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 I_vd, we obtained the following results for static complexity using I_vd1 (for ASC₁) and I_vd2 (for ASC₂):

I_vd1 = 3 × log₂3 + 3 × log₂3 + 2 × log₂2 = 11.51 bits

I_vd2 = 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).