Complexity Assessment of Assembly Supply Chains from the Sustainability Viewpoint
Testing and Comparison of ASC Complexity Indicators
Testing of C#1
C#1 is proposing the following statement:
If i is constant (i = k) and j is increasing, then the structural complexity of ASC(i,j-1,k) < ASC(i,j,k).
Let us test ASC1(3;4;3) and ASC2(3;5;3), shown in Figure 3. While in Figure 3a, ASC1 consists of three machines and operations (i = k = 3), and the number of parts equals four (j = 4), in Figure 3b, ASC2 contains three machines and operations (i = k = 3), and the number of parts equals five (j = 5).
Applying Equation (4), according to complexity indicator Ivd, we obtained the following results for static complexity using Ivd1 (for ASC1) and Ivd2 (for ASC2):
Ivd1 = 3 × log23 + 3 × log23 + 2 × log22 = 11.51 bits
Ivd2 = 3 × log23 + 4 × log24 + 2 × log22 = 14.76 bits
Applying Equation (5), according to complexity indicator PCI, we obtained the following results for PCI1 and PCI2:
PCI1 = −(0.5 × log20.5 + 0.5 × log20.5 + 0.5 × log20.5 + 0.5 × log20.5) = 4 bits
PCI2 = −(0.5 × log20.5 + 0.5 × log20.5 + 0.5 × log20.5 + 0.5 × log20.5 + 0.5 × log20.5 + 0.5 × log20.5) = 5 bits
Applying Equation (9), according to
complexity indicator system design complexity (SDC), we obtained the
following results for SDC1 and SDC2:
SDC1 = 4 × ln4 + 2 × ln2 + 2 × ln2 = 8.32 nats
SDC2 = 5 × ln5 + 2 × ln2 + 3 × ln3 = 12.73 nats
Applying Equation (10), according to complexity indicator MFC, we obtained the following results for MFC1 and MFC2:
MFC1 = 0 × 3 + 1 × 7 + 1 × 6 = 13
MFC2 = 0 × 3 + 1 × 8 + 1 × 7 = 15
According to these complexity indicators, it was proved that the complexity of ASC1(3,4,3) < ASC2(3,5,3), then ASC(i,j−1,k) < ASC(i,j,k).