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April  2011, 7(2): 365-383. doi: 10.3934/jimo.2011.7.365

Multi-objective aggregate production planning decisions using two-phase fuzzy goal programming method

Tien-Fu Liang 1, and  Hung-Wen Cheng 1,

1. 

Department of Industrial Engineering and Management, Hsiuping Institute of Technology, 11 Gungye Road, Dali City, Taichung 412, Taiwan, Taiwan

Received  January 2010 Revised  January 2011 Published  April 2011

In practical aggregate production planning (APP) decisions, the decision maker (DM) must simultaneously handle multiple conflicting goals that govern the use of the constrained resources. This study aims to present a two-phase fuzzy goal programming method to solve multi-objective APP problems with multiple products and multi-time periods. The designed fuzzy multi-objective linear programming model attempts to simultaneously minimize total costs, total carrying and backordering volume, and total rates of changes in labor levels with reference to inventory carrying levels, machine capacity, work-force levels, warehouse space and available budget. An industrial case is used to demonstrate the feasibility of applying the proposed method to real-life APP decisions. The contribution of this study lies in presenting a two-phase fuzzy goal programming methodology to solve multi-objective APP decision problems and provides a systematic decision-making framework that facilitates a DM to interactively adjust the search direction until the preferred efficient compromise solution is obtained.
Keywords: fuzzy sets, Aggregate production planning, fuzzy mathematical programming, multi-objective linear programming..
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Tien-Fu Liang, Hung-Wen Cheng. Multi-objective aggregate production planning decisions using two-phase fuzzy goal programming method. Journal of Industrial and Management Optimization, 2011, 7 (2) : 365-383. doi: 10.3934/jimo.2011.7.365
References:
[1]

R. A. Aliev, B. Fazlollahi, B. G. Guirimov and R. R. Aliev, Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management, Information Sciences, 177 (2007), 4241-4255. doi: 10.1016/j.ins.2007.04.012.

[2]

R. E. Bellman and L. A. Zadeh, Decision-making in a fuzzy environment,, Management Sciences, 17 ().  doi: 10.1287/mnsc.17.4.B141.

[3]

G. R. Bitran and H. H. Yanassee, Deterministic approximations to stochastic production problem, Operations Research, 32 (1984), 999-1018. doi: 10.1287/opre.32.5.999.

[4]

J. J. Buckley, Possibilistic linear programming with triangular fuzzy numbers, Fuzzy Sets and Systems, 26 (1988), 135-138. doi: 10.1016/0165-0114(88)90013-9.

[5]

M. D. Byrne and M. A. Bakir, Production planning using a hybrid simulation-analytical approach, International Journal of Production Economics, 59 (1999), 305-311. doi: 10.1016/S0925-5273(98)00104-2.

[6]

E. L. Castro de, M. T. Tabucanon and N. N. Nagarur, A Production order quantity model with stochastic demand for a chocolate milk manufacturer, International Journal of Production Economics, 49 (1997), 145-158. doi: 10.1016/S0925-5273(96)00117-X.

[7]

D. Dubois and P. Fortemps, Computing improved optimal solutions to max-min flexible constraint satisfaction problems, European Journal of Operational Research, 118 (1999), 95-126. doi: 10.1016/S0377-2217(98)00307-5.

[8]

B. R. Feiring, Production planning on stochastic demand environments, Mathematical and Computer Modelling, 15 (1991), 91-95. doi: 10.1016/0895-7177(91)90093-M.

[9]

S. E. Fleten and T. K. Kristoffersen, Short-term hydropower production planning by stochastic programming, Computers and Operations Research, 35 (2008), 2656-2671.

[10]

R. Y. K. Fung, J. Tang and D. Wang, Multiproduct aggregate production planning with fuzzy demands and fuzzy capacities, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 33 (2003), 302-313. doi: 10.1109/TSMCA.2003.817032.

[11]

S. M. Guu and Y. K. Wu, Two-phase approach for solving the fuzzy linear programming problems, Fuzzy Sets and Systems, 107 (1999), 191-195. doi: 10.1016/S0165-0114(97)00304-7.

[12]

E. L. Hannan, Linear programming with multiple fuzzy goals, Fuzzy Sets and Systems, 6 (1981), 235-248. doi: 10.1016/0165-0114(81)90002-6.

[13]

C. C. Holt, F. Modigliani and H. A. Simon, Linear decision rule for production and employment scheduling, Management Science, 2 (1955), 1-30. doi: 10.1287/mnsc.2.1.1.

