ORIGINAL_ARTICLE
Linear programming problem with generalized interval-valued fuzzy numbers
In this paper, we concentrate on linear programming problems in which the cost vector, the technological coefficients and the right-hand side values are interval-valued generalized trapezoidal fuzzy numbers. To the best of our knowledge, till now there is no method described in the literature to find the optimal solution of the linear programming problems with interval-valued generalized trapezoidal fuzzy numbers. We apply the signed distance for defuzzification of this problem. The crisp problem obtained after the defuzzification is solved by the linear programming methods. Finally, we give an illustrative example and its numerical solutions.
https://aotp.fabad-ihe.ac.ir/article_58381_a9b86c96007308f6d3316bfc2eccec6c.pdf
2018-05-01
1
9
10.22121/aotp.2018.119731.1010
Linear programming problem
Generalized trapezoidal fuzzy number
Interval-valued generalized trapezoidal fuzzy number
Rohollah
Taghaodi
taghaode@yahoo.com
1
Department of Mathematics, Kashan Branch, Islamic Azad University, Kashan, Iran
LEAD_AUTHOR
Fatemeh
Kardani
fkardani@gmail.com
2
Department of Industrial Engineering, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran
AUTHOR
Allahviranloo, T., Lotfi, F. H., Kiasary, M. K., Kiani, N. A., & Alizadeh, L. (2008). Solving fully fuzzy linear programming problem by the ranking function. Applied mathematical sciences, 2(1), 19-32.
1
Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17(4), B-141.
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Baranifar, S. (2018). A credibility-constrained programming for closed-loop supply chain network design problem under uncertainty. Annals of Optimization Theory and Practice, 1(1), 69-83.
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Bazaraa, M. S., Jarvis, J. J., & Sherali, H. D. (1990). Linear programming and network flows. John Wiley, New York, Second Edition.
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Chen, J. H. C. S. M., & Chen, S. M. (2006). A new method for ranking generalized fuzzy numbers for handling fuzzy risk analysis problems. In Proceedings of the Ninth Conference on Information Sciences, 1196–1199.
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Chen, S.H. (1985). Operations on fuzzy numbers with function principal. Tamkang Journal of Management Science, 6 (1), 13–25.
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Chen, T. Y. (2012). Multiple criteria group decision-making with generalized interval-valued fuzzy numbers based on signed distances and incomplete weights. Applied Mathematical Modelling, 36, 3029–3052.
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Chen,S.H. (1985). Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems, 17, 13–129.
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Ebrahimnejad, A. (2016). Fuzzy linear programming approach for solving transportation problems with interval-valued trapezoidal fuzzy numbers. Sadhana, 41 (3), 299–316.
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Farhadinia, B. (2014). Sensitivity analysis in interval-valued trapezoidal fuzzy number linear programming problems. Applied Mathematical Modelling, 38, 50–62.
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Gorzalczany, M. B. (1987). A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems, 21(1), 1–17.
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Hong, D. H., Lee, S. (2002). Some algebraic properties and a distance measure for interval-valued fuzzy numbers. Information Sciences, 148 (1), 1–10.
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Turksen, I. B. (1996). Interval-valued strict preference with Zadeh triples. Fuzzy Sets and Systems, 78 (2), 183–195.
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Wang, G., Li, Xi. (1998). The applications of interval-valued fuzzy numbers and interval-distribution numbers. Fuzzy Sets and Systems, 98, 331–335.
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Wei, S. H., & Chen, S. M. (2009). Fuzzy risk analysis based on interval-valued fuzzy numbers. Expert Systems with Applications, 36(2), 2285-2299.
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Wang, G., & Li, X. (2001). Correlation and information energy of interval-valued fuzzy numbers. Fuzzy sets and systems, 103, 69-175.
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Zadeh, A. (1965). Fuzzy Sets. Information and Control, 8, 338-353.
