  We present a new theoretical and numerical assessment methodology for a
one-dimensional process chain with general applicability to management problems
such as the optimization of decision chains or production chains. The process
is thereby seen as a chain of subsequently arranged units with random
parameters influencing the objective function. For solving such complex chain
problems, analytical methods usually fail and statistical methods only provide
approximate solutions while requiring massive computing power. We took insights
from physics to develop a new methodology based on homogenization and
clustering. The core idea is to replace the complex real chain with a virtual
chain that homogenizes the involved parameters and clusters the working units
into global units to facilitate computation. This methodology drastically
reduces computing time, allows for the derivation of analytical formulas, and
provides fast and objective insights about the optimization problem under
investigation. We illustrate the analytical potency of this methodology by
applying it to the production problem of selecting the economically superior
quality maintenance strategy. It can further be applied to all sequential
multi-parametrical chain problems commonly found in business.
