# Process Planning, Scheduling, and Layout Optimization for Multi-Unit Mass-Customized Products in Sustainable Reconfigurable Manufacturing System

^{*}

## Abstract

**:**

## 1. Introduction

- including the environmental sustainability for this integrated production management problem in RMS, which is limited in previous research;
- modifying the Pareto efficiency by combining the characteristics of this problem to get a reasonable number of Pareto-optimal solutions for decision makers; and
- surveying the appropriate parameters to design a decent heuristic approach in order to solve this problem effectively and efficiently.

## 2. Literature Review

## 3. Problem Formulation

#### 3.1. Assumptions

- Parameters about a WIP’s transportation time, cost, energy consumption, and holding cost are only dependent on the type of part variant this WIP belongs to;
- Parameters about an operation’s processing time, processing cost, processing energy consumption, hazardous waste, setup time, setup cost, and setup energy consumption are dependent on the type of part variant the corresponding WIP belongs to, the kind of this operation, the executing machine, and the configuration;
- Parameters about reconfiguration time, cost, and energy consumption on a machine depend on the former configuration and the latter configuration;
- Energy consumed from different activities is quantified with the same unit, which can be added directly to estimate the amount of GHG emissions;
- Parts and the final mass-customized products are qualified without any defect during production in RMS;
- All machines are idle without configurations and setups at the beginning of the task to produce a given number of mass-customized products; and
- All the raw materials and handling devices are available.

#### 3.2. Notations

#### 3.2.1. Sets and Indices

#### 3.2.2. Parameters

#### 3.2.3. Independent Decision Variables

#### 3.2.4. Auxiliary Decision Variables

#### 3.3. Mathematical Model

#### 3.3.1. Objective Functions

- The total penalty of tardiness for all the delayed products accomplished after the due date;
- The total cost including the total setup cost, the total processing cost, the total WIP transport cost, the total WIP holding cost, the total machine reconfiguration cost, and the total layout reconfiguration cost; and
- The value of the environment indicator defined as the aggregate of the normalized hazardous waste item (the ratio of the total amount of hazardous waste and the allowed amount of hazardous waste) and the normalized GHG emissions item (the ratio of the total amount of GHG emissions and the allowed amount of GHG emissions).

#### 3.3.2. Constraints

## 4. Numerical Experiment

#### 4.1. Modified Pareto Efficiency

#### 4.2. Exact Pareto-Optimal Solutions Obtained from Brute-Force Search

#### 4.3. Comparison with Exact Pareto-Optimal Solutions for No Environmental Indicator Model

## 5. Approximate Optimization

#### 5.1. Approximate Pareto-Optimal Solutions Obtained from NSGA-III

#### 5.2. Parameter Tunning

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Parameters about products and part variants in the numerical example (authors’ own study).

**Figure 3.**Reconfiguration time, cost, and energy consumption: (

**a**) on machine 1; (

**b**) on machine 2 (author’s own study).

**Figure 4.**Processing and setup parameters to produce a part belong to: (

**a**) part variant 1; (

**b**) part variant 2 (authors’ own study).

**Figure 8.**Pareto charts of standardized effects about: (

**a**) effectivity; (

**b**) efficiency (authors’ own study).

Abbreviations | Implication |
---|---|

RMS | reconfigurable manufacturing system |

MC | mass customization |

NSGA-II | non-dominated sorting genetic algorithm II |

NSGA-III | non-dominated sorting genetic algorithm III |

AMOSA | archived multi-objective simulated annealing |

GHG | greenhouse gases |

WIP | work in progress |

FJSP | flexible job-shop scheduling |

NP-hard | non-deterministic polynomial-time hardness |

$TSC$ | the total setup cost |

$TPC$ | the total processing cost |

$TFC$ | the total WIP transport cost |

$THC$ | the total WIP holding cost |

$TRC$ | the total machine reconfiguration cost |

$TLC$ | the total layout reconfiguration cost |

$THW$ | the total amount of hazardous waste |

$LHW$ | the allowed amount of hazardous waste |

${E}_{GHG}$ | the total amount of GHG emissions |

$LGE$ | the allowed amount of GHG emissions |

**Table 2.**The values of the multi-objective functions in the exact Pareto-optimal solutions for the small numerical example (authors’ own study).

Solutions | First Objective Function | Second Objective Function | Third Objective Function |
---|---|---|---|

Solution 1 | 3 | 70 | 0.9811320754716981 |

Solution 2 | 10 | 69 | 0.8662131519274376 |

Solution 3 | 10 | 69 | 0.8662131519274376 |

**Table 3.**The optimal layout in the exact Pareto-optimal solutions for the small numerical example (authors’ own study).

