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 ASC₁(3,4,3) and ASC₂(4,4,4), shown in Figure 4. While in Figure 4a, ASC₁ consists of three machines and operations (i = k = 3), and the number of parts equals four (j = 4), in Figure 4b, ASC₂ 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 × log₂3 + 3 × log₂3 + 2 × log₂2 = 11.51 bits

I_vd2 = 3 × log₂3 + 3 × log₂3 + 3 × log₂3 + 3 × log₂3 = 19.02 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 + 2 × ln2 + 2 × ln2 + 2 × ln2 = 9.7 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 × 9 = 17

According to these complexity indicators, it was proved that ASC₁(3,4,3) < ASC₂(4,4,4), then ASC(i−1,j,k) ˂ ASC(i,j,k).