Skip to main content

Advertisement

Log in

A column generation-based heuristic algorithm for an inventory routing problem with perishable goods

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

An inventory routing problem is a variation of the vehicle routing problem in which inventory and routing decisions are determined simultaneously over a given time horizon. The objective is to minimize the sum of transportation and inventory costs. In this paper, we study a specific inventory routing problem in which goods are perishable (PIRP). We develop a mathematical model for PIRP and exploit its structure to develop a column generation-based solution approach. Cutting planes are added to improve the formulation. We present computational experiments to demonstrate that our methodology is effective, and that the integration of routing and inventory can yield significant cost savings.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Andersson H., Hoff A., Christiansen M., Hasle G., Lokketangen A.: Industrial aspects and literature survey: combined inventory management and routing. Comput. Oper. Res. 37(1), 1515–1536 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. 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), 382–391 (2007)

    Article  Google Scholar 

  3. Atamturk A., Kucukyavuz S.: Lot sizing with inventory bounds and fixed costs: polyhedral study and computation. Oper. Res. 53, 711–730 (2005)

    Article  Google Scholar 

  4. Barany I., Roy T.J.V., Wolsey A.: Strong formulation for multi-item capacitated lot sizing. Manag. Sci. 30(19), 1255–1261 (1984)

    Article  MATH  Google Scholar 

  5. Bell W.J., Dalberto M., Fisher M.L., Greenfield A.J., Jaikuma R.: Improving the distribution of industrial gases with an on-line computerized routing and scheduling optimizer. Interface 13, 4–23 (1983)

    Article  Google Scholar 

  6. Bertazzi L., Palettta G., Speranza M.G.: Deterministic order-up-to level policies in an inventory routing problem. Transp. Sci. 36(1), 119–132 (2002)

    Article  MATH  Google Scholar 

  7. Campbell A., Clarke L., Savelsbergh M.W.P.: Inventory routing in practice. In: Toth, D., Vigo, D. (eds) The Vehicle Routing Problem, Society for Industrial and Applied Mathematics, Philadelphia (2002)

    Google Scholar 

  8. Christiansen M., Fagerholt K., Nygreen B., Ronen D.: Maritime transportation. Transportation 14, 189–284 (2007)

    Article  Google Scholar 

  9. Christiansen M., Fagerholt K., Ronen D.: Ship routing and scheduling: status and perspectives. Transp. Sci. 38(1), 1 (2004)

    Article  Google Scholar 

  10. Dell’Amico M., Francesco M., Värbrand P.: On prize-collecting tours and the asymmetric travelling salesman problem. Int. Trans. Oper. Res. 39(2), 188–205 (1995)

    Google Scholar 

  11. Desaulniers G., Desrosiers J., Solomon M.: Column Generation. Springer, Berlin (2005)

    Book  MATH  Google Scholar 

  12. Dong Y., Xu K.: A supply chain model of vendor managed inventory. Transp. Res. Part E: Logist. Transp. Rev. 38(2), 75–95 (2002)

    Article  Google Scholar 

  13. Dror M., Ball M.: Inventory/routing: reduction from an annual to a short period problem. Nav. Res. Logist. 33, 891–905 (1987)

    Article  MathSciNet  Google Scholar 

  14. Federgruen A., Prastacos G., Zipkin P.: An allocation and distribution model for perishable products. Oper. Res. 34, 75–82 (1986)

    Article  MATH  Google Scholar 

  15. Fisher, M.L.: Real-time scheduling of a bulk delivery fleet: practical application of Lagrangian relaxation. University of Pennsylvania, Philadelphia (1982)

  16. Gaur V., Fisher M.L.: A period inventory routing problem at a supermarket chain. Oper. Res. 52(6), 813–822 (2004)

    Article  MATH  Google Scholar 

  17. Gendreau M., Hertz A., Laporte G.: New insertion and postoptimization procedures for the traveling salesman problem. Oper. Res. 40, 1086–1094 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  18. Giri B.C., Chaudhuri K.S.: Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost. Eur. J. Oper. Res. 105, 467–474 (1998)

    Article  MATH  Google Scholar 

  19. Gronhaug R., Christiansen M., Desaulniers G, Desrosiers J.: A branch-and-price method for a liquefied natural gas inventory routing problem. Transp. Sci. 44(3), 400–415 (2010)

    Article  Google Scholar 

  20. Hsu C., Hung S., Li H.: Vehicle routing problem with time-windows for perishable food delivery. J. Food Eng. 80(1), 465–475 (2007)

    Article  Google Scholar 

  21. ILOG: Ilog Cplex 10.2-User’s Manual. ILOG S.A. and ILOG, Inc. (2007)

  22. Mamlin J., Kimaiyo S., Lewis S, Tadayo H., Jerop F.K., Gichunge C., Petersen T., Yih Y., Braitstein P., Einterz R.: Integrating nutrition support for food-insecure patients and their dependents into an HIV care and treatment program in western Kenya. Am. J. Public Health 99(2), 215–221 (2009)

    Article  Google Scholar 

  23. Panda S., Senapati S., Basu M.: Optimal replenishment policy for perishable seasonal products in a season with ramp-type time dependent demand. Comput. Ind. Eng. 54(2), 301–314 (2008)

    Article  Google Scholar 

  24. Ronen D.: Marine inventory routing: shipments planning. J. Oper. Res. Soc. 53, 108–114 (2002)

    Article  MATH  Google Scholar 

  25. Tarantilis C.T., Kiranoudis C.D. : A meta-heuristic algorithm for the efficient distribution of perishable foods. J. Food Eng. 50(1), 1–9 (2001)

    Article  Google Scholar 

  26. Toth P., Vigo D.: An overview of vehicle routing problems. In: Toth, D., Vigo, D. (eds) The Vehicle Routing Problem, Society for Industrial and Applied Mathematics, Philadelphia (2002)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ali Diabat.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Le, T., Diabat, A., Richard, JP. et al. A column generation-based heuristic algorithm for an inventory routing problem with perishable goods. Optim Lett 7, 1481–1502 (2013). https://doi.org/10.1007/s11590-012-0540-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-012-0540-2

Keywords

Navigation