# Simulation-Based Study of the Resilience of Flexible Manufacturing Layouts Subject to Uncertain Demands of Product Variants

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Comparison Studies of Functional and Cellular Layouts

#### 2.2. Numerical Approaches and the Concept of Criticiality

## 3. Manufacturing System Modeling and the Study Case

#### 3.1. Basic System Model

_{1}, v

_{2}, …, v

_{r}}, representing r different product variants. The set of parts consists of n different types of parts, denoted as P = {p

_{1}, p

_{2}, …, p

_{n}}, which are required to produce the product family. Suppose that the manufacturing system has m machines, denoted as a set M = {m

_{1}, m

_{2}, …, m

_{m}}, representing the total machine resources. Some machines can be duplicated, meaning that they belong to the same type of machines and perform the same manufacturing functions. Suppose that there are q types of machines, and the set of machine types is denoted as T = {t

_{1}, t

_{2}, …, t

_{q}}. To better track the notations of these elements, Table 1 lists the sets of these elements along with their subscript indices and the total number of elements in each set.

_{1}is made of two pieces of part p

_{1}and two pieces of part p

_{3}. To define these relationships, a part-variant matrix, denoted as PV = [pv

_{ih}], is used, where pv

_{ih}is the number of part p

_{i}required to make product variant v

_{h}.

_{ik}], where pt

_{ik}= 1 if machine type t

_{k}is required to make part p

_{i}(otherwise, pt

_{ik}= 0). Furthermore, machine duplication is allowed within each machine type. For example, Figure 1 shows that machines m

_{1}and m

_{2}are duplicates for machine type t

_{1}. Then, as part p

_{1}requires the service of machine type t

_{1}, part p

_{1}can use either machine m

_{1}or m

_{2}to complete the job. To capture these relationships, let us denote a machine-type matrix, MT = [mt

_{jk}], where mt

_{jk}= 1 if machine m

_{j}belongs to machine type t

_{k}(otherwise, mt

_{jk}= 0).

#### 3.2. Introduction to the Study Case

_{ih}], which describes the number of part p

_{i}required to make product variant v

_{h}, is provided in Table 2. For example, Table 2 shows that pv

_{21}= 2, indicating that two pieces of part p

_{2}are required to make product variant v

_{1}. Furthermore, the matrix of parts and machine types, PT = [pt

_{ik}], is provided in Table 3.

_{5}→ m

_{7}, m

_{8}, m

_{9}), it implies that this machine type has machine duplication (e.g., there are three machines for the drilling function). At this point, the manufacturer can choose between the functional or cellular layout, which will affect the processing time, transfer time, and part routing. These layouts are further explained in next two sections.

#### 3.3. Functional Layout

_{1}, the notation (m

_{1}, m

_{2}) means that p

_{1}can be processed by either m

_{1}or m

_{2}. When a part is moved from one station to another station (including receiving and shipping), it takes about 1 min.

_{3}as an example. Starting from the receiving station, p

_{3}is first moved to station 1 for cutting (a 3 min process). It is then moved to station 2 for edging using m

_{4}(a 4 min process) and then to station 3 for drilling (a 9 min process). The total transfer time is 4 min as it involves four transitions (e.g., receiving → station 1 → station 2 → station 3 → shipping). Then, the total time required to make p

_{3}without waiting in the machine queues is 3 + 4 + 9 + 4 = 20 min.

#### 3.4. Cellular Layout

_{8}and m

_{9}are duplicated machines in manufacturing cell 2.

_{3}again as an example. Starting from the receiving station, p

_{3}is first moved to the manufacturing cell 1, where it is processed through m

_{1}(a 2 min process), m

_{4}(a 3 min process), and m

_{7}(a 6 min process). After completing machine processing, p

_{3}is moved from the manufacturing cell 1 to the shipping station, resulting in a total transfer time of 2 min. Therefore, the total time required to make p

_{3}without waiting in the machine queues is 2 + 3 + 6 + 2 = 13 min. While it may seem that the cellular layout takes less time to process p

_{3}(compared to the functional layout, which takes 20 min), the cellular layout is less flexible. For example, m

_{7}is the only drilling machine in the manufacturing cell 1. If the parts assigned to this cell also heavily demand this machine, the waiting time in this machine queue will become the bottleneck of the overall manufacturing process.

