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Chance constrained programming models for uncertain hub covering location problems

  • Junbin Wang
  • Zhongfeng QinEmail author
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Abstract

Hub covering location problem is a typical strategic decision with the purpose of locating hubs and determining the assignments of other nodes to ensure the travel time is not exceeding a specific threshold. Since the parameters such as flows and travel times are difficult to be precisely obtained in advance, a feasible way is to estimate them following the experts’ subjective beliefs. Hence, this paper is devoted to study hub covering location problem by using uncertain measure to characterize the subjective belief and considering the flows and travel times by uncertain variables. The uncertain hub set covering location problem is first discussed under the purpose of covering the flows entirely with the minimum setup cost of hubs. Then the uncertain hub maximal covering problem is studied by maximizing the total flow covered when the number of hubs is confirmed previously. Chance constrained programming models for both problems are constructed, respectively, and their corresponding deterministic forms are derived. A hybrid intelligence algorithm named GA–VNS is proposed by combing the variable neighborhood search with the genetic algorithm. Finally, several numerical experiments are presented to indicate the efficiency of GA–VNS.

Keywords

Hub covering location problem Chance constrained programming Uncertain variable 

Notes

Acknowledgements

This work was supported in part by National Natural Science Foundation of China (No. 71771011).

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Calik H, Alumur SA, Kara BY, Karasan OE (2009) A tabu-search based heuristic for the hub covering problem over incomplete hub networks. Comput Oper Res 36(12):3088–3096CrossRefGoogle Scholar
  2. Campbell JF (1994) Integer programming formulations of discrete hub location problems. Eur J Oper Res 72(2):387–405CrossRefGoogle Scholar
  3. Castelli M, Vanneschi L (2014) Genetic algorithm with variable neighborhood search for the optimal allocation of goods in shop shelves. Oper Res Lett 42(5):355–360MathSciNetCrossRefGoogle Scholar
  4. Chanta S, Sangsawang O (2018) A single allocation p-hub maximal covering model for optimizing railway station location. In: International conference on intelligent computing & optimization. Springer, Cham, pp 522–530Google Scholar
  5. Correia I, Nickel S, Saldanha-da-Gama F (2018) A stochastic multi-period capacitated multiple allocation hub location problem: Formulation and inequalities. Omega 74:122–134CrossRefGoogle Scholar
  6. Dib O, Manier MA, Moalic L, Caminada A (2017) Combining VNS with genetic algorithm to solve the one-to-one routing issue in road networks. Comput Oper Res 78:420–430MathSciNetCrossRefGoogle Scholar
  7. Ernst AT, Jiang H, Krishanmoorthy M, Baatar D (2018) Reformulations and computational results for the uncapacitated single allocation hub covering problem. Data and decision sciences in action. Springer, Cham, pp 133–148Google Scholar
  8. Gao Y, Qin Z (2016) A chance constrained programming approach for uncertain p-hub center location problem. Comput Ind Eng 102:10–20CrossRefGoogle Scholar
  9. Hwang YH, Lee YH (2012) Uncapacitated single allocation p-hub maximal covering problem. Comput Ind Eng 63(2):382–389CrossRefGoogle Scholar
  10. Jankovic O, Miskovic S, Stanimirovic Z, Todosijevic R (2017) Novel formulations and VNS-based heuristics for single and multiple allocation p-hub maximal covering problems. Ann Oper Res 259(1–2):191–216MathSciNetCrossRefGoogle Scholar
  11. Kara BY, Tansel BC (2003) The single-assignment hub covering problem: Models and linearizations. J Oper Res Soc 54(1):59–64CrossRefGoogle Scholar
  12. Kara BY, Alumur S (2009) A hub covering network design problem for cargo applications in Turkey. J Oper Res Soc 60(10):1349–1359CrossRefGoogle Scholar
  13. Karimi H (2018) The capacitated hub covering location-routing problem for simultaneous pickup and delivery systems. Comput Ind Eng 116:47–58CrossRefGoogle Scholar
  14. Liu B (2007) Uncertainty theory. Springer, BerlinCrossRefGoogle Scholar
  15. Liu B (2009) Theory and practice of uncertain programming. Springer, BerlinCrossRefGoogle Scholar
  16. Lowe TJ, Sim T (2013) The hub covering flow problem. J Oper Res Soc 64(7):973–981CrossRefGoogle Scholar
  17. Mohammadi M, Jolai F, Tavakkoli-Moghaddam R (2013) Solving a new stochastic multi-mode p-hub covering location problem considering risk by a novel multi-objective algorithm. Appl Math Model 37(24):10053–10073MathSciNetCrossRefGoogle Scholar
  18. Peker M, Kara BY (2015) The p-hub maximal covering problem and extensions for gradual decay functions. Omega 54:158–172CrossRefGoogle Scholar
  19. Qin Z, Gao Y (2017) Uncapacitated p-hub location problem with fixed costs and uncertain flows. J Intell Manuf 28(3):705–716CrossRefGoogle Scholar
  20. Silva MR, Cunha CB (2017) A tabu search heuristic for the uncapacitated single allocation p-hub maximal covering problem. Eur J Oper Res 262(3):954–965MathSciNetCrossRefGoogle Scholar
  21. Tan PZ, Kara BY (2007) A hub covering model for cargo delivery systems. Networks 49(1):28–39MathSciNetCrossRefGoogle Scholar
  22. Yaman H (2011) Allocation strategies in hub networks. Eur J Oper Res 211(3):442–451MathSciNetCrossRefGoogle Scholar
  23. Yang TH (2009) Stochastic air freight hub location and flight routes planning. Appl Math Model 33(12):4424–4430CrossRefGoogle Scholar
  24. Yang K, Liu Y, Yang G (2013) Solving fuzzy p-hub center problem by genetic algorithm incorporating local search. Appl Soft Comput 13:2624–2632CrossRefGoogle Scholar
  25. Yang X, Liu B (2019) Uncertain time series analysis with imprecise observations. Fuzzy Optim Decis Making 18(3):263–278MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Economics and ManagementBeihang UniversityBeijingChina

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