# Joint Optimization of Process Flow and Scheduling in Service-Oriented Manufacturing Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. MRO Production System: Layout and Process Flow

#### 2.2. MRO Model and the Discrete-Event Simulation of the System

#### 2.2.1. Maintenance Sequence

#### 2.2.2. Production Process, Process Time, and Resources

#### 2.2.3. Simulation Runs

_{0}the number of initial replicates (set to 10), h

_{0}the initial half-width reached, h the desired half-width. Next, graphically the point is established where the transient period finishes.

## 3. Results

#### 3.1. Integrated Analysis of Process Flow and Dispatching Rule

#### 3.2. Logistic Operating Curves

## 4. Analysis and Discussion

#### 4.1. Operations Variability and Evaluation through the Taguchi Approach

#### 4.2. Cost Sensitivity Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Command | Function | Sequence | |
---|---|---|---|

Sec Mod TP | Inspection route for module TP | dye penetrant inspect—waiting area ^{(1)}—repair zone | |

Sec Mod SC | Inspection route for module SC | eddy current inspect—waiting area ^{(1)}—repair zone | |

Sec Mod SF | Inspection route for module SF | magnetic particles inspect—waiting area ^{(1)}—repair zone | |

Command | Function | Sequence | Assignation |

MEC1 | Special repair route assignation | machining—welding—machining—heat treatment—bonding—waiting area ^{(1)}—assembly area | Mod. TP: 36% Mod. SC: 15% Mod. SF: 46% |

MEC2 | Special repair route assignation | machining—welding—machining—heat treatment—bonding—waiting area ^{(1)}—assembly area | Mod. TP: 30% Mod. SC: 0% Mod. SF: 15% |

SOL1 | Special repair route assignation | machining—welding—machining—heat treatment—bonding—waiting area ^{(1)}—assembly area | Mod. TP: 14% Mod SC: 25% Mod. SF: 16% |

SOL2 | Special repair route assignation | welding—machining—bonding—waiting area ^{(1)}—assembly area | Mod. TP: 9% Mod. SC: 20% Mod. SF: 12% |

REC1 | Special repair route assignation | bonding—waiting area ^{(1)}—assembly area | Mod. TP: 11% Mod. SC: 40% Mod. SF: 11% |

Engine assy | Assembly engine route assignation | waiting area—assembly area |

^{(1)}Applicable only to simulation in model A.

PROCESS TIME [man hour] | Min | Mean | Max | PROCESS TIME [man hour] | Min | Mean | Max |
---|---|---|---|---|---|---|---|

Initial inspection | 10.6 | 12 | 14.3 | Welding repair (SC) | 6.1 | 7 | 8.3 |

Disassembly/Inspection (TP) module | 22 | 26 | 29.8 | Welding repair (SF) | 19.3 | 23 | 26.1 |

Disassembly/Inspection (SC) module | 20 | 24 | 27 | Heat treatment (TP) | 8.4 | 10 | 11.4 |

Disassembly/Inspection (SF) module | 40.7 | 48 | 55.1 | Heat treatment (SC) | 4.9 | 6 | 6.6 |

Engine disassembly | 14.9 | 18 | 20.1 | Heat treatment (SF) | 13.8 | 16 | 18.6 |

Eddy current inspection (SC) | 3.6 | 4 | 4.8 | Bonding repair (TP) | 10.1 | 12 | 13.7 |

Magnetic particles inspection (SF) | 30.1 | 35 | 40.7 | Bonding repair (SC) | 9.8 | 12 | 13.3 |

Dye penetrant inspection (TP) | 25.6 | 30 | 34.6 | Bonding repair (SF) | 33 | 39 | 44.7 |

Dye penetrant inspection (SC) | 4.2 | 5 | 5.6 | Assembly TP | 51.8 | 61 | 70 |

Dye penetrant inspection (SF) | 35.6 | 42 | 48.1 | Assembly SC | 37.1 | 44 | 50.2 |

General repair (TP) module | 85.6 | 101 | 115.9 | Assembly SF | 136.4 | 160 | 184.5 |

General repair (SC) module | 24.5 | 29 | 33.2 | Balancing (TP) | 13.1 | 15 | 17.7 |

General repair (SF) module | 283.1 | 333 | 383.1 | Balancing (SC) | 9.5 | 11 | 12.9 |

Machining repair (TP) | 13.1 | 15 | 17.8 | Balancing (SF) | 8.9 | 11 | 12.1 |

Machining repair (SC) | 3.7 | 4 | 5 | Engine assembly | 22.3 | 26 | 30.2 |

Machining repair (SF) | 55.3 | 65 | 74.8 | Inspection and final test | 10.7 | 13 | 14.5 |

