# Staff Task-Based Shift Scheduling Solution with an ANP and Goal Programming Method in a Natural Gas Combined Cycle Power Plant

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Shift Scheduling Problem (SSP)

## 3. Related Works

## 4. Methods

#### 4.1. Goal Programming (GP)

#### 4.2. Analytic Network Process (ANP)

- Unweighted Super Matrix: A square matristor consisting of super matrices, vectors that take into account all interactions between the problem criterion, sub criterion, and alternatives. - Weighted Super Matrix: The unweighted super matrix is equal to 1 column sum.
- Limit Super Matrix: The weighted super matrix is formed by taking the strength of the lines until they are not changed.

## 5. Case Study

#### 5.1. Determining the Workers’ Skill Weights with Analytic Network Process (ANP)

#### 5.2. Proposed Goal Programming Model

#### 5.2.1. Notations

- (1st Seniority-Shift Supervisor, 2nd Seniority-Foreman, 3rd Seniority-Expert, 4th Seniority-Assistant)
- There are 80 People in the department (4 Shift Supervisors, 12 Foremen, 24 Experts, 40 Assistants)
- 3 Shifts (Morning, Evening and Night Shifts)

- At least 1 Shift Supervisor must be present in each shift. (1st Seniority Level)
- There must be at least 3 in each shift from the Foremen. (2nd Seniority Level)
- There must be at least 6 in each shift from the Experts. (3rd Seniority Level)
- There must be at least 10 in each shift from the Assistants. (4th Seniority Level)

_{ijk}and h

_{ij}, here notation of i, j and k are the indices for 80 workers, 30 days and three shifts, respectively. Variable X

_{ijk}indicates worker i is assigned to work on day j for shift k and h

_{ij}, indicate the assignment of worker i to be in day-off, respectively, on day j.

#### 5.2.2. Parameters: All Parameters Are Given in the Model Below

_{i}: Weights of the skills of each personnel, i = 1,2,…,l

_{ij}: Decision variable for day-off of i

^{th}personnel, j

^{th}day i = 1,2,…,l j = 1…m

#### 5.2.3. Decision Variables: There Are Two Decision Variables on the Model. Those Are ${X}_{ijk}$ and ${h}_{ij}$

#### 5.2.4. Constraints

#### 5.2.5. Goal Constraints

#### 5.2.6. Objective Function

#### 5.3. Analysis of The Result

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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C1: Intervention to SCADA system | C5: Intervention to hydraulic lubrication system |

C2: Subcontracting and removal of execution unit | C6: Intervention to central internal demand system |

C3: Intervention to fault SCADA faults | C7: Intervention to water proofing equipment |

C4: Intervention to main power transformer and equipments | C8: Interference to generator defects |

C9: Intervention to switchgear equipment |

P1 to P10 | P11 to P20 | P21 to P30 | P31 to P40 | P41 to P50 | P51 to P60 | P61 to P70 | P71 to P80 |
---|---|---|---|---|---|---|---|

0.040845070 | 0.008450700 | 0.040845070 | 0.000069897 | 0.006960000 | 0.009990010 | 0.000069897 | 0.000069897 |

0.135560010 | 0.005865000 | 0.000868010 | 0.000021550 | 0.000025010 | 0.005665500 | 0.000021550 | 0.000021550 |

0.040840010 | 0.065868010 | 0.002567600 | 0.000021554 | 0.040845070 | 0.000860010 | 0.000021554 | 0.000021554 |

0.040045070 | 0.040111070 | 0.002240010 | 0.000002150 | 0.040845070 | 0.040775070 | 0.000002150 | 0.000002150 |

0.030845070 | 0.039845060 | 0.040845070 | 0.000000454 | 0.040845070 | 0.040845070 | 0.000000454 | 0.000000454 |

0.006960000 | 0.009990010 | 0.040845070 | 0.040845070 | 0.008450700 | 0.040663070 | 0.040845007 | 0.040845070 |

0.000025010 | 0.005665500 | 0.005686800 | 0.135560010 | 0.005865001 | 0.000868010 | 0.005686800 | 0.005686800 |

0.040845070 | 0.000860010 | 0.001235600 | 0.040840010 | 0.065868010 | 0.002567600 | 0.001235600 | 0.001235600 |

0.033945070 | 0.040845070 | 0.035655000 | 0.040045070 | 0.040845070 | 0.002240010 | 0.035655000 | 0.035655000 |

0.040740070 | 0.040845070 | 0.000000450 | 0.030845070 | 0.040845070 | 0.040845070 | 0.000000450 | 0.000000450 |

Shift Supervisor’s Weight | Foremen’s Weight | Expert’s Weight | Assistant’s Weight |
---|---|---|---|

