TABLE OF CONTENTS Chapters Three and Six presented the material recycle pinch diagram and the cascade analysis for the graphical and the algebraic targeting of direct recycle problems. As mentioned in Chapter Six, graphical tools may become cumbersome for problems with numerous sources or sinks and for problems with a wide range of flowrate or load scale. Additionally, algebraic techniques cannot easily handle problems with multiple fresh resources. Therefore, it is beneficial to develop a mathematical programming approach to the targeting of material recycle. Such approach can also be integrated with other optimization techniques. This chapter provides an optimization-based formulation for the mathematical solution of the direct recycle problem. First, the problem addressed in Chapters Three and Six will be re-stated. Then, a structural representation of the solution alternatives will be presented. Next, the mathematical programming formulation will be discussed along with its solution applied to a case study.
The problem can be expressed as follows:
Given a process with:
A set of process sinks (units): SINKS = { j=1,2, ..., N Sinks}. Each sink requires a feed with a given flowrate, G j, and a composition, 
, that satisfies the following constraint:
where 
and 
are given lower and upper bounds on admissible compositions to unit j.
A set of process sources: SOURCES = { i=1,2, ..., N Sources} which can be recycled/reused in process sinks. Each source has a given flowrate, W i, and a given...
