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We present a new theoretical and numerical assessment methodology for aone-dimensional process chain with general applicability to management problemssuch as the optimization of decision chains or production chains. The processis thereby seen as a chain of subsequently arranged units with randomparameters influencing the objective function. For solving such complex chainproblems, analytical methods usually fail and statistical methods only provideapproximate solutions while requiring massive computing power. We took insightsfrom physics to develop a new methodology based on homogenization andclustering. The core idea is to replace the complex real chain with a virtualchain that homogenizes the involved parameters and clusters the working unitsinto global units to facilitate computation. This methodology drasticallyreduces computing time, allows for the derivation of analytical formulas, andprovides fast and objective insights about the optimization problem underinvestigation. We illustrate the analytical potency of this methodology byapplying it to the production problem of selecting the economically superiorquality maintenance strategy. It can further be applied to all sequentialmulti-parametrical chain problems commonly found in business.

Homogenization and Clustering as a Non-Statistical Methodology to Assess Multi-Parametrical Chain Problems