A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment.

*(English)*Zbl 1187.90184Summary: This paper models supply chain (SC) uncertainties by fuzzy sets and develops a fuzzy linear programming model for tactical supply chain planning in a multi-echelon, multi-product, multi-level, multi-period supply chain network. In this approach, the demand, process and supply uncertainties are jointly considered. The aim is to centralize multi-node decisions simultaneously to achieve the best use of the available resources along the time horizon so that customer demands are met at a minimum cost. This proposal is tested by using data from a real automobile SC. The fuzzy model provides the decision maker (DM) with alternative decision plans with different degrees of satisfaction.

##### MSC:

90B90 | Case-oriented studies in operations research |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C05 | Linear programming |

##### Software:

CPLEX
PDF
BibTeX
XML
Cite

\textit{D. Peidro} et al., Eur. J. Oper. Res. 205, No. 1, 65--80 (2010; Zbl 1187.90184)

Full Text:
DOI

**OpenURL**

##### References:

[1] | 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 |

[2] | Alonso-Ayuso, A.; Escudero, L.F.; Garin, A.; Ortuno, M.T.; Perez, G., An approach for strategic supply chain planning under uncertainty based on stochastic 0-1 programming, Journal of global optimization, 26, 1, 97-124, (2003) · Zbl 1116.90383 |

[3] | Amid, A.; Ghodsypour, S.H.; O’Brien, C., Fuzzy multiobjective linear model for supplier selection in a supply chain, International journal of production economics, 104, 2, 394-407, (2006) |

[4] | Bhatnagar, R.; Sohal, A.S., Supply chain competitiveness: measuring the impact of location factors, uncertainty and manufacturing practices, Technovation, 25, 5, 443-456, (2005) |

[5] | Buckley, J.J., Solving possibilistic linear-programming problems, Fuzzy sets and systems, 31, 3, 329-341, (1989) · Zbl 0671.90049 |

[6] | Cadenas, J.M.; Verdegay, J.L., Using fuzzy numbers in linear programming, IEEE transactions on systems man and cybernetics part B - cybernetics, 27, 6, 1016-1022, (1997) |

[7] | Carlsson, C.; Fuller, R., A fuzzy approach to taming the bullwhip effect, Advances in computational intelligence and learning: methods and applications international series in intelligent technologies, 18, 247-262, (2002) |

[8] | Carlsson, C.; Korhonen, P., A parametric approach to fuzzy linear-programming, Fuzzy sets and systems, 20, 1, 17-30, (1986) · Zbl 0603.90093 |

[9] | Chanas, S., The use of parametric programming in fuzzy linear-programming, Fuzzy sets and systems, 11, 3, 243-251, (1983) · Zbl 0534.90056 |

[10] | Chanas, S.; Delgado, M.; Verdegay, J.L.; Vila, M.A., Interval and fuzzy extensions of classical transportation problems, Transportation planning and technology, 17, 2, 203-218, (1993) |

[11] | Chen, S.P.; Chang, P.C., A mathematical programming approach to supply chain models with fuzzy parameters, Engineering optimization, 38, 6, 647-669, (2006) |

[12] | Childerhouse, P.; Towill, D.R., Analysis of the factors affecting real-world value stream performance, International journal of production research, 40, 15, 3499-3518, (2002) |

[13] | Christopher, M., Logistics and supply chain management, (1998), Pitman London |

[14] | Clark, T.H.; Scarf, H., Optimal polices for a multi-echelon inventory problem, Management science, 6, 475-490, (1960) |

[15] | Davis, T., Effective supply chain management, Sloan management review, 34, 4, 35-46, (1993) |

[16] | de Kok, T.; Inderfurth, K., Nervousness in inventory management: comparison of basic control rules, European journal of operational research, 103, 1, 55-82, (1997) · Zbl 0922.90049 |

[17] | Donselaar, K.V.; Nieuwenhof, J.V.; Visschers, J., The impact of material coordination concepts on planning stability in supply chains, International journal of production economics, 68, 169-176, (2000) |

[18] | Dubois, D., Prade, H., (1988). Possibility Theory. New York, London. · Zbl 0645.68108 |

[19] | Dubois, D.; Fargier, H.; Fortemps, P., Fuzzy scheduling: modelling flexible constraints vs. coping with incomplete knowledge, European journal of operational research, 147, 2, 231-252, (2003) · Zbl 1037.90028 |

[20] | Fazel, Z.; Turksen, I.B.; Saghiri, S., Supply chain: crisp and fuzzy aspects, International journal of applied mathematical computer sciences, 12, 3, 423-435, (2002) |

[21] | Gen, M.; Tsujimura, Y.; Ida, K., Method for solving multiobjective aggregate production planning problem with fuzzy parameters, Computers and industrial engineering, 23, 1-4, 117-120, (1992) |

