# An ANN-Based Approach for Real-Time Scheduling in Cloud Manufacturing

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## Abstract

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## 1. Introduction

**Demander**- Users who publish manufacturing tasks to the platform, and request to purchase the manufacturing resource services provided by the platform.
**Provider**- Users who register manufacturing resources on the platform, providing virtualized manufacturing resources, such as software, equipment, materials, and labor.
**Operator**- Users who operate and manage the platform; they (1) decompose the demands into manufacturing tasks, (2) encapsulate the registered manufacturing resources through virtualization technology, and (3) match the manufacturing services and provide decision support applications.

- Demanders publish MP (Manufacturing Project) to the platform;
- Platform decomposes MP into MTs (Manufacturing Tasks);
- Platform discovers and matches MR (Manufacturing Resource) in type-matched MS (Manufacturing Service) for these MTs;
- Platform allocates MR for the processing of MT.
- Providers arrange MTs using professional software and deliver the completed MTs to demanders.

## 2. Mathematical Modeling for the CMfg Scheduling Problem

- The set-up time for MT is already included in the processing time;
- No interruption is considered in the processing of MTs;
- The capacity of MR occupied by task processing will be released when the processing is completed;
- Transportation logistics need to be considered before and after the processing of MT.

#### 2.1. Formal Expression of the Main Components

#### 2.2. Optimization Objectives for Real-Time Scheduling

#### 2.3. Constraints for Real-Time Scheduling

## 3. Artificial Neural Network based Resource Allocation Methodology

## 4. Numerical Results

#### 4.1. Experimental Environment Setting

**Exp-30**- Each MP in this group contains 30 MTs;
**Exp-60**- Each MP in this group contains 60 MTs;
**Exp-90**- Each MP in this group contains 90 MTs;
**Exp-120**- Each MP in this group contains 120 MTs;
**Exp-mix**- MT scale of each MP in this group can be any value in $\{30,60,90,120\}$.

#### 4.2. Preparation for Real-Time ANN-Based Scheduling Approach

#### 4.3. Performance with Discussions

## 5. Application Design of ANN-Based Real-Time Scheduling in the Cloud Manufacturing Environment

## 6. Conclusions

- We constructed a mathematical model for real-time scheduling in the CMfg environment with optimization objectives as minimizing the cost, minimizing the make-span, and maximizing the service satisfaction constrained by task precedence, resource occupation, and logistics duration;
- An ANN-based approach for real-time scheduling has been designed, it uses the MT attributes and process pending queue of MR as inputs to predict the completion status of MT if it will be allocated to any of the candidate MRs;
- We conducted the comparison experiments and modified the NSGA-II as the referred scheduling method, the results show that:
- The proposed ANN-based approach performs better than the NSGA-II in terms of objective values;
- The response time of the ANN is only about $4.4\%$ of the NSGA-II on average;
- Using ANN, the average decision time for MR allocation is under 50 ms, which indicates that the proposed ANN-based approach is suitable for the real-time scheduling.

- We designed the application of ANN-based real-time scheduling to show how to implement this method to help coordinate providers of MR in the CMfg environment.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Activity-on-Vertex of Manufacturing Project (MP) ${\mathbb{P}}_{c}$ (n/a means not applicable).

**Figure 5.**Precedence constraint of ${\mathbb{T}}_{6}^{\left(c\right)}$ with logistics duration considered.

**Figure 6.**Allocating ${\mathbb{T}}_{j}^{\left(c\right)}$ to one of the candidate MRs in ${\mathbb{S}}_{k}$, the capability type is matched.

**Figure 7.**Procedure of Manufacturing Task (MT) completion status prediction on candidate Manufacturing Resources (MRs.)

**Figure 11.**Performance comparison on various MT Scales, ($\alpha $) represents NSGA-II($\alpha $) in the x-labels, $\alpha \in \{0.05,0.25,0.50,1.00\}$.

