Skip to main content
Top
Published in: Soft Computing 17/2018

12-07-2017 | Focus

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

Authors: Liying Liu, Bo Zhang, Weimin Ma

Published in: Soft Computing | Issue 17/2018

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
go back to reference Bhatia H, Swarup K, Puri M (1976) Time minimizing solid transportation problem. Math Oper Stat 7:395–403MathSciNetMATH Bhatia H, Swarup K, Puri M (1976) Time minimizing solid transportation problem. Math Oper Stat 7:395–403MathSciNetMATH
go back to reference Chen X, Gao J (2013) Uncertain term structure model of interest rate. Soft Comput 17(4):597–604CrossRefMATH Chen X, Gao J (2013) Uncertain term structure model of interest rate. Soft Comput 17(4):597–604CrossRefMATH
go back to reference Cui Q, Sheng Y (2012) Uncertain programming model for solid transportation problem. Information 15(12):342–348 Cui Q, Sheng Y (2012) Uncertain programming model for solid transportation problem. Information 15(12):342–348
go back to reference Gao R (2016) Milne method for solving uncertain differential equations. Appl Math Comput 11(274):774–785MathSciNet Gao R (2016) Milne method for solving uncertain differential equations. Appl Math Comput 11(274):774–785MathSciNet
go back to reference Gao J, Yao K (2015) Some concepts and theorems of uncertain random process. Int J Intell Syst 30(1):52–65CrossRef Gao J, Yao K (2015) Some concepts and theorems of uncertain random process. Int J Intell Syst 30(1):52–65CrossRef
go back to reference Guo C, Gao J (2017) Optimal dealer pricing under transaction uncertainty. J Intell Manuf 28(3):657–665CrossRef Guo C, Gao J (2017) Optimal dealer pricing under transaction uncertainty. J Intell Manuf 28(3):657–665CrossRef
go back to reference 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):159–181MathSciNetCrossRef 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):159–181MathSciNetCrossRef
go back to reference Gao Y, Yang L, Li S (2016) Uncertain models on railway transportation planning problem. Appl Math Model 40:4921–4934MathSciNetCrossRef Gao Y, Yang L, Li S (2016) Uncertain models on railway transportation planning problem. Appl Math Model 40:4921–4934MathSciNetCrossRef
go back to reference Gao J, Yang X, Liu D (2017) Uncertain Shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput 56:551–556CrossRef Gao J, Yang X, Liu D (2017) Uncertain Shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput 56:551–556CrossRef
go back to reference Haley K (1962) The solid transportation problem. Oper Res 11:446–448MATH Haley K (1962) The solid transportation problem. Oper Res 11:446–448MATH
go back to reference Kennington J, Unger V (1976) A new branch and bound algorithm for the fixed charge transportation problem. Manag Sci 22:1116–1126MathSciNetCrossRefMATH Kennington J, Unger V (1976) A new branch and bound algorithm for the fixed charge transportation problem. Manag Sci 22:1116–1126MathSciNetCrossRefMATH
go back to reference Li X, Qin Z (2014) Interval portfolio selection models within the framework of uncertainty theory. Econ Model 41:338–344CrossRef Li X, Qin Z (2014) Interval portfolio selection models within the framework of uncertainty theory. Econ Model 41:338–344CrossRef
go back to reference Li Y, Ida K, Gen M, Kobuchi R (1997) Neural network approach for multicriteria solid transportation problem. Comput Ind Eng 33(3–4):465–468CrossRef Li Y, Ida K, Gen M, Kobuchi R (1997) Neural network approach for multicriteria solid transportation problem. Comput Ind Eng 33(3–4):465–468CrossRef
go back to reference Liu B (2008) Fuzzy process: hybrid process and uncertain process. J Uncertain Syst 2(1):3–16 Liu B (2008) Fuzzy process: hybrid process and uncertain process. J Uncertain Syst 2(1):3–16
go back to reference Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10 Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10
go back to reference Liu B (2010) Uncertain set theory and uncertain inference rule with application to uncertain control. J Uncertain Syst 4(2):83–98 Liu B (2010) Uncertain set theory and uncertain inference rule with application to uncertain control. J Uncertain Syst 4(2):83–98
go back to reference Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, BerlinCrossRef Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, BerlinCrossRef
go back to reference Lotif MM, Moghaddam RT (2013) A genetic algorithm using priority-based encoding with new operators for fixed charge transportation problems. Appl Soft Comput 13:2711–2722CrossRef Lotif MM, Moghaddam RT (2013) A genetic algorithm using priority-based encoding with new operators for fixed charge transportation problems. Appl Soft Comput 13:2711–2722CrossRef
