Piecewise Linearization-based Inexact Nonlinear Programming for Waste Management
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Effects of economies-of-scale can often bring about nonlinearities in objective functions in a municipal solid waste management planning under uncertainties. Previously, two types of approaches were employed to deal with the scale effects within an inexact optimization framework. One approach was to find efficient algorithms to directly solve the resulting nonlinear objective functions with inexact information. The other type of approach was to approximate nonlinear expressions so that existing algorithms could be applied. In fact, nonlinear systems usually can be approximated more accurately by piecewise linear functions through splitting the state space into piecewise regions and assuming sub-system is linear within each region. Thus, this study aims to develop piecewise linearization-based inexact nonlinear programming and apply it to hypothesis cases of waste allocation planning. Interactive algorithms were designed for solving the proposed methods. The results showed that a more accurate approximation for nonlinearities reflecting effects of economies-of-scale between unit transportation costs and waste flows as well as between unit operation costs and waste treatment amounts were obtained. Most of unit transportation costs or unit operation costs were less than those in conventional programming, which finally contributed to a lower net system costs. This implied that the often ignored effects of economies-of-scale should be considered accurately in the real-world waste management system.