17
ORIGINAL_ARTICLE
A Fuzzy multi-product two-stage supply chain network design with possibility of direct shipment
The configuration of the supply chain network (SCN) is one of the strategic issues that have a major impact on the overall performance of the supply chain. A well designed SCN leads to an ability to reduce the supply chain total cost. These purposes are influenced by the supply chain strategy, which is based either on direct or indirect supply or shipment. In the case of direct shipment, the products are directly transported from the point of origin to the customers. In the classic transportation problems, it is usually assumed that the transportation time and costs are certain. Most existing mathematical models neglect the presence of uncertainty within a programming environment. This uncertainty might come about because of traffic jam, machine malfunctioning, defect in raw material, interpretation of various events and etc. These emprise parameters can be considering as fuzzy numbers. In this study, for the first time a mathematical model for a responsive, multi-product two-stage, SCN with possibility of direct shipment is proposed. Because of the unpredictable factors that mentioned above, cost coefficients are considered as trapezoidal fuzzy numbers. Therefore, for validation, the proposed model is coded by GAMS software. The results showed that relevant model is valid.
https://aotp.fabad-ihe.ac.ir/article_63490_d17677e0ff2525aca943756ac3e6e384.pdf
2018-05-01
11
22
10.22121/aotp.2018.130632.1013
Supply chain network
Direct shipment
mathematical model
Fuzzy theory
Saber
Molla-Alizadeh-Zavardehi
saber.alizadeh@gmail.com
1
Department of Industrial Engineering, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran
LEAD_AUTHOR
Abbas
Shoja
abbas.sh61@yahoo.com
2
Department of Industrial Engineering, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran
AUTHOR
Basirzadeh, H. & Abbasi, R. (2008). A new approach for ranking fuzzy numbers based on cuts. Journal of Applied Mathematics and Informatics, 11, 767–78.
1
Chanas, S. & Kuchta, D. (1996). A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets and Systems, 82, 299–305.
2
Ebrahimnejad, A. (2016). A New Method for Solving Fuzzy Transportation Problem with LR Flat Fuzzy Numbers. Information Sciences, 357, 108-124.
3
Farahani, R.Z., Rezapour, S., Drezner, T. & Fallah, S. (2014). Competitive supply chain network design: An overview of classifications, models, solution techniques and applications. Omega, 45, 92-118.
4
Gao, S.P. & Liu, S.Y. (2004). Two-phase fuzzy algorithms for multi-objective transportation problem. The Journal of Fuzzy Mathematics, 12, 147-155.
5
Giri, P.K., Maiti, M.K. & Maiti, M. (2015). Fully fuzzy fixed charge multi-item solid transportation problem. Applied Soft Computing, 27, 77-91.
6
Hirsch, W.M. & Dantzig, G.B. (1968). The fixed charge problem. Naval Research Logistics, 15, 413–424.
7
Jimenez, F. & Verdegay, J.L. (1998). Uncertain solid transportation problems. Fuzzy Sets and Systems, 100, 45–57.
8
Jimenez, F. & Verdegay, J.L. (1999). Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach. European Journal of Operational Research, 117, 485–510.
9
Kocken, H. G. & Sivri M. (2016). a simple parametric method to generate all optimal solutions of Fuzzy Solid Transportation Problem. Applied Mathematical Modelling, 40, 4612-4624.
10
Li, Y., Ida, K. & Gen, M. (1997). Improved genetic algorithm for solving multiobjective solid transportation problem with fuzzy numbers. Computers & Industrial Engineering, 33, 589–592.
11
Liu, P., Yang, L., Wang, L. & Shukai. L. (2014). A solid transportation problem with type-2 fuzzy variables. Applied Soft Computing, 24, 543–558.
12
Lin, L. Gen, M. & Wang, X. (2009). Integrated multistage logistics network design by using hybrid evolutionary algorithm. Computers & Industrial Engineering, 56, 854–873.
13
Molla-Alizadeh-Zavardehi, S., Sadi Nezhad, S., Tavakkoli-Moghaddam, R. & Yazdani, M. (2013). Solving a fuzzy fixed charge solid transportation problem by metaheuristics. Mathematical and Computer Modelling, 57, 1543–1558.
14
Mahmoodirad, A. & Sanei, M. (2016). Solving a multi-stage multi-product solid supply chain network design problem by meta-heuristics. Scientia Iranica E, 23, 1429-1440.
15
Omar, M.S. & Samir, A.A. (2003). A parametric study on transportation problem under fuzzy environment. Engineering Journal of the University of Qatar, 15, 165-176.
16
Pishvaee, M.S., Rabbani, M. (2011). A graph theoretic-based heuristic algorithm for responsive supply chain network design with direct and indirect shipment. Advances in Engineering Software, 42, 57–63.
17
Pramanik, S., Jana, D.K. & Maiti, M. (2013). Multi-objective solid transportation problem in imprecise environments. Journal of Transportation Security, 6, 131-150.
