##
**Application of fuzzy sets to manufacturing/distribution planning decisions in supply chains.**
*(English)*
Zbl 1208.90008

Summary: In the real-world manufacturing/distribution planning decision (MDPD) integration problems in supply chains, the environmental coefficients and parameters are normally imprecise due to incomplete and/or unavailable information. This work presents a fuzzy linear programming approach based on the possibility theory. It applies this approach to solve multi-product and multi-time period MDPD problems with imprecise goals and forecast demand by considering the time value of money of related operating cost categories. The proposed approach attempts to minimize the total manufacturing and distribution costs by considering the levels of inventory, subcontracting and backordering, the available machine capacity and labor levels at each source, forecast demand and available warehouse space at each destination. This study utilizes an industrial case study to demonstrate the feasibility of applying the proposed approach to practical MDPD problems. The primary contribution of this paper is a fuzzy mathematical programming methodology for solving the MDPD integration problems in uncertain environments.

### MSC:

90B05 | Inventory, storage, reservoirs |

90C05 | Linear programming |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

### Keywords:

fuzzy sets; manufacturing/distribution planning decisions; supply chains; fuzzy linear programming; possibility theory
Full Text:
DOI

### 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, 4241-4255 (2007) · Zbl 1142.90416 |

[2] | Ana Maria, S.; Rakesh, N., A review of integrated analysis of production and distribution systems, IIE Transactions, 31, 1061-1074 (1999) |

[3] | Barbarsoğlu, G.; Özgür, D., Hierarchical design of an integrated production and 2-echelon distribution system, European Journal of Operational Research, 118, 464-484 (1999) · Zbl 0933.90018 |

[4] | Beamon, B. M., Supply chain design and analysis models: models and methods, International Journal of Production Economics, 55, 281-294 (1998) · Zbl 0951.90521 |

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

[6] | Bilgen, B.; Ozkarahan, I., Strategic tactical and operational production-distribution models: a review, International Journal of Technology Management, 28, 151-171 (2004) |

[7] | Buckley, J. J., Possibilistic linear programming with triangular fuzzy numbers, Fuzzy Sets and Systems, 26, 135-138 (1988) · Zbl 0644.90059 |

[8] | Buckley, J. J., Stochastic versus possibilistic programming, Fuzzy Sets and Systems, 34, 43-59 (1990) · Zbl 0692.90075 |

[9] | Byrne, M. D.; Bakir, M. A., Production planning using a hybrid simulation-analytical approach, International Journal of Production Economics, 59, 305-311 (1999) |

[10] | Byrne, M. D.; Hossain, M. M., Production planning: an improved hybrid approach, International Journal of Production Economics, 93-94, 225-229 (2005) |

[11] | Chandra, P.; Fisher, M. L., Coordination of production and distribution planning, European Journal of Operational Research, 72, 503-517 (1994) · Zbl 0805.90051 |

[12] | Chen, C. T.; Huang, S. F., Order-fulfillment ability analysis in the supply-chain system with fuzzy operation times, International Journal of Production Economics, 101, 185-193 (2006) |

[13] | Chen, C. L.; Lee, W. C., Multi-objective optimization of multi-echelon supply chain networks with uncertain product demands and prices, Computers and Chemical Engineering, 28, 1131-1144 (2004) |

[14] | Chen, C. T.; Lin, C. T.; Huang, S. F., A fuzzy approach for supplier evaluation and selection in supply chain management, International Journal of Production Economics, 102, 289-301 (2006) |

[15] | Cohen, M. A.; Lee, H. L., Strategic analysis of integrated production-distribution systems: models and methods, Operations Research, 36, 216-228 (1988) |

[16] | Erengüc, S. S.; Simpson, N. C.; Vakharia, A. J., Integrated production/distribution planning in supply chains: an invited review, European Journal of Operational Research, 115, 219-236 (1999) · Zbl 0949.90658 |

[17] | 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, 302-313 (2003) |

[18] | Gen, M.; Syarif, A., Hybrid genetic algorithm for multi-time period production/distribution planning, Computers and Industrial Engineering, 48, 799-809 (2005) |

[19] | Giannoccaro, H.; Pontrandolfo, P.; Scozzi, B., A fuzzy echelon approach for inventory management in supply chains, European Journal of Operational Research, 149, 185-196 (2003) · Zbl 1035.90002 |

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

[21] | Inuiguchi, M.; Ramik, 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, 3-28 (2000) · Zbl 0938.90074 |

[22] | Inuiguchi, M.; Sakawa, M., A possibilistic linear programming program in equivalent to a stochastic linear program in special case, Fuzzy Sets and Systems, 76, 309-318 (1995) · Zbl 0856.90131 |

[23] | Inuiguchi, M.; Sakawa, M., Possible and necessary efficiency in possibilistic multiobjective linear programming problems and possible efficiency test, Fuzzy Sets and Systems, 78, 231-241 (1996) · Zbl 0869.90079 |

[24] | Jang, Y. J.; Jang, S. Y.; Chang, B. M.; Park, J., A combined model of network design and Production/distribution planning for a supply network, Computers and Industrial Engineering, 43, 263-281 (2002) |

