zbMATH — the first resource for mathematics

A multi-objective bi-level location planning problem for stone industrial parks. (English) Zbl 1348.90390
Summary: This paper focuses on a stone industrial park location problem with a hierarchical structure consisting of a local government and several stone enterprises under a random environment. In contrast to previous studies, conflicts between the local authority and the stone enterprises are considered. The local government, being the leader in the hierarchy, aims to minimize both total pollution emissions and total development and operating costs. The stone enterprises, as the followers in the hierarchy, only aim to minimize total costs. In addition, unit production cost and unit transportation cost are considered random variables. This complicated multi-objective bi-level optimization problem poses several challenges, including randomness, two-level decision making, conflicting objectives, and difficulty in searching for the optimal solutions. Various approaches are employed to tackle these challenges. In order to make the model trackable, expected value operator is used to deal with the random variables in the objective functions and a chance constraint-checking method is employed to deal with such variables in the constraints. The problem is solved using a bi-level interactive method based on a satisfactory solution and Adaptive Chaotic Particle Swarm Optimization (ACPSO). Finally, a case study is conducted to demonstrate the practicality and efficiency of the proposed model and solution algorithm. The performance of the proposed bi-level model and ACPSO algorithm was highlighted by comparing to a single-level model and basic PSO and GA algorithms.

90B80 Discrete location and assignment
90B90 Case-oriented studies in operations research
90C15 Stochastic programming
90C29 Multi-objective and goal programming
Full Text: DOI
[1] Al-Jabari M, Sawalha H. Treating stone cutting waste by flocculation-sedimentation. In: Proceedings of the 28th WEDC conference on sustainable environmental sanitation and water services conference, Calcutta, India; 2002.
[2] Almeida, N.; Branco, F.; Santos, J., Recycling of stone slurry in industrial activities: application to concrete mixtures, Build Environ, 42, 2, 810-819, (2007)
[3] Barahona, F.; Jensen, D., Plant location with minimum inventory, Math Program, 83, 1, 101-111, (1998) · Zbl 0920.90088
[4] Berman, O.; Krass, D.; Wang, J., The probabilistic gradual covering location problem on a network with discrete random demand weights, Comput Oper Res, 38, 11, 1493-1500, (2011) · Zbl 1210.90041
[5] Akgün İ, Gümüşbugˇa F, Tansel B. Risk based facility location by using fault tree analysis in disaster management. Omega 2014, http://dx.doi.org/10.1016/j.omega.2014.04.003, in press.
[6] Hernández, P.; Alonso-Ayuso, A.; Bravo, F.; Escudero, L. F.; Guignard, M.; Marianov, V.; Weintraub, A., A branch-and-cluster coordination scheme for selecting prison facility sites under uncertainty, Comput Oper Res, 39, 9, 2232-2241, (2012) · Zbl 1251.90239
[7] Verma, M.; Gendreau, M.; Laporte, G., Optimal location and capability of oil-spill response facilities for the south coast of newfoundland, Omega, 41, 5, 856-867, (2013)
[8] Lai, Y. J., Hierarchical optimizationa satisfactory solution, Fuzzy Set Syst, 77, 3, 321-335, (1996) · Zbl 0869.90042
[9] Lee, E. S., Fuzzy multiple level programming, Appl Math Comput, 120, 1-3, 79-90, (2001) · Zbl 1032.90078
[10] Gao, D.; Zhao, X.; Geng, W., A delay-in-payment contract for Pareto improvement of a supply chain with stochastic demand, Omega, 49, 60-68, (2014)
[11] Nasserdine, K.; Mimi, Z.; Bevan, B.; Elian, B., Environmental management of the stone cutting industry, J Environ Manag, 90, 1, 466-470, (2009)
[12] Syam, S., A model and methodologies for the location problem with logistical components, Comput Oper Res, 29, 9, 1173-1193, (2002) · Zbl 0994.90089
[13] Tragantalerngsak, S.; Holt, J.; Ronnqvist, M., An exact method for the two echelon, single-source, capacitated facility location problem, Eur J Oper Res, 123, 3, 473-489, (2000) · Zbl 0991.90083
[14] Xu, J.; Yao, L., Random-like multiple objective decision making, (2011), Berlin, Heidelberg: Springer
[15] Yao L, Xu J, Guo F. A stone resource assignment model under the fuzzy environment. In; Mathematical problems in engineering, vol. 2012. Hindawi Publishing. Article ID 265837. 2012; p. 26. · Zbl 1264.90198
[16] Zhou, G.; Min, H.; Gen, M., The balanced allocation of customers to multiple distribution centers in the supply chain networka genetic algorithm approach, Comput Ind Eng, 43, 1-2, 251-261, (2002)
[17] Sakawa, M.; Nishizaki, I., Interactive fuzzy programming for decentralized two-level linear programming problems, Fuzzy Sets Syst, 125, 3, 301-315, (2002) · Zbl 1014.90119
[18] Tiryaki, F., Interactive compensatory fuzzy programming for decentralized multi-level linear programming (DMLLP) problems, Fuzzy Sets Syst, 157, 23, 3072-3090, (2006) · Zbl 1114.90491
[19] Arora, S. R.; Gupta, R., Interactive fuzzy goal programming approach for bi-level programming problem, Eur J Oper Res, 194, 2, 368-376, (2009) · Zbl 1154.90583
[20] Rossi R, Kilic OA, Tarim SA. Piecewise linear approximations for the static-dynamic uncertainty strategy in stochastic lot-sizing. Omega 2015;50:126-40.