18
Pramanik, S., Jana, D. K., Mondal ,S.K. & Maiti, M. (2015). A fixed-charge transportation problem in two-stage supply chain network in Gaussian type-2 fuzzy environments. Information Sciences, 325, 190-214.
19
Rani D. & Gulati, T.R. (2014). A new approach to solve unbalanced transportation problems in imprecise environment. Journal of Transportation Security, 7, 277-287.
20
Sakawa, M. & Yano, H. (1986). Interactive fuzzy decision making for multiobjective nonlinear programming using augmented minimax problems. Fuzzy Sets and Systems, 20, 31-43.
21
Sakawa, M., Yano, H. & Yumine, T. (1987). An Interactive fuzzy satisfying method for multi-objective linear programming problems and its application. IEEE Transactions on Man, Systems, and Cybernetics, 17, 654–661.
22
Samanta, B. & Roy, T.K. (2005). Multi-objective entropy transportation model with trapezoidal fuzzy number penalties, sources and destination. Journal of Transportation Engineering, 131, 419–428.
23
Singh, S. & Gupta, G. (2014). A new approach for solving cost minimization balanced transportation problem under uncertainty. Journal of Transportation Security, 7, 339-345.
24
Sanei, M. Mahmoodirad, A. & Niroomand, S. (2016). Two-Stage Supply Chain Network Design Problem with Interval Data. International Journal of e-Navigation and Maritime Economy, 5, 074 – 084.
25
Yang, L. & Liu, L. (2007). Fuzzy fixed charge solid transportation problem and algorithm. Applied Soft Computing, 7, 879–889.
26
ORIGINAL_ARTICLE
Country risk assessment by applying multi-criteria decision-making methods: a case study to rank countries in the Middle East & North Africa
The Middle East and North Africa (MENA) have been attracting many international investors for decades, but the current geopolitical situation has not shown a welcoming face towards foreign investors. Consequences of war, terror and political changes in the region have forced many international companies to reconsider their plans or withdraw their investments. On the other hand, there are companies that have faith in investing in the emerging market of the MENA with fewer competitors. It must be mentioned that narrowing down the best possible decision needs research on the current situation as well as analyzing and forecasting of the upcoming situations in terms of many factors within the country concerned and the region. The Multi-Criteria Decision Making (MCDM) analysis helps investors to choose the best alternative from a set of relevant criteria. In this paper, one of the well-known MCDM methods, TOPSIS, was used to rank twenty-three countries based on twenty key indicators within the years 2000-2015. The outcome of these findings provides a set of country rankings for an interested group of decision makers, policy makers, stakeholders, and other involved parties based on their interest in the MENA region in the so-called Arab Spring and post-Arab Spring environment.
https://aotp.fabad-ihe.ac.ir/article_65263_7b9190c5de531be2b10cebad9981f857.pdf
2018-05-01
23
34
10.22121/aotp.2018.126114.1011
Multi-criteria decision making
TOPSIS
Country risk ranking
International investors
Ahmad
Mohammadi Dehcheshmeh
dehcheshmeh.m.a@gmail.com
1
Businesses Administration, Faculty of Economic and administrative science, Istanbul Aydin University, Florya, Istanbul, Turkey
LEAD_AUTHOR
Nima
Mirzaei
nimamirzaei@aydin.edu.tr
2
Department of Industrial Engineering, Faculty of Engineering, Istanbul Aydin University, Florya, Istanbul, Turkey
AUTHOR
Abdullah, L. (2013). Fuzzy multi criteria decision making and its applications: A brief review of category. Procedia-Social and Behavioral Sciences, 97, 131-136.
1
Akbaş, H., & Bilgen, B. (2017). An integrated fuzzy QFD and TOPSIS methodology for choosing the ideal gas fuel at WWTPs. Energy, 125, 484-497.
2
Bilbao-Terol, A., Arenas-Parra, M., Cañal-Fernández, V., & Antomil-Ibias, J. (2014). Using TOPSIS for assessing the sustainability of government bond funds. Omega, 49, 1-17.
3
Hwang, C. L., & Masud, A. S. M. (2012). Multiple objective decision making—methods and applications: a state-of-the-art survey (Vol. 164). Springer Science & Business Media.
