## Complexity Assessment of Assembly Supply Chains from the Sustainability Viewpoint

The main point of the paper is to address supply chain networks in terms of sustainability. How can customization of physical networks help to better manage demand?

### 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).