Application of two-phase fuzzy optimization approach to multiproduct multistage integrated production planning with linguistic preference under uncertainty.

*(English)*Zbl 1394.90251Summary: This paper tackles the challenges for a production planning problem with linguistic preference on the objectives in an uncertain multiproduct multistage manufacturing environment. The uncertain sources are modelled by fuzzy sets and involve those induced by both the epistemic factors of process and external factors from customers and suppliers. A fuzzy multiobjective mixed integer programming model with different objective priorities is proposed to address the problem which attempts to simultaneously minimize the relevant operations cost and maximize the average safety stock holding level and the average service level. The epistemic and external uncertainty is simultaneously considered and formulated as flexible constraints. By defining the priority levels, a two-phase fuzzy optimization approach is used to manage the preference extent and convert the original model into an auxiliary crisp one. Then a novel interactive solution approach is proposed to solve this problem. An industrial case originating from a steel rolling plant is applied to implement the proposed approach. The numerical results demonstrate the efficiency and feasibility to handle the linguistic preference and provide a compromised solution in an uncertain environment.

##### MSC:

90B30 | Production models |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

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\textit{S. Lu} et al., Math. Probl. Eng. 2015, Article ID 780830, 20 p. (2015; Zbl 1394.90251)

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##### References:

[1] | Jans, R.; Degraeve, Z., Modeling industrial lot sizing problems: a review, International Journal of Production Research, 46, 6, 1619-1643, (2008) · Zbl 1160.90407 |

[2] | Kenné, J.-P.; Gharbi, A.; Beit, M., Age-dependent production planning and maintenance strategies in unreliable manufacturing systems with lost sale, European Journal of Operational Research, 178, 2, 408-420, (2007) · Zbl 1107.90012 |

[3] | Helber, S.; Sahling, F.; Schimmelpfeng, K., Dynamic capacitated lot sizing with random demand and dynamic safety stocks, OR Spectrum, 35, 1, 75-105, (2013) · Zbl 1260.90084 |

[4] | Peidro, D.; Mula, J.; Poler, R.; Verdegay, J.-L., Fuzzy optimization for supply chain planning under supply, demand and process uncertainties, Fuzzy Sets and Systems, 160, 18, 2640-2657, (2009) · Zbl 1279.90206 |

[5] | Mula, J.; Poler, R.; García-Sabater, J. P.; Lario, F. C., Models for production planning under uncertainty: a review, International Journal of Production Economics, 103, 1, 271-285, (2006) |

[6] | Gupta, A.; Maranas, C. D.; McDonald, C. M., Mid-term supply chain planning under demand uncertainty: customer demand satisfaction and inventory management, Computers & Chemical Engineering, 24, 12, 2613-2621, (2000) |

[7] | Santoso, T.; Ahmed, S.; Goetschalckx, M.; Shapiro, A., A stochastic programming approach for supply chain network design under uncertainty, European Journal of Operational Research, 167, 1, 96-115, (2005) · Zbl 1075.90010 |

[8] | Azaron, A.; Brown, K. N.; Tarim, S. A.; Modarres, M., A multi-objective stochastic programming approach for supply chain design considering risk, International Journal of Production Economics, 116, 1, 129-138, (2008) |

[9] | Birge, J. R.; Louveaux, F., Introduction to Stochastic Programming, (2011), Berlin, Germany: Springer, Berlin, Germany · Zbl 1223.90001 |

[10] | Kira, D.; Kusy, M.; Rakita, I., A stochastic linear programming approach to hierarchical production planning, Journal of the Operational Research Society, 48, 2, 207-211, (1997) · Zbl 0888.90081 |

[11] | Fleten, S.-E.; Kristoffersen, T. K., Short-term hydropower production planning by stochastic programming, Computers & Operations Research, 35, 8, 2656-2671, (2008) · Zbl 1169.90419 |

[12] | Zanjani, M. K.; Nourelfath, M.; Ait-Kadi, D., A multi-stage stochastic programming approach for production planning with uncertainty in the quality of raw materials and demand, International Journal of Production Research, 48, 16, 4701-4723, (2010) · Zbl 1197.90312 |

[13] | Inuiguchi, M.; Ramík, J., Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem, Fuzzy Sets and Systems, 111, 1, 3-28, (2000) · Zbl 0938.90074 |