[22] | Giannoccaro, I.; Pontrandolfo, P.; Scozzi, B., A fuzzy echelon approach for inventory management in supply chains, European journal of operational research, 149, 1, 185-196, (2003) · Zbl 1035.90002 |

[23] | Guillen, G.; Mele, E.; Bagajewicz, M.J.; Espuna, A.; Puigjaner, L., Multiobjective supply chain design under uncertainty, Chemical engineering science, 60, 6, 1535-1553, (2005) |

[24] | Gupta, A.; Maranas, C.D., Managing demand uncertainty in supply chain planning, Computers and chemical engineering, 27, 8-9, 1219-1227, (2003) |

[25] | Heilpern, S., The expected value of a fuzzy number, Fuzzy sets and systems, 47, 1, 81-86, (1992) · Zbl 0755.60004 |

[26] | Heisig, G., Planning stability under (s,S) inventory control rules, OR spectrum, 20, 4, 215-228, (1998) · Zbl 0917.90108 |

[27] | Herrera, F.; Verdegay, J.L., Three models of fuzzy integer linear programming, European journal of operational research, 83, 3, 581-593, (1995) · Zbl 0899.90160 |

[28] | Ho, C.F.; Chi, Y.P.; Tai, Y.M., A structural approach to measuring uncertainty in supply chains, International journal of electronic commerce, 9, 3, 91-114, (2005) |

[29] | ILOG Incorporation, (2003). CPLEX 9.0. USA. |

[30] | Jimenez, M., Ranking fuzzy numbers through the comparison of its expected intervals, International journal of uncertainty fuzziness and knowledge-based systems, 4, 4, 379-388, (1996) · Zbl 1232.03040 |

[31] | Jiménez, M.; Arenas, M.; Bilbao, A.; guez, M.V., Linear programming with fuzzy parameters: an interactive method resolution, European journal of operational research, 177, 1599-1609, (2007) · Zbl 1102.90345 |

[32] | Julien, B., An extension to possibilistic linear-programming, Fuzzy sets and systems, 64, 2, 195-206, (1994) |

[33] | Jung, J.Y.; Blau, G.; Pekny, J.F.; Reklaitis, G.V.; Eversdyk, D., A simulation based optimization approach to supply chain management under demand uncertainty, Computers and chemical engineering, 28, 10, 2087-2106, (2004) |

[34] | Kumar, M.; Vrat, P.; Shankar, R., A fuzzy goal programming approach for vendor selection problem in a supply chain, Computers and industrial engineering, 46, 1, 69-85, (2004) |

[35] | Kumar, M.; Vrat, P.; Shankar, R., A fuzzy programming approach for vendor selection problem in a supply chain, International journal of production economics, 101, 2, 273-285, (2006) |

[36] | Kumar, V.; Prakash; Tiwari, M.K.; Chan, F.T.S., Stochastic make-to-stock inventory deployment problem: an endosymbiotic psychoclonal algorithm based approach, International journal of production research, 44, 11, 2245-2263, (2006) |

[37] | Lababidi, H.M.S.; Ahmed, M.A.; Alatiqi, I.M.; Al Enzi, A.F., Optimizing the supply chain of a petrochemical company under uncertain operating and economic conditions, Industrial and engineering chemistry research, 43, 1, 63-73, (2004) |

[38] | Lai, Y.J.; Hwang, Ch. L., Fuzzy mathematical programming: methods and applications, (1992), Springer-Verlag Heidelberg |

[39] | Lai, Y.L.; Hwang, C.L., Fuzzy multiple objective decision making, (1994), Springer-Verlag Berlin, Heildelberg · Zbl 0823.90070 |

[40] | Lee, H.L.; Billington, C., Material management in decentralized supply chains, Operations research, 41, 5, 835-847, (1993) · Zbl 0800.90548 |

[41] | Liang, T.F., Distribution planning decisions using interactive fuzzy multi-objective linear programming, Fuzzy sets and systems, 157, 10, 1303-1316, (2006) · Zbl 1132.90384 |

[42] | Liang, T.F., Applying fuzzy goal programming to production/transportation planning decisions in a supply chain so, International journal of systems science, 38, 4, 293-304, (2007) · Zbl 1115.93056 |

[43] | Liu, S.T.; Kao, C., Solving fuzzy transportation problems based on extension principle, European journal of operational research, 153, 3, 661-674, (2004) · Zbl 1099.90507 |

[44] | Mason-Jones, R.; Towill, D.R., Shrinking the supply chain uncertainty circle, IOM control, 17-22, (1998) |

[45] | Maximal Software Incorporation, (2004). MPL Modeling System. Release 4.2e. USA. |