## 4. Criticality Analysis

#### 4.1. Development of Criticality Scores

_{ik}be the processing time of part p

_{i}using machine type t

_{k}. Recall that pt

_{ik}is a binary matrix element that indicates whether machine type t

_{k}is required to make part p

_{i}. Then, the criticality score (cs) of machine type t

_{k}, denoted as cs(t

_{k}), can be evaluated as follows.

_{i}) be the criticality score of part p

_{i}, and its formulation is given below.

_{ih}is a matrix element that indicates the number of part p

_{i}required to make product variant v

_{h}. Let cs(v

_{h}) be the criticality score of product variant v

_{h}, and its formulation is given below.

#### 4.2. Criticality Analysis with Machine Duplication

_{1}, md

_{2}, …, md

_{k}, …, md

_{q}) be the vector of machine duplicates, where md

_{k}is the number of duplicates of machine type t

_{k}. In our criticality analysis, a machine becomes less critical if it is duplicated. Thus, we suppose that the criticality score of a machine is inversely proportional to the number of its duplicates. To apply this notion, we define a vector of machine fraction, denoted as MF = (mf

_{1}, mf

_{2}, …, mf

_{j}, …, mf

_{m}), where mf

_{j}is the fraction of its duty share (essentially the reciprocal of the number of its duplicates). Then, when machine m

_{j}belongs to machine type t

_{k}, we have $m{f}_{j}=1/m{d}_{k}$.

_{ij}], to indicate pm

_{ij}= 1 if machine m

_{j}is required to make part p

_{i}(otherwise, pm

_{ij}= 0). Also, let proc

_{ij}be the processing time of part p

_{i}using machine m

_{j}. Then, the criticality score of machine m

_{j}, denoted as $cs\text{\_}md\left({m}_{j}\right)$, can be calculated as follows.

#### 4.3. Criticality Ratios for Product Variant and Production

_{h}. Also, as discussed in Section 3.2, machine duplication tends to make the functional layout more beneficial. Therefore, if there is a significant drop from $cs\left({v}_{h}\right)$ to $cs\text{\_}md\left({v}_{h}\right)$, the functional layout would tend to be more beneficial for producing product variant v

_{h}. This idea leads to the formulation of criticality ratios for comparing the functional and cellular layouts.

_{h}, and its formulation is provided in Equation (7). Based on the reasoning discussed earlier, if machine duplication can effectively reduce the criticality of a product variant (i.e., smaller $cs\text{\_}md\left({v}_{h}\right)$ → higher $CR\left({v}_{h}\right)$), it is more beneficial to produce this product variant in the functional layout. In other words, higher values of $CR\left({v}_{h}\right)$ imply that the functional layout tends to be more efficient than the cellular layout for producing product variant v

_{h}.

_{1}, pd

_{2}…, pd

_{h}, …pd

_{r}) be the vector of product demands, where pd

_{h}is the number of product variant v

_{h}that needs to be produced in a production. Given a production that specifies the product demands as PD, let cs(PD) be the score of production criticality, and its formulation is provided below. Using the same rationale, if the manufacturer expects to have more productions with high production criticality (i.e., $cs\left(PD\right)$), they should choose the functional layout in the long run.

#### 4.4. Criticality Analysis of the Study Case

_{4}for demonstration. From Table 4, we know that machine type t

_{4}has two machine duplicates: m

_{5}and m

_{6}. Then, we can check (m

_{5}, m

_{6}) in Table 5, which indicates that this machine type is required to make p

_{4}(6 min), p

_{5}(6 min), p

_{6}(9 min), p

_{7}(9 min), p

_{8}(9 min), p

_{13}(6 min), p

_{14}(6 min), and p

_{15}(6 min). As a result, we can calculate $cs\left({t}_{4}\right)$ = 57 using Equation (1). With two machine duplicates, we have $cs\text{\_}md\left({m}_{5}\right)=cs\text{\_}md\left({m}_{6}\right)=$ 57/2 = 28.5 using Equation (4). As observed from Table 7, while machine type t

_{5}(i.e., drilling machine) is the most critical (i.e., $cs\left({t}_{5}\right)$ = 67), it has three machine duplicates (e.g., m

_{7}, m

_{8}, m

_{9}), leading to a relatively lower criticality score for each machine. In contrast, machine type t

_{7}(or machine m

_{11}) is the least critical as it is only required by part p

_{8}(7 min) (see Table 5).

