ABSTRACT The traditional production planning model based upon the famous linear programming formulation has been well known in the literature. The consideration of uncertainty in manufacturing systems supposes a great advance. Models for production planning which do not recognize the uncertainty can be expected to generate inferior planning decisions as compared to models that explicitly account the uncertainty. This paper deals with production planning problem with fuzzy parameters in both of the objective function and constraints. We have a planning problem to maximize revenues net of the production inventory and lost sales cost. The existing results concerning the qualitative and quantitative analysis of basic notions in parametric production planning problem with fuzzy parameters. These notions are the set of feasible parameters, the solvability set and the stability set of the first kind.
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nullS. Abass, "Stability of Production Planning Problem with Fuzzy Parameters," Open Journal of Applied Sciences, Vol. 2 No. 3, 2012, pp. 188-192. doi: 10.4236/ojapps.2012.23028.
 P. J. Billington, J. O. McClain and L. J. Thomas, “Mathematical Programming Approaches to Capacity Constrained MRP Systems: Review, Formulation and Problem Reduction,” Management Science, Vol. 29, No. 15, 1983, PP. 1126-1141.
 A. C. Hax and D. Candea, “Production and Inventory Management,” Prentice-Hall, Englewood, 1984.
 B. Kim and S. Kim, “Extended Model for a Hybrid Production Planning Approach,” International Journal of Production Economics, Vol. 73, No. 2, 2001, 165-173.
 J. Galbraith, “Designing Complex Organizations,” Addison-Wesley, Boston, 1973.
 J. Mula, R. Poler, J. P. Garcia-Sabater and F. C. Lario, “Models for Production Planning under Uncertainty: A Review,” International journal of production economics, Vol. 103, No. 1, 2006, pp. 271-285.
 A. Jamalnia and M. Ali Aoukhakian, “A Hybrid Fuzzy Goal Programming Approach with Different Goal Priorities to Aggregate Production Planning,” Computers & Industrial Engineering, Vol. 56, No. 4, 2009, pp. 14741486.
 L. Zrinka, K. Soric and V. V. Rosenzweig, “Production Planning Problem with Sequence Dependent Setups as a Bilevel Programming Problem,” European Journal of Operational Research, Vol. 187, No. 3, 2008, pp. 1504-1512.
 C. Ho, “Evaluating the Impact of Operating Environments on MRP System Nervousness,” International Journal of Production Research, Vol. 27, No. 7, 1989, PP. 1115-1135.
 S. P. Sethi, H. Yan, and Q. Zang, “Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey,” Manufacturing and Service Operations Management Journal, Vol. 4, No. 2, 2002, pp. 133170.
 C. A. Yano and H. L. Lee, “Lot Sizing with Random Yields: A Review,” Operations Research, Vol. 43, No. 2, 1995, PP. 311-334.
 D. Dubois and H. Prade, “Fuzzy Sets and Systems, Theory and Applications,” Academic Press, New York, 1980.
 D. Dubois and H. Prade, “Operations on Fuzzy Numbers,” International Journal of System Science, Vol. 9, No. 6, 1978, pp. 613-626.
 M. osman, “Qualitative Analysis of Basic Notions in Parametric Programming, II (parameters in the objective function),” Applied Mathematics, Vol. 22, No. 5, 1977, pp. 333-348.
 M. osman and A. H. El-Banna, “Stability of Multiobjective Nonlinear Programming Problems with Fuzzy Parameters,” Mathematics and Computers in Simulation, Vol. 35, No. 4, 1993, pp. 321-326.