[14]

H. M. Hsu, and W. P. Wang, Possibilistic programming in production planning of assemble-to-order environments. Optimization and decision, Fuzzy Sets and Systems, 119 (2001), 59-70. doi: 10.1016/S0165-0114(99)00086-X.

[15]

A. Jain and U. S. Palekar, Aggregate production planning for a continuous reconfigurable manufacturing process, Computers and Operations Research, 32 (2005), 1213-1236.

[16]

G. Klir and B. Yuan, "Fuzzy Set and Fuzzy Logic: Theory and Applications," PTR: Prentice Hall (1995)

[17]

Y. J. Lai and C. L. Hwang, A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems, 49 (1992), 121-133. doi: 10.1016/0165-0114(92)90318-X.

[18]

E. S. Lee and R. J. Li, Fuzzy multiple objective programming and computing programming with Pareto optimum, Fuzzy Sets and Systems, 53 (1993), 275-283. doi: 10.1016/0165-0114(93)90399-3.

[19]

S. C. H. Leung and S .S. W. Chan, A goal programming model for aggregate production planning with resource utilization constraint, Computers and Industrial Engineering, 56 (2009), 1053-1064. doi: 10.1016/j.cie.2008.09.017.

[20]

X. Q. Li, B. Zhang and H. Li, Computing efficient solutions to fuzzy multiple objective linear programming problems, Fuzzy Sets and Systems, 157 (2006), 1328-1332. doi: 10.1016/j.fss.2005.12.003.

[21]

T. F. Liang, Application of interactive possibilistic linear programming to aggregate production planning with multiple imprecise objectives, Production Planning and Control, 18 (2007), 548-560. doi: 10.1080/09537280701530033.

[22]

T. F. Liang, Application of fuzzy sets to multi-objective project management decisions in uncertain environments, International Journal of General Systems, 38 (2009), 311-330. doi: 10.1080/03081070701785833.

[23]

S. M. Masud and C. L. Hwang, An aggregate production planning model and application of three multiple objective decision methods, International Journal of Production Research, 18 (1980), 741-752. doi: 10.1080/00207548008919703.

[24]

M. S. Moreno and J. M. Montagna, A multiperiod model for production planning and design in a multiproduct batch environment, Mathematical and Computer Modelling, 49 (2009), 1372-1385. doi: 10.1016/j.mcm.2008.11.004.

[25]

S. J. Nam and R. Logendran, Aggregate production planning - A survey of models and methodologies, European Journal of Operational Research, 61 (1992), 255-272. doi: 10.1016/0377-2217(92)90356-E.

[26]

D. özgen, S. önut, B. Gülsün, U. R. Tuzkaya and G. Tuzkaya, A two-phase methodology for multi- objective supplier evaluation and order allocation problems, Information Sciences, 178 (2008), 485-500. doi: 10.1016/j.ins.2007.08.002.

[27]

D. Petrovic, R. Roy and R. Petrovic, Supply chain modeling using fuzzy sets, International Journal of Production Economics, 59 (1999), 443-453. doi: 10.1016/S0925-5273(98)00109-1.

[28]

J. Ramik and J. Rimanek, Inequality relation between fuzzy numbers and its use in fuzzy optimization, Fuzzy Sets and Systems, 16 (1985), 123-138. doi: 10.1016/S0165-0114(85)80013-0.

[29]

H. Rommelfanger, Fuzzy linear programming and applications, European Journal of Operational Research, 92 (1996), 512-527. doi: 10.1016/0377-2217(95)00008-9.

[30]

G. Saad, An overview of production planning model: structure classification and empirical assessment, International Journal of Production Research, 20 (1982), 105-114. doi: 10.1080/00207548208947752.

[31]

Y. Shi and C. Haase, Optimal trade-offs of aggregate production planning with multi-objective and multi-capacity-demand levels, International Journal of Operations and Quantitative Management, 2 (1996), 127-143.

[32]

A. Singhvy, K. P. Madhavan and U. V. Shenoy, Pinch analysis for aggregate production planning in supply chains, Computers and Chemical Engineering, 28 (2004), 993-999. doi: 10.1016/j.compchemeng.2003.09.006.

[33]

C. H. L. Stephen, Y. Wu and K. K. Lai, Multi-site aggregate production planning with multiple objectives: a goal programming approach, Production Planning and Control, 14 (2003), 425-436. doi: 10.1080/0953728031000154264.

