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 co mbines the ideas of grey fuzzy linear programming (GFLP) and fuzzy qua dratic programming (FQP) within a general optimization framework. It i mproves upon the previous GFLP method by using n grey control variable s, x (lambda(i))(i = 1, 2,...,n), for n constraints instead of one x ( lambda) for n constraints in order to incorporate the independent prop erties 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 wit h the GFLP method, the GFQP approach is helpful for better satisfying model objective/constraints and providing grey solutions with higher s ystem certainty and lower system cost; compared with the FQP method, m ore information of the independent uncertain features of not only the stipulations but also the lefthand side coefficients are effectively r eflected in the GFQP method. The GFQP modelling approach is applied to a hypothetical case study of waste flow allocation planning under unc ertainty, with the input model stipulations fluctuating within wide in tervals and having independent uncertain characteristics. The results indicated that reasonable solutions have been generated. Comparisons b etween the GFQP and FQP/GFLP solutions are also provided, which demons trate that the GFQP method could better reflect system uncertainties a nd provide more realistic and applicable solutions with lower system u ncertainties and higher system benefits.