zbMATH — the first resource for mathematics

Uncertain random multilevel programming with application to production control problem. (English) Zbl 1364.90236
Summary: For modeling decentralized decision-making problems with uncertain random parameters, an uncertain random multilevel programming is proposed. For some special case, an equivalent crisp mathematical programming to the established uncertain random programming is presented. A searching method by integrating uncertain random simulations, neural network, and genetic algorithm is produced to search the quasi-optimal solution under some decision-making criterion. Finally, the proposed uncertain random multilevel programming is applied to a production control problem.

90C15 Stochastic programming
90B30 Production models
Full Text: DOI
[1] Aiyoshi, E; Shimizu, K, Hierarchical decentralized systems and its new solution by a barrier method, IEEE T Syst Man Cyb, 11, 444-449, (1981)
[2] Amouzegar, MA; Moshirvaziri, K, Determining optimal pollution control policies: an application of bilevel programming, Eur J Oper Res, 119, 100-120, (1999) · Zbl 0934.91044
[3] Arora, SR; Gupta, R, Interactive fuzzy goal programming approach for bilevel programming problem, Eur J Oper Res, 194, 368-376, (2009) · Zbl 1154.90583
[4] Ben-Ayed, O; Blair, CE, Computational difficulties of bilevel linear programming, Oper Res, 38, 556-560, (1990) · Zbl 0708.90052
[5] Bialas, WF; Karwan, MH, Two-level linear programming, Manage Sci, 30, 1004-1020, (1984) · Zbl 0559.90053
[6] Bracken, J; McGill, JM, Mathematical programs with optimization problems in the constraints, Oper Res, 21, 37-44, (1973) · Zbl 0263.90029
[7] Chen, X; Gao, J, Uncertain term structure model of interest rate, Soft Comput, 17, 597-604, (2013) · Zbl 1264.91128
[8] Cybenko, C, Approximations by superpositions of a sigmoidal function, Math Control Signal Syst, 2, 183-192, (1989)
[9] Etoa, JBE, Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm, J Glob Optim, 47, 615-637, (2010) · Zbl 1237.90176
[10] Gao, J; Liu, B; Gen, M, A hybrid intelligent algorithm for stochastic multilevel programming, IEEJ T Elect Infor Syst, 124, 1991-1998, (2004)
[11] Gao, J; Liu, B, Fuzzy multilevel programming with a hybrid intelligent algorithm, Comput Math Appl, 49, 1539-1548, (2005) · Zbl 1138.90508
[12] Gao, Y, Uncertain models for single facility location problems on networks, Appl Math Model, 36, 2592-2599, (2012) · Zbl 1246.90083
[13] Jiang, Y; Li, X; Huang, C; Wu, X, Application of particle swarm optimization based on CHKS smoothing function for solving nonlinear bilevel programming problem, Appl Math Comput, 219, 4332-4339, (2013) · Zbl 1401.90273
[14] Lai, YJ, Hierachical optimization: A satisfactory solution, Fuzzy Set Syst, 77, 321-335, (1996) · Zbl 0869.90042
[15] Lan, Y; Zhao, R; Tang, W, A bilevel fuzzy principal-agent model for optimal nonlinear taxation problems, Fuzzy Optim Decis Ma, 10, 211-232, (2011) · Zbl 1219.91059
[16] Lasdon, LS, Duality and decomposition in mathematical programming, IEEE T Syst Sci Cyb, 4, 86-100, (1968) · Zbl 0181.22804
[17] Lasdon LS (1970) Optimizing theory for large system. Macmillan Publishing, New York
[18] Lee ES, Shih HS (2001) Fuzzy and multi-level decision making: An interactive computational approach. Springer-Verlag, London
[19] Lim, C; Smith, JC, Algorithms for discrete and continuous multicommodity flow network interdiction problems, IIE Trans, 39, 15-26, (2007)
[20] Liu B (2002) Theory and practice of uncertain programming. Physica-Verlag, Heidelberg · Zbl 1029.90084
[21] Liu B (2007) Uncertainty theory, 2nd edn. Springer-Verlag, Berlin · Zbl 1141.28001
[22] Liu, B, Some research problems in uncertainty theory, J Uncertain Syst, 3, 3-10, (2009)
[23] Liu B (2010) Uncertainty theory: A branch of mathematics for modeling human uncertainty. Springer-Verlag, Berlin
[24] Liu, B, Extreme value theorems of uncertain process with application to insurance risk model, Soft Comput, 17, 549-556, (2013) · Zbl 1279.60009
[25] Liu, YH, Uncertain random variables: A mixture of uncertainty and randomness, Soft Comput, 17, 625-634, (2013) · Zbl 1281.60005
[26] Liu, YH, Uncertain random programming with applications, Fuzzy Optim Decis Ma, 12, 153-169, (2013) · Zbl 1428.90194
[27] Mesarovic MD, Macko D, Takahara Y (1970) Theory of multilevel hierarchical systems. Academic, New York · Zbl 0206.14501
[28] Patriksson, M; Wynter, L, Stochastic mathematical programs with equilibrium constraints, Oper Res Lett, 25, 159-167, (1999) · Zbl 0937.90076
[29] Rong, L, Two new uncertainty programming models of inventory with uncertain costs, J Inform Comput Sci, 8, 280-288, (2011)
[30] Saharidis, GK; Ierapetritou, MG, Resolution method for mixed integer bi-level linear problems based on decomposition technique, J Glob Optim, 44, 29-51, (2009) · Zbl 1172.90451
[31] Sahling, F; Buschkuhl, L; Tempelmeier, H; Helber, S, Solving a multi-level capacitated lot sizing problem with multi-period setup carry-over via a fix-and-optimize heuristic, Comput Oper Res, 36, 2546-2553, (2009) · Zbl 1179.90018
[32] Sheng, Y; Yao, K, Fixed charge transportation problem in uncertain environment, Ind Eng Manage Syst, 11, 183-187, (2012)
[33] Wang, G; Gao, Z; Xu, M; Sun, H, Models and a relaxation algorithm for continuous network design problem with a tradable credit scheme and equity constraints, Comput Oper Res, 41, 252-261, (2014) · Zbl 1348.90164
[34] Xu, P; Wang, L, An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions, Comput Oper Res, 41, 309-318, (2014) · Zbl 1348.90496
[35] Zhang, G; Lu, J, Fuzzy bilevel programming with multiple objectives and cooperative multiple followers, J Glob Optim, 47, 403-419, (2010) · Zbl 1222.90058
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.