[34]

H. Tanaka, H. Ichihashi and K. Asai, A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers, Control and Cybernetics, 13 (1984), 185-194.

[35]

J. Tang, R. Y. K. Fung and K. L. Yong, Fuzzy modelling and simulation for aggregate production planning, International Journal of Systems Science, 34 (2003), 661-673. doi: 10.1080/00207720310001624113.

[36]

J. Tang, D. Wang and R. Y. K. Fung, Fuzzy formulation for multi-product aggregate production planning, Production Planning and Control, 11 (2000), 670-676. doi: 10.1080/095372800432133.

[37]

S. A. Torabi and E. Hassini, An interactive possibilistic programming approach for multiple objective supply chain master planning, Fuzzy Sets and Systems, 159 (2008), 193-214. doi: 10.1016/j.fss.2007.08.010.

[38]

P. Vasant, Fuzzy decision making of profit function in production planning using S-curve membership function, Computers and Industrial Engineering, 51 (2006), 715-725. doi: 10.1016/j.cie.2006.08.017.

[39]

D. Wang and S. C. Fang, A genetics-based approach for aggregate production planning in a fuzzy environment, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 27 (1997), 636-645. doi: 10.1109/3468.618262.

[40]

R. C. Wang and H. H. Fang, Aggregate production planning with multiple objectives in a fuzzy environment, European Journal of Operational Research, 133 (2001), 521-536. doi: 10.1016/S0377-2217(00)00196-X.

[41]

R. C. Wang and T. F. Liang, Application of fuzzy multi-objective linear programming to aggregate production planning, Computers and Industrial Engineering, 46 (2004), 17-41. doi: 10.1016/j.cie.2003.09.009.

[42]

R. C. Wang and T. F. Liang, Applying possibilistic linear programming to aggregate production planning, International Journal of Production Economics, 98 (2005), 328-341. doi: 10.1016/j.ijpe.2004.09.011.

[43]

R. C. Wang and T. F. Liang, Aggregate production planning with multiple fuzzy goals, International Journal of Advanced Manufacturing Technology, 25 (2005), 589-597. doi: 10.1007/s00170-003-1885-6.

[44]

Z. Xu and R. R. Yage, Dynamic intuitionistic fuzzy multiple attribute decision making, International Journal of Approximate Reasoning, 48 (2008), 246-262. doi: 10.1016/j.ijar.2007.08.008.

[45]

A. V. Yazenin, Fuzzy and stochastic programming, Fuzzy Sets and Systems, 22 (1987), 171-180. doi: 10.1016/0165-0114(87)90014-5.

[46]

L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X.

[47]

H. J. Zimmermann, Description and optimization of fuzzy systems, International Journal of General Systems, 2 (1976), 209-215. doi: 10.1080/03081077608547470.

[48]

H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1 (1978), 45-56. doi: 10.1016/0165-0114(78)90031-3.

[49]

H. J. Zimmermann, "Fuzzy Set Theory and its Application," Boston: Kluwer Academic, 1996.

show all references

References:
[1]

R. A. Aliev, B. Fazlollahi, B. G. Guirimov and R. R. Aliev, Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management, Information Sciences, 177 (2007), 4241-4255. doi: 10.1016/j.ins.2007.04.012.

[2]

R. E. Bellman and L. A. Zadeh, Decision-making in a fuzzy environment,, Management Sciences, 17 ().  doi: 10.1287/mnsc.17.4.B141.

[3]

G. R. Bitran and H. H. Yanassee, Deterministic approximations to stochastic production problem, Operations Research, 32 (1984), 999-1018. doi: 10.1287/opre.32.5.999.

[4]

J. J. Buckley, Possibilistic linear programming with triangular fuzzy numbers, Fuzzy Sets and Systems, 26 (1988), 135-138. doi: 10.1016/0165-0114(88)90013-9.

[5]

M. D. Byrne and M. A. Bakir, Production planning using a hybrid simulation-analytical approach, International Journal of Production Economics, 59 (1999), 305-311. doi: 10.1016/S0925-5273(98)00104-2.

[6]

E. L. Castro de, M. T. Tabucanon and N. N. Nagarur, A Production order quantity model with stochastic demand for a chocolate milk manufacturer, International Journal of Production Economics, 49 (1997), 145-158. doi: 10.1016/S0925-5273(96)00117-X.

