A transportation planning problem with transfer costs in uncertain environment
As a generalization of existing uncertain transportation models, this paper proposes a new uncertain transportation model with transfer costs, of which the demands and the transportation costs as well as the transfer costs are uncertain variables. The model is presented in a form with expected-value objective and chance constraints. Based on the operational laws of uncertain variables, the presented model is transformed into an equivalent crisp model. After that, a numerical experiment is performed to illustrate the application of the model.
KeywordsTransportation problem Transfer cost Uncertainty theory Uncertain variable
This research was supported by The Thirteenth Five-Year Plan of Tianjin Educational Science, titled “Research on the Professional Growth Path of Teachers in Professional Institutions of Higher Learning” (Grant No. HE4051).
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- Akpan NP, Iwok IA (2017) A minimum spanning tree approach of solving a transportation problem. Int J Math Stat Invent 5(3):9–18Google Scholar
- Chen L, Peng J, Zhang B (2017) Uncertain goal programming models for bicriteria solid transportation problem. Appl Soft Comput 51:49–59Google Scholar
- Dalman H (2018) Uncertain programming model for multi-item solid transportation problem. Int J Mach Learn Cybern 9:559–567Google Scholar
- Hajiaghaei-Keshteli M, Molla-Alizadeh-Zavardehi S, Tavakkoli-Moghaddam R (2010) Addressing a nonlinear fixed-charge transportation problem using a spanning tree-based genetic algorithm. Comput Ind Eng 59(2):259–271Google Scholar
- Karaoglan I, Kesen SE (2017) The coordinated production and transportation scheduling problem with a time-sensitive product: a branch-and-cut algorithm. Int J Prod Res 55(2):536–557Google Scholar
- Liu B (2009a) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10Google Scholar
- Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, BerlinGoogle Scholar
- Liu Y, Ha M (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186Google Scholar
- Mou D, Zhao W, Chang X (2013) A transportation problem with uncertain truck times and unit costs. Ind Eng Manag Syst 12(1):30–35Google Scholar
- Musa R, Arnaout JP, Jung H (2010) Ant colony optimization algorithm to solve for the transportation problem of cross-docking network. Comput Ind Eng 59(1):85–92Google Scholar
- Qi L (1985) Forest iteration method for stochastic transportation problem. In: Cottle RW (ed) Mathematical programming essays in honor of George B. Dantzig Part II. Springer, Berlin, pp 142–163Google Scholar
- Sheng Y, Yao K (2012b) Fixed charge transportation problem in uncertain environment. Ind Eng Manag Syst 11(2):183–187Google Scholar
- Zhang B, Peng J, Li S, Chen L (2016) Fixed charge solid transportation problem in uncertain environment and its algorithm. Comput Ind Eng 102:186–197Google Scholar