# Designing Cyclic Job Rotations to Reduce the Exposure to Ergonomics Risk Factors

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data

#### 2.2. The RGA

#### 2.2.1. Solution Encoding and Initial Population

_{w}× 1 + n

_{r}, where n

_{w}is the number of workers involved in the schedule and n

_{r}is the number of rotations during a working day (Figure 2). The number of workers must coincide with the number of workstations to be occupied and must be divisible by n

_{r}.

_{g}) is obtained by dividing the number of workers (n

_{w}) by the number of rotations (n

_{r}). That is, n

_{g}is the number of rotation groups in each schedule, each group consisting of n

_{w}/n

_{g}workers and workstations.

_{g}. Row n

_{g}+ 1 contains a worker of the first rotation group, row n

_{g}+ 2 a worker of the second group, and so on, i.e., row i indicates the jobs belonging to rotation group i − {n

_{g}× Integer_part [(i−1)/n

_{g}]} assigned to a worker in each rotation. For example, in the case of a job schedule with 4 rotations, 16 workers and 16 workstations (Figure 2), rows 1, 5, 9, and 13 contain the workers and workstations of rotation group 1; rows 2, 6, 10, and 14 those of group 2; rows 3, 7, 11, and 15 those of group 3; and rows 4, 8, 12, and 16 those of group 4.

_{g}rows are generated. These rows contain a worker from each rotation group. n

_{g}workers are randomly assigned to the cells in the column Workers. A workstation is also randomly assigned to the remaining cells of the rows. Since the number of cells is n

_{g}× n

_{r}, the workstations will not be repeated within the same row. In the second stage, the rest of the workers are randomly assigned to the first column of rows n

_{g}+ 1 to n

_{w}. The workers in the same rotation group should occupy the same set of workstations in different rotations.

#### 2.2.2. Measuring the Fitness of the Rotation Schedules

_{w}, n

_{r}, and n

_{i}are the number of workers, rotations, and items considered. The coefficient I

_{j}represents the relative importance of the item j with respect to the rest of the items, tj(mi(r)) is the score of the item j of the job allocated to the worker i in the rotation r and d

_{r}is the duration of the rotation r.

^{i}

_{j}(r) is the score of the item j of worker i in rotation r. The capacity of a worker to perform a particular movement must be recalculated after each rotation, considering the effects of the jobs performed in earlier rotations, i.e., cumulative effect of fatigue on the muscle groups involved. To do this, the values of the workers’ movement items w

^{i}

_{j}(r) are recalculated for each rotation using the Equation (2) that considers the movements already performed by the worker in preceding rotations. If a worker had been assigned to a workstation requiring, for example, elbow flexion, in a rotation before the current rotation, the score of the worker’s item for this movement would increase according to the physical effort and duration of the task. This will reduce the probability of assigning this worker to a job that requires elbow flexion in the next rotations:

^{i}

_{j}(r) is the value of the item j of the worker i in the rotation r). This equation considers that the effort required at each workstation is given by the values of the workstation’s movement items. How much the movement items of the workers will change in the rotation r depends on the duration of the tasks developed in previous rotations (l

_{h}is the duration of the rotation h performed previously to rotation r) and on the time elapsed since these tasks were performed (e

_{h}is the time elapsed between the end of the rotation h and the beginning of the rotation r). For example, the longer a task that requires elbow flexion has been performed in previous rotations, the more the elbow flexion item will increase in the current rotation. In the same way, the longer the time elapsed since the end of the tasks requiring elbow flexion, the lower the increment of the elbow flexion item. In this way, the chance of being assigned to a workstation that requires elbow flexion will gradually increase as time passes. To calculate the time elapsed between rotations (Equation (3)), the existence of breaks or pauses is considered. In Equation (3), t

_{h},

_{r}is the break time between the current rotation r and a previous rotation h, and l

_{g}is the duration of the rotation g performed between h and r:

_{d}regulates the size of the effect of tasks performed in preceding rotations on the items of the worker in later rotations. The bigger the value of r

_{d}, the lower the effect.

#### 2.2.3. Penalties

_{max}is defined as the maximum consecutive time that a worker can be assigned to a workstation. The solutions in the population are revised to check if some worker has been assigned to the same workstation for a time longer than t

_{max}. In this case, the solution is penalized by increasing its fitness value, hence reducing its chances to survive or reproduce.

