IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v56y2015icp112-121.html
   My bibliography  Save this article

Managing stochastic demand in an Inventory Routing Problem with transportation procurement

Author

Listed:
  • Bertazzi, Luca
  • Bosco, Adamo
  • Laganà, Demetrio

Abstract

We study an Inventory Routing Problem in which the supplier has a limited production capacity and the stochastic demand of the retailers is satisfied with procurement of transportation services. The aim is to minimize the total expected cost over a planning horizon, given by the sum of the inventory cost at the supplier, the inventory cost at the retailers, the penalty cost for stock-out at the retailers and the transportation cost. First, we show that a policy based just on the average demand can have a total expected cost infinitely worse than the one obtained by taking into account the overall probability distribution of the demand in the decision process. Therefore, we introduce a stochastic dynamic programming formulation of the problem that allows us to find an optimal policy in small size instances. Finally, we design and implement a matheuristic approach, integrating a rollout algorithm and an optimal solution of mixed-integer linear programming models, which is able to solve realistic size problem instances. Computational results allow us to provide managerial insights concerning the management of stochastic demand.

Suggested Citation

  • Bertazzi, Luca & Bosco, Adamo & Laganà, Demetrio, 2015. "Managing stochastic demand in an Inventory Routing Problem with transportation procurement," Omega, Elsevier, vol. 56(C), pages 112-121.
    • Handle: RePEc:eee:jomega:v:56:y:2015:i:c:p:112-121
    DOI: 10.1016/j.omega.2014.09.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048314001212
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2014.09.010?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. G. Clarke & J. W. Wright, 1964. "Scheduling of Vehicles from a Central Depot to a Number of Delivery Points," Operations Research, INFORMS, vol. 12(4), pages 568-581, August.
    2. Herer, Yale T. & Levy, Roberto, 1997. "The Metered Inventory Routing Problem, an integrative heuristic algorithm," International Journal of Production Economics, Elsevier, vol. 51(1-2), pages 69-81, August.
    3. Mansini, Renata & Savelsbergh, Martin W.P. & Tocchella, Barbara, 2012. "The supplier selection problem with quantity discounts and truckload shipping," Omega, Elsevier, vol. 40(4), pages 445-455.
    4. Nicola Secomandi, 2001. "A Rollout Policy for the Vehicle Routing Problem with Stochastic Demands," Operations Research, INFORMS, vol. 49(5), pages 796-802, October.
    5. Kim, Jung-Ug & Kim, Yeong-Dae, 1999. "A decomposition approach to a multi-period vehicle scheduling problem," Omega, Elsevier, vol. 27(4), pages 421-430, August.
    6. Awi Federgruen & Gregory Prastacos & Paul H. Zipkin, 1986. "An Allocation and Distribution Model for Perishable Products," Operations Research, INFORMS, vol. 34(1), pages 75-82, February.
    7. Kopanos, Georgios M. & Puigjaner, Luis & Georgiadis, Michael C., 2012. "Simultaneous production and logistics operations planning in semicontinuous food industries," Omega, Elsevier, vol. 40(5), pages 634-650.
    8. Andreas Stenger & Daniele Vigo & Steffen Enz & Michael Schwind, 2013. "An Adaptive Variable Neighborhood Search Algorithm for a Vehicle Routing Problem Arising in Small Package Shipping," Transportation Science, INFORMS, vol. 47(1), pages 64-80, February.
    9. Lars Magnus Hvattum & Arne Løkketangen & Gilbert Laporte, 2009. "Scenario Tree-Based Heuristics for Stochastic Inventory-Routing Problems," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 268-285, May.
    10. Day, Jamison M. & Daniel Wright, P. & Schoenherr, Tobias & Venkataramanan, Munirpallam & Gaudette, Kevin, 2009. "Improving routing and scheduling decisions at a distributor of industrial gasses," Omega, Elsevier, vol. 37(1), pages 227-237, February.
