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Mathematical Problems in Engineering
Volume 2015, Article ID 780830, 20 pages
Research Article

Application of Two-Phase Fuzzy Optimization Approach to Multiproduct Multistage Integrated Production Planning with Linguistic Preference under Uncertainty

1State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, China
2The West Pipeline Company of CNPC, Urumqi 830012, China
3Liaoning Key Lab of Advanced Control Systems for Industry Equipment, Dalian University of Technology, Dalian 116024, China

Received 27 March 2015; Revised 24 July 2015; Accepted 6 August 2015

Academic Editor: Sean Wu

Copyright © 2015 Shan Lu 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.


This paper tackles the challenges for a production planning problem with linguistic preference on the objectives in an uncertain multiproduct multistage manufacturing environment. The uncertain sources are modelled by fuzzy sets and involve those induced by both the epistemic factors of process and external factors from customers and suppliers. A fuzzy multiobjective mixed integer programming model with different objective priorities is proposed to address the problem which attempts to simultaneously minimize the relevant operations cost and maximize the average safety stock holding level and the average service level. The epistemic and external uncertainty is simultaneously considered and formulated as flexible constraints. By defining the priority levels, a two-phase fuzzy optimization approach is used to manage the preference extent and convert the original model into an auxiliary crisp one. Then a novel interactive solution approach is proposed to solve this problem. An industrial case originating from a steel rolling plant is applied to implement the proposed approach. The numerical results demonstrate the efficiency and feasibility to handle the linguistic preference and provide a compromised solution in an uncertain environment.