#### 2.2.4. Selection

_{r}is the number of the best solutions retained for the next generation (elitism rate).

_{c}, being n the population size and p

_{c}a parameter named crossover probability. The number of survivors selected by the roulette wheel selection method from the previous generation is n·(1 − p

_{c}) − E

_{r}.

#### 2.2.5. Crossover Operator

_{c}pairs of individuals (parents) are selected from the population. Each pair is crossed over and generates a new individual (offspring). The offspring passes directly to the new generation. The crossover procedure is performed as follows:

- Two ‘parent’ solutions are randomly selected from the population and called Parent A and Parent B.
- One of the first n
_{g}rows of the offspring that have not yet been selected (hereafter named row i) is randomly selected. - Each cell in the row i of the offspring is assigned the same value as the equivalent cell in the row i of parent A. If the value corresponding to a cell has already been assigned to any other cell of the offspring, then the cell will remain empty and will be marked as ‘to be completed later’.
- Parent A will be now Parent B, and Parent B will be now Parent A. Steps 2, 3, and 4 are repeated until all the n
_{g}rows of the offspring have been selected. - The cells of the offspring marked as ‘to be completed later’ are randomly assigned the jobs that have not yet been assigned to any other cell.
- After obtaining the first n
_{g}rows of the offspring, the remaining rows are generated by assignment extension (Section 2.2.1). - One of the parents is randomly selected and the values of the column 1 (workers) are copied in the column 1 of the offspring.

_{g}rows of the ‘parent’ individuals and creates only the first n

_{g}rows of the offspring. Then, the complete offspring is obtained using the assignment extension procedure (Section 2.2.1).

#### 2.2.6. Mutation Operator

_{m}, where n is the population size and p

_{m}is a parameter (mutation probability). The mutation procedure is divided in two phases. The first phase deals with the assignment of workstations to each rotation, and the second deals with the assignment of workers to each group. The procedure is repeated n·p

_{m}times:

- One individual is randomly selected from the population.
- A rotation group j is randomly selected.
- Two rows, between 1 and ng, are randomly selected (i1, i2).
- The jobs assigned to cells (i1, j) and (i2, j) are swapped.
- The assignment is extended (Section 2.2.1).
- Two workers of column 1 are randomly swapped.

## 3. Case Study

#### 3.1. Scores of the Workers and the Workstations

#### 3.2. Parameters Used in the RGA

_{max}(the maximum consecutive time that a worker can be assigned to a workstation) was set to 2 h. In this way, the solutions that assigned a worker to the same workstation in two consecutive rotations were penalized. The coefficients I

_{1}to I

_{18}were set to 1 (see Equation (1)). These coefficients represent the relative importance of each item with respect to the rest of the items. In this case, all of them were considered to have the same level of importance.

_{d}regulates the size of the effect of tasks performed in preceding rotations on the items of the worker in later rotations. Considering the advice of the medical staff, the value of the parameter th was set to 1.5 and r

_{d}was set to 3.

_{c}) was set to 0.6, and the mutation probability (p

_{m}) to 0.3. The elitism rate (E

_{r}) was set to 1.

## 4. Results

## 5. Discussion

## 6. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Example of a job rotation schedule with four rotations. (

**a**) 16 workers rotate in 16 workstations. (

**b**) Four workers rotate in four rotation groups with four workstations each one.

**Figure 4.**Example of generation of offspring through crossover of two parents. The numbers 1 to 4 represent the sequence followed to generate the offspring.

**Table 1.**Criteria employed to characterize workers and workstations. The skills and capacity to perform the movements of the workers are matched with those required by the jobs.

