不确定与损毁情景下可靠性设施选址鲁棒优化模型与算法研究
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摘要
设施选址是长期战略性决策问题,选址决策面临各种不确定因素,设计一个可靠的选址网络具有重要的战略意义.本文同时考虑需求的不确定性及设施可能损毁的情景,扩展无容量限制的固定费用可靠性选址模型,建立不确定与损毁情景下服务能力有限的可靠性设施选址鲁棒优化模型.基于Bertsimas和Sim鲁棒优化方法提出一个新的混合整数规划模型,通过引入辅助变量和对偶变换实现非线性鲁棒优化模型转化为鲁棒对应模型,提出蝙蝠算法(BA)对模型予以求解,并通过算例仿真验证模型和算法的可行性,为设施选址决策提供模型和方法设计.
Facility location is a long-term strategic decision problem, but the location decision-making is confronted with various uncertain factors. Therefore, it is of strategic importance to design a reliable location network. This paper considers both demand uncertainty and facility failures, extends uncapacitated fix-charge location problem to establish reliability facility location robust optimization model under uncertainty and failure scenarios. A new mixed integer programming model is proposed based on Bertsimas and Sim robust method, the nonlinear robust optimization model is transformed into a robust correspondence model by introducing the auxiliary variable and dual transformation. We develop bat algorithm(BA) to solve the model, our computational results show the feasibility of the presented model and algorithm. This paper provides model and method design for facility location decision.
Facility location is a long-term strategic decision problem, but the location decision-making is confronted with various uncertain factors. Therefore, it is of strategic importance to design a reliable location network. This paper considers both demand uncertainty and facility failures, extends uncapacitated fix-charge location problem to establish reliability facility location robust optimization model under uncertainty and failure scenarios. A new mixed integer programming model is proposed based on Bertsimas and Sim robust method, the nonlinear robust optimization model is transformed into a robust correspondence model by introducing the auxiliary variable and dual transformation. We develop bat algorithm(BA) to solve the model, our computational results show the feasibility of the presented model and algorithm. This paper provides model and method design for facility location decision.
引文
[1] Snyder L V, Daskin M S. Reliability models for facility location:The expected failure cost case[J]. Transportation Science, 2005, 39(3):400-416.
[2] Li Q, Savachkin A. Reliable distribution networks design with nonlinear fortification function[J]. International Journal of Systems Science, 2016, 47(4):805-813.
[3] Bahri S, Rusman M. Reliable facility location model considering disruption risk in logistic model[J]. Journal of Engineering and Applied Sciences, 2013, 8(6):177-182.
[4] Cui T, Ouyang Y, Shen Z J M. Reliable facility location design under the risk of disruptions[J]. Operations Research, 2010, 58(4-part-1):998-1011.
[5] Berman O, Krass D, Menezes M B C. Locating facilities in the presence of disruptions and incomplete information[J]. Decision Sciences, 2009, 40(4):845-868.
[6]朱建明.损毁情景-下应急设施选址的多目标决策方法[J].系统工程理论-与实践,2015, 35(3):720-727.Zhu J M. Methods of multi-objective decision-making for emergency facility location problem under failure scenario[J]. Systems Engineering—Theory&Practice, 2015, 35(3):720-727.
[7] Shen Z J M, Zhan R L, Zhang J. The reliable facility location problem:Formulations, heuristics, and approxi?mation algorithms[J].INFORMS Journal on Computing, 2011, 23(3):470-482.
[8] Yu G, Haskell W B, Liu Y. Resilient facility location against the risk of disruptions[J]. rTransportation Research Part B:Methodological, 2017, 104(C):82-105.
[9] Jalali S, Seifbarghy M, Sadeghi J, et al. Optimizing a bi-objective reliable facility location problem with adapted stochastic measures using tuned-parameter multi-objective algorithms[J]. Knowledge-Based Systems,2016, 95(C):45-57.
[10] An Y,Zeng B, Zhang Y, et al. Reliable p-median facility location problem:Two-stage robust models and algorithms[J』. Transportation Research Part B:Methodological, 2014, 64(C):54-72.
