Grey integer programming An application to waste management.pdfVIP

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH ELSEVIER European Journal of Operational Research 83 (1995) 594-620 Theory and Methodology Grey integer programming: An application to waste management planning under uncertainty Guo H. Huang a, Brian W. Baetz a,., Gilles G. Patry b a Department o f Civil Engineering, McMaster University, Hamilton, Ont., Canada L8S 4L7 b Faculty o f Engineering, University of Ottawa, Ottawa, Ont., Canada KIN 6N5 Received July 1993; revised December 1993 Abstract This paper introduces a grey integer programming (GIP) method for facility expansion planning under uncer- tainty, by incorporating the concepts of grey number and grey mathematical programming into a mixed integer linear programming optimization framework. The approach is an improvement upon previous integer programming methods in terms of its technical characteristics and applicability. It allows uncertain information to be effectively communicated into the optimization process and the resulting solutions. It also has low computational requirements and is thus applicable to practical problems. The modelling approach is applied to a hypothetical planning problem of waste flow allocation and treatment/disposal facility expansion within a regional solid waste management system. The binary variable solutions provide the ranges of different development alternatives within a multi-period, multi-facility and multi-scale context, and the continuous variable solutions provide optimal schemes for waste flow allocation corresponding to the upper and lower bounds of the objective function value. The results indicate that reasonable and useful solutions can be achieved through the developed approach. Keywords: Grey integer programming; Mixed integer linear programming; Regional solid waste management; Optimization; Uncertainty 1. Introduct ion A significant number of municipal solid waste management planning problems involve facility capacity issues, where a rel