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Journal of Optimization
Volume 2014, Article ID 896756, 10 pages
Research Article

Polymorphic Uncertain Linear Programming for Generalized Production Planning Problems

1School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China
2School of Business, Central South University, Changsha, Hunan 410083, China

Received 24 June 2013; Revised 28 December 2013; Accepted 2 January 2014; Published 19 February 2014

Academic Editor: Cheng-Hong Yang

Copyright © 2014 Xinbo Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A polymorphic uncertain linear programming (PULP) model is constructed to formulate a class of generalized production planning problems. In accordance with the practical environment, some factors such as the consumption of raw material, the limitation of resource and the demand of product are incorporated into the model as parameters of interval and fuzzy subsets, respectively. Based on the theory of fuzzy interval program and the modified possibility degree for the order of interval numbers, a deterministic equivalent formulation for this model is derived such that a robust solution for the uncertain optimization problem is obtained. Case study indicates that the constructed model and the proposed solution are useful to search for an optimal production plan for the polymorphic uncertain generalized production planning problems.