    11. Alan S. Minkoff, 1993. "A Markov Decision Model and Decomposition Heuristic for Dynamic Vehicle Dispatching," Operations Research, INFORMS, vol. 41(1), pages 77-90, February.
    12. Archetti, Claudia & Bertazzi, Luca & Grazia Speranza, M., 2014. "Polynomial cases of the economic lot sizing problem with cost discounts," European Journal of Operational Research, Elsevier, vol. 237(2), pages 519-527.
    13. Dimitris Bertsimas & Ramazan Demir, 2002. "An Approximate Dynamic Programming Approach to Multidimensional Knapsack Problems," Management Science, INFORMS, vol. 48(4), pages 550-565, April.
    14. Yossi Sheffi, 2004. "Combinatorial Auctions in the Procurement of Transportation Services," Interfaces, INFORMS, vol. 34(4), pages 245-252, August.
    15. Novoa, Clara & Storer, Robert, 2009. "An approximate dynamic programming approach for the vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 196(2), pages 509-515, July.
    16. Côté, Jean-François & Potvin, Jean-Yves, 2009. "A tabu search heuristic for the vehicle routing problem with private fleet and common carrier," European Journal of Operational Research, Elsevier, vol. 198(2), pages 464-469, October.
    17. Yugang Yu & Chengbin Chu & Haoxun Chen & Feng Chu, 2012. "Large scale stochastic inventory routing problems with split delivery and service level constraints," Annals of Operations Research, Springer, vol. 197(1), pages 135-158, August.
    18. Jonathan F. Bard & Liu Huang & Patrick Jaillet & Moshe Dror, 1998. "A Decomposition Approach to the Inventory Routing Problem with Satellite Facilities," Transportation Science, INFORMS, vol. 32(2), pages 189-203, May.
    19. Stéphane Dauzère-Pérès & Atle Nordli & Asmund Olstad & Kjetil Haugen & Ulrich Koester & Myrstad Per Olav & Geir Teistklub & Alf Reistad, 2007. "Omya Hustadmarmor Optimizes Its Supply Chain for Delivering Calcium Carbonate Slurry to European Paper Manufacturers," Interfaces, INFORMS, vol. 37(1), pages 39-51, February.
    20. Luca Bertazzi, 2012. "Minimum and Worst-Case Performance Ratios of Rollout Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 378-393, February.
    21. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2004. "Dynamic Programming Approximations for a Stochastic Inventory Routing Problem," Transportation Science, INFORMS, vol. 38(1), pages 42-70, February.
    22. Walter J. Bell & Louis M. Dalberto & Marshall L. Fisher & Arnold J. Greenfield & R. Jaikumar & Pradeep Kedia & Robert G. Mack & Paul J. Prutzman, 1983. "Improving the Distribution of Industrial Gases with an On-Line Computerized Routing and Scheduling Optimizer," Interfaces, INFORMS, vol. 13(6), pages 4-23, December.
    23. Awi Federgruen & Paul Zipkin, 1984. "A Combined Vehicle Routing and Inventory Allocation Problem," Operations Research, INFORMS, vol. 32(5), pages 1019-1037, October.
    24. M-C Bolduc & J Renaud & F Boctor & G Laporte, 2008. "A perturbation metaheuristic for the vehicle routing problem with private fleet and common carriers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(6), pages 776-787, June.
    25. Vishal Gaur & Marshall L. Fisher, 2004. "A Periodic Inventory Routing Problem at a Supermarket Chain," Operations Research, INFORMS, vol. 52(6), pages 813-822, December.
    26. Chu, Ching-Wu, 2005. "A heuristic algorithm for the truckload and less-than-truckload problem," European Journal of Operational Research, Elsevier, vol. 165(3), pages 657-667, September.
    27. F. Guerriero, 2008. "Hybrid Rollout Approaches for the Job Shop Scheduling Problem," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 419-438, November.
    28. Pan, Feng & Nagi, Rakesh, 2013. "Multi-echelon supply chain network design in agile manufacturing," Omega, Elsevier, vol. 41(6), pages 969-983.
    29. J-Y Potvin & M-A Naud, 2011. "Tabu search with ejection chains for the vehicle routing problem with private fleet and common carrier," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(2), pages 326-336, February.
    30. 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.
    31. Yehuda Bassok & Ricardo Ernst, 1995. "Dynamic Allocations for Multi-Product Distribution," Transportation Science, INFORMS, vol. 29(3), pages 256-266, August.