Movements | General Skills | Mental and Communication Skills |
---|---|---|

Arm abduction | Standing | Reasoning |

Arm extension | Sitting | Taking complex decision |

Arm flexion | Walking | Responsibility |

Elbow flexion | Climbing | Cooperation |

Neck extension | Coordinating movements | Attention |

Neck flexion | Applying force standing | Initiative |

Neck turning | Applying force in movement | Autonomy |

Neck lateralization | Driving vehicles | Long distance vision |

Shoulder raising | Working at height | Color vision |

Trunk flexion | Using personal protection equipment | Hearing |

Trunk rotation | Staying in confined/restricted spaces | Locating direction of sound |

Trunk extension | Tactile sensitivity | |

Trunk lateralization | Smelling/tasting | |

Pinching with fingers | Writing | |

Hand flexion | Speaking | |

Hand extension | Using a keyboard | |

Pronation/Supination of hands | Using a mouse | |

Radial/Cubital deviation of hands |

**Table 2.**Score assigned to the workstations depending on the frequency of movements that must be performed.

Frequency (Movements/Minute) | Score |
---|---|

0 | 0 |

1–2 | 1 |

3–7 | 2 |

> 7 | 3 |

**Table 3.**Scores of the items of the “Movements” group for the 16 workstation and workers. The first number in each cell is the workstation score, the second one is the worker score.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Arm-abduction | 1|0 | 2|0 | 2|0 | 2|0 | 1|0 | 0|0 | 1|0 | 1|0 | 1|0 | 1|0 | 1|0 | 2|0 | 1|0 | 1|0 | 2|0 | 1|0 |

Arm-extension | 0|0 | 1|0 | 1|0 | 1|0 | 1|0 | 1|0 | 1|0 | 0|0 | 0|0 | 1|0 | 1|0 | 2|0 | 1|0 | 1|0 | 1|0 | 1|0 |

Arm-flexion | 3|0 | 2|0 | 2|0 | 2|0 | 1|0 | 2|0 | 2|0 | 2|0 | 3|0 | 2|0 | 2|0 | 2|0 | 3|0 | 2|0 | 2|0 | 2|0 |

Elbow-flexion | 3|0 | 1|0 | 1|0 | 1|0 | 1|0 | 2|0 | 2|0 | 2|0 | 3|0 | 2|0 | 2|0 | 1|0 | 2|0 | 2|0 | 2|0 | 2|0 |

Neck-extension | 0|0 | 0|0 | 0|0 | 0|0 | 1|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|2 | 0|0 | 0|0 |

Neck-flexion | 3|0 | 3|0 | 3|0 | 3|0 | 1|0 | 2|0 | 1|0 | 2|0 | 3|0 | 3|0 | 3|0 | 2|0 | 3|0 | 3|1 | 3|0 | 3|0 |

Neck-turning | 2|0 | 1|0 | 1|0 | 1|0 | 1|0 | 1|0 | 1|0 | 2|0 | 3|0 | 3|0 | 2|0 | 2|0 | 2|0 | 3|1 | 2|0 | 2|0 |

Neck-lat. | 0|0 | 0|0 | 0|0 | 0|0 | 1|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|2 | 0|0 | 0|0 |

Shoulder raising | 0|0 | 1|0 | 1|0 | 1|0 | 1|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|2 | 0|0 | 0|1 | 0|0 | 0|0 |

Pinching | 2|0 | 2|0 | 2|0 | 2|0 | 1|0 | 1|0 | 1|0 | 2|0 | 2|0 | 2|0 | 2|0 | 2|0 | 2|0 | 2|0 | 2|0 | 2|0 |

Hand-flexion | 3|0 | 1|0 | 1|0 | 1|0 | 2|0 | 1|0 | 2|0 | 2|0 | 2|0 | 2|0 | 3|0 | 2|0 | 2|0 | 2|0 | 1|0 | 2|0 |

Hand-extension | 1|0 | 0|0 | 0|0 | 0|0 | 1|0 | 0|0 | 1|0 | 1|0 | 1|0 | 0|0 | 1|0 | 0|0 | 1|0 | 1|0 | 1|0 | 1|0 |

Hand-turning | 1|0 | 1|0 | 1|0 | 1|0 | 1|0 | 2|0 | 1|0 | 2|0 | 2|0 | 1|0 | 2|0 | 1|0 | 2|0 | 2|0 | 2|0 | 2|0 |

Hand-lat. | 1|0 | 1|0 | 1|0 | 1|0 | 1|0 | 0|0 | 1|0 | 1|0 | 1|0 | 1|0 | 0|0 | 0|0 | 1|0 | 1|0 | 1|0 | 1|0 |