4
Özcan, E. C., Ünlüsoy, S., & Eren, T. (2017). A combined goal programming–AHP approach supported with TOPSIS for maintenance strategy selection in hydroelectric power plants. Renewable and Sustainable Energy Reviews, 78, 1410-1423.
5
Ervural, B. C., Zaim, S., Demirel, O. F., Aydin, Z., & Delen, D. (2017). An ANP and fuzzy TOPSIS-based SWOT analysis for Turkey’s energy planning. Renewable and Sustainable Energy Reviews.
6
Gul, M., Celik, E., Aydin, N., Gumus, A. T., & Guneri, A. F. (2016). A state of the art literature review of VIKOR and its fuzzy extensions on applications. Applied Soft Computing, 46, 60-89.
7
Kumar, A., Sah, B., Singh, A. R., Deng, Y., He, X., Kumar, P., & Bansal, R. C. (2017). A review of multi criteria decision making (MCDM) towards sustainable renewable energy development. Renewable and Sustainable Energy Reviews, 69, 596-609.
8
Majumder, M. (2015). Multi criteria decision making. In Impact of urbanization on water shortage in face of climatic aberrations (pp. 35-47). Springer, Singapore.
9
Mandic, K., Delibasic, B., Knezevic, S., & Benkovic, S. (2014). Analysis of the financial parameters of Serbian banks through the application of the fuzzy AHP and TOPSIS methods. Economic Modelling, 43, 30-37.
10
Othman, M. K., Fadzil, M. N., & Rahman, N. S. F. A. (2015). The Malaysian Seafarers Psychological Distraction Assessment Using a TOPSIS Method. International Journal of e-Navigation and Maritime Economy, 3, 40-50.
11
Radmehr, A., & Araghinejad, S. (2015). Flood vulnerability analysis by fuzzy spatial multi criteria decision making. Water resources management, 29(12), 4427-4445.
12
Roszkowska, E. (2013). Rank ordering criteria weighting methods–a comparative overview.
13
Sánchez-Lozano, J. M., García-Cascales, M. S., & Lamata, M. T. (2016). Comparative TOPSIS-ELECTRE TRI methods for optimal sites for photovoltaic solar farms. Case study in Spain. Journal of Cleaner Production, 127, 387-398.
14
Torlak, G., Sevkli, M., Sanal, M., & Zaim, S. (2011). Analyzing business competition by using fuzzy TOPSIS method: An example of Turkish domestic airline industry. Expert Systems with Applications, 38(4), 3396-3406.
15
Yan, X. P., Wan, C. P., Zhang, D., & Yang, Z. L. (2017). Safety management of waterway congestions under dynamic risk conditions—A case study of the Yangtze River. Applied Soft Computing, 59, 115-128.
16
ORIGINAL_ARTICLE
Refueling station location problem under uncertain environment
Development of the infrastructure of alternative fuel stations is one of the best ways to extend the use of alternative fuel vehicles. Hence, constructing refueling stations with minimum cost is an important issue. On the other hand, considering the exact value of cost is not match with real cases. In this regard, the cost of building station is considered as a trapezoidal fuzzy value and a mathematical fuzzy programming model is presented in this paper. In order to solve the fuzzy model, first the model is converted to an interval programming model, then the equivalent bi-objective crisp model of the interval programming problem is written. Finally, two interactive fuzzy solution approaches are used to solve the respective bi-objective crisp model. The results show that the performance of the solution approaches is the same.
https://aotp.fabad-ihe.ac.ir/article_65264_51572994fe8ccfddc92ace0056fb8732.pdf
2018-05-01
35
45
10.22121/aotp.2018.129441.1012
Refueling station
Facility location
Fuzzy programming
Farzaneh
Ferdowsi
f.ferdowsi@sutech.ac.ir
1
Faculty of Mathematics, Shiraz University of Technology, Shiraz, Iran
LEAD_AUTHOR
Milad
Nasiri
traumamedicalinfo@sums.ac.ir
2
Rajaee hospital (Emtiaz), Trauma Research Center, Shiraz University of Medical Sciences, Shiraz, Iran
AUTHOR
Upchurch, C., & Kuby, M. (2010). Comparing the p-median and flow-refueling models for locating alternative-fuel stations. Journal of Transport Geography, 18(6), 750-758.
1
Upchurch, C., Kuby, M., & Lim, S. (2009). A Model for Location of Capacitated Alternative‐Fuel Stations. Geographical Analysis, 41(1), 85-106.
