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MCFP: A Monte Carlo Simulation-based Fuzzy Programming Approach for Optimization under Dual Uncertainties of Possibility and Continuous Probability

B. Chen1,2*, P. Li2, H. J. Wu2, T. Husain2 and F. Khan2

  1. Key Laboratory of Regional Energy and Environmental Systems Optimization, Ministry of Education, Resources and Environmental Research Academy, North China Electric Power University, Beijing 102206, China
  2. Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John’s NL A1B 3X5, Canada

*Corresponding author. Tel: +1-709-8648958 Fax: +1-709-8644042 Email:


The efficiency and confidence of decision making much rely on accurate information and objective judgement, however, which are usually compromised by uncertainties existing in the system. Although in many studies uncertainties are reflected during optimization processes, few models considered the dual uncertainties of possibility and continuous probability. This study proposed a Monte Carlo simulation-based fuzzy programming (MCFP) approach to handle such dual uncertainties. The developed approach was tested by a municipal solid waste management (MSW) problem to demonstrate its feasibility and efficiency. The results indicated that the proposed approach could obtain a reliable solution and adequately support the decision making process in MSW management. It is significantly advantageous in handling the coexistence of various fuzzy sets and complex probability distributions when compared to the conventional fuzzy stochastic programming approaches. Furthermore, three levels of the optimal results to help decision makers effectively manage the composting facility: the entire distributions for general policy makers in long term policy making and trade-off, risk and reliability analyses of the system; the range of most frequent occurrences for project/plant managers in a medium arrangement; and the expected values for the plant operators for short term operating and adjusting the facility to minimize the system cost. Such different levels of decision supports could make the MCFP approach highly feasible, flexible and adaptable in real-work applications.

Keywords: dual uncertainties, possibility, probability, Monte Carlo simulation, optimization, municipal waste management (MSW)

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