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Scenario-Based Methods for Interval Linear Programming Problems

M. F. Cao and G. H. Huang*

MOE Key Laboratory of Regional Energy Systems Optimization, S&C Academy of Energy and Environmental Research, North China Electric Power University, Beijing 102206, China

*Corresponding author. Email:


In this study, a total of twelve system-condition scenarios are considered for the management system. The scenarios correspond on different attitudes of decision makers to the study system. In detail, variations in concerns on objective function values (aggressive, conservative, or neutral), the attitude to the constraints (optimistic or pessimistic), and the preferred types of constricting ratios (consistent or varied) lead to twelve scenarios. Consequently, twelve planning models and solution methods corresponding to different scenarios have been developed. To demonstrate the applicability of the developed methods, a municipal solid waste management problem has been provided in the case study section. The inherent mechanism of the study system could be reflected through a series of considered scenarios. Thus the decision makers could understand the targeted system comprehensively and identify the scenario which best fits the practical condition. Moreover, a number of feasible schemes could be generated under each scenario which allows decision makers to further adjust the obtained solutions and indentify a desired one through incorporation of their experiences, economic situations, social and cultural conditions. In addition, the possibility of infeasible solutions has been greatly reduced with the consideration of twelve scenarios instead of one.

Keywords: interval linear programming, scenario analysis, constricting ratio, three-step method, solid waste management

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