Fuzzy Programming Approach to a Multi-Objective Fuzzy Stochastic Routing and Siting Hazardous Wastes

S. Dutta, S. Acharya, Rajashree Mishra

Abstract


The aim of the research article is not only to propose a solution procedure to solve multi-objective fuzzy stochastic programming problem by using genetic-algorithm-based fuzzy programming method, but also to apply the computational techniques for transportation of the hazardous waste materials. In this article, routing and siting problems for nuclear hazardous waste material are studied and solved. The amount of waste materials generated in the nuclear reactors follows normal distribution. The two considered objective functions are about route selection which includes minimum travel time and minimum number of houses along the way, taking the safety measures into consideration. A multi-objective fuzzy stochastic mathematical model is formulated with the above mentioned objective functions and the route selection as the constraints. The proposed solution procedure is illustrated by a numerical example and a case study.


Keywords


Fuzzy Stochastic Programming; Multi-Objective Programming; Fuzzy Programming; Genetic Algorithm

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References


Ardjmand E, Weckman G, Park N, et al. Applying genetic algorithm to a new location and routing model of hazardous materials. International Journal of Production Research 2015; 53(3): 916–928.

Ardjmand E, Young WA, Weckman GR, et al. Applying genetic algorithm to a new biobjective stochastic model for transportation, location, and allocation of hazardous materials. Expert Systems with Applications 2016; 51: 49–58.

Karadimas NV, Kouzas G, Anagnostopoulos I, et al. Urban solid waste collection and routing: The ant colony strategic approach. International Journal of Simulation: Systems, Science & Technology 2005; 6(12-13): 45–53.

Samanlioglu F. A multi-objective mathematical model for the industrial hazardous waste location-routing problem. European Journal of Operational Research 2013; 226(2): 332–340.

Current J, Ratick S. A model to assess risk, equity and efficiency in facility location and transportation of hazardous materials. Location Science 1995; 3(3): 187–201.

Giannikos I. A multiobjective programming model for locating treatment sites and routing hazardous wastes. European Journal of Operational Research 1998; 104(2): 333–342.

List G, Mirchandani P. An integrated network/planar multiobjective model for routing and siting for hazardous materials and wastes. Transportation Science 1991; 25(2): 146–156.

List G, Mirchandani P. Community-focused routing and siting model for hazardous materials and wastes. Proceedings of the National Conference on Hazardous Materials Transportation; ASCE; 1991.

Nema AK, Gupta SK. Optimization of regional hazardous waste management systems: An improved formulation. Waste Management 1999; 19(7): 441–451.

Gomez JR, Pacheco J, Gonzalo-Orden H. A tabu search method for a bi-objective urban waste collection problem. Computer-Aided Civil and Infrastructure Engineering 2015; 30(1): 36–53.

Warmerdam JM, Jacobs TL. Fuzzy set approach to routing and siting hazardous waste operations. Information Sciences-Applications 1994; 2(1): 1–14.

Liu B. Minimax chance constrained programming models for fuzzy decision systems. Information Sciences 1998; 112(1): 25–38.

Chang NB, Davila E. Siting and routing assessment for solid waste management under uncertainty using the grey mini-max regret criterion. Environmental Management 2006; 38(4): 654–672.

Bit AK, Biswal MP, Alam SS. Fuzzy programming approach to multicriteria decision making transportation problem. Fuzzy Sets and Systems 1992; 50(2): 135–141.

Hulsurkar S, Biswal MP, Sinha SB. Fuzzy programming approach to multi-objective stochastic linear programming problems. Fuzzy Sets and Systems 1997; 88(2): 173–181.

Kumar M, Vrat P, Shankar R. A fuzzy programming approach for vendor selection problem in a supply chain. International Journal of Production Economics 2006; 101(2): 273–285.

Liu ST, Kao C. Solving fuzzy transportation problems based on extension principle. European Journal of Operational Research 2004; 153(3): 661–674.

Zadeh LA. Fuzzy sets. Information and Control 1965; 8(3): 338–353.

Charnes A, Cooper WW. Chance-constrained programming. Management Science 1959; 6(1): 73–79.

Mohan C, Nguyen HT. A fuzzifying approach to stochastic programming. Opsearch 1997; 34: 73–96.

Acharya S, Biswal MP. Solving probabilistic programming problems involving multi-choice parameters. Opsearch 2011; 48(3): 217–235.

Sakawa M, Nishizaki I, Katagiri H. Fuzzy stochastic multiob-jective programming. Science & Business Media 2011; 159.

Wang S, Watada J. Fuzzy stochastic optimization: Theory, models and applications. Science & Business Media 2012.

Mousavi SM, Jolai F, Tavakkoli-Moghaddam R. A fuzzy stochastic multi-attribute group decision-making approach for selection problems. Group Decision and Negotiation 2013; 22(2): 207–233.

Sakawa M, Matsui T. Interactive fuzzy programming for stochastic two-level linear programming problems through probability maximization. Artificial Intelligence Research 2013; 2(2): 109–124.

Aiche F, Abbas M, Dubois D. Chance-constrained programming with fuzzy stochastic coefficients. Fuzzy Optimization and Decision Making 2013; 12(2): 125–152.

Acharya S, Ranarahu N, Dash JK, et al. Solving multi-objective fuzzy probabilistic programming problem. Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology 2014; 26(2): 935–948.

Acharya S, Ranarahu N, Dash JK, et al. Computation of a multi-objective fuzzy stochastic transportation problem. International Journal of Fuzzy Computation and Modelling 2014; 1(2): 212–233.

Li Y, Liu J, Huang G. A hybrid fuzzy-stochastic programming method for water trading within an agricultural system. Agricultural Systems 2014; 123: 71–83.

Holland JH. Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. United States: University of Michigan Press; 1975.

Liu B, Iwamura K. Fuzzy programming with fuzzy decisions and fuzzy simulation-based genetic algorithm. Fuzzy Sets and Systems 2001; 122(2): 253–262.

Jana RK, Biswal MP. Stochastic simulation-based genetic algorithm for chance constraint programming problems with continuous random variables. International Journal of Computer Mathematics 2004; 81(9): 1069–1076.

Jana RK, Biswal MP. Genetic based fuzzy goal programming for multiobjective chance constrained programming problems with continuous random variables. International Journal of Computer Mathematics 2006; 83(2): 171–179.

Dutta S, Sahoo BC, Mishra R, et al. Fuzzy stochastic genetic algorithm for obtaining optimum crops pattern and water balance in a farm. Water Resources Management 2016; 30(12): 4097–4123.

Dutta S, Acharya S, Mishra R. Genetic algorithm based fuzzy stochastic transportation programming problem with continuous random variables. Opsearch 2016; 53(4): 835–872.

Lai YJ, Hwang CL. A new approach to some possibilistic linear programming problems. Fuzzy Sets and Systems 1992; 49(2): 121–133.

Buckley JJ. Fuzzy probabilities: New approach and applications. Science & Business Media 2005; 115.

Nanda S, Kar K. Convex fuzzy mappings. Fuzzy Sets and Systems 1992; 48(1): 129–132.

Buckley JJ, Eslami E. Uncertain probabilities ii: The continuous case. Soft Computing 2004; 8(3): 193–199.

ReVelle C, Cohon J, Shobrys D. Simultaneous siting and routing in the disposal of hazardous wastes. Transportation Science 1991; 25(2): 138–145.




DOI: http://dx.doi.org/10.24294/tm.v3i1.616

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