An interactive possibilistic programming approach for a multi-objective hub location problem: Economic and environmental design

Display Omitted Presenting a new multi-objective mathematical model for a p-hub location problem.Considering environmental aspects of noise pollution caused by vehicles.Considering different transportation modes.Applying an Me-based possibilistic programming method to cope with the uncertainty.Developing hybrid differential evolution and hybrid imperialist competitive algorithms to solve large-sized problems. This paper presents a new multi-objective mathematical model for a multi-modal hub location problem under a possibilistic-stochastic uncertainty. The presented model aims to minimize the total transportation and traffic noise pollution costs. Furthermore, it aims to minimize the maximum transportation time between origin-destination nodes to ensure a high probability of meeting the service guarantee. In order to cope with the uncertainties and the multi-objective model, we propose a two-phase approach, including fuzzy interactive multi-objective programming approach and an efficient method based on the Me measure. Due to the NP-hardness of the presented model, two meta-heuristic algorithms, namely hybrid differential evolution and hybrid imperialist competitive algorithm, are developed. Furthermore, a number of sensitivity analyses are provided to demonstrate the effectiveness of the presented model. Finally, the foregoing meta-heuristics are compared together through different comparison metrics.

[1]  Masao Fukushima,et al.  ON THE HUB-AND-SPOKE MODEL WITH ARC CAPACITY CONATRAINTS , 2003 .

[2]  Inge Norstad,et al.  Reducing fuel emissions by optimizing speed on shipping routes , 2010, J. Oper. Res. Soc..

[3]  Swagatam Das,et al.  A new differential evolution with improved mutation strategy , 2010, IEEE Congress on Evolutionary Computation.

[4]  David J. Sheskin,et al.  Handbook of Parametric and Nonparametric Statistical Procedures , 1997 .

[5]  W. T. Sulaiman,et al.  Inequalities via convex functions , 1999 .

[6]  Mir Saman Pishvaee,et al.  Credibility-based fuzzy mathematical programming model for green logistics design under uncertainty , 2012, Comput. Ind. Eng..

[7]  Jamie Ebery,et al.  Solving large single allocation p-hub problems with two or three hubs , 2001, Eur. J. Oper. Res..

[8]  K. Lai,et al.  An Organizational Theoretic Review of Green Supply Chain Management Literature , 2011 .

[9]  Kaisa Miettinen,et al.  On initial populations of a genetic algorithm for continuous optimization problems , 2007, J. Glob. Optim..

[10]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

[11]  Gilbert Laporte,et al.  Stochastic uncapacitated hub location , 2011, Eur. J. Oper. Res..

[12]  Gang Liu,et al.  Enhanced differential evolution using random-based sampling and neighborhood mutation , 2015, Soft Comput..

[13]  R. Tavakkoli-Moghaddam,et al.  Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty , 2016 .

[14]  Zbigniew Michalewicz,et al.  Evolutionary algorithms for constrained engineering problems , 1996, Computers & Industrial Engineering.

[15]  Baoding Liu,et al.  Dependent-chance programming with fuzzy decisions , 1999, IEEE Trans. Fuzzy Syst..

[16]  Andreas T. Ernst,et al.  The capacitated multiple allocation hub location problem: Formulations and algorithms , 2000, Eur. J. Oper. Res..

[17]  Seyed Ali Torabi,et al.  Resilient supplier selection and order allocation under operational and disruption risks , 2015 .

[18]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[19]  Antonio González.  A study of the ranking function approach through mean values , 1990 .

[20]  Ioannis Mallidis,et al.  Operations Research for green logistics - An overview of aspects, issues, contributions and challenges , 2011, Eur. J. Oper. Res..

[21]  Reza Tavakkoli-Moghaddam,et al.  Solving a new stochastic multi-mode p-hub covering location problem considering risk by a novel multi-objective algorithm , 2013 .

[22]  玄 光男,et al.  進化技術ハンドブック = Handbook of evolutionary technology : computation and applications , 2010 .

[23]  D. Skorin-Kapov,et al.  Tight linear programming relaxations of uncapacitated p-hub median problems , 1996 .

[24]  Vladimir Marianov,et al.  A conditional p-hub location problem with attraction functions , 2009, Comput. Oper. Res..

[25]  Elise Miller-Hooks,et al.  A Green Vehicle Routing Problem , 2012 .

[26]  Jiuping Xu,et al.  Approximation based fuzzy multi-objective models with expected objectives and chance constraints: Application to earth-rock work allocation , 2013, Inf. Sci..

[27]  S.A. Torabi,et al.  An interactive possibilistic programming approach for multiple objective supply chain master planning , 2008, Fuzzy Sets Syst..

