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.
Transportation problem Uncertainty programming Uncertain variable
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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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Conflicts of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants performed by any of the authors.
Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10Google Scholar
Liu B (2010) Uncertain set theory and uncertain inference rule with application to uncertain control. J Uncertain Syst 4(2):83–98Google Scholar
Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, BerlinCrossRefGoogle Scholar
Lotif MM, Moghaddam RT (2013) A genetic algorithm using priority-based encoding with new operators for fixed charge transportation problems. Appl Soft Comput 13:2711–2722CrossRefGoogle 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 10:100–110CrossRefGoogle Scholar