**Figure 15.**Logical flow chart of application design of ANN-based scheduling in the CMfg environment.

Symbol | Description |
---|---|

${b}_{j}^{\left(c\right)}$ | The processing start time of ${\mathbb{T}}_{j}^{\left(c\right)}$. |

c | Label of MP ($c\in \mathcal{C}$). |

${d}_{j}^{\left(c\right)}$ | The ideal due time of ${\mathbb{T}}_{j}^{\left(c\right)}$, its upper and lower bound are ${\overline{d}}_{j}^{\left(c\right)}$ and ${\underline{d}}_{j}^{\left(c\right)}$. |

${e}_{j}^{\left(c\right)}$ | The finish time of ${\mathbb{T}}_{j}^{\left(c\right)}$. |

${g}_{j}^{\left(c\right)}$ | The ready time of ${\mathbb{T}}_{j}^{\left(c\right)}$. |

i | Label of MP ($i\in {\mathcal{I}}_{k}$). |

j | Label of MT ($j\in {\mathcal{J}}_{c}$). |

k | Label of MS ($k\in \mathcal{K}$). |

${l}_{j}^{\left(c\right)}$ | The logistics duration of ${\mathbb{T}}_{j}^{\left(c\right)}$. |

${p}_{j}^{\left(c\right)}$ | The processing duration of ${\mathbb{T}}_{j}^{\left(c\right)}$. |

${v}_{j}^{\left(c\right)}$ | The required resource capacity of ${\mathbb{T}}_{j}^{\left(c\right)}$. |

${x}_{i,j}^{\left(c\right)}$ | 0–1 decision variable to indicate if ${\mathbb{T}}_{j}^{\left(c\right)}$ will be allocated to ${\mathbb{R}}_{i}^{\left(k\right)}$ or not. |

$\mathbf{y}(j,c,i,k)$ | The actual completion status of ${\mathbb{T}}_{j}^{\left(c\right)}$ after processed in ${\mathbb{R}}_{i}^{\left(k\right)}$. |

$\widehat{\mathbf{y}}(j,c,i,k)$ | The predicted completion status of ${\mathbb{T}}_{j}^{\left(c\right)}$ after processed in ${\mathbb{R}}_{i}^{\left(k\right)}$. |

${B}_{c}$ | The publish time of ${\mathbb{P}}_{c}$. |

${C}_{i}^{\left(k\right)}$ | The unit cost of ${\mathbb{R}}_{i}^{\left(k\right)}$. |

${D}_{i}^{\left(k\right)}\left({\mathbb{T}}_{j}^{\left(c\right)}\right)$ | The preference function of ${\mathbb{T}}_{j}^{\left(c\right)}$ allocated on ${\mathbb{R}}_{i}^{\left(k\right)}$. |

${L}_{c,i}^{\left(k\right)}$ | The logistics duration between ${\mathbb{P}}_{c}$ and ${\mathbb{S}}_{i}$. |

${\mathit{L}}_{c}$ | The logistics duration vector of ${\mathbb{P}}_{c}$, each element corresponds to a type-matched MR. |

${\mathcal{M}}_{i}^{\left(k\right)}\left(t\right)$ | The in-processing set of MT in ${\mathbb{R}}_{i}^{\left(k\right)}$ at time t. |

${\mathbb{P}}_{c}$ | MP labeled in c. |

${P}_{i}^{\left(k\right)}$ | The service quality of ${\mathbb{R}}_{i}^{\left(k\right)}$. |

${\mathcal{P}}_{j}^{\left(c\right)}$ | The immediate predecessor set of ${\mathbb{T}}_{j}^{\left(c\right)}$. |

${\mathcal{Q}}_{i}^{\left(k\right)}\left(t\right)$ | The processing pending queue of MTs in ${\mathbb{R}}_{i}^{\left(k\right)}$ at time t. |

${\mathbb{R}}_{i}^{\left(k\right)}$ | MR labeled in $(i,k)$. |

${\mathbb{S}}_{k}$ | MS in type k. |

${\mathcal{S}}_{j}^{\left(c\right)}$ | The immediate successor set of ${\mathbb{T}}_{j}^{\left(c\right)}$. |

