## 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#2

C#2 is proposing the following statement:

If j is constant and i is increasing (i = k), then the structural complexity of ASC(i−1,j,k) ˂ ASC(i,j,k).

Let us test ASC

_{1}(3,4,3) and ASC_{2}(4,4,4), shown in Figure 4. While in Figure 4a, ASC_{1}consists of three machines and operations (i = k = 3), and the number of parts equals four (j = 4), in Figure 4b, ASC_{2}contains four machines and operations (i = k = 4), and the number of parts equals four (j = 4).Applying Equation (4), according to complexity indicator I

_{vd}, we obtained the following results for I_{vd1}and I_{vd2}:
I

_{vd1}= 3 × log_{2}3 + 3 × log_{2}3 + 2 × log_{2}2 = 11.51 bits
I

_{vd2}= 3 × log_{2}3 + 3 × log_{2}3 + 3 × log_{2}3 + 3 × log_{2}3 = 19.02 bitsApplying Equation (5), according to complexity indicator PCI, we obtained the following results for PCI

_{1}and PCI_{2}:
PCI

_{1}= −(0.5 × log_{2}0.5 + 0.5 × log_{2}0.5 + 0.5 × log_{2}0.5 + 0.5 × log_{2}0.5) = 4 bits
PCI

_{2}= −(0.5 × log_{2}0.5 + 0.5 × log_{2}0.5 + 0.25 × log_{2}0.25 + 0.25 × log_{2}0.25 + 0.5 × log_{2}0.5 + 0.25 × log_{2}0.25 + 0.25 × log_{2}0.25 + 0.5 × log_{2}0.5 + 0.5 × log_{2}0.5 + 0.5 × log_{2}0.5) = 5 bitsApplying Equation (9), according to complexity indicator SDC, we obtained the following results for SDC

_{1}and SDC_{2}:
SDC

_{1}= 4 × ln4 + 2 × ln2 + 2 × ln2 = 8.32 nats
SDC2 = 4 × ln4 + 2 × ln2 + 2 × ln2 + 2 × ln2 = 9.7 nats

Applying Equation (10), according to complexity indicator MFC, we obtained the following results for MFC

_{1}and MFC_{2}:
MFC

_{1}= 0 × 3 + 1 × 7 + 1 × 6 = 13
MFC

_{2}= 0 × 3 + 1 × 8 + 1 × 9 = 17According to these complexity indicators, it was proved that ASC

_{1}(3,4,3) < ASC_{2}(4,4,4), then ASC(i−1,j,k) ˂ ASC(i,j,k).