Grey linear programming, its solving approach, and its application

In systems analysis, uncertainties may exist in model parameters and input data. Those uncertainties can propagate through the analysis and generate uncertainty in the results. Grey systems theory offers a method for incorporating uncertainties into systems analysis. In this paper, a new method of solution for a grey linear programming (GLP) model is advanced. The GLP model allows grey messages concerning the model parameters and input data to be communicated into optimization processes and solutions. A new application field—grey systems analysis of water resource planning and decision making under uncertainty—is introduced, and a case study is reported of water quantity allocation and quality planning in a drainage basin area connected to a water delivery canal in Xiamen, China. The results indicate that the solutions derived are feasible for the study area. Sensitivity tests of the effects of grey inputs on grey outputs are reported. It is indicated that the grey degrees of the solutions increase along with increases of those of input grey coefficients. When the grey degrees of input grey coefficients increase from 10% to 15% and 20%, those of grey solutions increase from 18.76% to 35.00% and 82.35%, correspondingly. The test results indicate that the grey solutions (grey outputs) can reflect the effects of input grey messages.