Determining a subsidy rate for Taiwan's recycling glass industry: an application of bi-level programming

Abstract

This study attempts to optimize the operations of the Recycling Fund Management Board (RFMB), founded by the Environmental Protection Administration of the R.O.C. Government (on Taiwan), through the decision of a subsidy rate for the domestic glass recycling industry. The hierarchical and interactive nature between the two parties is modelled by bi-level programming, where the RFMB plays the upper-level decision unit while the recycling industry is the lower-level counterpart. In order to solve the problem by optimization software, the bi-level formulation is transformed to a single-level problem via Karush-Kuhn-Tucker optimality conditions and is further transformed to a 0−1 mixed integer programming problem by variable substitution. The problem is solved with real-world data, and the obtained solutions are analysed and compared with the RFMB’s current operations. The results suggest that the proposed approach can improve the operations of the RFMB.

Keywords:

• bi-level programming problem
• glass recycling industry
• subsidy rate
• recycling and treatment fee
• 0−1 mixed integer programming
• KKT conditions

Acknowledgements

This study was supported by the National Science Council of Taiwan under Grant numbers NSC95-2221-E-032-030-MY3 and NSC98-2221-E-032-015. The authors would like to thank two anonymous reviewers and the editor for their comments.