_{4}, which requires machine types of t

_{1}, t

_{4}, and t

_{5}(see Table 3). Using Equation (2), we can obtain cs(p

_{4}) = cs(t

_{1}) + cs(t

_{4}) + cs(t

_{5}) = 171. As observed from Table 8, part p

_{13}is the most critical as it requires four machine types and one relatively critical machine, m

_{4}(see Table 5).

_{2}has the highest criticality ratio and can sensitively cause the delay of the completion time. It implies that if the demand of product variant v

_{2}tends to be high (relative to other product variants), we should consider the functional layout. In contrast, product variant v

_{3}has the lowest criticality ratio. In this case, we should lean towards the cellular layout if the demand for product variant v

_{3}tends to be high.

## 5. Simulation Setup, Results and Discussion

#### 5.1. Simulation Setup

- Even production: (20, 20, 20, 20, 20), where each product variant is produced with 20 units.
- One-dominating-product production: (60, 10, 10, 10, 10), where one product variant is produced with 60 units and others with 10 units.
- Two-dominating-product production: (38, 38, 8, 8, 8), where two product variants are produced with 38 units and others with 8 units.
- Three-dominating-product production: (30, 30, 30, 5, 5), where three product variants are produced with 30 units and others with 5 units.
- Four-dominating-product production: (24, 24, 24, 24, 4), where four product variants are produced with 24 units and another with 4 units.

_{2}, v

_{4}, and v

_{5}can sensitively reduce the relative performance of the cellular layout. The purpose of this simulation study is to verify how well the criticality analysis can indicate the sensitivity of the layout’s performance concerning the uncertain demands of product variants.

#### 5.2. Simulation Results

_{1}and m

_{2}; m

_{5}and m

_{6}) tend to have even utilization, and they can effectively share the workloads. One exception is machine m

_{9}, which has lower utilization since it is only used when m

_{7}and m

_{8}are busy. In contrast, the duplicated machines in the cellular layout tend to have more uneven utilization. In particular, machine m

_{6}in the cellular layout has the highest utilization (e.g., 0.97). Here, the duplicated machine m

_{5}(utilization = 0.44) cannot effectively share the workload of m

_{6}, as both machines belong to different manufacturing cells. Despite the uneven utilization, since the cellular layout has the advantages of shorter processing and transfer times, it can still yield a shorter completion time overall.

_{2}and v

_{5}, respectively) are dominant in the production. In contrast, when product variant v

_{3}, which is the least critical, has a high demand in the case of I-3, it gives an advantage to the cellular layout, resulting in a shorter completion time by 956 min.

^{2}= 0.8044. The positive correlation suggests that the cellular layout tends to yield a higher completion time when the value of production criticality is high. The value of R

^{2}indicates that the linear regression model can account for 80.44% of the variability in the data. In our interpretation, production criticality can adequately explain the time difference between the functional and cellular layouts. This provides evidence to support that the proposed criticality analysis can discern the relative performance between these two layouts.

^{2}= 0.3740. Compared to the cases of the one-dominating product production (i.e., Figure 5), both the positive correlation and the R

^{2}value decrease. This indicates that the positive trend of production criticality favoring the functional layout is weaker.

#### 5.3. Discussion

## 6. Conclusions

- The criticality analysis relies on the information of machine resources and production requirements, without necessitating extensive operational details (e.g., part demands and routing), which are often unavailable for layout decisions. Despite utilizing relatively limited information, the criticality analysis can reveal the sensitivity of product variant demands to layout performance through the simulation study.
- In practice, manufacturers can use the criticality analysis to inform their layout decisions. For example, if they anticipate a higher production of critical product variants, they should consider more flexible layouts and encourage resource pooling in the layout design.

- More production factors can be incorporated in the manufacturing system model, such as flexible fixtures, setup times, lot sizes, and scheduling decisions.
- More market factors can be incorporated in the criticality analysis. For example, the selling prices of product variants can be associated with their criticality scores in order to influence their market demands.
- The criticality analysis can be extended to develop a decision-making method for the facility layout design in the presence of market uncertainty.
- The study of uncertain demands using simulations calls for more computational techniques since the demand profiles of product variants can be complex. Potential techniques to consider include experimental design and Monte Carlo simulation.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Relational graph of manufacturing system elements (Note: numbers on the links indicate the numbers of parts demanded by the product variants.).