    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. Wadi Khalid Anuar & Lai Soon Lee & Hsin-Vonn Seow & Stefan Pickl, 2021. "A Multi-Depot Vehicle Routing Problem with Stochastic Road Capacity and Reduced Two-Stage Stochastic Integer Linear Programming Models for Rollout Algorithm," Mathematics, MDPI, vol. 9(13), pages 1-44, July.
    2. Chih-Kang Lin & Shangyao Yan & Fei-Yen Hsiao, 2021. "Optimal Inventory Level Control and Replenishment Plan for Retailers," Networks and Spatial Economics, Springer, vol. 21(1), pages 57-83, March.
    3. Feki, Yassin & Hajji, Adnène & Rekik, Monia, 2016. "A hedging policy for carriers’ selection under availability and demand uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 85(C), pages 149-165.
    4. Alvarez, Aldair & Cordeau, Jean-François & Jans, Raf & Munari, Pedro & Morabito, Reinaldo, 2021. "Inventory routing under stochastic supply and demand," Omega, Elsevier, vol. 102(C).
    5. Rossi, Roberto & Tomasella, Maurizio & Martin-Barragan, Belen & Embley, Tim & Walsh, Christopher & Langston, Matthew, 2019. "The Dynamic Bowser Routing Problem," European Journal of Operational Research, Elsevier, vol. 275(1), pages 108-126.
    6. Cárdenas-Barrón, Leopoldo E. & Melo, Rafael A., 2021. "A fast and effective MIP-based heuristic for a selective and periodic inventory routing problem in reverse logistics," Omega, Elsevier, vol. 103(C).
    7. Beltran-Royo, C., 2017. "Two-stage stochastic mixed-integer linear programming: The conditional scenario approach," Omega, Elsevier, vol. 70(C), pages 31-42.
    8. Bertazzi, Luca & Bosco, Adamo & Laganà, Demetrio, 2016. "Min–Max exact and heuristic policies for a two-echelon supply chain with inventory and transportation procurement decisions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 57-70.
    9. Bertazzi, Luca & Moezi, Sarem Deilami & Maggioni, Francesca, 2021. "The value of integration of full container load, less than container load and air freight shipments in vendor–managed inventory systems," International Journal of Production Economics, Elsevier, vol. 241(C).
    10. Rahimi, Mohammad & Baboli, Armand & Rekik, Yacine, 2017. "Multi-objective inventory routing problem: A stochastic model to consider profit, service level and green criteria," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 101(C), pages 59-83.
    11. Zhang, Juliang & Xiang, Jie & Cheng, T.C. Edwin & Hua, Guowei & Chen, Cheng, 2019. "An optimal efficient multi-attribute auction for transportation procurement with carriers having multi-unit supplies," Omega, Elsevier, vol. 83(C), pages 249-260.
    12. A. Mor & M. G. Speranza, 2020. "Vehicle routing problems over time: a survey," 4OR, Springer, vol. 18(2), pages 129-149, June.
    13. Liu, Ming & Liu, Xin & Chu, Feng & Zheng, Feifeng & Chu, Chengbin, 2019. "Distributionally robust inventory routing problem to maximize the service level under limited budget," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 126(C), pages 190-211.
    14. Wadi Khalid Anuar & Lai Soon Lee & Hsin-Vonn Seow & Stefan Pickl, 2022. "A Multi-Depot Dynamic Vehicle Routing Problem with Stochastic Road Capacity: An MDP Model and Dynamic Policy for Post-Decision State Rollout Algorithm in Reinforcement Learning," Mathematics, MDPI, vol. 10(15), pages 1-70, July.
    15. Mahmutoğulları, Özlem & Yaman, Hande, 2023. "A Branch-and-Cut Algorithm for the Inventory Routing Problem with Product Substitution," Omega, Elsevier, vol. 115(C).
    16. A. Mor & M. G. Speranza, 2022. "Vehicle routing problems over time: a survey," Annals of Operations Research, Springer, vol. 314(1), pages 255-275, July.
    17. Amit Verma & Ann Melissa Campbell, 2019. "Strategic placement of telemetry units considering customer usage correlation," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(1), pages 35-64, March.
    18. Mosca, Alyssa & Vidyarthi, Navneet & Satir, Ahmet, 2019. "Integrated transportation – inventory models: A review," Operations Research Perspectives, Elsevier, vol. 6(C).

