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A Scheduling Solution for Robotic Arm-Based Batching Systems with Multiple Conveyor Belts^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Scheduling Problems for Robotic Arms in Automated Systems

#### 2.2. Scheduling Problems for Robotic Arms with Conveyor Belts

#### 2.3. Solution Algorithms for Scheduling Robotic Arm-Based Batching Systems

## 3. A Robotic Arm-Based Food Processing System

#### 3.1. Problem Descriptions

- Which robotic arm will pick up an item;
- When and where an item on a conveyor belt will be picked up;
- On which tray on which side of the conveyor belt an item will be placed.

#### 3.2. The Complexity of the Target Scheduling Problem

- The initial position and weight of items are unknown until they enter the conveyor belt;
- The position of an item on a conveyor belt is continuously moving;
- Processing time of a robotic arm depends on (1) the position of an item to pick up and (2) the position of the tray where the robotic arm placed the previous item picked up before the current one;
- A tray track is advanced only when the tray at the end of the track exceeds the target weight, affecting the positions of the entire trays in the system;
- Each robotic arm can handle items in a designated operational area.

## 4. The Proposed Solution Approach

#### A Goal Program for a Sub-Problem: Scheduling Robotic Arms Only for a Single Tray

- There is enough time for a robotic arm to move to field f after completing all the tasks scheduled to be done before the time when item i arrives at field f;
- Placing item i on the tray after the nth advancement does not delay any following tasks scheduled by upstream sub-problems.

## 5. Computational Burden of the Proposed Solution Approach

## 6. Discussion

#### 6.1. The Objective Function of the Sub-Problem

#### 6.2. A Robotic Arm-Based Batching System Configuration

## 7. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Simplified flow chart of the robotic batching system. t_plan is the time between planning newly arrived groups of items (deterministic), t_computing is the time to compute the plan (fixed threshold), t_a is the arrival times of items (stochastic), t_timestep is a single time step, conveyor moves all the time (deterministic), t_movements is the time that the robotic arm needs to conduct a task (deterministic), and t_adv is the time for the tray lane to advance (deterministic).

Study | Target System/Problem | Decision | Tray/Bin Lane Number |
---|---|---|---|

[17] | A meat processing system | Batch or trim pieces? (with respect to weights) | 1 |

[18] | A fillet batching operation in a poultry processing plant | Which tray? (with respect to weights) | 1 |

[19] | Batching food items for a specific weight target | Which bin? (with respect to weights) | 2 |

[20] | Poultry processing plants with batchers | Which tray? (with respect to weights) | 1 |

[21] | Bin covering with a target weight for a poultry processing plant | Which tray? (with respect to weights) | 1 |

[22] | Packing in a conveyor-based automatic sorting system | Which action? - Do {stay, put, pick} - For {current box, buffer} | 1 |

[23] | A robotic arm system with multiple conveyor belts | Which tray? (with respect to weights and conveyor belt track) | 2 |

Study | Conveyor Belt Type | Buffer | Machine Type |
---|---|---|---|

[17] | Two conveyor belts | Yes | Grader (diverter) |

[18] | 4 track line conveyor belt | Yes | Grader |

[19] | 1 track line conveyor belt | Yes | Grader |

[20] | 1 track line conveyor belt | Yes | Batcher (drop) |

[21] | 1 track line conveyor belt | Yes | Batcher (drop) |

[22] | Unidirectional 1 track conveyor belt A circular conveyor for boxes | Yes (for unused product) | Robotic arm |

[23] | 2 track line conveyor belt | Yes | Robotic arm |

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**MDPI and ACS Style**

Nielsen, K.G.; Sung, I.; El Yafrani, M.; Kılıç, D.K.; Nielsen, P.
A Scheduling Solution for Robotic Arm-Based Batching Systems with Multiple Conveyor Belts. *Algorithms* **2023**, *16*, 172.
https://doi.org/10.3390/a16030172

**AMA Style**

Nielsen KG, Sung I, El Yafrani M, Kılıç DK, Nielsen P.
A Scheduling Solution for Robotic Arm-Based Batching Systems with Multiple Conveyor Belts. *Algorithms*. 2023; 16(3):172.
https://doi.org/10.3390/a16030172

**Chicago/Turabian Style**

Nielsen, Kasper Gaj, Inkyung Sung, Mohamed El Yafrani, Deniz Kenan Kılıç, and Peter Nielsen.
2023. "A Scheduling Solution for Robotic Arm-Based Batching Systems with Multiple Conveyor Belts" *Algorithms* 16, no. 3: 172.
https://doi.org/10.3390/a16030172