**Figure 6.**Time difference versus production criticality in the two-, three- and four-dominating-product productions.

Set Expression | Subscript Index | Total Number of Elements in the Set | |
---|---|---|---|

Product variant | V = {v_{1}, v_{2}, …, v_{r}} | h | r |

Part | P = {p_{1}, p_{2}, …, p_{n}} | i | n |

Machine | M = {m_{1}, m_{2}, …, m_{m}} | j | m |

Machine types | T = {t_{1}, t_{2}, …, t_{q}} | k | q |

Product Variant v_{1} | Product Variant v_{2} | Product Variant v_{3} | Product Variant v_{4} | Product Variant v_{5} | |
---|---|---|---|---|---|

Part p_{1} | 0 | 0 | 2 | 2 | 0 |

Part p_{2} | 2 | 0 | 3 | 0 | 1 |

Part p_{3} | 0 | 0 | 0 | 2 | 4 |

Part p_{4} | 0 | 3 | 0 | 3 | 3 |

Part p_{5} | 0 | 2 | 0 | 1 | 3 |

Part p_{6} | 0 | 4 | 0 | 0 | 0 |

Part p_{7} | 0 | 0 | 1 | 2 | 0 |

Part p_{8} | 0 | 2 | 0 | 0 | 0 |

Part p_{9} | 0 | 0 | 3 | 0 | 0 |

Part p_{10} | 0 | 2 | 0 | 0 | 0 |

Part p_{11} | 0 | 0 | 0 | 0 | 2 |

Part p_{12} | 0 | 1 | 0 | 1 | 0 |

Part p_{13} | 2 | 0 | 1 | 1 | 2 |

Part p_{14} | 2 | 0 | 0 | 0 | 1 |

Part p_{15} | 0 | 0 | 0 | 2 | 2 |

Part p_{16} | 0 | 0 | 0 | 0 | 4 |

Machine Type t_{1} | Machine Type t_{2} | Machine Type t_{3} | Machine Type t_{4} | Machine Type t_{5} | Machine Type t_{6} | Machine Type t_{7} | |
---|---|---|---|---|---|---|---|

Part p_{1} | 1 | 0 | 0 | 0 | 0 | 0 | 0 |

Part p_{2} | 1 | 0 | 1 | 0 | 0 | 0 | 0 |

Part p_{3} | 1 | 0 | 1 | 0 | 1 | 0 | 0 |

Part p_{4} | 1 | 0 | 0 | 1 | 1 | 0 | 0 |

Part p_{5} | 1 | 0 | 0 | 1 | 1 | 0 | 0 |

Part p_{6} | 1 | 0 | 0 | 1 | 1 | 0 | 0 |

Part p_{7} | 1 | 0 | 0 | 1 | 1 | 0 | 0 |

Part p_{8} | 1 | 0 | 0 | 1 | 0 | 0 | 1 |

Part p_{9} | 1 | 0 | 1 | 0 | 0 | 1 | 0 |

Part p_{10} | 1 | 0 | 1 | 0 | 1 | 0 | 0 |

Part p_{11} | 1 | 0 | 0 | 0 | 1 | 0 | 0 |

Part p_{12} | 1 | 0 | 0 | 0 | 0 | 1 | 0 |

Part p_{13} | 1 | 0 | 1 | 1 | 1 | 0 | 0 |

Part p_{14} | 1 | 1 | 0 | 1 | 1 | 0 | 0 |

Part p_{15} | 1 | 1 | 0 | 1 | 1 | 0 | 0 |

Part p_{16} | 1 | 1 | 0 | 0 | 1 | 0 | 0 |

Machine Type | Label of Machine Type | Label of Machine |
---|---|---|

Cutting machine | t_{1} | m_{1}, m_{2} |

One-side edging machine | t_{2} | m_{3} |

Two-side edging machine with gutter making | t_{3} | m_{4} |

Two-side edging machine | t_{4} | m_{5}, m_{6} |

Drilling machine | t_{5} | m_{7}, m_{8}, m_{9} |

Multi-purpose machining center | t_{6} | m_{10} |

Drilling machining center | t_{7} | m_{11} |

Part Label | Part Routing | Processing Time |
---|---|---|

p_{1} | (m_{1}, m_{2}) | 3 min |

p_{2} | (m_{1}, m_{2}) → m_{4} | 3 min → 4 min |

p_{3} | (m_{1}, m_{2}) → m_{4} → (m_{7}, m_{8}, m_{9}) | 3 min → 4 min → 9 min |

p_{4} | (m_{1}, m_{2}) → (m_{5}, m_{6}) → (m_{7}, m_{8}, m_{9}) | 3 min → 6 min → 6 min |