Trunk-flexion | 2|0 | 1|0 | 1|0 | 1|0 | 2|0 | 1|0 | 1|0 | 1|0 | 2|0 | 2|0 | 1|0 | 1|2 | 2|0 | 2|1 | 1|0 | 1|0 |

Trunk-extension | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 | 0|0 |

Trunk-rotation | 1|0 | 0|0 | 0|0 | 0|0 | 1|0 | 1|0 | 1|0 | 1|0 | 1|0 | 2|0 | 0|0 | 1|3 | 1|0 | 2|2 | 0|0 | 0|0 |

Trunk-lat. | 0|0 | 0|0 | 0|0 | 0|0 | 1|0 | 0|0 | 1|0 | 0|0 | 0|0 | 1|0 | 0|0 | 0|3 | 0|0 | 1|1 | 0|0 | 0|0 |

Legs-flexion | 2|0 | 0|0 | 0|0 | 0|0 | 1|0 | 0|0 | 1|0 | 0|0 | 0|0 | 1|0 | 0|0 | 0|2 | 1|0 | 1|0 | 1|2 | 0|0 |

**Table 4.**Penalized assignments as a result of limitations of the workers’ capacities and job requirements.

Workstation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Worker 12 | ● | ● | ● | ● | ● | ● | ● | ● | ● | ● | ● | |||||

Worker 13 | ● | ● | ● | ● | ● | ● | ||||||||||

Worker 14 | ● | ● | ● | |||||||||||||

Worker 15 | ● | ● |

Run | Iteration | Best Fitness | Workers Mean Value | Standard Deviation of Workers Mean Value |
---|---|---|---|---|

1 | 2969 | 492.83 | 31.62 | 9.61 |

2 | 2857 | 492.83 | 32.05 | 11.14 |

3 | 2353 | 492.80 | 32.30 | 14.26 |

4 | 3071 | 496.40 | 32.17 | 9.87 |

5 | 8276 | 492.83 | 32.09 | 12.32 |

6 | 5363 | 492.83 | 31.30 | 11.19 |

7 | 1397 | 494.37 | 31.40 | 10.41 |

8 | 1888 | 492.83 | 31.69 | 11.86 |

9 | 6777 | 494.37 | 31.43 | 9.97 |

10 | 1479 | 493.65 | 32.35 | 11.82 |

Mean values | 3643 | 493.57 | 31.84 | 11.24 |

Runs | Iteration | Best Fitness | Workers Mean Value | Standard Deviation of Workers Mean Value |
---|---|---|---|---|

1 | 3141 | 477.77 | 29.86 | 8.03 |

2 | 6153 | 479.32 | 29.96 | 7.87 |

3 | 3230 | 480.71 | 30.05 | 7.92 |

4 | 7071 | 479.54 | 29.97 | 7.49 |

5 | 2545 | 479.93 | 30.00 | 7.86 |

6 | 6345 | 477.33 | 29.83 | 7.15 |

7 | 8697 | 478.52 | 29.91 | 6.72 |

8 | 4479 | 479.73 | 29.98 | 7.56 |

9 | 5421 | 480.07 | 30.00 | 6.35 |

10 | 1537 | 480.92 | 30.06 | 6.41 |

Mean values | 4861.90 | 479.38 | 29.96 | 7.33 |

Cycle | Workers | Rotation 1 | Rotation 2 | Rotation 3 | Rotation 4 | Cost |
---|---|---|---|---|---|---|

1 | Worker 6 | Workstation 15 | Workstation 5 | Workstation 13 | Workstation 10 | 24.37 |

2 | Worker 3 | Workstation 3 | Workstation 9 | Workstation 7 | Workstation 16 | 24.70 |

3 | Worker 1 | Workstation 1 | Workstation 8 | Workstation 12 | Workstation 6 | 32.25 |

4 | Worker 2 | Workstation 11 | Workstation 4 | Workstation 14 | Workstation 2 | 30.89 |

1 | Worker 9 | Workstation 5 | Workstation 13 | Workstation 10 | Workstation 15 | 24.23 |

2 | Worker 16 | Workstation 9 | Workstation 7 | Workstation 16 | Workstation 3 | 29.22 |

3 | Worker 10 | Workstation 8 | Workstation 12 | Workstation 6 | Workstation 1 | 26.20 |