[14] | Petrovic, D.; Roy, R.; Petrovic, R., Supply chain modelling using fuzzy sets, International Journal of Production Economics, 59, 1, 443-453, (1999) |

[15] | Guiffrida, A. L.; Nagi, R., Fuzzy set theory applications in production management research: a literature survey, Journal of Intelligent Manufacturing, 9, 1, 39-56, (1998) |

[16] | Bellman, R. E.; Zadeh, L. A., Decision-making in a fuzzy environment, Management Science, 17, 4, B-141-B-164, (1970) · Zbl 0224.90032 |

[17] | Zimmermann, H.-J., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 1, 45-55, (1978) · Zbl 0364.90065 |

[18] | Fung, R. Y. K.; Tang, J.; Wang, D., Multiproduct aggregate production planning with fuzzy demands and fuzzy capacities, IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, 33, 3, 302-313, (2003) |

[19] | Wang, R.-C.; Liang, T.-F., Application of fuzzy multi-objective linear programming to aggregate production planning, Computers & Industrial Engineering, 46, 1, 17-41, (2004) |

[20] | Wang, R.-C.; Liang, T.-F., Applying possibilistic linear programming to aggregate production planning, International Journal of Production Economics, 98, 3, 328-341, (2005) |

[21] | Vasant, P. M., Fuzzy production planning and its application to decision making, Journal of Intelligent Manufacturing, 17, 1, 5-12, (2006) |

[22] | Mula, J.; Poler, R.; Garcia, J. P., MRP with flexible constraints: a fuzzy mathematical programming approach, Fuzzy Sets and Systems, 157, 1, 74-97, (2006) · Zbl 1085.90062 |

[23] | Torabi, S. A.; Hassini, E., An interactive possibilistic programming approach for multiple objective supply chain master planning, Fuzzy Sets and Systems, 159, 2, 193-214, (2008) · Zbl 1168.90352 |

[24] | Torabi, S. A.; Ebadian, M.; Tanha, R., Fuzzy hierarchical production planning (with a case study), Fuzzy Sets and Systems, 161, 11, 1511-1529, (2010) · Zbl 1186.90046 |

[25] | Taghizadeh, K.; Bagherpour, M.; Mahdavi, I., Application of fuzzy multi-objective linear programming model in a multi-period multi-product production planning problem, International Journal of Computational Intelligence Systems, 4, 2, 228-243, (2011) |

[26] | Aliev, R. A.; Fazlollahi, B.; Guirimov, B. G.; Aliev, R. R., Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management, Information Sciences, 177, 20, 4241-4255, (2007) · Zbl 1142.90416 |

[27] | Hsu, H.-M.; Wang, W.-P., Possibilistic programming in production planning of assemble-to-order environments, Fuzzy Sets and Systems, 119, 1, 59-70, (2001) |

[28] | Lan, Y.-F.; Liu, Y.-K.; Sun, G.-J., Modeling fuzzy multi-period production planning and sourcing problem with credibility service levels, Journal of Computational and Applied Mathematics, 231, 1, 208-221, (2009) · Zbl 1167.90004 |

[29] | Figueroa-García, J. C.; Kalenatic, D.; Lopez-Bello, C. A., Multi-period mixed production planning with uncertain demands: fuzzy and interval fuzzy sets approach, Fuzzy Sets and Systems, 206, 21-38, (2012) · Zbl 1252.90019 |

[30] | Yaghin, R. G.; Torabi, S. A.; Ghomi, S. M. T. F., Integrated markdown pricing and aggregate production planning in a two echelon supply chain: a hybrid fuzzy multiple objective approach, Applied Mathematical Modelling, 36, 12, 6011-6030, (2012) · Zbl 1349.90295 |

[31] | Su, T.-S.; Lin, Y.-F., Fuzzy multi-objective procurement/production planning decision problems for recoverable manufacturing systems, Journal of Manufacturing Systems, (2014) |

[32] | Li, S.; Hu, C., Two-step interactive satisfactory method for fuzzy multiple objective optimization with preemptive priorities, IEEE Transactions on Fuzzy Systems, 15, 3, 417-425, (2007) |

[33] | Tiwari, R. N.; Dharmar, S.; Rao, J. R., Fuzzy goal programming—an additive model, Fuzzy Sets and Systems, 24, 1, 27-34, (1987) · Zbl 0627.90073 |