[11] Lu M, Ran L, Shen Z J M. Reliable facility location design under uncertain correlated disruptions[J]. Manufac?turing&Service Operations Management, 2015, 17(4):445-455.
[12] Mohammadi M, Tavakkoli-Moghaddam R, Siadat A, et al. Design of a reliable logistics network with hub disruption under uncertainty[J]. Applied Mathematical Modelling, 2016, 40(9):5621-5642.
[13] Murali P, Fernando Ord6ez F, Dessouky M M. Facility location under demand uncertainty:Response to a large-scale bio-terror attack[J]! Socio-Economic Planning Sciences, 2012, 46(1):78-87.
[14]王海军,刘畅,王婧.应急储备库选址与资源配置随机规划模型研究[J].管理学报,2013, 10(10):1507-1511.Wang H J, Liu C, Wang J. Stochastic optimization models for emergency supplies location and allocation[J].Chinese Journal of Management, 2013, 10(10):1507-1511.
[15] Jamalian A, Salahi M. Robust solutions to multi-facility Weber location problem under interval and ellipsoidal uncertainty[J]. Applied Mathematics and Computation, 2014, 242(3):179-186.
[16] Zhang L, Wu S. Robust solutions to Euclidean facility location problems with uncertain data[J]. Journal of Industrial and Management Optimization, 2010, 6(1):751-760.
[17] Zhang B, Peng J, Li S. Covering location problem of emergency service facilities in an uncertain environment[J].Applied Mathematical Modelling, 2017, 51(3):429-447.
[18] Cavdur F, Kose-Kucuk M, Sebatli A. Allocation of temporary disaster response facilities under demand uncer?tainty:An earthquake case study[J]. International Journal of Disaster Risk Reduction, 2016, 19(4):159-166.
[19] Puga M S, Tancrez J S. A heuristic algorithm for solving large location-inventory problems with demand uncer?tainty[j]. European Journal of Operational Research, 2017, 259(2):413-423.
[20] Boukani F H, Moghaddam B F, Pishvaee M S. Robust optimization approach to capacitated single and multiple allocation hub location problems[J]. Computational and Applied Mathematics, 2016, 35(1):45-60.
[21] Bertsimas D, Sim M. The price of robustness[J]. Operations Research, 2004, 52(1):35-53.
[22] Soyster A L. Convex programming with set-inclusive constraints and applications to inexact linear programming[J]. Operations Research, 1973, 21(5):1154-1157.
[23] Yang X S. A new metaheuristic bat-inspired algorithm[C]//Nature Inspired Cooperative Strategies for Optimization, Berlin Heidelberg:Springer Berlin Heidelberg, 2010, 28(4):65-74.
[24] Yang X S, Gandomi A H. Bat algorithm:A novel approach for global engineering optimization[J]. Engineering Computations, 2012, 29(5):464-483.
[25] Yang X S, He X. Bat algorithm:Literature review and applications[J]. International Journal of Bio-Inspired Computation, 2013, 5(3):141-149.
[26] Mirjalili S, Mirjalili S M, Yang X S. Binary bat algorithm[J]. Neural Computing and Applications, 2014, 25(3-4):663-681.
[2] Li Q, Savachkin A. Reliable distribution networks design with nonlinear fortification function[J]. International Journal of Systems Science, 2016, 47(4):805-813.
[3] Bahri S, Rusman M. Reliable facility location model considering disruption risk in logistic model[J]. Journal of Engineering and Applied Sciences, 2013, 8(6):177-182.
[4] Cui T, Ouyang Y, Shen Z J M. Reliable facility location design under the risk of disruptions[J]. Operations Research, 2010, 58(4-part-1):998-1011.
[5] Berman O, Krass D, Menezes M B C. Locating facilities in the presence of disruptions and incomplete information[J]. Decision Sciences, 2009, 40(4):845-868.
[6]朱建明.损毁情景-下应急设施选址的多目标决策方法[J].系统工程理论-与实践,2015, 35(3):720-727.Zhu J M. Methods of multi-objective decision-making for emergency facility location problem under failure scenario[J]. Systems Engineering—Theory&Practice, 2015, 35(3):720-727.