4 | Worker 4 | Workstation 4 | Workstation 14 | Workstation 2 | Workstation 11 | 26.72 |

1 | Worker 11 | Workstation 13 | Workstation 10 | Workstation 15 | Workstation 5 | 36.32 |

2 | Worker 14 | Workstation 7 | Workstation 16 | Workstation 3 | Workstation 9 | 47.49 |

3 | Worker 5 | Workstation 12 | Workstation 6 | Workstation 1 | Workstation 8 | 26.12 |

4 | Worker 13 | Workstation 14 | Workstation 2 | Workstation 11 | Workstation 4 | 31.74 |

1 | Worker 8 | Workstation 10 | Workstation 15 | Workstation 5 | Workstation 13 | 27.03 |

2 | Worker 15 | Workstation 16 | Workstation 3 | Workstation 9 | Workstation 7 | 31.37 |

3 | Worker 7 | Workstation 6 | Workstation 1 | Workstation 8 | Workstation 12 | 28.01 |

4 | Worker 12 | Workstation 2 | Workstation 11 | Workstation 4 | Workstation 14 | 46.06 |

Average cost | 30.80 | |||||

Standard deviation | 7.07 | |||||

Total fitness | 492.80 |

Workers | Rotation 1 | Rotation 2 | Rotation 3 | Rotation 4 | Cost |
---|---|---|---|---|---|

Worker 1 | Workstation 6 | Workstation 10 | Workstation 3 | Workstation 11 | 23.48 |

Worker 2 | Workstation 15 | Workstation 5 | Workstation 1 | Workstation 6 | 21.48 |

Worker 3 | Workstation 7 | Workstation 14 | Workstation 2 | Workstation 1 | 22.53 |

Worker 4 | Workstation 4 | Workstation 13 | Workstation 10 | Workstation 16 | 32.98 |

Worker 5 | Workstation 12 | Workstation 8 | Workstation 13 | Workstation 7 | 29.92 |

Worker 6 | Workstation 2 | Workstation 1 | Workstation 6 | Workstation 10 | 25.62 |

Worker 7 | Workstation 5 | Workstation 9 | Workstation 4 | Workstation 14 | 20.04 |

Worker 8 | Workstation 10 | Workstation 16 | Workstation 15 | Workstation 5 | 32.72 |

Worker 9 | Workstation 9 | Workstation 4 | Workstation 8 | Workstation 13 | 34.42 |

Worker 10 | Workstation 13 | Workstation 7 | Workstation 14 | Workstation 3 | 28.46 |

Worker 11 | Workstation 1 | Workstation 6 | Workstation 12 | Workstation 8 | 27.39 |

Worker 12 | Workstation 11 | Workstation 2 | Workstation 11 | Workstation 4 | 42.04 |

Worker 13 | Workstation 14 | Workstation 3 | Workstation 16 | Workstation 12 | 31.43 |

Worker 14 | Workstation 3 | Workstation 11 | Workstation 7 | Workstation 15 | 45.55 |

Worker 15 | Workstation 16 | Workstation 12 | Workstation 9 | Workstation 2 | 34.31 |

Worker 16 | Workstation 8 | Workstation 15 | Workstation 5 | Workstation 9 | 24.96 |

Average cost | 29.83 | ||||

Standard deviation | 7.14 | ||||

Total fitness | 477.33 |

© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Diego-Mas, J.A. Designing Cyclic Job Rotations to Reduce the Exposure to Ergonomics Risk Factors. *Int. J. Environ. Res. Public Health* **2020**, *17*, 1073.
https://doi.org/10.3390/ijerph17031073

**AMA Style**

Diego-Mas JA. Designing Cyclic Job Rotations to Reduce the Exposure to Ergonomics Risk Factors. *International Journal of Environmental Research and Public Health*. 2020; 17(3):1073.
https://doi.org/10.3390/ijerph17031073

**Chicago/Turabian Style**

Diego-Mas, Jose Antonio. 2020. "Designing Cyclic Job Rotations to Reduce the Exposure to Ergonomics Risk Factors" *International Journal of Environmental Research and Public Health* 17, no. 3: 1073.
https://doi.org/10.3390/ijerph17031073