Welding repair (TP) | 5.1 | 6 | 6.8 | Delivery to customer | 2.6 | 3 | 3.5 |

Engine assembly total [man hour] | 1265.17 | ||||||

TP module total [man hour] | 292.68 | ||||||

SC module total [man hour] | 160.64 | ||||||

SF module total [man hour] | 787.42 |

Rule Name | Formulation |
---|---|

Critical Ratio and Shortest Processing Time (CR+SPT) [27] | $Z=\mathrm{processing}\text{}\mathrm{time}\times \mathrm{max}\left\{\frac{\mathrm{due}\text{}\mathrm{date}-\mathrm{current}\text{}\mathrm{date}}{\mathrm{remaining}\text{}\mathrm{processing}\text{}\mathrm{time}},1\right\}$ |

Critical Ratio (CR) | $Z=\frac{\mathrm{due}\text{}\mathrm{date}-\mathrm{current}\text{}\mathrm{date}}{\mathrm{remaining}\text{}\mathrm{processing}\text{}\mathrm{time}}$ |

Slack Time Remaining (STR) | $Z=\mathrm{due}\text{}\mathrm{date}-\mathrm{current}\text{}\mathrm{date}-\mathrm{remaining}\text{}\mathrm{processing}\text{}\mathrm{time}$ |

Slack Time Remaining/Operation (STR/OP) | $Z=\frac{\mathrm{due}\text{}\mathrm{date}-\mathrm{current}\text{}\mathrm{date}-\mathrm{remaining}\text{}\mathrm{processing}\text{}\mathrm{time}}{\mathrm{remaining}\text{}\mathrm{operations}}$ |

Earliest Due Date (EDD) | $Z=\mathrm{due}\text{}\mathrm{date}-\mathrm{current}\text{}\mathrm{date}$ |

First In, First Out (FIFO) | Ordering according to entrance time to the system |

Largest Processing Time (LPT) | Ordering according to processing time |

Shortest Processing Time (SPT) | Ordering according to processing time |

Priority Rule | # Completed Works | # Due Works | % Late Works | Work in Progress (WIP) (units) | ||||||

S | A | S | A | S | A | S | A | |||

CR | 413 | 425 | 152 | 153 | 36.8 | 36.0 | 10.7 | 10.8 | ||

CR+SPT | 413 | 414 | 152 | 136 | 36.8 | 32.9 | 10.6 | 10.2 | ||

STR/OP | 412 | 410 | 163 | 143 | 39.6 | 34.9 | 11.1 | 10.4 | ||

STR | 421 | 415 | 169 | 150 | 40.1 | 36.1 | 11.2 | 11.0 | ||

EDD | 415 | 417 | 153 | 128 | 36.9 | 30.7 | 10.9 | 10.5 | ||

LPT | 421 | NA | 186 | NA | 36.9 | NA | 12.7 | NA | ||

SPT | 415 | NA | 151 | NA | 36.9 | NA | 10.5 | NA | ||

FIFO | 412 | 414 | 159 | 148 | 36.9 | 35.7 | 10.7 | 10.4 | ||

average | 415.3 | 415.8 | 160.6 | 143.0 | 37.6 | 34.4 | 11.0 | 10.6 | ||

NA: Due to Arena software restrictions, it was not possible to take data | ||||||||||

Priority Rule | Value Added (days) | Wait Time (days) | Lead Time (days) | Value Added Time (%) | Utilization (%) | |||||

S | A | S | A | S | A | [%] | A | S | A | |

CR | 48.3 | 48.3 | 71.5 | 66.0 | 48.2 | 46.5 | 40.3 | 42.2 | 67.4 | 69.1 |

CR+SPT | 48.2 | 48.3 | 67.6 | 62.6 | 46.8 | 44.9 | 41.6 | 43.5 | 67.9 | 68.1 |

STR/OP | 48.2 | 48.2 | 74.1 | 67.2 | 49.3 | 46.6 | 39.4 | 41.8 | 67.8 | 67.4 |

STR | 48.3 | 48.3 | 71.9 | 71.5 | 48.9 | 48.5 | 40.2 | 40.3 | 68.4 | 68.2 |

EDD | 48.2 | 48.2 | 72.8 | 68.6 | 48.1 | 46.5 | 39.8 | 41.3 | 67.5 | 68.1 |

LPT | 48.1 | NA | 87.6 | NA | 54.8 | NA | 35.5 | NA | 68.6 | NA |

SPT | 48.3 | NA | 66.7 | NA | 46.3 | NA | 42.0 | NA | 68.1 | NA |

FIFO | 48.3 | 48.3 | 69.5 | 65.9 | 47.6 | 46.6 | 41.0 | 42.3 | 67.6 | 67.5 |

average | 48.2 | 48.2 | 72.7 | 66.9 | 48.8 | 46.6 | 40.0 | 41.9 | 67.9 | 68.1 |

NA: solution not reached under setup constraints due to inventory overflow | ||||||||||