0.06432254 | 0.026957512 | 0.022802299 | 0.016094762 |

P1 | 27 | P9 | 19 | P17 | 26 | P25 | 25 | P33 | 20 | P41 | 22 | P49 | 20 | P57 | 19 | P65 | 20 | P73 | 22 |

P2 | 11 | P10 | 23 | P18 | 19 | P26 | 20 | P34 | 14 | P42 | 22 | P50 | 26 | P58 | 27 | P66 | 20 | P74 | 30 |

P3 | 17 | P11 | 26 | P19 | 24 | P27 | 27 | P35 | 16 | P43 | 21 | P51 | 24 | P59 | 27 | P67 | 17 | P75 | 30 |

P4 | 20 | P12 | 25 | P20 | 25 | P28 | 26 | P36 | 21 | P44 | 27 | P52 | 17 | P60 | 21 | P68 | 15 | P76 | 19 |

P5 | 25 | P13 | 26 | P21 | 27 | P29 | 28 | P37 | 23 | P45 | 11 | P53 | 30 | P61 | 16 | P69 | 19 | P77 | 22 |

P6 | 21 | P14 | 20 | P22 | 20 | P30 | 17 | P38 | 22 | P46 | 25 | P54 | 12 | P62 | 22 | P70 | 21 | P78 | 16 |

P7 | 26 | P15 | 19 | P23 | 26 | P31 | 25 | P39 | 26 | P47 | 21 | P55 | 30 | P63 | 23 | P71 | 27 | P79 | 23 |

P8 | 22 | P16 | 24 | P24 | 23 | P32 | 10 | P40 | 24 | P48 | 22 | P56 | 24 | P64 | 26 | P72 | 22 | P80 | 22 |

P1 | 23 | P9 | 23 | P17 | 23 | P25 | 23 | P33 | 23 | P41 | 23 | P49 | 23 | P57 | 20 | P65 | 23 | P73 | 23 |

P2 | 23 | P10 | 22 | P18 | 23 | P26 | 23 | P34 | 23 | P42 | 22 | P50 | 23 | P58 | 23 | P66 | 22 | P74 | 23 |

P3 | 23 | P11 | 23 | P19 | 23 | P27 | 23 | P35 | 22 | P43 | 22 | P51 | 23 | P59 | 23 | P67 | 23 | P75 | 23 |

P4 | 23 | P12 | 23 | P20 | 22 | P28 | 22 | P36 | 22 | P44 | 23 | P52 | 22 | P60 | 22 | P68 | 23 | P76 | 23 |

P5 | 22 | P13 | 23 | P21 | 23 | P29 | 23 | P37 | 22 | P45 | 22 | P53 | 22 | P61 | 22 | P69 | 23 | P77 | 23 |

P6 | 23 | P14 | 23 | P22 | 23 | P30 | 23 | P38 | 23 | P46 | 22 | P54 | 22 | P62 | 23 | P70 | 23 | P78 | 23 |

P7 | 22 | P15 | 22 | P23 | 22 | P31 | 23 | P39 | 22 | P47 | 23 | P55 | 23 | P63 | 23 | P71 | 23 | P79 | 23 |

P8 | 23 | P16 | 23 | P24 | 22 | P32 | 22 | P40 | 23 | P48 | 23 | P56 | 22 | P64 | 23 | P72 | 23 | P80 | 23 |

Criteria | Existing Schedule | Proposed Schedule |
---|---|---|

Unsatisfied preference | 4 | 0 |

Satisfied preference | 6 | 10 |

Total preference | 10 | 10 |

Percentage of satisfaction | %60.00 | %100.00 |

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## Share and Cite

**MDPI and ACS Style**

Özder, E.H.; Özcan, E.; Eren, T.
Staff Task-Based Shift Scheduling Solution with an ANP and Goal Programming Method in a Natural Gas Combined Cycle Power Plant. *Mathematics* **2019**, *7*, 192.
https://doi.org/10.3390/math7020192

**AMA Style**

Özder EH, Özcan E, Eren T.
Staff Task-Based Shift Scheduling Solution with an ANP and Goal Programming Method in a Natural Gas Combined Cycle Power Plant. *Mathematics*. 2019; 7(2):192.
https://doi.org/10.3390/math7020192

**Chicago/Turabian Style**

Özder, Emir Hüseyin, Evrencan Özcan, and Tamer Eren.
2019. "Staff Task-Based Shift Scheduling Solution with an ANP and Goal Programming Method in a Natural Gas Combined Cycle Power Plant" *Mathematics* 7, no. 2: 192.
https://doi.org/10.3390/math7020192