p_{5} | (m_{1}, m_{2}) → (m_{5}, m_{6}) → (m_{7}, m_{8}, m_{9}) | 3 min → 6 min → 9 min |

p_{6} | (m_{1}, m_{2}) → (m_{5}, m_{6}) → (m_{7}, m_{8}, m_{9}) | 3 min → 9 min → 6 min |

p_{7} | (m_{1}, m_{2}) → (m_{5}, m_{6}) → (m_{7}, m_{8}, m_{9}) | 3 min → 9 min → 6 min |

p_{8} | (m_{1}, m_{2}) → (m_{5}, m_{6}) → m_{11} | 3 min → 9 min → 7 min |

p_{9} | (m_{1}, m_{2}) → m_{4} → m_{10} | 3 min → 9 min → 7 min |

p_{10} | (m_{1}, m_{2}) → m_{4} → (m_{7}, m_{8}, m_{9}) | 3 min → 4 min → 6 min |

p_{11} | (m_{1}, m_{2}) → (m_{7}, m_{8}, m_{9}) | 3 min → 9 min |

p_{12} | (m_{1}, m_{2}) → m_{10} | 2 min → 13 min |

p_{13} | (m_{1}, m_{2}) → m_{4} → (m_{5}, m_{6}) → (m_{7}, m_{8}, m_{9}) | 3 min → 6 min → 6 min → 4 min |

p_{14} | (m_{1}, m_{2}) → m_{3} → (m_{5}, m_{6}) → (m_{7}, m_{8}, m_{9}) | 3 min → 6 min → 6 min → 4 min |

p_{15} | (m_{1}, m_{2}) → m_{3} → (m_{5}, m_{6}) → (m_{7}, m_{8}, m_{9}) | 3 min → 3 min → 6 min → 4 min |

p_{16} | (m_{1}, m_{2}) → m_{3} → (m_{7}, m_{8}, m_{9}) | 3 min → 3 min → 4 min |

Part Label | Part Routing | Manufacturing Cell | Processing Time |
---|---|---|---|

p_{1} | m_{1} | Cell 1 | 2 min |

p_{2} | m_{1} → m_{4} | Cell 1 | 2 min → 3 min |

p_{3} | m_{1} → m_{4} → m_{7} | Cell 1 | 2 min → 3 min → 6 min |

p_{4} | m_{2} → m_{6} → (m_{8}, m_{9}) | Cell 2 | 2 min → 4 min → 4 min |

p_{5} | m_{2} → m_{6} → (m_{8}, m_{9}) | Cell 2 | 2 min → 4 min → 6 min |

p_{6} | m_{2} → m_{6} → (m_{8}, m_{9}) | Cell 2 | 2 min → 6 min → 4 min |

p_{7} | m_{2} → m_{6} → (m_{8}, m_{9}) | Cell 2 | 2 min → 6 min → 4 min |

p_{8} | m_{2} → m_{6} → m_{11} | Cell 2 | 2 min → 6 min → 5 min |

p_{9} | m_{1} → m_{4} → m_{10} | Cell 1 | 2 min → 6 min → 5 min |

p_{10} | m_{1} → m_{4} → m_{7} | Cell 1 | 2 min → 3 min → 4 min |

p_{11} | m_{2} → (m_{8}, m_{9}) | Cell 2 | 2 min → 6 min |

p_{12} | m_{1} → m_{10} | Cell 1 | 1 min → 10 min |

p_{13} | m_{1} → m_{4} → m_{5} → m_{7} | Cell 1 | 2 min → 4 min → 4 min → 3 min |

p_{14} | m_{1} → m_{3} → m_{5} → m_{7} | Cell 1 | 2 min → 4 min → 4 min → 3 min |

p_{15} | m_{1} → m_{3} → m_{5} → m_{7} | Cell 1 | 2 min → 2 min → 4 min → 3 min |

p_{16} | m_{1} → m_{3} → m_{7} | Cell 1 | 2 min → 2 min → 3 min |

Criticality Score of Machine Types | Criticality Score of Machines | ||
---|---|---|---|

