# An entropy based solid transportation problem in uncertain environment

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## Abstract

The uncertain solid transportation problem considers material dispatching with uncertain elements like demands. Now, it plays an increasingly important role in logistics managements. Traditionally, the transportation cost is used as the optimization objective, while the dispersals of trips between origins and destinations are usually neglected. In order to minimize the transportation penalties and ensure uniform distribution of goods between origins and destinations, this paper employs entropy function of dispersals of trips between origins and destinations as a second objective function. Within the framework of uncertainty theory, the uncertain entropy based solid transportation model is transformed into its deterministic equivalent, which can be solved by general optimization methods. Finally, a numerical example is given for illustrating purpose.

## Keywords

Solid transportation problem Entropy function Uncertain variable Expected value## Notes

### Acknowledgements

This study was funded by Henan Soft Science Research Program under Grant no. 172400410168.

## References

- Chen H, Wang X, Liu Z, Zhao R (2017) Impact of risk levels on optimal selling to heterogeneous retailers under dual uncertainties. J Ambient Intell Hum Comput. doi: 10.1007/s12652-017-0481-9 Google Scholar
- Chen X, Gao J (2013) Uncertain term structure model of interest rate. Soft Comput 17(4):597–604CrossRefzbMATHGoogle Scholar
- Cui Q, Sheng Y (2013) Uncertain programming model for solid transportation problem. Inf Int Interdiscip J 16(2):1207–1214MathSciNetGoogle Scholar
- Das A, Bera U (2015) A bi-objective solid transportation model under uncertain environment. Facets of uncertainties and applications. Springer, IndiazbMATHGoogle Scholar
- Gao J, Yao K (2015) Some concepts and theorems of uncertain random process. Int J Intell Syst 30(1):52–65CrossRefGoogle Scholar
- Gao J, Yang X, Liu D (2017) Uncertain Shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput 56:551–556CrossRefGoogle Scholar
- Guo C, Gao J (2017) Optimal dealer pricing under transaction uncertainty. J Intell Manuf 28(3):657–665CrossRefGoogle Scholar
- Haley K (1962) The solid transportation problem. Oper Res Int J 10(4):448–464zbMATHGoogle Scholar
- Liu B (2007) Uncertainty theory, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
- Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10Google Scholar
- Liu B (2009) Theory and practice of uncertain programming, 2nd edn. Springer, BerlinCrossRefzbMATHGoogle Scholar
- Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, BerlinCrossRefGoogle Scholar
- Liu B (2012) Why is there a need for uncertainty theory? J Uncertain Syst 6(1):3–10Google Scholar
- Liu B (2013) Toward uncertain finance theory. J Uncertain Anal Appl 1:1CrossRefGoogle Scholar
- Liu Y, Yao K (2017) Uncertain random logic and uncertain random entailment. J Ambient Intell Hum Comput. doi: 10.1007/s12652-017-0465-9 Google Scholar
- Xiao C, Zhang Y, Fu Z (2016) Valuing interest rate swap contracts in uncertain financial market. Sustainability 8(11):1186–1196CrossRefGoogle Scholar
- Yang X, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertain Anal Appl 1:17CrossRefGoogle Scholar
- Yang X, Gao J (2016) Linear-quadratic uncertain differential games with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819–826MathSciNetCrossRefGoogle Scholar
- Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf 28(3):515–525CrossRefGoogle Scholar
- Yang X, Ni Y (2017) Existence and uniqueness theorem for uncertain heat equation. J Ambient Intell Hum Comput. doi: 10.1007/s12652-017-0479-3 Google Scholar
- Yao K, Gao J, Gao Y (2013) Some stability theorems of uncertain differential equation. Fuzzy Optim Decis Mak 12(1):3–13MathSciNetCrossRefGoogle Scholar
- Yao K, Gao J (2015) Uncertain random alternating renewal process with application to interval availability. IEEE Trans Fuzzy Syst 23(5):1333–1342CrossRefGoogle Scholar
- Yao K, Liu B (2017) Uncertain regression analysis: an approach for imprecise observations. Soft Comput. doi: 10.1007/s00500-017-2521-y zbMATHGoogle Scholar
- Zhang B, Peng J, Chen L (2016) Fixed charge solid transportation problem in uncertain environment and its algorithm. Comput Ind Eng 102:186–197CrossRefGoogle Scholar
- Zhang Y, Gao J, Fu Z (2017) Valuing currency swap contracts in uncertain financial market. Fuzzy Optim Decis Mak
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