[46] | Minegishi, S.; Thiel, D., System dynamics modeling and simulation of a particular food supply chain, Simulation practice and theory, 8, 5, 321-339, (2000) · Zbl 1003.68649 |

[47] | Mula, J.; Poler, R.; Garcı´a, J.P.; Ortiz, A., Demand uncertainty effects of first tier suppliers of an automobile industry supply chain, The ICFAI journal of supply chain management, 2, 3, 19-39, (2005) |

[48] | Mula, J.; Poler, R.; Garcı´a, J.P., MRP with flexible constraints: a fuzzy mathematical programming approach, Fuzzy sets and systems, 157, 1, 74-97, (2006) · Zbl 1085.90062 |

[49] | Park, Y.B., An integrated approach for production and distribution planning in supply chain management, International journal of production research, 43, 6, 1205-1224, (2005) · Zbl 1068.90557 |

[50] | Peidro, D., 2007. Models for centralized supply chain planning under uncertainty. Application to an Automobile Supply Chain. Polytechnic University of Valencia, Thesis. ISBN: 978-84-690-5107-8. |

[51] | Peidro, D., Mula, J., Poler, R., 2007. Supply chain planning under uncertainty: a fuzzy linear programming approach. In: IEEE International Fuzzy Systems Conference, FUZZ-IEEE, pp. 1-6. · Zbl 1190.90299 |

[52] | Peidro, D.; Mula, J.; Poler, R.l.; Lario, F.C., Quantitative models for supply chain planning under uncertainty: a review, The international journal of advanced manufacturing technology, 43, 3-4, 400-420, (2009) |

[53] | Petrovic, D., Simulation of supply chain behaviour and performance in an uncertain environment, International journal of production economics, 71, 1-3, 429-438, (2001) |

[54] | Petrovic, D.; Roy, R.; Petrovic, R., Modelling and simulation of a supply chain in an uncertain environment, European journal of operational research, 109, 2, 299-309, (1998) · Zbl 0937.90047 |

[55] | Petrovic, D.; Roy, R.; Petrovic, R., Supply chain modelling using fuzzy sets, International journal of production economics, 59, 1-3, 443-453, (1999) |

[56] | Rommelfanger, H.; Slowinski, R., Fuzzy linear programming with single or multiple objective functions, () · Zbl 0944.90048 |

[57] | Saaty, T.M., How to make a decision: the analytic hierarchy process, European journal of operational research, 48, 9-16, (1990) · Zbl 0707.90002 |

[58] | Sakawa, M., Fuzzy sets and interactive multi-objective optimization, (1993), Plenum Press New York |

[59] | Sakawa, M.; Nishizaki, I.; Uemura, Y., Fuzzy programming and profit and cost allocation for a production and transportation problem, European journal of operational research, 131, 1, 1-15, (2001) · Zbl 0979.90126 |

[60] | 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 |

[61] | Selim, H.; Araz, C.; Ozkarahan, I., Collaborative production – distribution planning in supply chain: a fuzzy goal programming approach, Transportation research part E: logistics and transportation review, 44, 3, 396-419, (2008) |

[62] | Shih, L.H., Cement transportation planning via fuzzy linear programming, International journal of production economics, 58, 3, 277-287, (1999) |

[63] | Sodhi, M.S., Managing demand risk in tactical supply chain planning for a global consumer electronics company, Production and operations management, 14, 1, 69-79, (2005) |

[64] | Sridharan, V.; Berry, W.; Udayabhanu, V., Freezing the master production schedule stability under rolling planning horizons, Management science, 33, 9, 1137-1149, (1987) |

[65] | 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 |

[66] | Vasant, P.M., Fuzzy linear programming for decision making and planning under uncertainty, International journal of information technology and decision making, 4, 4, 647-662, (2005) |

[67] | Wang, X.; Kerre, E., On the classification and the dependencies of the ordering methods, (), 73-90 · Zbl 0906.04003 |

[68] | Wang, J.T.; Shu, Y.F., Fuzzy decision modeling for supply chain management, Fuzzy sets and systems, 150, 1, 107-127, (2005) · Zbl 1075.90532 |

[69] | Wang, J.; Shu, Y.F., A possibilistic decision model for new product supply chain design, European journal of operational research, 177, 2, 1044-1061, (2007) · Zbl 1111.90331 |

[70] | Xie, Y.; Petrovic, D.; Burnham, K., A heuristic procedure for the two-level control of serial supply chains under fuzzy customer demand, International journal of production economics, 102, 1, 37-50, (2006) |

[71] | Zadeh, L.A., Fuzzy sets, Information and control, 8, 3, 338, (1965) · Zbl 0139.24606 |

[72] | Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002 |

[73] | Zimmermann, H.J., Description and optimization of fuzzy systems, International journal of general systems, 2, 4, 209-215, (1976) · Zbl 0338.90055 |

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

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.