Labels of Machine Type | Critical Score, $\mathit{c}\mathit{s}\left({\mathit{t}}_{\mathit{k}}\right)$ | Labels of Machine | Critical Score, $\mathit{c}\mathit{s}\mathbf{\text{\_}}\mathit{m}\mathit{d}\left({\mathit{m}}_{\mathit{j}}\right)$ |

t_{1} | 47 | m_{1}, m_{2} | 23.5 |

t_{2} | 12 | m_{3} | 12 |

t_{3} | 27 | m_{4} | 27 |

t_{4} | 57 | m_{5}, m_{6} | 28.5 |

t_{5} | 67 | m_{7}, m_{8}, m_{9} | 22.3 |

t_{6} | 20 | m_{10} | 20 |

t_{7} | 7 | m_{11} | 7 |

Criticality Score of Parts | ||
---|---|---|

Without Machine Duplication, $\mathit{c}\mathit{s}\left({\mathit{p}}_{\mathit{i}}\right)$ | With Machine Duplication, $\mathit{c}\mathit{s}\mathbf{\text{\_}}\mathit{m}\mathit{d}\left({\mathit{p}}_{\mathit{i}}\right)$ | |

Part p_{1} | 47 | 23.5 |

Part p_{2} | 74 | 50.5 |

Part p_{3} | 141 | 72.8 |

Part p_{4} | 171 | 74.3 |

Part p_{5} | 171 | 74.3 |

Part p_{6} | 171 | 74.3 |

Part p_{7} | 171 | 74.3 |

Part p_{8} | 111 | 59.0 |

Part p_{9} | 94 | 70.5 |

Part p_{10} | 141 | 72.8 |

Part p_{11} | 114 | 45.8 |

Part p_{12} | 67 | 43.5 |

Part p_{13} | 198 | 101.3 |

Part p_{14} | 183 | 86.3 |

Part p_{15} | 183 | 86.3 |

Part p_{16} | 126 | 57.8 |

Criticality Score of Product Variants | Criticality Ratios, $\mathit{C}\mathit{R}\left({\mathit{v}}_{\mathit{h}}\right)$ | ||
---|---|---|---|

Without Machine Duplication, $\mathit{c}\mathit{s}\left({\mathit{v}}_{\mathit{h}}\right)$ | With Machine Duplication, $\mathit{c}\mathit{s}\mathbf{\text{\_}}\mathit{m}\mathit{d}\left({\mathit{v}}_{\mathit{h}}\right)$ | ||

Product variant v_{1} | 910 | 476.3 | 1.91 |

Product variant v_{2} | 2110 | 976.2 | 2.16 |

Product variant v_{3} | 967 | 585.7 | 1.65 |

Product variant v_{4} | 2033 | 956.2 | 2.13 |

Product variant v_{5} | 3341 | 1572.5 | 2.12 |

Machine Type | Machine Labels | Machine Utilization | |
---|---|---|---|

Functional Layout | Cellular Layout | ||

Cutting machine | m_{1} | 0.73 | 0.66 |

m_{2} | 0.73 | 0.44 | |

One-side edging machine | m_{3} | 0.31 | 0.24 |

Two-side edging machine with gutter making | m_{4} | 0.89 | 0.72 |

Two-side edging machine | m_{5} | 0.94 | 0.44 |

m_{6} | 0.92 | 0.97 | |

Drilling machine | m_{7} | 0.89 | 0.81 |

m_{8} | 0.81 | 0.75 | |

m_{9} | 0.55 | 0.20 | |

Multi-purpose machining center | m_{10} | 0.35 | 0.30 |

Drilling machining center | m_{11} | 0.10 | 0.09 |

Case Label | Product Demand | Production Criticality | Completion Time | Time Difference | |
---|---|---|---|---|---|

Functional Layout | Cellular Layout | ||||

I-1 | (60, 10, 10, 10, 10) | 195.26 | 2208 min | 1810 min | −398 min |

I-2 | (10, 60, 10, 10, 10) | 207.81 | 3384 min | 3960 min | 576 min |

I-3 | (10, 10, 60, 10, 10) | 182.29 | 3476 min | 2520 min | −956 min |

I-4 | (10, 10, 10, 60, 10) | 206.05 | 2784 min | 2560 min | −224 min |

I-5 | (10, 10, 10, 10, 60) | 205.97 | 3599 min | 3730 min | 131 min |

**Table 12.**Production criticality and completion time of the demand profiles in the two-, three- and four-dominating-product productions.