S = synchronous model; A = asynchronous model |

Factor | Type | Range | Number of Levels (#) |
---|---|---|---|

Dispatching rule (A) | Controllable | CR-EDD-CR+SPT | CR (1)-EDD (2)-CR+SPT (3) |

Type of component (B) | Controllable | Engines: 0–100% | 60 (1)–70 (2)–80 (3) |

Monthly demand (C) | Noise | 6–10 units | 6 (1)–8 (2) |

Learning curve (D) | Noise | 95%–85% | 95 (1)–85 (2) |

Rework (E) | Noise | 5%–15% | 5 (1)–15 (2) |

Response Variable | Magnitude | Objective | Maximizing | |||
---|---|---|---|---|---|---|

Total Time (TT) | days | Smaller-the-better | $S/N\left[db\right]=10\xb7Log\left[\frac{1}{\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}T{T}_{i}^{2}}\right]=10\xb7Log\left[\frac{1}{T{T}^{2}+{\sigma}_{n-1}^{2}}\right]$ | |||

Due Works (DW) | work orders | Smaller-the-better | $S/N\left[db\right]=10\xb7Log\left[\frac{1}{\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}D{W}_{i}^{2}}\right]=10\xb7Log\left[\frac{1}{D{W}^{2}+{\sigma}_{n-1}^{2}}\right]$ | |||

% Busy resource cost (BRC) | $\mathrm{BRC}\%=\frac{\mathrm{Busyresourcecost}}{\mathrm{Total}\text{}\mathrm{resourcecost}}$ | Larger-the-better | $S/N\left[db\right]=10\xb7Log\left[\frac{1}{\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}BR{C}_{i}^{2}}\right]=-10\xb7Log\left[\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}\frac{1}{BR{C}_{i}^{2}}\right]$ | |||

Work-in-process (WIP) | work orders in process | Smaller-the-better | $S/N\left[db\right]=10\xb7Log\left[\frac{1}{\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}WI{P}_{i}^{2}}\right]=10\xb7Log\left[\frac{1}{WI{P}^{2}+{\sigma}_{n-1}^{2}}\right]$ | |||

L_{9} (3^{2}) Inner Array | L_{4} (2^{3}) Outer Array | |||||

Treatments | Controllable factors | Treatments | Noise factors | |||

A | B | C | D | E | ||

1 | 1 | 1 | 1 | 1 | 1 | 1 |

2 | 1 | 2 | 2 | 1 | 2 | 2 |

3 | 1 | 3 | 3 | 2 | 1 | 2 |

4 | 2 | 1 | 4 | 2 | 2 | 1 |

5 | 2 | 2 | DEGREES OF FREEDOM (DOF) | |||

6 | 2 | 3 | ||||

7 | 3 | 1 | factor | Quantity | Level | Number of DOF |

8 | 3 | 2 | Controllable | 2 | 3 | 2 × (3 − 1) = 4 |

9 | 3 | 3 | Noise | 3 | 2 | 2 × (2 − 1) = 2 |

Process Flow Model | Resp. | Signal-to-Noise Ratio | Mean Response | Signal-to-Noise Ratio Nominal the Best | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Mix | Rule | Mix | Rule | Mix | Rule | ||||||||

LEV | VAR | LEV | VAR | LEV | VAR | LEV | VAR | LEV | VAR | LEV | VAR | ||

S | TT | 60 | 90 | 60 | 90 | 60 | 80 | CR+SPT | 10 | ||||

DW | 60 | 60 | EDD | 30 | 60 | 50 | EDD | 40 | 60 | 75 | EDD | 20 | |

BRC | 80 | 99 | 80 | 99 | 60 | 85 | CR+SPT | 10 | |||||

WIP | 60 | 90 | 60 | 90 | 60 | 80 | CR+SPT | 10 | |||||

A | TT | 60 | 90 | 60 | 90 | 60 | 70 | ||||||

DW | 60 | 70 | CR+SPT | 25 | 60 | 65 | EDD | 30 | 60 | 80 | CR+SPT | 15 | |

BRC | 80 | 99 | 80 | 99 | 60 | 75 | |||||||

WIP | 60 | 99 | 60 | 90 | 60 | 70 |

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**MDPI and ACS Style**

Vargas, J.; Calvo, R.
Joint Optimization of Process Flow and Scheduling in Service-Oriented Manufacturing Systems. *Materials* **2018**, *11*, 1559.
https://doi.org/10.3390/ma11091559

**AMA Style**

Vargas J, Calvo R.
Joint Optimization of Process Flow and Scheduling in Service-Oriented Manufacturing Systems. *Materials*. 2018; 11(9):1559.
https://doi.org/10.3390/ma11091559

**Chicago/Turabian Style**

Vargas, Joe, and Roque Calvo.
2018. "Joint Optimization of Process Flow and Scheduling in Service-Oriented Manufacturing Systems" *Materials* 11, no. 9: 1559.
https://doi.org/10.3390/ma11091559