Inexact Piecewise Quadratic Programming for Waste Flow Allocation under Uncertainty and Nonlinearity

Abstract

In practical waste management systems, most relationships among different system components are nonlinear in nature. Effects of economies-of-scale can often bring about such nonlinearity in objective functions within an inexact optimization framework. To handle both nonlinearity and uncertainty, an inex act piecewise quadratic programming (IPQP) model was developed through coupling piecewise linear regression with interval linear programming. In IPQP, uncertainties expressed as intervals for transportation/operation costs, treatment capacities, waste generation rates, waste flows/amounts were reflected; a more accurate approximation for nonlinearities reflecting effects of economies-o f-scale between unit transportation costs and waste flows as well as between unit operation costs and waste treatment amounts were provided. An interactive algorithm was designed for solving IPQP. IPQP was applied to a hypothesis case of waste allocation planning and compared with a conventional inexact quadratic programming model (IQP). The results indicated that, in the investigated waste allocation system, the optimized waste flows from the districts to the waste treatment facilities (WTFs) and the optimized waste treatment amounts in WTFs had no significant differences between both models. However, most of unit transportation costs or unit operation costs in IPQP were less than those in IQP, which finally contributed to a lower net system costs in IPQP than IQP. Th is implied that the often ignored effects of economies-of-scale should be considered accurately in the real-world waste management system to obtain lower costs. Strategies to balance the tradeoff between approximation accuracy and computational complexity for IPQP were also discussed.

Keywords: quadratic programming, piecewise linear regression, waste management, operation costs, transportation costs, economies of scale