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Recent Progress Using Matheuristics for Strategic Maritime Inventory Routing

  • Dimitri J. PapageorgiouEmail author
  • Myun-Seok Cheon
  • Stuart Harwood
  • Francisco Trespalacios
  • George L. Nemhauser
Chapter
Part of the Intelligent Systems Reference Library book series (ISRL, volume 131)

Abstract

This chapter presents an extensive computational study of simple, but prominent matheuristics (i.e., heuristics that rely on mathematical programming models) to find high quality ship schedules and inventory policies for a class of maritime inventory routing problems. Our computational experiments are performed on a test bed of the publicly available MIRPLib instances. This class of inventory routing problems has few constraints relative to some operational problems, but is complicated by long planning horizons. We compare several variants of rolling horizon heuristics, K-opt heuristics, local branching, solution polishing, and hybrids thereof. Many of these matheuristics substantially outperform the commercial mixed-integer programming solvers CPLEX 12.6.2 and Gurobi 6.5 in their ability to quickly find high quality solutions. New best known incumbents are found for 26 out of 70 yet-to-be-proved-optimal instances and new best known bounds on 56 instances.

Keywords

Deterministic inventory routing Matheuristics Maritime transportation Mixed-integer linear programming Time decomposition 

Notes

Acknowledgements

We wish to thank two anonymous referees for their feedback, in particular Reviewer 1 whose perceptive comments helped improve the quality of the chapter.

