Municipal solid waste management under uncertainty: A mixed interval parameter fuzzy-stochastic robust programming approach

A mixed interval parameter fuzzy-stochastic robust programming (MIFSRP) model is developed and applied to the planning of solid waste management systems under uncertainty. The MIFSRP can explicitly address system uncertainties with multiple presentations. It can be used as an extension of the existing interval-parameter fuzzy robust programming, interval-parameter linear programming, and chance constraint programming methods. In this MIFSRP model, the hybrid uncertainties can be directly communicated into the optimization process and resulting solution through representing the uncertain parameters as interval numbers and fuzzy membership functions with random characteristics. Highly uncertain information arising from simultaneous appearance of fuzziness and randomness for the lower and upper bounds of interval parameters can be effectively addressed through integrating chance constraint programming, interval linear programming, and fuzzy robust programming methods into a general optimization framework. This can enhance the robustness of the optimization process and solution. Results of the case study indicate that useful solutions for planning municipal solid waste management practices have been generated. The compromise between optimality and stability of the study system, and the tradeoff between system costs and risk can be reflected with the introduction of fuzzy interval and fuzzy random parameters. The results also suggest that the proposed methodology is applicable to practical problems that are associated with hybrid uncertain information existing as randomness and fuzziness.