[21] Sakawa, M.; Nishizaki, I.; Uemura, Y., Interactive fuzzy programming for linear and linear fractional production and allocation problemsa case study, Eur J Oper Res, 135, 142-157, (2001) · Zbl 1077.90564
[22] Xu, J.; Tu, Y.; Zeng, Z., Bi-level optimization of regional water resources allocation problem under fuzzy random environment, J Water Resour Plan Manag, 139, 3, 246-264, (2013)
[23] Simaarn, M.; Cruz, J. B., On the Stackelberg strategy in nonzero-sum games, J Optim Theory Appl, 11, 5, 533-555, (1973) · Zbl 0243.90056
[24] Sakawa, M.; Nishizaki, I.; Oka, Y., Interactive fuzzy programming for multiobjective two-level linear programming problems with partial information of preference, Int J Fuzzy Syst, 2, 79-86, (2000)
[25] Lee, E. S.; Shih, H. S., Fuzzy and multi-level decision making: an interactive computation approach, (2001), Springer-Verlag London
[26] Ai, T. J.; Kachitvichyanukul, V., A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery, Comput Oper Res, 36, 1693-1702, (2009) · Zbl 1179.90068
[27] Caponetto, R.; Fortuna, L.; Fazzino, S., Sequences to improve the performance of evolutionary algorithms, IEEE Trans Evolution Comput, 7, 3, 289-304, (2003)
[28] Valenzuela, J.; Mazumdar, M., Monte Carlo computation of power generation production costs under operating constraints, IEEE Trans Power Syst, 16, 4, 671-677, (2001)
[29] Valenzuela, J.; Mazumdar, M., Statistical analysis of electric power production costs, IIE Trans, 32, 12, 1139-1148, (2000)
[30] Louveaux, F. V.; Peeters, D., A dual-based procedure for stochastic facility location, Oper Res, 40, 3, 564-573, (1992) · Zbl 0773.90044
[31] Sibdari, S.; Pyke, D. F., Dynamic pricing with uncertain production costan alternating-move approach, Eur J Oper Res, 236, 1, 218-228, (2014) · Zbl 1338.91072
[32] Santoso, T.; Ahmed, S.; Goetschalckx, M.; Shapiro, A., A stochastic programming approach for supply chain network design under uncertainty, Eur J Oper Res, 167, 1, 96-115, (2005) · Zbl 1075.90010
[33] Zhang, T.; Hu, T.; Guo, X.; Chen, Z.; Zheng, Y., Solving high dimensional bilevel multiobjective programming problem using a hybrid particle swarm optimization algorithm with crossover operator, Knowl-Based Syst, 53, 13-19, (2013)
[34] Deb, K.; Sinha, A., Solving bilevel multi-objective optimization problems using evolutionary algorithms, Evol Multi-Criterion Optim., 110-124, (2008)
[35] Sinha A, Deb K. Towards understanding evolutionary bilevel multi-objective optimization algorithm. In: IFAC workshop on control applications of optimization, vol. 7; 2009. p. 338-43.
[36] Deb, K.; Sinha, A., An efficient and accurate solution methodology for bilevel multi-objective programming problems using a hybrid evolutionary-local-search algorithm, Evolution Comput, 18, 3, 403-449, (2010)
[37] Gao, Y.; Zhang, G.; Ma, J.; Lu, J., A λ-cut and goal-programming-based algorithm for fuzzy-linear multiple-objective bilevel optimization, IEEE Trans Fuzzy Syst, 18, 1, 1-13, (2010)
[38] Ahmed, S.; King, A. J.; Parija, G., A multi-stage stochastic integer programming approach for capacity expansion under uncertainty, J Glob Optim, 26, 1, 3-24, (2003) · Zbl 1116.90382
[39] Maqsood, I.; Huang, G. H.; Scott Yeomans, J., An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty, Eur J Oper Res, 167, 1, 208-225, (2005) · Zbl 1074.90541
[40] Xu J, Tu Y, Lei X. Applying multi-objective bi-level optimization under fuzzy random environment to traffic assignment problem: case study of large-scale construction project. J Infrastruct Syst: 05014003. 2014; 20(3), doi:10.1061/(ASCE)IS.1943-555X.0000147.
[41] Yang, N.; Wen, F., A chance constrained programming approach to transmission system expansion planning, Electr Power Syst Res, 75, 2, 171-177, (2005)
[42] Li, P.; Arellano-Garcia, H.; Wozny, G., Chance constrained programming approach to process optimization under uncertainty, Comput Chem Eng, 32, 1, 25-45, (2008)
[43] Miller, L. B.; Wagner, H., Chance-constrained programming with joint constraints, Oper Res, 13, 930-945, (1965) · Zbl 0132.40102
[44] Charnes, A.; Cooper, W. W., Chance-constrained programming, Manag Sci, 6, 1, 73-79, (1959) · Zbl 0995.90600
[45] Pongchairerks P, Kachitvichyanukul V. A non-homogenous particle swarm optimization with multiple social structures. In: Proceedings of the international conference on simulation and modeling 2005. Bangkok, Thailand; 2005. · Zbl 1168.90466
[46] Kennedy, J.; Eberhart, R. C.; Shi, Y., Swarm intelligence, (2001), Morgan Kaufmann San Francisco, CA
[47] Wan, Z.; Wang, G.; Sun, B., A hybrid intelligent algorithm by combining particle swarm optimization with chaos searching technique for solving nonlinear bilevel programming problems, Swarm Evolution Comput, 8, 26-32, (2013)
[48] Wee, H. M.; Widyadana, G. A., A production model for deteriorating items with stochastic preventive maintenance time and rework process with FIFO rule, Omega, 41, 6, 559-573, (2013)
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.