References

  1. 1.
    Agra, A., Andersson, H., Christiansen, M., Wolsey, L.: A maritime inventory routing problem: discrete time formulations and valid inequalities. Networks 62(4), 297–314 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Agra, A., Christiansen, M., Delgado, A., Simonetti, L.: Hybrid heuristics for a short sea inventory routing problem. Eur. J. Oper. Res. 236(3), 924–935 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Al-Ameri, T.A., Shah, N., Papageorgiou, L.G.: Optimization of vendor-managed inventory systems in a rolling horizon framework. Comput. Ind. Eng. 54(4), 1019–1047 (2008)CrossRefGoogle Scholar
  4. 4.
    Al-Khayyal, F., Hwang, S.: Inventory constrained maritime routing and scheduling for multi-commodity liquid bulk, Part I: Applications and model. Eur. J. Oper. Res. 176(1), 106–130 (2007)CrossRefzbMATHGoogle Scholar
  5. 5.
    Andersson, H., Hoff, A., Christiansen, M., Hasle, G., Løkketangen, A.: Industrial aspects and literature survey: combined inventory management and routing. Comput. Oper. Res. 37(9), 1515–1536 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Archetti, C., Speranza, M.G.: A survey on matheuristics for routing problems. EURO J. Comput. Optim. 2(4), 223–246 (2014)CrossRefzbMATHGoogle Scholar
  7. 7.
    Asokan, B.V., Furman, K.C., Goel, V., Shao, Y., Li, G.: Parallel large-neighborhood search techniques for LNG inventory routing. Submitted for publication (2014)Google Scholar
  8. 8.
    Bertazzi, L., Speranza, M.G.: Matheuristics for inventory routing problems. In: Hybrid Algorithms for Service, Computing and Manufacturing Systems: Routing and Scheduling Solutions, p. 488. IGI Global, Hershey (2011)Google Scholar
  9. 9.
    Bixby, R., Rothberg, E.: Progress in computational mixed integer programming—a look back from the other side of the tipping point. Ann. Oper. Res. 149(1), 37–41 (2007)Google Scholar
  10. 10.
    Boschetti, M.A., Maniezzo, V., Roffilli, M., Röhler, A.B.: Matheuristics: optimization, simulation and control. In: Hybrid Metaheuristics, pp. 171–177. Springer (2009)Google Scholar
  11. 11.
    Brouer, B.D., Desaulniers, G., Pisinger, D.: A matheuristic for the liner shipping network design problem. Transp. Res. Part E: Logist. Transp. Rev. 72, 42–59 (2014)CrossRefGoogle Scholar
  12. 12.
    Campbell, A., Clarke, L., Kleywegt, A., Savelsbergh, M.W.P.: The inventory routing problem. In: Crainic, T.G., Laporte, G. (eds.) Fleet Management and Logistics, pp. 95–113. Kluwer (1998)Google Scholar
  13. 13.
    Christiansen, M., Fagerholt, K., Flatberg, T., Haugen, O., Kloster, O., Lund, E.H.: Maritime inventory routing with multiple products: a case study from the cement industry. Eur. J. Oper. Res. 208(1), 86–94 (2011)CrossRefGoogle Scholar
  14. 14.
    Christiansen, M., Fagerholt, K., Nygreen, B., Ronen, D.: Maritime transportation. In: Barnhart, C., Laporte, G. (eds.) Transportation, Handbooks in Operations Research and Management Science, vol. 14, pp. 189–284. Elsevier (2007)Google Scholar
  15. 15.
    Coelho, L.C., Cordeau, J.F., Laporte, G.: Thirty years of inventory-routing. Transp. Sci. 48(1), 1–19 (2014)CrossRefGoogle Scholar
  16. 16.
    Cornuéjols, G.: Valid inequalities for mixed integer linear programs. Math. Programm. 112(1), 3–44 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Dauzère-Pérès, S., Nordli, A., Olstad, A., Haugen, K., Koester, U., Myrstad, P.O., Teistklub, G., Reistad, A.: Omya hustadmarmor optimizes its supply chain for delivering calcium carbonate slurry to European paper manufacturers. Interfaces 37(1), 39–51 (2007)CrossRefGoogle Scholar
  18. 18.
    Engineer, F.G., Furman, K.C., Nemhauser, G.L., Savelsbergh, M.W.P., Song, J.H.: A Branch-Price-And-Cut algorithm for single product maritime inventory routing. Oper. Res. 60(1), 106–122 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Fischetti, M., Lodi, A.: Local branching. Math. Programm. 98(1–3), 23–47 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Fodstad, M., Uggen, K.T., Rømo, F., Lium, A., Stremersch, G.: LNGScheduler: a rich model for coordinating vessel routing, inventories and trade in the liquefied natural gas supply chain. J. Energy Mark. 3(4), 31–64 (2010)CrossRefGoogle Scholar
  21. 21.
    Furman, K.C., Song, J.H., Kocis, G.R., McDonald, M.K., Warrick, P.H.: Feedstock routing in the ExxonMobil downstream sector. Interfaces 41(2), 149–163 (2011)CrossRefGoogle Scholar
  22. 22.
    Godfrey, G.A., Powell, W.B.: An adaptive dynamic programming algorithm for dynamic fleet management, I: Single period travel times. Transp. Sci. 36(1), 21–39 (2002)CrossRefzbMATHGoogle Scholar
  23. 23.
    Godfrey, G.A., Powell, W.B.: An adaptive dynamic programming algorithm for dynamic fleet management, II: Multiperiod travel times. Transp. Sci. 36(1), 40–54 (2002)CrossRefzbMATHGoogle Scholar
  24. 24.
    Goel, V., Furman, K.C., Song, J.H., El-Bakry, A.S.: Large neighborhood search for LNG inventory routing. J. Heurist. 18(6), 821–848 (2012)CrossRefGoogle Scholar
  25. 25.
    Goel, V., Slusky, M., van Hoeve, W.J., Furman, K.C., Shao, Y.: Constraint programming for LNG ship scheduling and inventory management. Eur. J. Oper. Res. 241(3), 662–673 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Halvorsen-Weare, E., Fagerholt, K.: Routing and scheduling in a liquefied natural gas shipping problem with inventory and berth constraints. Ann. Oper. Res. 203(1), 167–186 (2013)CrossRefzbMATHGoogle Scholar
