Development of dual-interval optimization methodologies for the management of regional environmental systems

In this dissertation research, dual interval mathematical programming (DIMP) and dual interval two-stage mathematical programming (DITSMP) methods were developed for decision making under multiple uncertainties, and applied to case studies of resources and environmental management planning. The DIMP/DITSMP approaches improved upon the existing mathematical programming methods, such as fuzzy mathematical programming, stochastic mathematical programming and interval mathematical programming by introducing the concept of dual interval into conventional mathematical programming (MP) and two-stage stochastic programming (TSP) frameworks. Highly uncertain information (presented as dual intervals) was allowed to be communicated into the optimization processes. As a result, feasible decision alternatives could be generated through analysis of the dual interval solutions. Moreover, the methods were applicable to practical problems due to their reasonable computational requirements.;The DITSMP method was applied to the planning of waste-flow allocation and facility expansion within the waste management system of the City of Regina, Canada. By examining the relationships among different system components, a DITSMP model was formulated. As a result of the case study, reasonable solutions for municipal solid waste management (MSW) decision making were generated. The obtained waste flow allocation plans were useful in adjusting the existing waste management practices, and the capacity expansion schemes provided optimal timing and sizing in terms of the developments or expansions of the related waste management facilities.;Four DIMP methods [i.e., dual interval linear programming (DILP), dual interval probabilistic integer programming (DIPIP), dual interval fuzzy programming (DIFP), and dual interval fuzzy-possibilistic integer programming (DIFPIP)] and four DITSMP methods [i.e., dual interval two-stage stochastic programming (DITSP), dual interval stochastic integer programming (DISIP), dual interval two-stage restricted-recourse programming (DITRP), and dual interval robust stochastic dynamic programming (DIRSDP)] were developed in association with the relevant solution methods. They were applied to resources and environmental management problems where DILP, DIPIP, DITSP, and DISIP methods were applied to waste flow allocation, and DIFP, DIFPIP, DITRP and DIRSDP methods were extended to air quality and water resources management. Iwo special characteristics of the DITSMP methods rendered them different from the DIMP. The DITSMP methods could reflect uncertainties expressed as single/dual intervals and probability distribution functions; the sequence of decision process in the DITSMP involved two stages where a desired plan could be identified after the random uncertainties were unveiled.