[28]  Rafay Ishfaq,et al.  Design of intermodal logistics networks with hub delays , 2012, Eur. J. Oper. Res..

[29]  Richard W. Eglese,et al.  Combinatorial optimization and Green Logistics , 2010, Ann. Oper. Res..

[30]  Reza Tavakkoli-Moghaddam,et al.  Sustainable hub location under mixed uncertainty , 2014 .

[31]  Paul R. Kleindorfer,et al.  ENVIRONMENTAL MANAGEMENT AND OPERATIONS MANAGEMENT: INTRODUCTION TO PART 1 (MANUFACTURING AND ECOLOGISTICS) , 2009 .

[32]  Caro Lucas,et al.  Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition , 2007, 2007 IEEE Congress on Evolutionary Computation.

[33]  Mohamed Shenify,et al.  The Expected Value of a Fuzzy Number , 2015 .

[34]  Andreas T. Ernst,et al.  Efficient algorithms for the uncapac-itated single allocation p-hub median problem , 1996 .

[35]  Barrett W. Thomas,et al.  The stochastic p-hub center problem with service-level constraints , 2009, Comput. Oper. Res..

[36]  L. V. Wassenhove,et al.  Sustainable Operations Management , 2005 .

[37]  Seyed Mahmoud Mousavi,et al.  Modeling of road-traffic noise with the use of genetic algorithm , 2011, Appl. Soft Comput..

[38]  Baoding Liu,et al.  Chance constrained programming with fuzzy parameters , 1998, Fuzzy Sets Syst..

[39]  Elise Miller-Hooks,et al.  Resilience: An Indicator of Recovery Capability in Intermodal Freight Transport , 2012, Transp. Sci..

[40]  Gilbert Laporte,et al.  The Pollution-Routing Problem , 2011 .

[41]  Mehrdad Mohammadi,et al.  Multi-objective hub network design under uncertainty considering congestion: An M/M/c/K queue system , 2016 .

[42]  Mehrdad Mohammadi,et al.  A multi-objective optimization model for hub network design under uncertainty: An inexact rough-interval fuzzy approach , 2015 .

[43]  Amir Azaron,et al.  Robust and fuzzy goal programming optimization approaches for a novel multi-objective hub location-allocation problem: A supply chain overview , 2015, Appl. Soft Comput..

[44]  Samir Elhedhli,et al.  A Lagrangean Heuristic for Hub-and-Spoke System Design with Capacity Selection and Congestion , 2010, INFORMS J. Comput..

[45]  P. Victer Paul,et al.  Performance analyses over population seeding techniques of the permutation-coded genetic algorithm: An empirical study based on traveling salesman problems , 2015, Appl. Soft Comput..

[46]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[47]  Jouni Lampinen,et al.  A Trigonometric Mutation Operation to Differential Evolution , 2003, J. Glob. Optim..

[48]  James F. Campbell,et al.  Integer programming formulations of discrete hub location problems , 1994 .

[49]  Lawrence V. Snyder,et al.  Facility location under uncertainty: a review , 2006 .

[50]  L. M. D. C. Ibáñez,et al.  A subjective approach for ranking fuzzy numbers , 1989 .

[51]  Qingfu Zhang,et al.  Enhancing the search ability of differential evolution through orthogonal crossover , 2012, Inf. Sci..

[52]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[53]  B. Naderi,et al.  A novel imperialist competitive algorithm for generalized traveling salesman problems , 2015, Appl. Soft Comput..

[54]  Andreas T. Ernst,et al.  A Stackelberg hub arc location model for a competitive environment , 2014, Comput. Oper. Res..

[55]  Mir Saman Pishvaee,et al.  Green and Reverse Logistics Management Under Fuzziness , 2014, Supply Chain Management Under Fuzziness.

[56]  D. Dubois,et al.  The mean value of a fuzzy number , 1987 .

[57]  Ehsan Nikbakhsh,et al.  Hub location problems: A review of models, classification, solution techniques, and applications , 2013, Comput. Ind. Eng..

[58]  Sibel A. Alumur,et al.  Hub location under uncertainty , 2012 .

[59]  Sh. Givargis,et al.  Converting the UK calculation of road traffic noise (CORTN) to a model capable of calculating LAeq,1h for the Tehran’s roads , 2008 .

[60]  Ponnuthurai N. Suganthan,et al.  An Adaptive Differential Evolution Algorithm With Novel Mutation and Crossover Strategies for Global Numerical Optimization , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[61]  Masoud Rabbani,et al.  A robust possibilistic programming approach to multiperiod hospital evacuation planning problem under uncertainty , 2018, Int. Trans. Oper. Res..

[62]  Morton E. O'Kelly,et al.  The Location of Interacting Hub Facilities , 1986, Transp. Sci..