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#4

C#4 is proposing the following statement:
If i, j, and k are constant and the number of routings is increasing, then the structural complexity of ASC(i,j,k) ˂ ASC(i,j,k) with an increasing number of routings.

Let us test ASC1(3,4,3) and ASC2(3,4,3), shown in Figure 6. While in Figure 6a, ASC1 consists of three machines and operations (i = k = 3), and the number of parts equals four (j = 4), in Figure 6b, ASC2 consists of three machines and operations (i = k = 3), and the number of parts equals four (j = 4), but P2 and P3 can be processed on M1 or M2.

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 = 4 × log24 + 4 × log24 + 2 × log22 = 18 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 + 0.25 × log20.25 + 0.25 × log20.25 + 0.5 × log20.5 + 0.25 × log20.25 + 0.25 × log20.25 + 0.5 × log20.5 + 0.5 × log20.5 + 0.5 × log20.5) = 5 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 + 3 × ln3 = 12.14 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 × 7 + 1 × 8 = 15

According to these complexity indicators, it was proved that the complexity of ASC1 ˂ ASC2, then ASC(i,j,k) ˂ ASC(i,j,k) with an increasing number of routings.