Metal Foams: A Design Guide

206 Metal Foams: A Design Guide
PV = 20,000 units/yr PV = 300,000 units/yr
Materials cost
Direct labor
Energy cost
Equipment cost
Auxillary
Tooling cost
Maintenance
Fixed overhead
Building cost
Working capital
Liquid PM, batch PM, continuous
Figure 16.4 Output of the TCM for the liquid-state foaming process of
aluminum
We now consider the final step in determining viability: that of value
modeling.
16.4 Value modeling
Multi-objective optimization and trade-off surfaces
When a design has two or more objectives, solutions rarely exist that optimize
all objectives simultaneously. The objectives are normally non-commensurate,
meaning that they are measured in different units, and in conflict, meaning that
any improvement in one is at the loss of another. The situation is illustrated for
two objectives by Figure 16.5 in which one performance metric, P2, is plotted
another, P1. It is usual to define the metrics such that a minimum is sought
for each. Each bubble describes a solution. The solutions which minimize P1
do not minimize P2, and vice versa. Some solutions, such as that at A, are far
from optimal: other solutions exist which have lower values of both P1 and P2,
such as B. Solutions like A are said to be dominated by others. Solutions like
that at B have the characteristic that no other solution exists with lower values
of both P1 and P2. These are said to be non-dominated solutions. The line or
surface on which they lie is called the non-dominated or optimum trade-off
surface (Hansen and Druckstein, 1982; Sawaragi and Nakayama, 1985). The
values of P1 and P2 corresponding to the non-dominated set of solutions are
called the Pareto set.