine, Pirmin & Minner, Stefan & Schiffer, Maximilian, 2023. "Smart and sustainable city logistics: Design, consolidation, and regulation," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1071-1084.
    10. Zhang, Juan & Campbell, James F. & Sweeney, Donald C., 2024. "A continuous approximation approach to integrated truck and drone delivery systems," Omega, Elsevier, vol. 126(C).
    11. Atieh Madani & Rajan Batta & Mark Karwan, 2021. "The balancing traveling salesman problem: application to warehouse order picking," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 442-469, July.
    12. Jabali, Ola & Gendreau, Michel & Laporte, Gilbert, 2012. "A continuous approximation model for the fleet composition problem," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1591-1606.
    13. Jaller, Miguel & Pahwa, Anmol, 2020. "Analytical Modeling Framework to Assess the Economic and Environmental Impacts of Residential Deliveries, and Evaluate Sustainable Last-Mile Strategies," Institute of Transportation Studies, Working Paper Series qt4143j4pr, Institute of Transportation Studies, UC Davis.
    14. Narayanan, Arunachalam & Robinson, Powell, 2010. "Evaluation of joint replenishment lot-sizing procedures in rolling horizon planning systems," International Journal of Production Economics, Elsevier, vol. 127(1), pages 85-94, September.
    15. Franceschetti, Anna & Honhon, Dorothée & Laporte, Gilbert & Woensel, Tom Van & Fransoo, Jan C., 2017. "Strategic fleet planning for city logistics," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 19-40.
    16. Janjevic, Milena & Merchán, Daniel & Winkenbach, Matthias, 2021. "Designing multi-tier, multi-service-level, and multi-modal last-mile distribution networks for omni-channel operations," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1059-1077.
    17. Huang, Michael & Smilowitz, Karen R. & Balcik, Burcu, 2013. "A continuous approximation approach for assessment routing in disaster relief," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 20-41.
    18. Mehdi Nourinejad & Matthew J. Roorda, 2017. "A continuous approximation model for the fleet composition problem on the rectangular grid," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 373-401, March.
    19. Arslan, Okan, 2021. "The location-or-routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 147(C), pages 1-21.
    20. Ongkunaruk, P. & Wahab, M.I.M. & Chen, Y., 2016. "A genetic algorithm for a joint replenishment problem with resource and shipment constraints and defective items," International Journal of Production Economics, Elsevier, vol. 175(C), pages 142-152.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:276:y:2019:i:3:p:1013-1033. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.