2
Ferdowsi, F., Maleki, H. R., & Niroomand, S. (2018). A credibility-based hybrid fuzzy programming approach for a bi-objective refueling alternative fuel vehicles problem under uncertainty. Journal of Intelligent & Fuzzy Systems, 34(4), 2385-2399.
3
Ferdowsi, F., Maleki, H. R., & Rivaz, S. (2018). Air refueling tanker allocation based on a multi-objective zero-one integer programming model. Operational Research, 1-26.
4
Alefeld, G., & Herzberger, J. (1983). Introduction to interval computation. Academic press.
5
Selim, H., & Ozkarahan, I. (2008). A supply chain distribution network design model: an interactive fuzzy goal programming-based solution approach. The International Journal of Advanced Manufacturing Technology, 36(3-4), 401-418.
6
Capar, I., & Kuby, M. (2011). An efficient formulation of the flow refueling location model for alternative-fuel stations. IIE Transactions
7
He, J., Yang, H., Tang, T. Q., & Huang, H. J. (2018). An optimal charging station location model with the consideration of electric vehicle’s driving range. Transportation Research Part C: Emerging Technologies, 86, 641-654.
8
Hodgson, M. J. (1990). A Flow‐Capturing Location‐Allocation Model. Geographical Analysis, 22(3), 270-279.
9
Hosseini, M., MirHassani, S. A., & Hooshmand, F. (2017). Deviation-flow refueling location problem with capacitated facilities: Model and algorithm. Transportation Research Part D: Transport and Environment, 54, 269-281.
10
Melendez, M., & Milbrandt, A. (2006). Geographically based hydrogen consumer demand and infrastructure analysis (No. NREL/TP-560-40373). National Renewable Energy Laboratory (NREL), Golden, CO..
11
Melendez, M., Theis, K., & Johnson, C. (2007). Lessons Learned from the Alternative Fuels Experience and How They Apply to the Development of a Hydrogen-Fueled Transportation System (No. NREL/TP-560-40753). National Renewable Energy Lab.(NREL), Golden, CO (United States).
12
Kuby, M., & Lim, S. (2005). The flow-refueling location problem for alternative-fuel vehicles. Socio-Economic Planning Sciences, 39(2), 125-145.
13
Kuby, M., & Lim, S. (2007). Location of alternative-fuel stations using the flow-refueling location model and dispersion of candidate sites on arcs. Networks and Spatial Economics, 7(2), 129-152.
14
Berman, O., Larson, R. C., & Fouska, N. (1992). Optimal location of discretionary service facilities. Transportation Science, 26(3), 201-211.
15
Grzegorzewski, P. (2002). Nearest interval approximation of a fuzzy number. Fuzzy Sets and systems, 130(3), 321-330.
16
Church, R., & ReVelle, C. (1974, December). The maximal covering location problem. In Papers of the Regional Science Association (Vol. 32, No. 1, pp. 101-118). Springer-Verlag.
17
Moore, R. E. (1979). Method and application of interval analysis, SLAM. Philadelphia, PA.
18
MirHassani, S. A., & Ebrazi, R. (2013). A flexible reformulation of the refueling station location problem. Transportation Science, 47(4), 617-628.
19
Das, S. K., Goswami, A., & Alam, S. S. (1999). Multiobjective transportation problem with interval cost, source and destination parameters. European Journal of Operational Research, 117(1), 100-112.
20
Sen, S., & Pal, B. B. (2015). Interval Goal Programming Approach to Multiobjective Programming Problems with Fuzzy Data Uncertainty. In Information Systems Design and Intelligent Applications (pp. 457-467). Springer, New Delhi.
21
Chen, Y. W., Cheng, C. Y., Li, S. F., & Yu, C. H. (2018). Location optimization for multiple types of charging stations for electric scooters. Applied Soft Computing, 67, 519-528.
22
Wang, Y. W., & Lin, C. C. (2009). Locating road-vehicle refueling stations. Transportation Research Part E: Logistics and Transportation Review, 45(5), 821-829.
23
Wang, Y. W., & Wang, C. R. (2010). Locating passenger vehicle refueling stations. Transportation Research Part E: Logistics and Transportation Review, 46(5), 791-801.
24
Lin, Z., Ogden, J., Fan, Y., & Chen, C. W. (2008). The fuel-travel-back approach to hydrogen station siting. International journal of hydrogen energy, 33(12), 3096-3101.
25