[7] Shen Z J M, Zhan R L, Zhang J. The reliable facility location problem:Formulations, heuristics, and approxi?mation algorithms[J].INFORMS Journal on Computing, 2011, 23(3):470-482.
[8] Yu G, Haskell W B, Liu Y. Resilient facility location against the risk of disruptions[J]. rTransportation Research Part B:Methodological, 2017, 104(C):82-105.
[9] Jalali S, Seifbarghy M, Sadeghi J, et al. Optimizing a bi-objective reliable facility location problem with adapted stochastic measures using tuned-parameter multi-objective algorithms[J]. Knowledge-Based Systems,2016, 95(C):45-57.
[10] An Y,Zeng B, Zhang Y, et al. Reliable p-median facility location problem:Two-stage robust models and algorithms[J』. Transportation Research Part B:Methodological, 2014, 64(C):54-72.
[11] Lu M, Ran L, Shen Z J M. Reliable facility location design under uncertain correlated disruptions[J]. Manufac?turing&Service Operations Management, 2015, 17(4):445-455.
[12] Mohammadi M, Tavakkoli-Moghaddam R, Siadat A, et al. Design of a reliable logistics network with hub disruption under uncertainty[J]. Applied Mathematical Modelling, 2016, 40(9):5621-5642.
[13] Murali P, Fernando Ord6ez F, Dessouky M M. Facility location under demand uncertainty:Response to a large-scale bio-terror attack[J]! Socio-Economic Planning Sciences, 2012, 46(1):78-87.
[14]王海军,刘畅,王婧.应急储备库选址与资源配置随机规划模型研究[J].管理学报,2013, 10(10):1507-1511.Wang H J, Liu C, Wang J. Stochastic optimization models for emergency supplies location and allocation[J].Chinese Journal of Management, 2013, 10(10):1507-1511.
[15] Jamalian A, Salahi M. Robust solutions to multi-facility Weber location problem under interval and ellipsoidal uncertainty[J]. Applied Mathematics and Computation, 2014, 242(3):179-186.
[16] Zhang L, Wu S. Robust solutions to Euclidean facility location problems with uncertain data[J]. Journal of Industrial and Management Optimization, 2010, 6(1):751-760.
[17] Zhang B, Peng J, Li S. Covering location problem of emergency service facilities in an uncertain environment[J].Applied Mathematical Modelling, 2017, 51(3):429-447.
[18] Cavdur F, Kose-Kucuk M, Sebatli A. Allocation of temporary disaster response facilities under demand uncer?tainty:An earthquake case study[J]. International Journal of Disaster Risk Reduction, 2016, 19(4):159-166.
[19] Puga M S, Tancrez J S. A heuristic algorithm for solving large location-inventory problems with demand uncer?tainty[j]. European Journal of Operational Research, 2017, 259(2):413-423.
[20] Boukani F H, Moghaddam B F, Pishvaee M S. Robust optimization approach to capacitated single and multiple allocation hub location problems[J]. Computational and Applied Mathematics, 2016, 35(1):45-60.
[21] Bertsimas D, Sim M. The price of robustness[J]. Operations Research, 2004, 52(1):35-53.
[22] Soyster A L. Convex programming with set-inclusive constraints and applications to inexact linear programming[J]. Operations Research, 1973, 21(5):1154-1157.
[23] Yang X S. A new metaheuristic bat-inspired algorithm[C]//Nature Inspired Cooperative Strategies for Optimization, Berlin Heidelberg:Springer Berlin Heidelberg, 2010, 28(4):65-74.
[24] Yang X S, Gandomi A H. Bat algorithm:A novel approach for global engineering optimization[J]. Engineering Computations, 2012, 29(5):464-483.
[25] Yang X S, He X. Bat algorithm:Literature review and applications[J]. International Journal of Bio-Inspired Computation, 2013, 5(3):141-149.
[26] Mirjalili S, Mirjalili S M, Yang X S. Binary bat algorithm[J]. Neural Computing and Applications, 2014, 25(3-4):663-681.