# Ant Colony Optimization Algorithm for Maintenance, Repair and Overhaul Scheduling Optimization in the Context of Industrie 4.0

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## Abstract

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## Featured Application

**Production scheduling for MRO sector.**

## Abstract

## 1. Introduction

## 2. Modelling of the Scheduling Optimization Problem of MRO Processes

- The machine’s set-up time and transportation time required between operations are not considered.
- There is no dependency between machines.
- A machine can only execute other operations if the current operation is completed.
- The precedence constraints which indicate the sequence to execute the operations are only applicable for the operations in the same job.
- Only one operation of the same job can be executed at a time.

## 3. Ant Colony Optimization (ACO) Algorithm

_{0}. Each ant of the colony builds a tour by repetitively using a random greedy rule called the state transition rule as defined in Equation (1). According to this rule, an ant will decide which path to follow based on the pheromone deposited on each feasible path.

## 4. Numerical Results

#### 4.1. Minimizing Make-Span

#### 4.2. Effect of Parameters

#### 4.3. Minimizing Total Weighted Tardiness

#### 4.4. Dynamic scheduling

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Convergence rate of the developed algorithm with different number of operations: (

**a**) 30 operations, (

**b**) 60 operations and (

**c**) 100 operations.

**Figure 6.**Tuning Number of Ants parameter, $A$, for a use-case of 60 operations and fixed value of $Q=9500$: (

**a**) $A=15$, (

**b**) $A=30$ and (

**c**) $A=45$.

**Figure 7.**Tuning parameter Q for a use-case of 60 operations and fixed value of parameter $A=30$: (

**a**) $Q=7000$, (

**b**) $Q=9500$, (

**c**) $Q=\mathrm{11,000}$ and (

**d**) $Q=\mathrm{50,000}$.

**Figure 8.**Tuning parameters for total weighted tardiness performance problem with varied number of operations: (

**a**) 30 operations, (

**b**) 60 operations and (

**c**) 100 operations.

**Table 1.**Required machines and processing times of operations in the use case to execute the ACO algorithm.

Operation | Operation 1 | Operation 2 | Operation 3 | Operation 4 | Operation 5 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Job | Process time | Machine | Process time | Machine | Process time | Machine | Process time | Machine | Process time | Machine | |

Job 1 | 5 (min) | 2 | 2 (min) | 9 | 3 (min) | 10 | - | - | - | - | |

Job 2 | 2 (min) | 1 | 4 (min) | 2 | 1 (min) | 3 | - | - | - | - | |

Job 3 | 1 (min) | 1 | 4 (min) | 3 | 3 (min) | 2 | - | - | - | - | |

Job 4 | 20 (min) | 1 | 5 (min) | 2 | 16 (min) | 3 | 15 (min) | 4 | 25 (min) | 5 | |

Job 5 | 15 (min) | 1 | 25 (min) | 10 | - | - | - | - | - | - | |

Job 6 | 15 (min) | 6 | 7 (min) | 5 | - | - | - | - | - | - | |

Job 7 | 10 (min) | 1 | 7 (min) | 2 | 20 (min) | 3 | - | - | - | - | |

Job 8 | 20 (min) | 4 | 5 (min) | 5 | 16 (min) | 6 | 15 (min) | 7 | 25 (min) | 8 | |

Job 9 | 15 (min) | 10 | 7 (min) | 8 | - | - | - | - | - | - | |

Job 10 | 15 (min) | 3 | 7 (min) | 6 | - | - | - | - | - | - |

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**MDPI and ACS Style**

Tran, L.V.; Huynh, B.H.; Akhtar, H.
Ant Colony Optimization Algorithm for Maintenance, Repair and Overhaul Scheduling Optimization in the Context of Industrie 4.0. *Appl. Sci.* **2019**, *9*, 4815.
https://doi.org/10.3390/app9224815

**AMA Style**

Tran LV, Huynh BH, Akhtar H.
Ant Colony Optimization Algorithm for Maintenance, Repair and Overhaul Scheduling Optimization in the Context of Industrie 4.0. *Applied Sciences*. 2019; 9(22):4815.
https://doi.org/10.3390/app9224815

**Chicago/Turabian Style**

Tran, Le Vu, Bao Huy Huynh, and Humza Akhtar.
2019. "Ant Colony Optimization Algorithm for Maintenance, Repair and Overhaul Scheduling Optimization in the Context of Industrie 4.0" *Applied Sciences* 9, no. 22: 4815.
https://doi.org/10.3390/app9224815