go back to reference 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 10:100–110CrossRef 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 10:100–110CrossRef
go back to reference Romeijna HE, Sargutb FZ (2011) The stochastic transportation problem with single sourcing. Eur J Oper Res 214(2):262–272MathSciNetCrossRef Romeijna HE, Sargutb FZ (2011) The stochastic transportation problem with single sourcing. Eur J Oper Res 214(2):262–272MathSciNetCrossRef
go back to reference Sheng Y, Yao K (2012) Fixed charge transportation problem and its uncertain programming model. Ind Eng Manag Syst 11(2):183–187 Sheng Y, Yao K (2012) Fixed charge transportation problem and its uncertain programming model. Ind Eng Manag Syst 11(2):183–187
go back to reference Sheng Y, Gao Y (2016) Shortest path problem of uncertain random network. Comput and Ind Eng 99:97–105CrossRef Sheng Y, Gao Y (2016) Shortest path problem of uncertain random network. Comput and Ind Eng 99:97–105CrossRef
go back to reference Sun M, Aronson JE, McKeown PG, Drinka D (1998) A tabu search heuristic procedure for the fixed charge transportation problem. Eur J Oper Res 106:441–456CrossRefMATH Sun M, Aronson JE, McKeown PG, Drinka D (1998) A tabu search heuristic procedure for the fixed charge transportation problem. Eur J Oper Res 106:441–456CrossRefMATH
go back to reference Wang X, Ning Y, Moughal T, Chen X (2015) Adams–Simpson method for solving uncertain differential equations. Appl Math Comput 271:209–219MathSciNet Wang X, Ning Y, Moughal T, Chen X (2015) Adams–Simpson method for solving uncertain differential equations. Appl Math Comput 271:209–219MathSciNet
go back to reference Williams A (1963) A stochastic transportation problem. Oper Res 11:759–770 Williams A (1963) A stochastic transportation problem. Oper Res 11:759–770
go back to reference Yang L, Feng Y (2007) A bicriteria solid transportation problem with fixed charge under stochastic environment. Appl Math Model 31:2668–2683CrossRefMATH Yang L, Feng Y (2007) A bicriteria solid transportation problem with fixed charge under stochastic environment. Appl Math Model 31:2668–2683CrossRefMATH
go back to reference Yang X, Gao J (2013) Uncertain differential games with applicatians to capitalism. J Uncertain Anal Appl l: Article 17 Yang X, Gao J (2013) Uncertain differential games with applicatians to capitalism. J Uncertain Anal Appl l: Article 17
go back to reference Yang X, Ralescu D (2015) Adams method for solving uncertain differential equations. Appl Math Comput 270:993–1003MathSciNet Yang X, Ralescu D (2015) Adams method for solving uncertain differential equations. Appl Math Comput 270:993–1003MathSciNet
go back to reference Yang X, Shen Y (2015) Runge-Kutta method for solving uncertain differential equations. J Uncertain Anal Appl 3 (Article 17) Yang X, Shen Y (2015) Runge-Kutta method for solving uncertain differential equations. J Uncertain Anal Appl 3 (Article 17)
go back to reference Yang X, Gao J (2016) Linear-quadratic uncertain differential games with applicatians to resource extraction problem. IEEE T Fuzzy Syst 24(4):819–826CrossRef Yang X, Gao J (2016) Linear-quadratic uncertain differential games with applicatians to resource extraction problem. IEEE T Fuzzy Syst 24(4):819–826CrossRef
go back to reference Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf 28(3):515–525CrossRef Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf 28(3):515–525CrossRef
go back to reference Yao K (2013) Extreme values and integral of solution of uncertain differential equation. J Uncertain Anal Appl 1: Article 2 Yao K (2013) Extreme values and integral of solution of uncertain differential equation. J Uncertain Anal Appl 1: Article 2
go back to reference Yao K (2015) Inclusion relationship of uncertain sets. J Uncertain Anal Appl 3: Article 13 Yao K (2015) Inclusion relationship of uncertain sets. J Uncertain Anal Appl 3: Article 13
go back to reference Yao K, Chen X (2013) A numerical method for solving uncertain differential equations. J Intell Fuzzy Syst 25(3):825–832MathSciNetMATH Yao K, Chen X (2013) A numerical method for solving uncertain differential equations. J Intell Fuzzy Syst 25(3):825–832MathSciNetMATH
go back to reference 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):186–197CrossRef 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):186–197CrossRef
Metadata
Title
Uncertain programming models for fixed charge multi-item solid transportation problem
Authors
Liying Liu
Bo Zhang
Weimin Ma
Publication date
12-07-2017
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 17/2018
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-017-2718-0

Other articles of this Issue 17/2018

Soft Computing 17/2018 Go to the issue

Premium Partner