Multi-objective non-linear programming problem with rough interval parameters: an application in municipal solid waste management

Abstract

In dealing with the real-world optimization problems, a decision-maker has to frequently face the ambiguity and hesitancy due to various uncontrollable circumstances. Rough set theory has emerged as an indispensable tool for representing this ambiguity because of its characteristic of incorporating agreement and understanding of all the involved specialists and producing more realistic conclusions. This paper studies an application of the rough set theory for a multi-objective non-linear programming problem that originates for the management of solid wastes. Municipal solid waste management is a global problem that affects every country. Because of the poor waste management system in many nations, the bulk of municipal solid waste is disposed of in open landfills with no recovery mechanism. Hence, an effective and long term waste management strategy is the demand of the day. This research offers an incinerating, composting, recycling, and disposing system for the long-term management of the municipal solid waste. A model for the municipal solid waste management with the goal of minimizing the cost of waste transportation, cost of waste treatment and maximizing the revenue generated from various treatment facilities is developed under rough interval environment. To tackle the conflicting nature of different objectives, an approach is proposed that gives the optimistic and pessimistic views of the decision-maker for optimizing the proposed model. Also, the biasness/preference of the decision-maker for a specific objective is handled by establishing the respective non-linear membership and non-membership functions instead of the linear ones. Finally, to demonstrates the practicality of the proposed methodology, a case study is solved and the obtained Pareto-optimal solution has been compared to those obtained by the existing approaches.