Abstract
This paper focuses on modeling and optimization of entropy-based uncertain multi-item solid transportation problems (MISTPs), in which direct costs, supplies, demands, conveyance capacities are uncertain nature. The purpose is to minimize the total uncertain cost via maximum entropy which ensures uniform delivery of products from sources to destinations through conveyances. The expected value programming and expected constrained programming models for optimizing the entropy-based uncertain MISTPs are constructed. These models are based on uncertainty theory. Subsequently, the constructed models are converted into their deterministic equivalences which are solved using two known mathematical programming methods. Finally, a numerical example is given to illustrate the models.
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References
Bhatia HL, Swarup K, Puri MC (1976) Time minimizing solid transportation problem. Stat J Theor Appl Stat 7(3):395–403
Chen X, Dai W (2011) Maximum entropy principle for uncertain variables. Int J Fuzzy Syst 13(3):232–236
Chen L, Peng J, Zhang B (2017) Uncertain goal programming models for bicriteria solid transportation problem. Appl Soft Comput 51:49–59
Chen B, Liu Y, Zhou T (2017) An entropy based solid transportation problem in uncertain environment. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-017-0535-z
Chen L, Peng J, Zhang B, Li S (2017) Uncertain programming model for uncertain minimum weight vertex covering problem. J Intell Manuf 28(3):625–632
Chen L, Peng J, Ralescu DA (2017) Uncertain vertex coloring problem. Soft Comput. https://doi.org/10.1007/s00500-017-2861-7
Cheng L, Rao C, Chen L (2017) Multidimensional knapsack problem based on uncertain measure. Sci Iran Trans E Ind Eng 24(5):2527–2539
Cui Q, Sheng Y (2013) Uncertain programming model for solid transportation problem. Int Inf Inst (Tokyo) Inf 16(2):1207
Dai W, Chen X (2012) Entropy of function of uncertain variables. Math Comput Model 55(3):754–760
Dalman H (2016) Uncertain programming model for multi-item solid transportation problem. Int J Mach Learn Cybern 9(4):559–567
Dalman H, Bayram M (2017) Interactive fuzzy goal programming based on Taylor series to solve multiobjective nonlinear programming problems with interval type 2 fuzzy numbers. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2017.2774191
Dalman H, Sivri M (2017) Multi-objective solid transportation problem in uncertain environment. Iran J Sci Technol Trans A Sci 41(2):505–514
Dalman H, Güzel N, Sivri M (2016) A fuzzy set-based approach to multi-objective multi-item solid transportation problem under uncertainty. Int J Fuzzy Syst 18(4):716–729
Ding S (2014) Uncertain minimum cost flow problem. Soft Comput 18(11):2201–2207
Gao J, Yang X, Liu D (2017) Uncertain Shapley value of coalitional game with application to supply chain alliance. Appl Soft Comput 56:551556
Guo C, Gao J (2017) Optimal dealer pricing under transaction uncertainty. J Intell Manuf 28(3):657665
Haley KB (1962) New methods in mathematical programming—the solid transportation problem. Oper Res 10(4):448–463
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
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2009) Theory and practice of uncertain programming, 2nd edn. Springer, Berlin
Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10
Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin
Liu B (2012) Why is there a need for uncertainty theory? J Uncertain Syst 6(1):310
Liu B (2013) Toward uncertain finance theory. J Uncertain Anal Appl. https://doi.org/10.1186/2195-5468-1-1
Liu B (2014) Uncertain random graph and uncertain random network. J Uncertain Syst 8(1):3–12
Liu B, Chen X (2015) Uncertain multiobjective programming and uncertain goal programming. J Uncertain Anal Appl. https://doi.org/10.1186/s40467-015-0036-6
Liu YH, Ha M (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186
Liu L, Zhang B, Ma W (2017) Uncertain programming models for fixed charge multi-item solid transportation problem. Soft Comput. https://doi.org/10.1007/s00500-017-2718-0
Majumder S, Kundu P, Kar S, Pal T (2018) Uncertain multi-objective multi-item fixed charge solid transportation problem with budget constraint. Soft Comput. https://doi.org/10.1007/s00500-017-2987-7
Ojha A, Das B, Mondal S, Maiti M (2009) An entropy based solid transportation problem for general fuzzy costs and time with fuzzy equality. Math Comput Model 50(1–2):166–178
Rosyida I, Peng J, Chen L, Widodo W, Indrati CR, Sugeng KA (2018) An uncertain chromatic number of an uncertain graph based on alpha-cut coloring. Fuzzy Optim Decis Mak 17(1):103–123
Schell ED (1955) Distribution of a product by several properties. In: Proceedings of 2nd symposium in linear programing, DCS/comptroller, HQ US Air Force, Washington DC, pp 615-642
Shannon CE, Weaver W (1949) The mathematical theory of communication. University of Illinois press, Urbana
Sheng Y, Gao J (2014) Chance distribution of the maximum flow of uncertain random network. J Uncertain Anal Appl 2(1):15
Shi G, Sheng Y, Ralescu DA (2017) The maximum flow problem of uncertain random network. J Ambient Intell Humaniz Comput 8(5):667–675
Xiao C, Zhang Y, Fu Z (2016) Valuing interest rate swap contracts in uncertain financial market. Sustainability. https://doi.org/10.3390/su8111186
Yang X, Gao J (2013) Uncertain differential games with application to capitalism. J Uncertain Anal Appl. https://doi.org/10.1186/2195-5468-1-17
Yang X, Gao J (2016) Linear-quadratic uncertain differential games with application to resource extraction problem. IEEE Trans Fuzzy Syst 24(4):819826
Yang X, Gao J (2017) Bayesian equilibria for uncertain bimatrix game with asymmetric information. J Intell Manuf 28(3):515525
Yao K, Liu B (2017) Uncertain regression analysis: an approach for imprecise observations. Soft Comput. https://doi.org/10.1007/s00500-017-2521-y
Yao K, Gao J, Gao Y (2013) Some stability theorems of uncertain differential equation. Fuzzy Optim Decis Mak 12(1):313
Zadeh LA (1968) Probability measures of fuzzy events. J Mathe Anal Appl 23(2):421–427
Zhang B, Peng J, Li S, Chen L (2016) Fixed charge solid transportation problem in uncertain environment and its algorithm. Comput Ind Eng 102:186–197
Zhou J, Yang F, Wang K (2014) Multi-objective optimization in uncertain random environments. Fuzzy Optim Decis Mak 13(4):397–413
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Dalman, H. Entropy-based multi-item solid transportation problems with uncertain variables. Soft Comput 23, 5931–5943 (2019). https://doi.org/10.1007/s00500-018-3255-1
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DOI: https://doi.org/10.1007/s00500-018-3255-1