## 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#5

C#5 is proposing the following statement:
If i, j, and k are constant and the number of echelons is increasing, then the complexity of ASC(i,j,k) ˂ ASC(i,j,k) with an increasing number of echelons.

Let us test ASC1(3,4,3) and ASC2(3,4,3), shown in Figure 7. While in Figure 7a, ASC1 consists of three machines and operations (i = k = 3), the number of parts equals four (j = 4), and the number of echelons equals two, in Figure 7b, ASC2 contains three machines (i = 3), four operations (k = 4), the number of parts equals four (j = 4), and the number of echelons equals three.

Applying Equation (4), according to complexity indicator Ivd, we obtained the following results for Ivd1 and Ivd2:

Ivd1 = 3 × log23 + 3 × log23 + 2 × log22 = 11.51 bits
Ivd2 = 3 × log23 + 3 × log23 + 2 × log22 = 11.51 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 = −(0.33 × log20.33 + 0.33 × log20.33 + 0.33 × log20.33 + 0.33 × log20.33 + 0.33 × log20.33 + 0.33 × log20.33 + 0.5 × log20.5 + 0.5 × log20.5 + 1 × log21) = 4.17 bits

Applying Equation (9), according to complexity indicator SDC, we obtained the following results for SDC1 and SDC2:

SDC1 = 4 × ln4 + 2 × ln2 + 2 × ln2 = 8.32 nats
SDC2 = 4 × ln4 + 3 × ln3 + 2 × ln2 = 10.23 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 × 4 + 1 × 7 + 1 × 6 = 13

According to the three complexity indicators PCI, SDC, and MFC, it was proved that the complexity of ASC1 ˂ the complexity of ASC2, then ASC(i,j,k) ˂ ASC(i,j,k) with an increasing number of echelons.