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 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 + 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.