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Uncertain programming models for fixed charge multi-item solid transportation problem

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Abstract

This paper investigates the fixed charge multi-item solid transportation problem, in which the fixed charges, direct costs, transportation capacities, supply and demand are uncertain variables. Based on the uncertainty theory, expected value programming model and chance-constrained programming model for fixed charge multi-item solid transportation problem are constructed, respectively. We can obtain the optimal solution of two models via solving the relevant deterministic models. Finally, a numerical experiment is implemented to illustrate the application of the models.

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References

  • Bhatia H, Swarup K, Puri M (1976) Time minimizing solid transportation problem. Math Oper Stat 7:395–403

    MathSciNet  MATH  Google Scholar 

  • Chen X, Liu B (2010) Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optim Decis Mak 9(1):69–81

    Article  MathSciNet  MATH  Google Scholar 

  • Chen X, Gao J (2013) Uncertain term structure model of interest rate. Soft Comput 17(4):597–604

    Article  MATH  Google Scholar 

  • Chen B, Liu Y, Zhou T (2017) An entropy based solid transportation problem in uncertain environment. J Ambient Intell Humaniz Comput. doi:10.1007/s12652-017-0535-z

  • Cui Q, Sheng Y (2012) Uncertain programming model for solid transportation problem. Information 15(12):342–348

    Google Scholar 

  • Dalman H (2017) Uncertain programming model for multi-item solid transportation problem. Int J Mach Leant Cybern. doi:10.1007/s13042-016-0538-7

  • Gao R (2016) Milne method for solving uncertain differential equations. Appl Math Comput 11(274):774–785

    MathSciNet  Google Scholar 

  • Gao J, Yao K (2015) Some concepts and theorems of uncertain random process. Int J Intell Syst 30(1):52–65

    Article  Google Scholar 

  • Guo C, Gao J (2017) Optimal dealer pricing under transaction uncertainty. J Intell Manuf 28(3):657–665

    Article  Google Scholar 

  • Gao X, Gao Y, Ralescu D (2010) On Liu’s inference rule for uncertain systems. Int J Uncertain Fuzz 18(1):1–11

    Article  MathSciNet  MATH  Google Scholar 

  • Gao R, Sun Y, Ralescu D (2016) Order statistics of uncertain random variables with application to k-out-of-n system. Fuzzy Optim Decis Mak 16(2):159–181

    Article  MathSciNet  Google Scholar 

  • Gao Y, Yang L, Li S (2016) Uncertain models on railway transportation planning problem. Appl Math Model 40:4921–4934

    Article  MathSciNet  Google Scholar 

  • Gao J, Yang X, Liu D (2017) Uncertain Shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput 56:551–556

    Article  Google Scholar 

  • Haley K (1962) The solid transportation problem. Oper Res 11:446–448

    MATH  Google Scholar 

  • Hirsch W, Dantzig G (1968) The fixed charge problem. Naval Res Logist Quart 15:413–424

    Article  MathSciNet  MATH  Google Scholar 

  • Kennington J, Unger V (1976) A new branch and bound algorithm for the fixed charge transportation problem. Manag Sci 22:1116–1126

    Article  MathSciNet  MATH  Google Scholar 

  • Li X, Qin Z (2014) Interval portfolio selection models within the framework of uncertainty theory. Econ Model 41:338–344

    Article  Google Scholar 

  • Li Y, Ida K, Gen M, Kobuchi R (1997) Neural network approach for multicriteria solid transportation problem. Comput Ind Eng 33(3–4):465–468

    Article  Google Scholar 

  • Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  • Liu B (2008) Fuzzy process: hybrid process and uncertain process. J Uncertain Syst 2(1):3–16

    Google Scholar 

  • Liu B (2009) Theory and practice of uncertain programming, 2nd edn. Springer, Berlin

    Book  MATH  Google Scholar 

  • Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10

    Google Scholar 

  • Liu B (2010) Uncertain set theory and uncertain inference rule with application to uncertain control. J Uncertain Syst 4(2):83–98

