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A capacitated facility location and inventory management problem with single sourcing

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Abstract

The current paper addresses the integrated location and inventory problem with capacity constraints. Adopting more realistic assumptions comes at the cost of increased complexity and inability to solve the model with existing methods, mainly due to the non-linear terms that arise. We attempt to render the extended formulation solvable by linearizing its non-linear terms. Certain terms are replaced by exact reformulations while for the rest a piecewise linearization is implemented. The contribution of this work is not only the development of a formulation that is more practical, but also the reformulation that enables its solving with commercial software. We test our proposed approach on a benchmark dataset from the literature, including both small and large instances of the problem. Results clearly demonstrate the superiority of this approach in terms of both solution quality and computational time.

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References

  1. Daskin, M., Coullard, C., Shen, Z.-J.: An inventory-location model: formulation, solution algorithm and computational results. Ann. Oper. Res. 110(1–4), 83–106 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Diabat, A.: Hybrid algorithm for a vendor managed inventory system in a two-echelon supply chain. Eur. J. Oper. Res. 238(1),114–121 (2014)

  3. Diabat, A., Abdallah, T., Henschel, A.: A closed-loop location-inventory problem with spare parts consideration. Comput. Oper. Res. 54, 245–256 (2015)

    Article  MathSciNet  Google Scholar 

  4. Diabat, A., Abdallah, T., Le, T.: A hybrid tabu search based heuristic for the periodic distribution inventory problem with perishable goods. Ann. Oper. Res. (2014). doi:10.1007/s10479-014-1640-4

    MathSciNet  Google Scholar 

  5. Diabat, A., Aouam, T., Ozsen, L.: An evolutionary programming approach for solving the capacitated facility location problem with risk pooling. Int. J. Appl. Dec. Sci. 2(4), 389–405 (2009)

    Google Scholar 

  6. Diabat, A., Battaïa, O., Nazzal, D.: An improved lagrangian relaxation-based heuristic for a joint location-inventory problem. Comput. Oper. Res. 61, 170–178 (2015)

  7. Diabat, A., Deskoores, R.M.: A hybrid genetic algorithm based heuristic for an integrated supply chain problem. J. Manufact. Syst. (2015). doi:10.1016/j.jmsy.2015.04.011

  8. Diabat, A., Richard, J.-P.: An integrated supply chain problem: a nested Lagrangian relaxation approach. Ann. Oper. Res. 229(1), 303–323 (2015)

  9. Diabat, A., Richard, J.-P., Codrington, C.: A Lagrangian relaxation approach to simultaneous strategic and tactical planning in supply chain design. Ann. Oper. Res. 203(1), 55–80 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Diabat, A., Theodorou, E.: A location-inventory supply chain problem: reformulation and piecewise linearization. Comput. Ind. Eng. 90, 381–389 (2015)

  11. Dolgui, A., Proth, J.-M.: Supply Chain Engineering: Useful Methods and Techniques. Springer, New York (2010)

    Book  Google Scholar 

  12. Jayaraman, V., Ross, A.: A simulated annealing methodology to distribution network design and management. Eur. J. Oper. Res. 144(3), 629–645 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kallrath, J., Rebennack, S.: Computing area-tight piecewise linear overestimators, underestimators and tubes for univariate functions. In: Optimization in Science and Engineering. Springer, New York, pp. 273–292 (2014)

  14. Le, T., Diabat, A., Richard, J.-P., Yih, Y.: A column generation-based heuristic algorithm for an inventory routing problem with perishable goods. Optim. Lett. 7(7), 1481–1502 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ozsen, L., Coullard, C.R., Daskin, M.S.: Capacitated DC location model with risk pooling. Naval Res. Log. (NRL) 55(4), 295–312 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Rebennack, S., Kallrath, J.: Continuous piecewise linear \(\delta \)-approximations for MINLP problems. I. Minimal breakpoint systems for univariate functions . Tech. Rep., Colorado School of Mines, Division of Economics and Business. Working paper series 2012-12 (2012)

  17. Rebennack, S., Kallrath, J.: Continuous Piecewise Linear \(\delta \)-Approximations for MINLP Problems. II, Bivariate and Multivariate Functions. Tech. Rep., Colorado School of Mines, Division of Economics and Business. Working paper series 2012-13 (2012)

  18. Roundy, R.: 98%-Effective Integer-Ratio Lot-Sizing for One-DC Multi-Retailer Systems. Manag. Sci. 31(11), 1416–1430 (1985)

    Article  MATH  Google Scholar 

  19. Shen, Z.-J.M., Coullard, C., Daskin, M.S.: A joint location-inventory model. Transp. Sci. 37(1), 40–55 (2003)

    Article  Google Scholar 

  20. Shu, J.: An efficient Greedy Heuristic for DC-retailer network design optimization. Transp. Sci. 44(2), 183–192 (2010)

    Article  Google Scholar 

  21. Simchi-Levi, D., Kaminsky, P., Simchi-Levi, E.: Designing and managing the supply chain: concepts, strategies, and case studies. Mc-Graw-Hill, New York (2003)

  22. Teo, C.-P., Shu, J.: DC-retailer network design problem. Oper. Res. 52(3), 396–408 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  23. Vidyarthi, N., Çelebi, E., Elhedhli, S., Jewkes, E.: Integrated production-inventory-distribution system design with risk pooling: model formulation and heuristic solution. Transp. Sci. 41(3), 392–408 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Systems and Management, Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates

    Ali Diabat

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  1. Ali Diabat
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Correspondence to Ali Diabat.

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Diabat, A. A capacitated facility location and inventory management problem with single sourcing. Optim Lett 10, 1577–1592 (2016). https://doi.org/10.1007/s11590-015-0950-z

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  • DOI: https://doi.org/10.1007/s11590-015-0950-z

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