    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. Leandro C. Coelho & Jean-François Cordeau & Gilbert Laporte, 2014. "Thirty Years of Inventory Routing," Transportation Science, INFORMS, vol. 48(1), pages 1-19, February.
    2. Yves Crama & Mahmood Rezaei & Martin Savelsbergh & Tom Van Woensel, 2018. "Stochastic Inventory Routing for Perishable Products," Transportation Science, INFORMS, vol. 52(3), pages 526-546, June.
    3. Cárdenas-Barrón, Leopoldo Eduardo & González-Velarde, José Luis & Treviño-Garza, Gerardo & Garza-Nuñez, Dagoberto, 2019. "Heuristic algorithm based on reduce and optimize approach for a selective and periodic inventory routing problem in a waste vegetable oil collection environment," International Journal of Production Economics, Elsevier, vol. 211(C), pages 44-59.
    4. Song, Ruidian & Zhao, Lei & Van Woensel, Tom & Fransoo, Jan C., 2019. "Coordinated delivery in urban retail," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 126(C), pages 122-148.
    5. Zhenzhen Zhang & Zhixing Luo & Hu Qin & Andrew Lim, 2019. "Exact Algorithms for the Vehicle Routing Problem with Time Windows and Combinatorial Auction," Transportation Science, INFORMS, vol. 53(2), pages 427-441, March.
    6. Jin-Hwa Song & Martin Savelsbergh, 2007. "Performance Measurement for Inventory Routing," Transportation Science, INFORMS, vol. 41(1), pages 44-54, February.
    7. Said Dabia & David Lai & Daniele Vigo, 2019. "An Exact Algorithm for a Rich Vehicle Routing Problem with Private Fleet and Common Carrier," Transportation Science, INFORMS, vol. 53(4), pages 986-1000, July.
    8. Rossi, Roberto & Tomasella, Maurizio & Martin-Barragan, Belen & Embley, Tim & Walsh, Christopher & Langston, Matthew, 2019. "The Dynamic Bowser Routing Problem," European Journal of Operational Research, Elsevier, vol. 275(1), pages 108-126.
    9. Jafarian, Ahmad & Asgari, Nasrin & Mohri, Seyed Sina & Fatemi-Sadr, Elham & Farahani, Reza Zanjirani, 2019. "The inventory-routing problem subject to vehicle failure," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 126(C), pages 254-294.
    10. Jeffrey W. Ohlmann & Michael J. Fry & Barrett W. Thomas, 2008. "Route Design for Lean Production Systems," Transportation Science, INFORMS, vol. 42(3), pages 352-370, August.
    11. Andreas Stenger & Daniele Vigo & Steffen Enz & Michael Schwind, 2013. "An Adaptive Variable Neighborhood Search Algorithm for a Vehicle Routing Problem Arising in Small Package Shipping," Transportation Science, INFORMS, vol. 47(1), pages 64-80, February.
    12. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2002. "The Stochastic Inventory Routing Problem with Direct Deliveries," Transportation Science, INFORMS, vol. 36(1), pages 94-118, February.
    13. Alvarez, Aldair & Cordeau, Jean-François & Jans, Raf & Munari, Pedro & Morabito, Reinaldo, 2021. "Inventory routing under stochastic supply and demand," Omega, Elsevier, vol. 102(C).
    14. Sayarshad, Hamid R. & Gao, H. Oliver, 2018. "A non-myopic dynamic inventory routing and pricing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 83-98.
    15. Mirzapour Al-e-hashem, Seyed M.J. & Rekik, Yacine & Mohammadi Hoseinhajlou, Ebrahim, 2019. "A hybrid L-shaped method to solve a bi-objective stochastic transshipment-enabled inventory routing problem," International Journal of Production Economics, Elsevier, vol. 209(C), pages 381-398.
    16. Ketzenberg, Michael E. & Metters, Richard D., 2020. "Adapting operations to new information technology: A failed “internet of things” application," Omega, Elsevier, vol. 92(C).
    17. Bertazzi, Luca & Maggioni, Francesca, 2018. "A stochastic multi-stage fixed charge transportation problem: Worst-case analysis of the rolling horizon approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 555-569.
    18. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2004. "Dynamic Programming Approximations for a Stochastic Inventory Routing Problem," Transportation Science, INFORMS, vol. 38(1), pages 42-70, February.
    19. Paul, J. & Agatz, N.A.H. & Spliet, R. & de Koster, M.B.M., 2017. "Shared Capacity Routing Problem – An Omni-channel Retail Study," ERIM Report Series Research in Management ERS-2017-012-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    20. Gahm, Christian & Brabänder, Christian & Tuma, Axel, 2017. "Vehicle routing with private fleet, multiple common carriers offering volume discounts, and rental options," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 97(C), pages 192-216.

    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:jomega:v:56:y:2015:i:c:p:112-121. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.