Determining Optimal Demand Rate and Production Decisions: A Geometric Programming Approach
In this paper a nonlinear model is presented to
demonstrate the relation between production and marketing
departments. By introducing some functions such as pricing cost and
market share loss functions it will be tried to show some aspects of
market modelling which has not been regarded before. The proposed
model will be a constrained signomial geometric programming
model. For model solving, after variables- modifications an iterative
technique based on the concept of geometric mean will be introduced
to solve the resulting non-standard posynomial model which can be
applied to a wide variety of models in non-standard posynomial
geometric programming form. At the end a numerical analysis will
be presented to accredit the validity of the mentioned model.
[1] W. J. Lee and K. C. Lee, "PROMISE: a distributed DSS approach to
coordinating production and marketing decisions," Comput.Oper.Res. ,
vol. 26, no. 9, pp. 901-920,1999
[2] W. J. Lee, "Determining order quantity and selling price by geometric
programming: optimal solution, bounds, and sensitivity," Decis. Sci.,
vol. 24, no. 1, pp. 76-87, Jan/Feb 1993
[3] W. J. Lee and D. Kim, "Optimal and Heuristic Decision Strategies for
Integrated Production and Marketing Planning," Decis. Sci. , vol. 24, no.
6, pp. 1203-1213, Nov/Dec 1993
[4] D. Kim and W.J Lee, "Optimal joint pricing and lot sizing with fixed and
variable capacity," Eur. J. Oper. Res. , vol. 109, no. 1, pp. 212-227,
1998
[5] C. K. Chen, "Optimal determination of quality level, selling quantity and
purchasing price for intermediate firms," prod. Plann. Control. , vol.11,
no. 7, pp. 706-712, 2000
[6] S. J. Sadjadi, M. Oroujee, and M.B. Aryanezhad, "Optimal Production
and Marketing Planning," Comput. Optim. Appl. , vol. 30, no. 2, pp.
195-203, 2005
[7] M. Fathian, S.J. Sadjadi, and S. Sajadi, "Optimal pricing model for
electronic products," Comput. Ind. Eng. , Article in press, 2008
[8] C. S. Beightler, D. T. Philips, Applied Geometric Programming, USA:
John Whiley, 1976
[9] N. Safaei, S.J. Sadjadi, and M. Babakhani, "An efficient genetic
algorithm for determining the optimal price discrimination," Appl. Math.
Comput, vol.181, no. 1, pp. 1693-1702, 2006
[10] M. Parlar and Z.K. Weng, "Coordinating pricing and production
decisions in the presence of price competition," Eur. J. Oper. Res., vol.
170, no. 1, pp. 211-227, 2006
[11] http://www.stanford.edu/~boyd/ggplab
[12] S. Boyd and L. Vandenberghe, Convex Optimization, UK: Cambridge
University Press, 2004, pp. 561- 630
[1] W. J. Lee and K. C. Lee, "PROMISE: a distributed DSS approach to
coordinating production and marketing decisions," Comput.Oper.Res. ,
vol. 26, no. 9, pp. 901-920,1999
[2] W. J. Lee, "Determining order quantity and selling price by geometric
programming: optimal solution, bounds, and sensitivity," Decis. Sci.,
vol. 24, no. 1, pp. 76-87, Jan/Feb 1993
[3] W. J. Lee and D. Kim, "Optimal and Heuristic Decision Strategies for
Integrated Production and Marketing Planning," Decis. Sci. , vol. 24, no.
6, pp. 1203-1213, Nov/Dec 1993
[4] D. Kim and W.J Lee, "Optimal joint pricing and lot sizing with fixed and
variable capacity," Eur. J. Oper. Res. , vol. 109, no. 1, pp. 212-227,
1998
[5] C. K. Chen, "Optimal determination of quality level, selling quantity and
purchasing price for intermediate firms," prod. Plann. Control. , vol.11,
no. 7, pp. 706-712, 2000
[6] S. J. Sadjadi, M. Oroujee, and M.B. Aryanezhad, "Optimal Production
and Marketing Planning," Comput. Optim. Appl. , vol. 30, no. 2, pp.
195-203, 2005
[7] M. Fathian, S.J. Sadjadi, and S. Sajadi, "Optimal pricing model for
electronic products," Comput. Ind. Eng. , Article in press, 2008
[8] C. S. Beightler, D. T. Philips, Applied Geometric Programming, USA:
John Whiley, 1976
[9] N. Safaei, S.J. Sadjadi, and M. Babakhani, "An efficient genetic
algorithm for determining the optimal price discrimination," Appl. Math.
Comput, vol.181, no. 1, pp. 1693-1702, 2006
[10] M. Parlar and Z.K. Weng, "Coordinating pricing and production
decisions in the presence of price competition," Eur. J. Oper. Res., vol.
170, no. 1, pp. 211-227, 2006
[11] http://www.stanford.edu/~boyd/ggplab
[12] S. Boyd and L. Vandenberghe, Convex Optimization, UK: Cambridge
University Press, 2004, pp. 561- 630
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:54271", author = "Farnaz G. Nezami and Mir B. Aryanezhad and Seyed J. Sadjadi", title = "Determining Optimal Demand Rate and Production Decisions: A Geometric Programming Approach", abstract = "In this paper a nonlinear model is presented to
demonstrate the relation between production and marketing
departments. By introducing some functions such as pricing cost and
market share loss functions it will be tried to show some aspects of
market modelling which has not been regarded before. The proposed
model will be a constrained signomial geometric programming
model. For model solving, after variables- modifications an iterative
technique based on the concept of geometric mean will be introduced
to solve the resulting non-standard posynomial model which can be
applied to a wide variety of models in non-standard posynomial
geometric programming form. At the end a numerical analysis will
be presented to accredit the validity of the mentioned model.", keywords = "Geometric programming, marketing, nonlinear
optimization, production.", volume = "3", number = "1", pages = "51-6", }