Solutions | Machines | Position on the X-Coordinate | Position on the Y-Coordinate |
---|---|---|---|

Solution 1 | Machine 1 | 3 | 3 |

Machine 2 | 9 | 7 | |

Solution 2 | Machine 1 | 3 | 3 |

Machine 2 | 9 | 7 | |

Solution 3 | Machine 1 | 3 | 3 |

Machine 2 | 9 | 7 |

**Table 4.**The optimal production scheme in the exact Pareto-optimal solutions for the small numerical example (authors’ own study).

Solutions | Independent Decision Variables | $\mathbf{Processes}(\mathit{i},\mathit{v},\mathit{j},\mathit{q})$ | |||||
---|---|---|---|---|---|---|---|

$\left(1,1,1,1\right)$ | $\left(1,1,1,2\right)$ | $\left(1,1,1,3\right)$ | $\left(2,2,1,1\right)$ | $\left(2,2,1,2\right)$ | $\left(2,2,1,3\right)$ | ||

Solution 1 | ${\rho}_{i,v,j,q}$ | 0 | 1 | 2 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 1 | 1 | 1 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 2 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 3 | 27 | 45 | 3 | 12 | 23 | |

Solution 2 | ${\rho}_{i,v,j,q}$ | 0 | 1 | 2 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 0 | 0 | 0 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 0 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 31 | 48 | 56 | 3 | 12 | 23 | |

Solution 3 | ${\rho}_{i,v,j,q}$ | 0 | 2 | 1 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 0 | 0 | 0 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 0 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 31 | 43 | 59 | 3 | 12 | 23 |

**Table 5.**The values of the multi-objective functions in the exact Pareto-optimal solutions for no environmental indicator model (authors’ own study).

Solutions | First Objective Function | Second Objective Function |
---|---|---|

Solution 1 | 3 | 70 |

Solution 2 | 10 | 69 |

Solution 3 | 10 | 69 |

Solution 4 | 36 | 63 |

Solution 5 | 36 | 63 |

Solution 6 | 36 | 63 |

Solution 7 | 36 | 63 |

**Table 6.**The optimal layout in the exact Pareto-optimal solutions for no environmental indicator model (authors’ own study).

Solutions | Machines | Position on the X-Coordinate | Position on the Y-Coordinate |
---|---|---|---|

Solution 1 | Machine 1 | 3 | 3 |

Machine 2 | 9 | 7 | |

Solution 2 | Machine 1 | 3 | 3 |

Machine 2 | 9 | 7 | |

Solution 3 | Machine 1 | 3 | 3 |

Machine 2 | 9 | 7 | |

Solution 4 | Machine 1 | 3 | 3 |

Machine 2 | 9 | 7 | |

Solution 5 | Machine 1 | 3 | 3 |

Machine 2 | 9 | 7 | |

Solution 6 | Machine 1 | 3 | 3 |

Machine 2 | 9 | 7 | |

Solution 7 | Machine 1 | 3 | 3 |

Machine 2 | 9 | 7 |

**Table 7.**The optimal production scheme in the exact Pareto-optimal solutions for no environmental indicator model (authors’ own study).

Solutions | Independent Decision Variables | $\mathbf{Processes}(\mathit{i},\mathit{v},\mathit{j},\mathit{q})$ | |||||
---|---|---|---|---|---|---|---|

$\left(1,1,1,1\right)$ | $\left(1,1,1,2\right)$ | $\left(1,1,1,3\right)$ | $\left(2,2,1,1\right)$ | $\left(2,2,1,2\right)$ | $\left(2,2,1,3\right)$ | ||

Solution 1 | ${\rho}_{i,v,j,q}$ | 0 | 1 | 2 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 1 | 1 | 1 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 2 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 3 | 27 | 45 | 3 | 12 | 23 | |

Solution 2 | ${\rho}_{i,v,j,q}$ | 0 | 1 | 2 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 0 | 0 | 0 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 0 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 31 | 48 | 56 | 3 | 12 | 23 | |

Solution 3 | ${\rho}_{i,v,j,q}$ | 0 | 2 | 1 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 0 | 0 | 0 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 0 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 31 | 43 | 59 | 3 | 12 | 23 | |