[25] | Kim, B.; Kim, S., Extended model of a hybrid production planning approach, International Journal of Production Economics, 73, 165-173 (2001) |

[26] | Kumar, M.; Vrat, P.; Shan, R., A fuzzy goal programming approach for vendor selection problem in a supply chain, Computers and Industrial Engineering, 46, 69-85 (2004) |

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

[28] | Lai, Y. J.; Hwang, C. L., Fuzzy Mathematical Programming: Methods and Applications (1992), Spring-Verlag: Spring-Verlag Berlin · Zbl 0793.90094 |

[29] | Lee, Y. H.; Kim, S. H., Production-distribution planning in supply chain considering capacity constraints, Computers and Industrial Engineering, 43, 169-190 (2002) |

[30] | Lee, Y. H.; Kim, S. H.; Moon, S. H., Production-distribution planning in supply chain using a hybrid approach, Production Planning and Control, 13, 35-46 (2002) |

[31] | Li, L.; Lai, K. K., A fuzzy approach to the multiobjective transportation problem, Computers and Operations Research, 27, 43-57 (2000) · Zbl 0973.90010 |

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

[33] | Liang, T. F., Applying fuzzy goal programming to production/transportation planning decisions in a supply chain, International Journal of Systems Science, 38, 293-304 (2007) · Zbl 1115.93056 |

[34] | Min, H.; Zhou, Z., Supply chain modeling: past, present and future, Computers and Industrial Engineering, 43, 231-249 (2002) |

[35] | Ozdamar, L.; Yazgac, T., A hierarchical planning approach for a production-distribution system, International Journal of Production Research, 37, 3759-3772 (1999) · Zbl 0948.90533 |

[36] | Özgen, D.; Önut, S.; Gülsün, B.; Tuzkaya, U. R.; Tuzkaya, G., A two-phase methodology for multi-objective supplier evaluation and order allocation problems, Information Sciences, 178, 485-500 (2008) · Zbl 1149.90190 |

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

[38] | Petrovic, D., Simulation of supply chain behavior and performance in an uncertain environment, International Journal of Production Economics, 71, 429-438 (2001) |

[39] | Petrovic, D.; Roy, R.; Petrovic, R., Modelling and simulation of a supply chain in an uncertain environment, European Journal of Operational Research, 109, 299-309 (1998) · Zbl 0937.90047 |

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

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

[42] | Rizk, N.; Martel, A.; Amours, S. D., Multi-item dynamic production-distribution planning in process industries with divergent finishing stages, Computers and Operations Research, 33, 3600-3623 (2005) · Zbl 1125.90346 |

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

[44] | Sabri, E. H.; Beamon, B. M., A multi-objective approach to simultaneous strategic and operational planning in supply chain design, Omega, 28, 581-598 (2000) |

[45] | Simpson, N. C.; Vakharia, A. J., Integrated production/distribution planning in supply chains: an invited review, European Journal of Operational Research, 115, 219-236 (1999) · Zbl 0949.90658 |

[46] | Tanaka, H.; Guo, P.; Zimmermann, H.-J., Possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems, Fuzzy Sets and Systems, 113, 323-332 (2000) · Zbl 0961.90136 |

[47] | Tanaka, H.; Ichihashi, H.; Asai, K., A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers, Control and Cybernetics, 13, 185-194 (1984) · Zbl 0551.90062 |

[48] | Tang, J.; Wang, D.; Fung, R. Y.K., Formulation of general possibilistic linear programming problems for complex systems, Fuzzy Sets and Systems, 119, 41-48 (2001) |

[49] | Thomas, D. J.; Griffin, P. M., Coordinated supply chain management, European Journal of Operational Research, 94, 1-15 (1996) · Zbl 0929.90004 |

[50] | Vidal, C. J.; Goetschalckx, M., Strategic production-distribution models: a critical review with emphasis on global supply chain model, European Journal of Operational Research, 98, 1-18 (1997) · Zbl 0922.90062 |

[51] | Wang, R. C.; Fang, H. H., Aggregate production planning with multiple objectives in a fuzzy environment, European Journal of Operational Research, 133, 521-536 (2001) · Zbl 1053.90541 |

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

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

[54] | Wang, J.; Shu, Y. F., Fuzzy decision modeling for supply chain management, Fuzzy Sets and Systems, 150, 107-127 (2005) · Zbl 1075.90532 |

[55] | 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, 37-50 (2006) |

[56] | Yang, T.; Ingizio, J. P.; Kim, H. J., Fuzzy programming with nonlinear membership functions: piecewise linear approximation, Fuzzy Sets and Systems, 11, 39-53 (1991) · Zbl 0743.90115 |

[57] | Yazenin, A. V., Fuzzy and stochastic programming, Fuzzy Sets and Systems, 22, 171-180 (1987) · Zbl 0623.90058 |

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

[59] | Zimmermann, H.-J., Description and optimization of fuzzy systems, International Journal of General Systems, 2, 209-215 (1976) · Zbl 0338.90055 |

[60] | Zimmermann, H.-J., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 45-56 (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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.