[34] | Lin, C.-C., A weighted max–min model for fuzzy goal programming, Fuzzy Sets and Systems, 142, 3, 407-420, (2004) · Zbl 1045.90091 |

[35] | Tiwari, R. N.; Dharmar, S.; Rao, J. R., Priority structure in fuzzy goal programming, Fuzzy Sets and Systems, 19, 3, 251-259, (1986) · Zbl 0602.90078 |

[36] | Chen, L.-H.; Tsai, F.-C., Fuzzy goal programming with different importance and priorities, European Journal of Operational Research, 133, 3, 548-556, (2001) · Zbl 1053.90140 |

[37] | Mula, J.; Peidro, D.; Poler, R., The effectiveness of a fuzzy mathematical programming approach for supply chain production planning with fuzzy demand, International Journal of Production Economics, 128, 1, 136-143, (2010) |

[38] | Kanyalkar, A. P.; Adil, G. K., An integrated aggregate and detailed planning in a multi-site production environment using linear programming, International Journal of Production Research, 43, 20, 4431-4454, (2005) · Zbl 1095.90534 |

[39] | Liu, S.; Papageorgiou, L. G., Multiobjective optimisation of production, distribution and capacity planning of global supply chains in the process industry, Omega, 41, 2, 369-382, (2013) |

[40] | Chen, S.-P.; Huang, W.-L., A membership function approach for aggregate production planning problems in fuzzy environments, International Journal of Production Research, 48, 23, 7003-7023, (2010) · Zbl 1210.90072 |

[41] | Abad, P. L., Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale, European Journal of Operational Research, 144, 3, 677-685, (2003) · Zbl 1012.90002 |

[42] | Perea-López, E.; Ydstie, B. E.; Grossmann, I. E., A model predictive control strategy for supply chain optimization, Computers and Chemical Engineering, 27, 8-9, 1201-1218, (2003) |

[43] | Peidro, D.; Mula, J.; Jiménez, M.; del Mar Botella, M., A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment, European Journal of Operational Research, 205, 1, 65-80, (2010) · Zbl 1187.90184 |

[44] | Jamalnia, A.; Soukhakian, M. A., A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning, Computers & Industrial Engineering, 56, 4, 1474-1486, (2009) |

[45] | Rommelfanger, H., Fuzzy linear programming and applications, European Journal of Operational Research, 92, 3, 512-527, (1996) · Zbl 0914.90265 |

[46] | Liang, T.-F., Application of fuzzy sets to manufacturing/distribution planning decisions in supply chains, Information Sciences, 181, 4, 842-854, (2011) · Zbl 1208.90008 |

[47] | Li, D. F.; Nan, J. X.; Zhang, M. J., A ranking method of triangular intuitionistic fuzzy numbers and application to decision making, International Journal of Computational Intelligence Systems, 3, 5, 522-530, (2010) |

[48] | Tanaka, H.; Asai, K., Fuzzy linear programming problems with fuzzy numbers, Fuzzy Sets and Systems, 13, 1, 1-10, (1984) · Zbl 0546.90062 |

[49] | Lai, Y.-J.; Hwang, C.-L., A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems, 49, 2, 121-133, (1992) |

[50] | Yeh, C.-H.; Deng, H., A practical approach to fuzzy utilities comparison in fuzzy multicriteria analysis, International Journal of Approximate Reasoning, 35, 2, 179-194, (2004) · Zbl 1068.91013 |

[51] | Bortolan, G.; Degani, R., A review of some methods for ranking fuzzy subsets, Fuzzy Sets and Systems, 15, 1, 1-19, (1985) · Zbl 0567.90056 |

[52] | Ramík, J.; ímánek, J., Inequality relation between fuzzy numbers and its use in fuzzy optimization, Fuzzy Sets and Systems, 16, 2, 123-138, (1985) · Zbl 0574.04005 |

[53] | Tsai, K.-M.; You, S.-Y.; Lin, Y.-H.; Tsai, C.-H., A fuzzy goal programming approach with priority for channel allocation problem in steel industry, Expert Systems with Applications, 34, 3, 1870-1876, (2008) |

[54] | Hu, C.-F.; Teng, C.-J.; Li, S.-Y., A fuzzy goal programming approach to multi-objective optimization problem with priorities, European Journal of Operational Research, 176, 3, 1319-1333, (2007) · Zbl 1109.90070 |

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