    Google Scholar 

  • Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin

    Book  Google Scholar 

  • Lotif MM, Moghaddam RT (2013) A genetic algorithm using priority-based encoding with new operators for fixed charge transportation problems. Appl Soft Comput 13:2711–2722

    Article  Google Scholar 

  • Ojha A, Das B, Mondal S, Maiti M (2010) A solid transportation problem for an item with fixed charge vechicle cost and price discounted varying charge using genetic algorithm. Appl Soft Comput 10:100–110

    Article  Google Scholar 

  • Romeijna HE, Sargutb FZ (2011) The stochastic transportation problem with single sourcing. Eur J Oper Res 214(2):262–272

    Article  MathSciNet  Google Scholar 

  • Sheng Y, Yao K (2012) Fixed charge transportation problem and its uncertain programming model. Ind Eng Manag Syst 11(2):183–187

  • Sheng Y, Gao Y (2016) Shortest path problem of uncertain random network. Comput and Ind Eng 99:97–105

    Article  Google Scholar 

  • Sun M, Aronson JE, McKeown PG, Drinka D (1998) A tabu search heuristic procedure for the fixed charge transportation problem. Eur J Oper Res 106:441–456

    Article  MATH  Google Scholar 

  • Wang X, Ning Y, Moughal T, Chen X (2015) Adams–Simpson method for solving uncertain differential equations. Appl Math Comput 271:209–219

    MathSciNet  Google Scholar 

  • Williams A (1963) A stochastic transportation problem. Oper Res 11:759–770

  • Yang L, Feng Y (2007) A bicriteria solid transportation problem with fixed charge under stochastic environment. Appl Math Model 31:2668–2683

    Article  MATH  Google Scholar 

  • Yang X, Gao J (2013) Uncertain differential games with applicatians to capitalism. J Uncertain Anal Appl l: Article 17

  • Yang X, Ralescu D (2015) Adams method for solving uncertain differential equations. Appl Math Comput 270:993–1003

    MathSciNet  Google Scholar 

  • Yang X, Shen Y (2015) Runge-Kutta method for solving uncertain differential equations. J Uncertain Anal Appl 3 (Article 17)

  • Yang X, Gao J (2016) Linear-quadratic uncertain differential games with applicatians to resource extraction problem. IEEE T Fuzzy Syst 24(4):819–826

    Article  Google Scholar 

  • Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf 28(3):515–525

    Article  Google Scholar 

  • Yao K (2013) Extreme values and integral of solution of uncertain differential equation. J Uncertain Anal Appl 1: Article 2

  • Yao K (2015) Inclusion relationship of uncertain sets. J Uncertain Anal Appl 3: Article 13

  • Yao K, Chen X (2013) A numerical method for solving uncertain differential equations. J Intell Fuzzy Syst 25(3):825–832

    MathSciNet  MATH  Google Scholar 

  • Zhang B, Peng J, Li S, Chen L (2016) Fixed charge solid transportation Pproblem in uncertain environment and its algorithm. Comput Ind Eng 102(2016):186–197

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Natural Science Foundation of China (No. 11626234), the Hubei Provincial Natural Science Foundation (No. 2016CFB308), the Higher Educational Science and Technology Program Foundation of Shandong Province (No. J13LI10), and the Foundation of Liaocheng University (No. 318011303).

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Authors and Affiliations

  1. School of Economics and Management, Tongji University, Shanghai, 200092, China

    Liying Liu & Weimin Ma

  2. School of Mathematics Science, Liaocheng University, Liaocheng, 252059, China

    Liying Liu

  3. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China

    Bo Zhang

Authors
  1. Liying Liu
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  2. Bo Zhang
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  3. Weimin Ma
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Correspondence to Liying Liu.

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

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Communicated by Y. Ni.

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Liu, L., Zhang, B. & Ma, W. Uncertain programming models for fixed charge multi-item solid transportation problem. Soft Comput 22, 5825–5833 (2018). https://doi.org/10.1007/s00500-017-2718-0

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