Case Label | Product Demand | Production Criticality | Completion Time | Time Difference | |
---|---|---|---|---|---|

Functional Layout | Cellular Layout | ||||

II-1 | (38, 38, 8, 8, 8) | 201.95 | 2707 min | 2640 min | −67 min |

II-2 | (38, 8, 38, 8, 8) | 186.64 | 2920 min | 2128 min | −792 min |

II-3 | (38, 8, 8, 38, 8) | 200.89 | 2346 min | 1972 min | −374 min |

II-4 | (38, 8, 8, 8, 38) | 200.84 | 2806 min | 2854 min | 48 min |

II-5 | (8, 38, 38, 8, 8) | 194.17 | 2950 min | 2790 min | −160 min |

II-6 | (8, 38, 8, 38, 8) | 208.42 | 3192 min | 3450 min | 258 min |

II-7 | (8, 38, 8, 8, 38) | 208.38 | 3364 min | 3330 min | −34 min |

II-8 | (8, 8, 38, 38, 8) | 193.11 | 2755 min | 2350 min | −405 min |

II-9 | (8, 8, 38, 8, 38) | 193.06 | 3295 min | 3118 min | −177 min |

II-10 | (8, 8, 8, 38, 38) | 207.32 | 3153 min | 3106 min | −47 min |

III-1 | (30, 30, 30, 5, 5) | 192.95 | 2486 min | 2160 min | −326 min |

III-2 | (30, 30, 5, 30, 5) | 204.82 | 2799 min | 2710 min | −89 min |

III-3 | (30, 30, 5, 5, 30) | 204.78 | 2873 min | 2610 min | −263 min |

III-4 | (30, 5, 30, 30, 5) | 192.06 | 2588 min | 2096 min | −492 min |

III-5 | (30, 5, 30, 5, 30) | 192.02 | 3038 min | 2722 min | −316 min |

III-6 | (30, 5, 5, 30, 30) | 203.90 | 2805 min | 2727 min | −78 min |

III-7 | (5, 30, 30, 30, 5) | 198.34 | 2641 min | 2835 min | 194 min |

III-8 | (5, 30, 30, 5, 30) | 198.30 | 3061 min | 2735 min | −326 min |

III-9 | (5, 30, 5, 30, 30) | 210.18 | 3277 min | 3285 min | 8 min |

III-10 | (5, 5, 30, 30, 30) | 197.42 | 2969 min | 3043 min | 74 min |

IV-1 | (24, 24, 24, 24, 4) | 196.88 | 2395 min | 2290 min | −105 min |

IV-2 | (24, 24, 24, 4, 24) | 196.85 | 2633 min | 2287 min | −346 min |

IV-3 | (24, 24, 4, 24, 24) | 206.35 | 2904 min | 2650 min | −254 min |

IV-4 | (24, 4, 24, 24, 24) | 196.14 | 2714 min | 2700 min | −14 min |

IV-5 | (4, 24, 24, 24, 24) | 201.16 | 2971 min | 2746 min | −225 min |

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**MDPI and ACS Style**

Li, S.; Eshragh, B.; Ebufegha, A.J.
Simulation-Based Study of the Resilience of Flexible Manufacturing Layouts Subject to Uncertain Demands of Product Variants. *Sustainability* **2023**, *15*, 14946.
https://doi.org/10.3390/su152014946

**AMA Style**

Li S, Eshragh B, Ebufegha AJ.
Simulation-Based Study of the Resilience of Flexible Manufacturing Layouts Subject to Uncertain Demands of Product Variants. *Sustainability*. 2023; 15(20):14946.
https://doi.org/10.3390/su152014946

**Chicago/Turabian Style**

Li, Simon, Bahareh Eshragh, and Akposeiyifa Joseph Ebufegha.
2023. "Simulation-Based Study of the Resilience of Flexible Manufacturing Layouts Subject to Uncertain Demands of Product Variants" *Sustainability* 15, no. 20: 14946.
https://doi.org/10.3390/su152014946