  27. 27.
    Hemmati, A., Hvattum, L.M., Christiansen, M., Laporte, G.: An iterative two-phase hybrid matheuristic for a multi-product short sea inventory-routing problem. Eur. J. Oper. Res. 252(3), 775–788 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Hemmati, A., Stålhane, M., Hvattum, L.M., Andersson, H.: An effective heuristic for solving a combined cargo and inventory routing problem in tramp shipping. Comput. Oper. Res. 64, 274–282 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Hewitt, M., Nemhauser, G.L., Savelsbergh, M.W.P.: Branch-and-price guided search for integer programs with an application to the multicommodity fixed-charge network flow problem. INFORMS J. Comput. (2012)Google Scholar
  30. 30.
    Hewitt, M., Nemhauser, G.L., Savelsbergh, M.W.P., Song, J.H.: A Branch-and-price guided search approach to maritime inventory routing. Comput. Oper. Res. 40(5), 1410–1419 (2013)CrossRefzbMATHGoogle Scholar
  31. 31.
    Jiang, Y., Grossmann, I.E.: Alternative mixed-integer linear programming models of a maritime inventory routing problem. Comput. Chem. Eng. 77, 147–161 (2015)CrossRefGoogle Scholar
  32. 32.
    Munguía, L.M., Ahmed, S., Bader, D.A., Nemhauser, G.L., Shao, Y.: Alternating criteria search: a parallel large neighborhood search algorithm for mixed integer programs. Submitted for publication (2016)Google Scholar
  33. 33.
    Mutlu, F., Msakni, M.K., Yildiz, H., Snmez, E., Pokharel, S.: A comprehensive annual delivery program for upstream liquefied natural gas supply chain. Eur. J. Oper. Res. (2015)Google Scholar
  34. 34.
    Papageorgiou, D.J., Cheon, M.S., Nemhauser, G., Sokol, J.: Approximate dynamic programming for a class of long-horizon maritime inventory routing problems. Transp. Sci. 49(4), 870–885 (2014)CrossRefGoogle Scholar
  35. 35.
    Papageorgiou, D.J., Keha, A.B., Nemhauser, G.L., Sokol, J.: Two-stage decomposition algorithms for single product maritime inventory routing. INFORMS J. Comput. 26(4), 825–847 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Papageorgiou, D.J., Nemhauser, G.L., Sokol, J., Cheon, M.S., Keha, A.B.: MIRPLib—a library of maritime inventory routing problem instances: survey, core model, and benchmark results. Eur. J. Oper. Res. 235(2), 350–366 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Rakke, J.G., Andersson, H., Christiansen, M., Desaulniers, G.: A new formulation based on customer delivery patterns for a maritime inventory routing problem. Transp. Sci. 49(2), 384–401 (2014)CrossRefGoogle Scholar
  38. 38.
    Rakke, J.G., Stålhane, M., Moe, C.R., Christiansen, M., Andersson, H., Fagerholt, K., Norstad, I.: A rolling horizon heuristic for creating a liquefied natural gas annual delivery program. Transp. Res. Part C: Emerg. Technol. 19(5), 896–911 (2011)CrossRefGoogle Scholar
  39. 39.
    Rothberg, E.: An evolutionary algorithm for polishing mixed integer programming solutions. INFORMS J. Comput. 19(4), 534–541 (2007)CrossRefzbMATHGoogle Scholar
  40. 40.
    Savelsbergh, M.W.P., Song, J.: An optimization algorithm for the inventory routing problem with continuous moves. Comput. Oper. Res. 35(7), 2266–2282 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Shao, Y., Furman, K.C., Goel, V., Hoda, S.: A hybrid heuristic strategy for liquefied natural gas inventory routing. Transp. Res. Part C: Emerg. Technol. 53, 151–171 (2015)CrossRefGoogle Scholar
  42. 42.
    Song, J.H., Furman, K.C.: A maritime inventory routing problem: practical approach. Comput. Oper. Res. 40(3), 657–665 (2013)CrossRefzbMATHGoogle Scholar
  43. 43.
    Stålhane, M., Rakke, J.G., Moe, C.R., Andersson, H., Christiansen, M., Fagerholt, K.: A construction and improvement heuristic for a liquefied natural gas inventory routing problem. Comput. Ind. Eng. 62(1), 245–255 (2012)CrossRefGoogle Scholar
  44. 44.
    Topaloglu, H.: A parallelizable dynamic fleet management model with random travel times. Eur. J. Oper. Res. 175(2), 782–805 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Topaloglu, H., Powell, W.B.: Dynamic-programming approximations for stochastic time-staged integer multicommodity-flow problems. INFORMS J. Comput. 18(1), 31–42 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Toriello, A., Nemhauser, G.L., Savelsbergh, M.W.P.: Decomposing inventory routing problems with approximate value functions. Naval Res. Logist. 57(8), 718–727 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Uggen, K., Fodstad, M., Nørstebø, V.: Using and extending fix-and-relax to solve maritime inventory routing problems. TOP 21(2), 355–377 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    UNCTAD: Review of Maritime Transport United Nations, New York and Geneva (2015)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Dimitri J. Papageorgiou
    • 1
    Email author
  • Myun-Seok Cheon
    • 1
  • Stuart Harwood
    • 1
  • Francisco Trespalacios
    • 1
  • George L. Nemhauser
    • 2
  1. 1.Corporate Strategic Research, ExxonMobil Research and Engineering CompanyAnnandaleUSA
  2. 2.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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