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Uncertain models on railway transportation planning problem. (English) Zbl 1459.90021
Summary: This paper investigates the frequency service network design problem in a railway freight transportation system, in which the fixed charge and transportation costs are both nondeterministic. In order to deal with nondeterministic system, uncertain variables are introduced. Here we propose two uncertain programming models, namely, budget-constrained model and possibility-constrained model, to design the fright transportation system. It is proved that the possibility-constrained model can be transformed to an equivalent deterministic transportation model using inverse uncertainty distribution. Based on this equivalence relation, the possibility-constrained optimal transportation plan can be obtained and then the solution of the budget-constrained model can be approximated. Finally, the idea of uncertain models is illustrated by a numerical experiment.

MSC:
90B06 Transportation, logistics and supply chain management
90B10 Deterministic network models in operations research
90C11 Mixed integer programming
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[1] Assad, A., Models for rail transportation, Transp. Res. Part A: gen., 14, 3, 205-220 (1980)
[2] Crainic, T.; Ferland, J.; Rousseau, J., A tactical planning model for rail freight transportation, Transp. Sci., 18, 2, 165-184 (1984)
[3] Harris, R., Economies of traffic density in the rail freight industry, Bell J. Econ., 8, 2, 556-564 (1977)
[4] Crainic, T.; Laporte, G., Planning models for freight transportation, Eur. J. Oper. Res., 97, 3, 409-438 (1997) · Zbl 0919.90055
[5] Crainic, T., Service network design in freight transportation, Eur. J. Oper. Res., 122, 272-288 (2000) · Zbl 0961.90010
[6] Crainic, T.; Roy, J., O.R. tools for tactical freight transportation planning, Eur. J. Oper. Res., 33, 3, 290-297 (1988)
[7] Keaton, M. H., Designing optimal railroad operating plans: lagrangian relaxation and heuristic approaches, Transp. Res. Part B: Methodol., 23, 6, 415-431 (1989)
[8] Keaton, M. H., Designing optimal railroad operating plans: a dual adjustment method for implementing Lagrangian relaxation, Transp. Sci., 26, 263-279 (1992) · Zbl 0775.90299
[9] Newton, H.; Barnhart, C.; Vance, P., Constructing railroad blocking plans to minimize handling costs, Transp. Sci., 32, 4, 330-345 (1998) · Zbl 0987.90510
[10] Gorman, M. F., An application of genetic and tabu searches to the freight railroad operating plan problem, Ann. Oper. Res., 78, 51-69 (1998) · Zbl 0896.90137
[11] Gorman, M. F., Santa fe railway uses an operating-plan model to improve its service design, Interfaces, 28, 4, 1-12 (1998)
[12] Yang, L.; Gao, Z.; Li, K., Railway freight transportation planning with mixed uncertainty of randomness and fuzziness, Appl. Soft Comput., 11, 778-792 (2011)
[13] Yang, L.; Li, X.; Gao, Z.; Li, K., A fuzzy minimum risk model for the railway transportation planning problem, Iran. J. Fuzzy Syst., 8, 4, 39-60 (2011) · Zbl 1260.90036
[14] Liu, B., Uncertainty theory, second ed. (2007), Springer-Verlag: Springer-Verlag Berlin
[15] Liu, B., Uncertainty theory: a branch of mathematics for modeling human uncertainty (2010), Springer-Verlag: Springer-Verlag Berlin
[16] Dempster, A., Upper and lower probabilities induced by a multivalued mapping, Ann. Math. Stat., 38, 2, 325-339 (1967) · Zbl 0168.17501
[17] Tversky, A.; Kahneman, D., Rational choice and the framing of decisions, J. Bussiness, 59, 2, 251-278 (1986)
[18] Pawlak, Z., Rough sets, Int. J. Parallel Program., 11, 5, 341-356 (1982) · Zbl 0501.68053
[19] Zadeh, L., Fuzzy sets, Inf. Control, 8, 338-353 (1965) · Zbl 0139.24606
[20] Zadeh, L., Fuzzy sets as the basis for a theory of possibility, Fuzzy Set Syst., 1, 1, 3-28 (1978) · Zbl 0377.04002
[21] Ding, S., Uncertain random newsboy problem, J. Intell. Fuzzy Syst., 26, 1, 483-490 (2014) · Zbl 1306.90005
[22] Ding, S., Uncertain multi-product newsboy problem with chance constraint, Appl. Math. Comput., 223, 139-146 (2013) · Zbl 1329.90009
[23] Gao, Y.; Wen, M.; Ding, S., (s,S) policy for uncertain single-peorid inventroy problem, Int. J. Uncertain. Fuzziness Knowl.-Based Syst., 21, 6, 945-953 (2013) · Zbl 1401.90029
[24] Qin, Z.; Kar, S., Single-period inventory problem under uncertain environment, Appl. Math. Comput., 219, 18, 9630-9638 (2013) · Zbl 1290.90007
[25] Ding, S., Uncertain minimum cost flow problem, Soft Comput., 18, 11, 2201-2207 (2014) · Zbl 1330.90014
[26] Gao, Y., Shortest path problem with uncertain arc lengths, Comput. Math. Appl., 62, 6, 2591-2600 (2011) · Zbl 1231.90367
[27] Gao, Y., Uncertain models for single facility location problems on networks, Appl. Math. Model., 36, 6, 2592-2599 (2012) · Zbl 1246.90083
[28] Gao, Y.; Yang, L.; Li, S.; Kar, S., On distribution function of the diameter in uncertain graph, Inf. Sci., 296, 61-74 (2015) · Zbl 1360.05131
[29] Han, S.; Peng, Z.; Wang, S., The maximum flow problem of uncertain network, Inf. Sci., 265, 167-175 (2014) · Zbl 1328.90018
[30] Deng, L.; Zhu, Y., Uncertain optimal control of linear quadratic models with jump, Math. Comput. Model., 57, 9-10, 2432-2441 (2013) · Zbl 1286.93202
[31] Zhu, Y., Uncertain optimal control with application to a portfolio selection model, Cybern. Syst., 41, 7, 535-547 (2010) · Zbl 1225.93121
[32] Sheng, Y.; Yao, K., A transportation model with uncertain costs and demands, Inf.: An Int. Interdiscip. J., 15, 8, 3179-3186 (2012) · Zbl 1323.90010
[33] Sheng, Y.; Yao, K., Fixed charge transportation problem in uncertain environment, Ind. Eng. Manag. Syst., 11, 2, 183-187 (2012)
[34] Liu, B., Some research problems in uncertainty theory, J. Uncertain Syst., 3, 1, 3-10 (2009)
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