WASTE FLOW ALLOCATION PLANNING THROUGH A GREY FUZZY QUADRATIC PROGRAMMING APPROACH

This paper proposes a grey fuzzy quadratic programming (GFQP) approach as a means for optimization analysis under uncertainty. The method combines the ideas of grey fuzzy linear programming (GFLP) and fuzzy quadratic programming (FQP) within a general optimization famework. It improves upon the previous GFLP method by using n grey control variables, ® (A,j (i = 1,2,..., n), for n constraints instead of one ® (X) for n constraints in order to incorporate the independent properties of the stipulation uncertainties; it also improves upon the FQP method by further introducing grey numbers for coefficients in A and C to effectively reflect the lefthand side uncertainties. Compared with the GFLP method, the GFQP approach is helpful for better satisfying model objective/constraints and providing grey solutions with higher system certainty and lower system cost; compared with the FQP method, more information of the independent uncertain features of not only the stipulations but also the lefthand side coefficients are effectively reflected in the GFQP method. The GFQP modelling approach is applied to a hypothetical case study of waste flow allocation planning under uncertainty, with the input model stipulations fluctuating within wide intervals and having independent uncertain characteristics. The results indicated that reasonable solutions have been generated. Comparisons between the GFQP and FQP/GFLP solutions are also provided, which demonstrate that the GFQP method could better reflect system uncertainties and provide more realistic and applicable solutions with lower system uncertainties and higher system benefits.