BUS606: Operations and Supply Chain Management

To provide a detailed and reproducible case study for production flow analysis, an open-source benchmark model of modular wire-harness production was developed. The details of the model are given in the Appendix. The multilayer network model of the production flow analysis problem is formed and analyzed in the MuxViz framework developed for the interactive visualization and exploration of multilayer networks [49]. The established network is depicted in Figure 2.

4.1. Similarity and Modularity Analysis

Figure 7 Multilayer network representing the details of the work of the operators (built-in components, $C$; zones of the activities, $Z$; skills, $S$; assignment of the operators to the workstations, $O$; and activity types, $T$) (see Table 1 for the detailed definition of the layers).

Although our network defines part families indirectly in layer $M$ and also groups of these activities (in layer $T$), it is interesting to observe how the multilayer network is structured and how the analysis of the modularity of the network can form part and activity groups. For this purpose, a multilayer InfoMap algorithm was applied.

The analysis yielded useful and informative results. 26 modules were identified. Although layer $\mathbf{M}$ which represents how the activities are grouped according to different products, this analysis was able to detect the modules of the products $\left(m_{1}, \ldots, m_{7}\right)$ in terms of the types of the activities $\left(t_{1}, \ldots, t_{16}\right)$. This result confirms that the analysis of the modularity of the proposed multilayer network model is useful in fine-tuning the existing part families based on multiple aspects representing the layers of the model.

To demonstrate how such information is useful in the early process-design phase to define technical modules, layer T of the C-Z-S-O-T multilayer network is shown in Figure 9. As can be seen, the most significant module is separated into six smaller groups by following the structure of layer $Z$ that defines in which zone the activities occur. The central role of the most frequent and widely distributed $t_{10}$ type of activity (wire-terminal attachment) is also highlighted.

Figure 9 Layer T of the network defines the types of activities. The six clusters formed in this layer reflect the effects of how the activities are distributed among the zones (defined by layer Z), which illustrates the benefit of the multidimensional network-based visual exploration of the production data.

4.2. Workload Analysis

The balancing of modular production is challenging due to the great diversity of products. Besides group formation, the analysis of the workloads is also an important task in production flow analysis. The proposed bipartite network-based model can be directly applied for this purpose as the biadjacency matrices of the layers result in simple calculations. To illustrate this applicability, let us consider the analysis of how well the production line is balanced. The equation $\mathbf{L}_{a}=\mathbf{M P}_{p}^{\prime}$ represents the activities of the production of the $p$th product (where $\mathbf{P}_{p}$ represents the $p$ th column of the $\mathbf{P}$ productmodule matrix). As these activities are assigned to the workstations as $\mathbf{L}_{w}=\operatorname{diag}\left(\mathbf{L}_{a}\right) \mathbf{W}$ and $\mathbf{T}^{\prime} \mathbf{L}_{w}$ represents the number of activities grouped by activity types and $\mathbf{T}^{\prime} \mathbf{C C}^{\prime} \mathbf{L}_{w}$ is the number of built-in components at the workstations, the total activity time at the workstations can be calculated by the following equation, where $\theta_{t}$ represents the elementary activity times given in the appendix:

$\mathbf{I}_{\mathrm{time}}=\left[\mathbf{T}^{\prime} \mathbf{L}_{w}, \mathbf{T}^{\prime} \mathbf{C} \mathbf{C}^{\prime} \mathbf{L}_{w}\right] \theta_{t}.$

As Figure 10 illustrates, the calculations above can be used to check how the process is balanced and how the complexity of the product influences the workloads of the workstations.

(a) Number of built-in components at a given workstation. The figure shows how the workload differs during the production of the base module $p_1$and the most complex product $p_{64}$

(b) Total station times during the production of the 16th product

Figure 10 The workloads (number of activities, built-in components, and total activity times) can be easily calculated based on the biadjacency matrices of the proposed model, which supports the balancing of the conveyor belt.

4.3. Analysis of the Flexibility of Operator Assignment

In the early $80 \mathrm{~s}$, suggested that organisational research should incorporate network perspective. In the early $90 \mathrm{~s}$, six themes (turnover/absenteeism, power, work attitudes, job design, leadership, and motivation) dominated the research of microorganisational behaviour. Recently, multilayer networks are becoming widely used in the analysis of social networks where people interact with each other in multiple ways like via mobile phone and emails. In this paper, we make the first attempt to integrate such analysis to the modelling and optimisation of production process.

For successful line balancing of wire-harness production, the skills of the operators influencing the speed of the conveyor belt should also be studied and handled. Dynamic job rotation requires efficient allocation of the assembly tasks while taking into account the constraints related to the available skills of the operators. Figure 11 shows the distribution of the required skills as a function of different product modules, $\mathbf{M}^{\prime} \mathbf{T S}$. As can be seen, the most in demand is the $s_{3}$ terminal-attaching skill, while $s_{6}$ is the visual testing skill which is required only once during production. The abilities of the operators can also be calculated, for example, $\mathbf{W}^{\prime} \mathbf{T S O}^{\prime}$ yields how many activities can be performed at a given operator-workstation assignment (see Figure 11(a)).

(a) Distribution of the required skills as a function of the modules of the product

(b) The number of activities that can be performed during a given operator-workstation assignment. The skills of the operators constrain the flexibility of line balancing

Figure 11 Analysis of the demand of skills and the flexibility of the operator-workstation assignment.

The presented analysis can be useful in designing the sessions of the operators by determining the components of critical skills and knowledge. Figure 12 shows the layers $S$ and $O$ of the network. Five groups of activity, skill, and operator nodes were identified with the help of multilayer modularity analysis. The smallest module contains the $t_{15}$ clip installation activity type which requires specialist skills.

Figure 12 Skill (S) and operator (O) layers define the network that can be used to determine elements of critical knowledge which is useful in terms of the design of training programs for the operators.

As can be seen, the skill $s_4$ can be considered a key piece of knowledge, because it is related to five types of activities. Operators $o_9$ and $o_{10}$ possess specialist knowledge, while $s_3$ consists of group-wise knowledge because it is the most related to the operators.

The presented analysis demonstrated that the analysis of the node degrees can identify the critically essential skills and resources. Skills that have small degrees in the $O$ layer can be considered as the knowledge of specialist, while skills with large degrees are quantified as group-wise knowledge. Skills that have no links at the $S$ layer are useless, while skills that have a small degree at the $O$ layer and high degree at the $S$ layer are critical, as this reflects that a small number of operators can be assigned to a large number of tasks which requires this knowledge.