${\mathbb{T}}_{j}^{\left(c\right)}$ | MT labeled in $(j,c)$. |

${V}_{i}^{\left(k\right)}\left(t\right)$ | The maximum available capacity of ${\mathbb{R}}_{i}^{\left(k\right)}$ at time t, its upper bound is ${\overline{V}}_{i}^{\left(k\right)}$. |

${Z}_{x}^{\left(c\right)}$ | The object value of ${\mathbb{P}}_{c}$, $x\in \{d,m,u\}$ represents {make-span, cost, quality}. |

${\kappa}_{j}^{\left(c\right)}$ | The required service type of ${\mathbb{T}}_{j}^{\left(c\right)}$. |

${\mu}_{i,x}$ | The mean value of MTs in queue, $x\in \{g,p,l,v,\underline{d},\overline{d}\}$ represents the feature mark. |

${\sigma}_{i,x}$ | The standard deviation value of MTs in queue, $x\in \{g,p,l,v,\underline{d},\overline{d}\}$ represents the feature mark. |

${\phi}_{i,n}^{(c,j)}$ | The probability for due time value located in interval n of ${\mathbb{T}}_{j}^{\left(c\right)}$ if ${\mathbb{R}}_{i}^{\left(k\right)}$ is allocated ($n=0,1,2$). |

${\U0001d7d9}_{\mathrm{predicate}}$ | Indicator function (${\U0001d7d9}_{\mathrm{predicate}}=1$ if the predicate is true, else 0). |

$\left|\mathcal{S}\right|$ | The element count of set $\mathcal{S}$. |

MT Label (j) | Processing Time (${\mathit{p}}_{\mathit{j}}^{\left(\mathit{c}\right)}$) | MS Type (${\mathit{\kappa}}_{\mathit{j}}^{\left(\mathit{c}\right)}$) | MR Capacity (${\mathit{v}}_{\mathit{j}}^{\left(\mathit{c}\right)}$) | Successors (${\mathcal{S}}_{\mathit{j}}^{\left(\mathit{c}\right)}$) |
---|---|---|---|---|

1 | 0 | n/a | 0 | 2, 3, 4 |

2 | 8 | 0 | 4 | 6, 11, 15 |

⋮ | ⋮ | ⋮ | ⋮ | ⋮ |

31 | 2 | 2 | 2 | 32 |

32 | 0 | n/a | 0 | n/a |

Name | Value | Description |
---|---|---|

dist_max | 10 | Maximum distance |

dist_min | 0 | Minimum distance |

num_type | 4 | Number of capability type of MS |

n_max | 5 | Maximum number of MRs in each MS |

n_min | 1 | Minimum number of MRs in each MS |

c_max | 50 | Maximum unit cost of MR |

c_min | 1 | Minimum unit cost of MR |

v_max | 40 | Maximum capacity value of MR |

v_min | 10 | Minimum capacity value of MR |

p_max | 200 | Maximum service quality value of MR |

p_min | 5 | Minimum service quality value of MR |

Name | Value | Description |
---|---|---|

learning_rate | 0.001 | Learning rate of ANN |

batch_size | 64 | Batch size of dataset |

hidden_layer | (300,100,80,40) | Size of hidden layers |

num_exp_iter | 20 | Number of iterations in the training process |

num_epochs | 1000 | Number of epochs for gradient descent for each training iteration |

Label | Precision | Recall | F1-Score |
---|---|---|---|

Completion status 0 | 0.848 | 0.943 | 0.893 |

Completion status 1 | 0.848 | 0.700 | 0.767 |

Completion status 2 | 0.968 | 0.972 | 0.970 |

Macro average | 0.888 | 0.872 | 0.877 |

Weighted average | 0.944 | 0.944 | 0.943 |

Dataset Group | Method | Average Cost ($\overline{{\mathit{Z}}_{\mathit{m}}}$) | Average Satisfaction ($\overline{{\mathit{Z}}_{\mathit{u}}}$) | Average Make-span ($\overline{{\mathit{Z}}_{\mathit{d}}}$) |
---|---|---|---|---|

