Generalized production planning problem under interval uncertainty

Abstract Data in many real life engineering and economical problems suffer from inexactness. Herein we assume that we are given some intervals in which the data can simultaneously and independently perturb. We consider the generalized production planning problem with interval data. The interval data are in both of the objective function and constraints. The existing results concerning the qualitative and quantitative analysis of basic notions in parametric production planning problem. These notions are the set of feasible parameters, the solvability set and the stability set of the first kind.

[1]  David F. Pyke,et al.  Inventory management and production planning and scheduling , 1998 .

[2]  H. Zhang,et al.  Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey , 2002, Manuf. Serv. Oper. Manag..

[3]  Jeremy F. Shapiro,et al.  Chapter 8 Mathematical programming models and methods for production planning and scheduling , 1993, Logistics of Production and Inventory.

[4]  James P. Jarvis,et al.  A Hierarchical Production Planning and Scheduling Model , 1992 .

[5]  M. Osman,et al.  Qualitative analysis of basic notions in parametric convex programming. I. Parameters in the constraints , 1977 .

[6]  Jeremy F. Shapiro,et al.  Mathematical programming models and methods for production planning and scheduling , 1988 .

[7]  Arnoldo C. Hax,et al.  Hierarchical integration of production planning and scheduling , 1973 .

[8]  Jay R. Galbraith.  Designing Complex Organizations , 1973 .

[9]  G. P. Liu,et al.  A nonlinear interval number programming method for uncertain optimization problems , 2008, Eur. J. Oper. Res..

[10]  M. Osman,et al.  Qualitative analysis of basic notions in parametric convex programming. II. Parameters in the objective function , 1977 .

[11]  Mohammad Ali Soukhakian,et al.  A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning , 2009, Comput. Ind. Eng..

[12]  Stability of multiobjective nonlinear programming problems with fuzzy parameters , 1993 .

[13]  Hau L. Lee,et al.  Lot Sizing with Random Yields: A Review , 1995, Oper. Res..

[14]  Raul Poler,et al.  Models for production planning under uncertainty: A review ☆ , 2006 .

[15]  W. F. Abd El-Wahed,et al.  A Solution Methodology of Bi-Level Linear Programming Based on Genetic Algorithm , 2009 .

[16]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[17]  Zhang Quan,et al.  A Ranking Approach for Interval Numbers in Uncertain Multiple Attribute Decision Making Problems , 1999 .