Fuzzy Linear Programming Models for a Green Logistics Center Location and Allocation Problem under Mixed Uncertainties Based on Different Carbon Dioxide Emission Reduction Methods

This study explores a foundational logistics center location and allocation problem in a three-stage logistics network that consists of suppliers, logistics centers, and customers. In this study, the environmental sustainability of the logistics network is improved by optimizing the carbon dioxide emissions of the logistics network based on multi-objective optimization and carbon tax regulation. Mixed uncertainties in the planning stage, including the supply capacities of suppliers, operation capacities of logistics centers, and demands of customers, are modeled using triangular fuzzy numbers based on the fuzzy set theory to order to enhance the reliability of the logistics center location and allocation planning. To solve the green logistics center location and allocation problem under mixed uncertainties, we establish two fuzzy mixed integer linear programming models. The fuzzy credibilistic chance-constrained programming is then adopted to obtain the crisp and linear reformulations of the fuzzy programming models. A numerical case is given to verify the feasibility of the proposed methods, in which the performance of carbon tax regulation in reducing carbon dioxide emissions is then tested based on the benchmark provided by the multi-objective optimization. Lastly, sensitivity analysis and fuzzy simulation are utilized to reveal the effect of the mixed uncertainties on the logistics location and allocation planning and further determine the best confidence level in the fuzzy chance constraints to provide decision makers with a crisp plan.

[1]  Kaveh Khalili-Damghani,et al.  Type-II Fuzzy Multi-Product, Multi-Level, Multi-Period Location–Allocation, Production–Distribution Problem in Supply Chains: Modelling and Optimisation Approach , 2018 .

[2]  Baoding Liu,et al.  Fuzzy vehicle routing model with credibility measure and its hybrid intelligent algorithm , 2006, Appl. Math. Comput..

[3]  Shaligram Pokharel,et al.  The Design of Green Supply Chains under Carbon Policies: A Literature Review of Quantitative Models , 2019, Sustainability.

[4]  Jorge Pinho de Sousa,et al.  A two-phase MILP approach to integrate order, customer and manufacturer characteristics into Dynamic Manufacturing Network formation and operational planning , 2018, Expert Syst. Appl..

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

[6]  Saman Hassanzadeh Amin,et al.  A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return , 2013 .

[7]  Felix T.S. Chan,et al.  A three-stage and multi-objective stochastic programming model to improve the sustainable rescue ability by considering secondary disasters in emergency logistics , 2019, Comput. Ind. Eng..

[8]  C. Carter,et al.  REVERSE LOGISTICS: A REVIEW OF THE LITERATURE AND FRAMEWORK FOR FUTURE INVESTIGATION , 1998 .

[9]  Xiaofan Lai,et al.  A multi-objective optimization for green supply chain network design , 2011, Decis. Support Syst..

[10]  Xinya Li,et al.  A Fuzzy Programming Method for Modeling Demand Uncertainty in the Capacitated Road-Rail Multimodal Routing Problem with Time Windows , 2019, Symmetry.

[11]  Ziyou Gao,et al.  Modeling and optimization of a road-rail intermodal transport system under uncertain information , 2018, Eng. Appl. Artif. Intell..

[12]  Tong Shaocheng,et al.  Interval number and fuzzy number linear programmings , 1994 .

[13]  Tien-Fu Liang,et al.  Application of fuzzy sets to manufacturing/distribution planning decisions with multi-product and multi-time period in supply chains , 2009, Expert Syst. Appl..

[14]  Madjid Tavana,et al.  Multi-stage supply chain network solution methods: hybrid metaheuristics and performance measurement , 2018 .

[15]  Mitsuo Gen,et al.  Network model and optimization of reverse logistics by hybrid genetic algorithm , 2009, Comput. Ind. Eng..

[16]  Xinwang Liu,et al.  Measuring the satisfaction of constraints in fuzzy linear programming , 2001, Fuzzy Sets Syst..

[17]  Yoshiaki Shimizu,et al.  A flexible design of logistic network against uncertain demands through hybrid meta-heuristic method , 2006 .

[18]  Nico Vandaele,et al.  Multi-level reverse logistics network design under uncertainty , 2012 .