Exp-30 | NSGA-II(0.05) | 19936.50 | 520.00 | 3067.65 |

NSGA-II(0.25) | 18,899.10 | 520.00 | 2085.15 | |

NSGA-II(0.50) | 18,404.20 | 520.00 | 2467.45 | |

NSGA-II(1.00) | 18,078.50 | 520.00 | 2475.50 | |

ANN | 16,987.00 | 539.00 | 1201.00 | |

(${\rho}_{m}=1.064$) | (${\rho}_{u}=1.037$) | (${\rho}_{d}=2.055$) | ||

Exp-60 | NSGA-II(0.05) | 37,221.25 | 941.00 | 5881.85 |

NSGA-II(0.25) | 35,365.10 | 941.00 | 5057.35 | |

NSGA-II(0.50) | 34,854.95 | 940.00 | 5942.30 | |

NSGA-II(1.00) | 34,372.50 | 940.00 | 8026.00 | |

ANN | 33,231.00 | 940.00 | 4049.00 | |

(${\rho}_{m}=1.034$) | (${\rho}_{u}=0.999$) | (${\rho}_{d}=1.249$) | ||

Exp-90 | NSGA-II(0.05) | 57,029.15 | 521.15 | 6237.05 |

NSGA-II(0.25) | 52,598.70 | 493.00 | 6168.35 | |

NSGA-II(0.50) | 51,594.55 | 491.65 | 7100.70 | |

NSGA-II(1.00) | 50,818.75 | 491.45 | 8702.70 | |

ANN | 50,742.50 | 570.00 | 8563.50 | |

(${\rho}_{m}=1.002$) | (${\rho}_{u}=1.094$) | (${\rho}_{d}=0.984$) | ||

Exp-120 | NSGA-II(0.05) | 70,489.20 | 322.90 | 12,391.10 |

NSGA-II(0.25) | 65,013.05 | 320.00 | 15,160.20 | |

NSGA-II(0.50) | 66,264.75 | 320.00 | 13,435.25 | |

NSGA-II(1.00) | 64,586.50 | 320.00 | 20,547.70 | |

ANN | 63,318.00 | 320.00 | 14,171.00 | |

(${\rho}_{m}=1.020$) | (${\rho}_{u}=0.991$) | (${\rho}_{d}=0.874$) | ||

Exp-mix | NSGA-II(0.05) | 57,822.30 | 422.75 | 8406.95 |

NSGA-II(0.25) | 54,625.10 | 421.00 | 8344.35 | |

NSGA-II(0.50) | 53,559.60 | 420.50 | 9380.85 | |

NSGA-II(1.00) | 53,157.45 | 421.00 | 10,617.90 | |

ANN | 51,743.00 | 420.00 | 8823.00 | |

(${\rho}_{m}=1.027$) | (${\rho}_{u}=0.993$) | (${\rho}_{d}=0.946$) |

Dataset Group | MT Amount | Average Schedule Time (s) | Average Decision Time for MT (ms) |
---|---|---|---|

Exp-30 | 600 | 25.147 | 41.911 |

Exp-60 | 1200 | 32.909 | 27.424 |

Exp-90 | 1800 | 32.113 | 17.840 |

Exp-120 | 2400 | 38.990 | 16.246 |

Exp-mix | 1558 | 23.491 | 15.078 |

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**MDPI and ACS Style**

Chen, S.; Fang, S.; Tang, R.
An ANN-Based Approach for Real-Time Scheduling in Cloud Manufacturing. *Appl. Sci.* **2020**, *10*, 2491.
https://doi.org/10.3390/app10072491

**AMA Style**

Chen S, Fang S, Tang R.
An ANN-Based Approach for Real-Time Scheduling in Cloud Manufacturing. *Applied Sciences*. 2020; 10(7):2491.
https://doi.org/10.3390/app10072491

**Chicago/Turabian Style**

Chen, Shengkai, Shuliang Fang, and Renzhong Tang.
2020. "An ANN-Based Approach for Real-Time Scheduling in Cloud Manufacturing" *Applied Sciences* 10, no. 7: 2491.
https://doi.org/10.3390/app10072491