[7]

D. Dubois and P. Fortemps, Computing improved optimal solutions to max-min flexible constraint satisfaction problems, European Journal of Operational Research, 118 (1999), 95-126. doi: 10.1016/S0377-2217(98)00307-5.

[8]

B. R. Feiring, Production planning on stochastic demand environments, Mathematical and Computer Modelling, 15 (1991), 91-95. doi: 10.1016/0895-7177(91)90093-M.

[9]

S. E. Fleten and T. K. Kristoffersen, Short-term hydropower production planning by stochastic programming, Computers and Operations Research, 35 (2008), 2656-2671.

[10]

R. Y. K. Fung, J. Tang and D. Wang, Multiproduct aggregate production planning with fuzzy demands and fuzzy capacities, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 33 (2003), 302-313. doi: 10.1109/TSMCA.2003.817032.

[11]

S. M. Guu and Y. K. Wu, Two-phase approach for solving the fuzzy linear programming problems, Fuzzy Sets and Systems, 107 (1999), 191-195. doi: 10.1016/S0165-0114(97)00304-7.

[12]

E. L. Hannan, Linear programming with multiple fuzzy goals, Fuzzy Sets and Systems, 6 (1981), 235-248. doi: 10.1016/0165-0114(81)90002-6.

[13]

C. C. Holt, F. Modigliani and H. A. Simon, Linear decision rule for production and employment scheduling, Management Science, 2 (1955), 1-30. doi: 10.1287/mnsc.2.1.1.

[14]

H. M. Hsu, and W. P. Wang, Possibilistic programming in production planning of assemble-to-order environments. Optimization and decision, Fuzzy Sets and Systems, 119 (2001), 59-70. doi: 10.1016/S0165-0114(99)00086-X.

[15]

A. Jain and U. S. Palekar, Aggregate production planning for a continuous reconfigurable manufacturing process, Computers and Operations Research, 32 (2005), 1213-1236.

[16]

G. Klir and B. Yuan, "Fuzzy Set and Fuzzy Logic: Theory and Applications," PTR: Prentice Hall (1995)

[17]

Y. J. Lai and C. L. Hwang, A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems, 49 (1992), 121-133. doi: 10.1016/0165-0114(92)90318-X.

[18]

E. S. Lee and R. J. Li, Fuzzy multiple objective programming and computing programming with Pareto optimum, Fuzzy Sets and Systems, 53 (1993), 275-283. doi: 10.1016/0165-0114(93)90399-3.

[19]

S. C. H. Leung and S .S. W. Chan, A goal programming model for aggregate production planning with resource utilization constraint, Computers and Industrial Engineering, 56 (2009), 1053-1064. doi: 10.1016/j.cie.2008.09.017.

[20]

X. Q. Li, B. Zhang and H. Li, Computing efficient solutions to fuzzy multiple objective linear programming problems, Fuzzy Sets and Systems, 157 (2006), 1328-1332. doi: 10.1016/j.fss.2005.12.003.

[21]

T. F. Liang, Application of interactive possibilistic linear programming to aggregate production planning with multiple imprecise objectives, Production Planning and Control, 18 (2007), 548-560. doi: 10.1080/09537280701530033.

[22]

T. F. Liang, Application of fuzzy sets to multi-objective project management decisions in uncertain environments, International Journal of General Systems, 38 (2009), 311-330. doi: 10.1080/03081070701785833.

[23]

S. M. Masud and C. L. Hwang, An aggregate production planning model and application of three multiple objective decision methods, International Journal of Production Research, 18 (1980), 741-752. doi: 10.1080/00207548008919703.

[24]

M. S. Moreno and J. M. Montagna, A multiperiod model for production planning and design in a multiproduct batch environment, Mathematical and Computer Modelling, 49 (2009), 1372-1385. doi: 10.1016/j.mcm.2008.11.004.

[25]

S. J. Nam and R. Logendran, Aggregate production planning - A survey of models and methodologies, European Journal of Operational Research, 61 (1992), 255-272. doi: 10.1016/0377-2217(92)90356-E.

[26]

D. özgen, S. önut, B. Gülsün, U. R. Tuzkaya and G. Tuzkaya, A two-phase methodology for multi- objective supplier evaluation and order allocation problems, Information Sciences, 178 (2008), 485-500. doi: 10.1016/j.ins.2007.08.002.

[27]

D. Petrovic, R. Roy and R. Petrovic, Supply chain modeling using fuzzy sets, International Journal of Production Economics, 59 (1999), 443-453. doi: 10.1016/S0925-5273(98)00109-1.

