A Bi-level Multi-objective Optimization Model of Multiple Items for Stone Industry Under Fuzzy Environment

Abstract

Traditionally, stone industry is produced essential materials for the construction industry but stone industry is always debated as a high emission industry for stone dust and waste water. This emission has an adverse impact on environment, humans, agriculture and ground water. This paper focuses on how to optimize the stone industry. The government is considered as the leader level which will make a strategy to plan the exploring amount of every stone plant and sustainable development in stone industry to create employment opportunity and economic growth. The stone plants are considered as the lower-level decision-makers which optimize their objective functions under the constraint of leader. The stone plants have individual objectives of maximizing the profit and produce different product according to the demand constraints under the limited exploring amount. Due to the lack of historical data, some emission coefficients are considered as fuzzy numbers according to experts advices. Therefore, a bi-level multi-objective optimization model with possibilistic and predetermined constraints under the fuzzy environment is developed to control the pollution and get sustainable development in stone industry. For some special fuzzy coefficients, the equivalent model is obtained. At the end, a practical case is proposed to show the efficiency of the proposed model.