Gou H. Huang

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Civil Engineering


Brian W. Baetz


Gilles G. Patry


In this dissertation research, grey mathematical programming (GMP) and grey fuzzy mathematical programming (GFMP) methods have been developed for the first time for decision making under uncertainty, and applied to case studies for municipal solid waste (MSW) management planning in the Regional Municipality of Hamilton-Wentworth (RMHW), Ontario, Canada.

The GMP/GFMP approaches have improved upon existing mathematical programming methods, such as fuzzy mathematical programming, stochastic mathematical programming, and interval mathematical programming, by introducing concepts of grey systems and grey decisions into ordinary mathematical programming (MP) and fuzzy mathematical programming (FMP) framework. The developed methods allow uncertain information (presented as grey numbers) to be effectively communicated into the optimization processes and resulting solutions, such that feasible decision alternatives can be generated through the interpretation and analysis of the grey solutions according to projected applicable system conditions. Moreover, the proposed GMP/GFMP solution algorithms do not lead to more complicated intermediate models, and thus have lower computational requirements and are applicable to practical problems.

Four GMP (grey linear programming (GLP), grey quadratic programming (GQP), grey integer programming (GIP), and grey dynamic programming (GDP)) and four GFMP (grey fuzzy linear programming (GFLP), grey fuzzy quadratic programming (GFQP), grey fuzzy integer programing (GFIP), and grey fuzzy dynamic programming (GFDP)) methods have been developed. The GFMP improved upon the GMP through the introduction of concepts of fuzzy decisions and FMP into the GMP frameworks to better reflect system uncertainties and generate grey solutions with higher certainty and improved applicability. The use of the GFMP approaches may be particularly pertinent for GMP problems with model stipulations fluctuating within wide intervals but the related membership function information for admissible violations of system objectives and constraints is known. The GMP/GFMP pairs are all directly linked (GLP-GFLP, GIP-GFIP, and GDP-GFDP) except for the GFQP which is not linked to the GQP but instead is linked to and improves upon the GFLP since it enables the modelling of constraints with independent uncertain characteristics. In comparison, the GQP was formulated by including the effects of economies of scale within the GLP modelling framework. In terms of the difference between the GIP/GFIP and GDP/GFDP, the GIP/GFIP methods provide a "one step" optimization process which is convenient for modelling formulation and solution, but may require computers with high capacities and speeds when large scale problems with a multitude of variables and time stages are to be solved, while the GDP/GFDP methods could potentially solve such a problem by dividing the planning horizon into several stages, but may require more effort for the dynamic analysis and computation of the stage submodels. The effectiveness of the methods and their solution algorithms have been demonstrated through a series of comparisons between the MP/GMP/GFMP solutions, as well as related sensitivity analyses.

The GMP and GFMP methodologies were applied to case studies of short term waste flow allocation and long term facility expansion for the waste management system in the RMHW. Through examining the relationships and conflicts between different system components, a GLP model was formulated for the waste flow allocation planning problem, and a GIP model was formulated for the facility expansion planning problem. The grey solutions provided optimal and stable ranges for system objective function values and decision variables, which could be used for generating decision alternatives through adjusting/shifting the decision variable values within their solution intervals and making relevant tradeoffs between different system objectives/restrictions according to projected applicable conditions. Generally, the short term waste flow allocation solutions were useful for adjusting or justifying the existing waste flow allocation patterns, and the long term capacity planning solutions provided optimal times, sizes and locations of the waste management facility developments/expansions. Sensitivity analyses of the effects of system condition variations on the model solutions were also conducted.

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