[19]  Yan Sun,et al.  A Bi-Objective Fuzzy Credibilistic Chance-Constrained Programming Approach for the Hazardous Materials Road-Rail Multimodal Routing Problem under Uncertainty and Sustainability , 2019, Sustainability.

[20]  Yan Sun,et al.  How Uncertain Information on Service Capacity Influences the Intermodal Routing Decision: A Fuzzy Programming Perspective , 2018, Inf..

[21]  Xinya Li,et al.  Fuzzy Programming Approaches for Modeling a Customer-Centred Freight Routing Problem in the Road-Rail Intermodal Hub-and-Spoke Network with Fuzzy Soft Time Windows and Multiple Sources of Time Uncertainty , 2019, Mathematics.

[22]  M. Gen,et al.  Method for solving multiobjective aggregate production planning problem with fuzzy parameters , 1992 .

[23]  Dezhi Zhang,et al.  A multimodal logistics service network design with time windows and environmental concerns , 2017, PloS one.

[24]  J. Mula,et al.  The effectiveness of a fuzzy mathematical programming approach for supply chain production planning with fuzzy demand , 2010 .

[25]  Cao Erbao,et al.  A hybrid differential evolution algorithm to vehicle routing problem with fuzzy demands , 2009 .

[26]  Chin-Shan Lu,et al.  Comparing carbon dioxide emissions of trucking and intermodal container transport in Taiwan , 2009 .

[27]  Turan Paksoy,et al.  Interactive fuzzy programming approaches to the strategic and tactical planning of a closed-loop supply chain under uncertainty , 2014 .

[28]  Der-Horng Lee,et al.  Dynamic network design for reverse logistics operations under uncertainty , 2009 .

[29]  Mir Saman Pishvaee,et al.  A memetic algorithm for bi-objective integrated forward/reverse logistics network design , 2010, Comput. Oper. Res..

[30]  Mohammad Hossein Fazel Zarandi,et al.  The multi-depot capacitated location-routing problem with fuzzy travel times , 2011, Expert Syst. Appl..

[31]  R. Lamming,et al.  Developing eco-innovations: A three-stage typology of supply networks , 2016 .

[32]  Fariborz Jolai,et al.  Robust and reliable forward–reverse logistics network design under demand uncertainty and facility disruptions , 2014 .

[33]  Wei Zhang,et al.  Integrating the logistics network design with order quantity determination under uncertain customer demands , 2014, Expert Syst. Appl..

[34]  Chen Zhang,et al.  A Time-Dependent Fuzzy Programming Approach for the Green Multimodal Routing Problem with Rail Service Capacity Uncertainty and Road Traffic Congestion , 2018, Complex..

[35]  Mir Saman Pishvaee,et al.  A stochastic optimization model for integrated forward/reverse logistics network design , 2009 .

[36]  Carlos A. Méndez,et al.  Multi-period design and planning of closed-loop supply chains with uncertain supply and demand , 2014, Comput. Chem. Eng..

[37]  Jean-François Cordeau,et al.  An integrated model for logistics network design , 2006, Ann. Oper. Res..

[38]  Jacek Żak,et al.  The Selection of the Logistics Center Location Based on MCDM/A Methodology☆ , 2014 .

[39]  Shad Dowlatshahi,et al.  Developing a Theory of Reverse Logistics , 2000, Interfaces.

[40]  Bartosz Sawik,et al.  Weighted-Sum Approach for Bi-objective Optimization of Fleet Size with Environmental Aspects , 2018, Applications of Management Science.

[41]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[42]  Shiwei He,et al.  Robust Optimization Model and Algorithm for Logistics Center Location and Allocation under Uncertain Environment , 2009 .

[43]  Mingyuan Chen,et al.  The distributionally robust newsvendor problem with dual sourcing under carbon tax and cap-and-trade regulations , 2016, Comput. Ind. Eng..

[44]  Teodor Gabriel Crainic,et al.  Service network design in freight transportation , 2000, Eur. J. Oper. Res..

[45]  Kannan Govindan,et al.  A fuzzy multi-objective optimization model for sustainable reverse logistics network design , 2016 .