[28]

J. Ramik and J. Rimanek, Inequality relation between fuzzy numbers and its use in fuzzy optimization, Fuzzy Sets and Systems, 16 (1985), 123-138. doi: 10.1016/S0165-0114(85)80013-0.

[29]

H. Rommelfanger, Fuzzy linear programming and applications, European Journal of Operational Research, 92 (1996), 512-527. doi: 10.1016/0377-2217(95)00008-9.

[30]

G. Saad, An overview of production planning model: structure classification and empirical assessment, International Journal of Production Research, 20 (1982), 105-114. doi: 10.1080/00207548208947752.

[31]

Y. Shi and C. Haase, Optimal trade-offs of aggregate production planning with multi-objective and multi-capacity-demand levels, International Journal of Operations and Quantitative Management, 2 (1996), 127-143.

[32]

A. Singhvy, K. P. Madhavan and U. V. Shenoy, Pinch analysis for aggregate production planning in supply chains, Computers and Chemical Engineering, 28 (2004), 993-999. doi: 10.1016/j.compchemeng.2003.09.006.

[33]

C. H. L. Stephen, Y. Wu and K. K. Lai, Multi-site aggregate production planning with multiple objectives: a goal programming approach, Production Planning and Control, 14 (2003), 425-436. doi: 10.1080/0953728031000154264.

[34]

H. Tanaka, H. Ichihashi and K. Asai, A formulation of fuzzy linear programming problem based on comparison of fuzzy numbers, Control and Cybernetics, 13 (1984), 185-194.

[35]

J. Tang, R. Y. K. Fung and K. L. Yong, Fuzzy modelling and simulation for aggregate production planning, International Journal of Systems Science, 34 (2003), 661-673. doi: 10.1080/00207720310001624113.

[36]

J. Tang, D. Wang and R. Y. K. Fung, Fuzzy formulation for multi-product aggregate production planning, Production Planning and Control, 11 (2000), 670-676. doi: 10.1080/095372800432133.

[37]

S. A. Torabi and E. Hassini, An interactive possibilistic programming approach for multiple objective supply chain master planning, Fuzzy Sets and Systems, 159 (2008), 193-214. doi: 10.1016/j.fss.2007.08.010.

[38]

P. Vasant, Fuzzy decision making of profit function in production planning using S-curve membership function, Computers and Industrial Engineering, 51 (2006), 715-725. doi: 10.1016/j.cie.2006.08.017.

[39]

D. Wang and S. C. Fang, A genetics-based approach for aggregate production planning in a fuzzy environment, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 27 (1997), 636-645. doi: 10.1109/3468.618262.

[40]

R. C. Wang and H. H. Fang, Aggregate production planning with multiple objectives in a fuzzy environment, European Journal of Operational Research, 133 (2001), 521-536. doi: 10.1016/S0377-2217(00)00196-X.

[41]

R. C. Wang and T. F. Liang, Application of fuzzy multi-objective linear programming to aggregate production planning, Computers and Industrial Engineering, 46 (2004), 17-41. doi: 10.1016/j.cie.2003.09.009.

[42]

R. C. Wang and T. F. Liang, Applying possibilistic linear programming to aggregate production planning, International Journal of Production Economics, 98 (2005), 328-341. doi: 10.1016/j.ijpe.2004.09.011.

[43]

R. C. Wang and T. F. Liang, Aggregate production planning with multiple fuzzy goals, International Journal of Advanced Manufacturing Technology, 25 (2005), 589-597. doi: 10.1007/s00170-003-1885-6.

[44]

Z. Xu and R. R. Yage, Dynamic intuitionistic fuzzy multiple attribute decision making, International Journal of Approximate Reasoning, 48 (2008), 246-262. doi: 10.1016/j.ijar.2007.08.008.

[45]

A. V. Yazenin, Fuzzy and stochastic programming, Fuzzy Sets and Systems, 22 (1987), 171-180. doi: 10.1016/0165-0114(87)90014-5.

[46]

L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X.

[47]

H. J. Zimmermann, Description and optimization of fuzzy systems, International Journal of General Systems, 2 (1976), 209-215. doi: 10.1080/03081077608547470.

[48]

H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1 (1978), 45-56. doi: 10.1016/0165-0114(78)90031-3.

[49]

H. J. Zimmermann, "Fuzzy Set Theory and its Application," Boston: Kluwer Academic, 1996.

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