A GREY LINEAR PROGRAMMING APPROACH FOR MUNICIPAL SOLID WASTE MANAGEMENT PLANNING UNDER UNCERTAINTY

TLDR

Uncertainties in linear‑programming coefficients and constraints can propagate through analyses, yet existing methods are either too complex for practical use or fail to fully capture input and output uncertainties. This study introduces a grey linear‑programming (GLP) model to civil engineering for handling such uncertainties. The GLP framework incorporates input uncertainties into the optimization process, yielding solutions that reflect inherent variability, and can be solved efficiently by repeatedly running a simplex algorithm, as demonstrated on a hypothetical municipal solid‑waste allocation problem. The approach produces reasonable solutions for both lower‑ and upper‑bound objective‑function cases. Keywords: grey systems theory, grey linear programming, uncertainty, municipal solid waste management, decision making.

Abstract

Abstract In optimization analysis by linear programming, uncertainties may exist in model coefficients and stipulations (right-hand side constraints). These uncertainties can propagate through the analysis and generate uncertainties in the results. However, among the previous methods dealing with uncertainty, some were too complicated to be applied to actual problems, and some were unable to reflect completely the uncertainties of the input and output information. In this paper, a grey linear programming (GLP) model is introduced to the civil engineering area. This method allows uncertainties in the model inputs to be communicated into the optimization process, and thereby solutions reflecting the inherent uncertainties can be derived. A grey linear programming problem can be solved easily by running a simplex program several times. The modelling approach is applied to a hypothetical problem of waste flow allocation planning within a municipal solid waste management system. The results indicate that reasonable solutions can be generated for both the lower and upper limit objective function cases. KEY WORDS: grey systems theorygrey linear rjrogramminguncertaintymunicipal solid waste managementdecision making