Solution 4 | ${\rho}_{i,v,j,q}$ | 0 | 1 | 2 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 0 | 0 | 0 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 0 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 5 | 44 | 52 | 13 | 22 | 33 | |

Solution 5 | ${\rho}_{i,v,j,q}$ | 0 | 1 | 2 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 0 | 0 | 0 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 0 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 11 | 44 | 52 | 3 | 22 | 33 | |

Solution 6 | ${\rho}_{i,v,j,q}$ | 0 | 2 | 1 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 0 | 0 | 0 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 0 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 5 | 39 | 55 | 13 | 22 | 33 | |

Solution 7 | ${\rho}_{i,v,j,q}$ | 0 | 2 | 1 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 0 | 0 | 0 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 0 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 11 | 39 | 55 | 3 | 22 | 33 |

**Table 8.**The values of the multi-objective functions in the approximate Pareto-optimal solutions for the small numerical example (authors’ own study).

Solutions | First Objective Function | Second Objective Function | Third Objective Function |
---|---|---|---|

Solution 1 | 6 | 74 | 1.0242587601078168 |

Solution 2 | 36 | 65 | 0.910411622276029 |

Solution 3 | 36 | 65 | 0.910411622276029 |

**Table 9.**The optimal layout in the approximate Pareto-optimal solutions for the small numerical example (authors’ own study).

Solutions | Machines | Position on the X-Coordinate | Position on the Y-Coordinate |
---|---|---|---|

Solution 1 | Machine 1 | 3 | 3 |

Machine 2 | 8 | 7 | |

Solution 2 | Machine 1 | 3 | 3 |

Machine 2 | 8 | 7 | |

Solution 3 | Machine 1 | 3 | 3 |

Machine 2 | 8 | 7 |

**Table 10.**The optimal production scheme in the Exact Pareto-optimal solutions for the small numerical example (authors’ own study).

Solutions | Independent Decision Variables | $\mathbf{Processes}(\mathit{i},\mathit{v},\mathit{j},\mathit{q})$ | |||||
---|---|---|---|---|---|---|---|

$\left(1,1,1,1\right)$ | $\left(1,1,1,2\right)$ | $\left(1,1,1,3\right)$ | $\left(2,2,1,1\right)$ | $\left(2,2,1,2\right)$ | $\left(2,2,1,3\right)$ | ||

Solution 1 | ${\rho}_{i,v,j,q}$ | 0 | 1 | 2 | 1 | 0 | 2 |

${\alpha}_{i,v,j,q}$ | 1 | 1 | 1 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 2 | 0 | 0 | 1 | 0 | |

${\beta}_{i,v,j,q}$ | 3 | 27 | 45 | 3 | 13 | 24 | |

Solution 2 | ${\rho}_{i,v,j,q}$ | 0 | 1 | 2 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 0 | 0 | 0 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 0 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 5 | 44 | 52 | 13 | 22 | 33 | |

Solution 3 | ${\rho}_{i,v,j,q}$ | 0 | 2 | 1 | 0 | 1 | 2 |

${\alpha}_{i,v,j,q}$ | 0 | 0 | 0 | 0 | 0 | 0 | |

${\phi}_{i,v,j,q}$ | 1 | 0 | 0 | 1 | 0 | 0 | |

${\beta}_{i,v,j,q}$ | 5 | 39 | 55 | 13 | 22 | 33 |

Solutions | Low Level | High Level |
---|---|---|

Number of reference point | 6 | 15 |

Mutation probability | 0.05 | 0.1 |

Generation limit | 1000 | 2000 |

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**MDPI and ACS Style**

Gao, S.; Daaboul, J.; Le Duigou, J.
Process Planning, Scheduling, and Layout Optimization for Multi-Unit Mass-Customized Products in Sustainable Reconfigurable Manufacturing System. *Sustainability* **2021**, *13*, 13323.
https://doi.org/10.3390/su132313323

**AMA Style**

Gao S, Daaboul J, Le Duigou J.
Process Planning, Scheduling, and Layout Optimization for Multi-Unit Mass-Customized Products in Sustainable Reconfigurable Manufacturing System. *Sustainability*. 2021; 13(23):13323.
https://doi.org/10.3390/su132313323

**Chicago/Turabian Style**

Gao, Sini, Joanna Daaboul, and Julien Le Duigou.
2021. "Process Planning, Scheduling, and Layout Optimization for Multi-Unit Mass-Customized Products in Sustainable Reconfigurable Manufacturing System" *Sustainability* 13, no. 23: 13323.
https://doi.org/10.3390/su132313323