- freely available
Entropy 2013, 15(10), 4285-4299; doi:10.3390/e15104285
2. Related Works
3. Generating of Assembly Supply Chain Classes
- The initial nodes “i” in topological alternatives are allocated to possible tiers tl (l = 1,...,m), ordered from left to right, except the tier tm, in which a final assembler is situated. We assume to model ASCs only with one final assembler. In a case when a real assembly process consists of more than one final assembler (for example 3) then it is advisable, for the purpose of the complexity measuring, to split the assembly network into three independent networks.
- The minimal number of initial nodes “i” in the first tier tl equals 2.
- In case of non-modular assembly supply chain structure, the number of initial nodes “i” in the most upstream echelon is equal to the number of individual assembly parts or inputs (in = 1,..., r).
- R1: If the numerical combination “K” consists only of numeric characters (digits), assigned by symbol “n”, n ≤ 2, e.g. K = (2;1) or K = (2;2;1) then M(2;1) or M(2;2;1) = 1.
- R2: If the numerical combination “K” consists just of one digit “3” and other digits are < 3, e.g., K = (3;1) or (3;2;2), then M(3;1) or M(3;2;2) = 2.
- R3: If the numerical combination “K” consists just of one digit “4” and other digits are < 3, e.g., K = (4;2), then M(4;2) = 5.
|The highest digit of combination set under condition that other digits are < 3||Number of alternatives for the given combinations|
4. Static Structural Complexity Metrics for ASC Structures
4.1. Some Terminology and Definitions
4.2. Specifications of ASC Networks Complexity Measure
4.3. Selection of ASC Networks with Non-repeated Sets of Vertex Degrees
5. The Concept of Quantitative Complexity Scale for ASC Networks
- A new exact framework for creating topological classes of ASC networks is developed. This methodological framework enables one to determine all relevant topological graphs for any class of ASC structure. The usefulness of such a framework is especially notable in cases when it is necessary to apply relative complexity metrics to compare the complexity of the existing configuration against the simplest or/and the most complex one.
- In order to parameterize properties of vertices of the ASC networks, an efficient method to identify total number of the graphs with non-repeated sets of vertex degrees structure is presented. The determination of the non-repeated sets of vertex degrees structure (for selected classes of ASC networks are described in Figure 5) shows that the total numbers of such graphs follows the Omar integer sequence , with the first number omitted.
- The Vertex degree index was applied to a new area of configuration complexity.
- The quantitative object-oriented model for defining degrees of configuration complexity of ASC networks was outlined.
Conflicts of Interest
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