# Realizing Energy Savings in Integrated Process Planning and Scheduling

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Methodological Approach and Advantages

- In this research, frequent machine turning “ons” and “offs” as well as changeable processing times are not allowed to make the resultant scheduling scheme of the energy-efficient IPPS problem more practical. The energy consumption reduction of the IPPS problem is realized by the optimal scheduling scheme.
- Based on the two scenarios, we analyze the impacts of different machine automation levels (different types of machine tools, represented by the $\alpha $ value in Figure 2) and different workloads (represented by the $\beta $ value in Figure 2) on the energy consumptions of IPPS instances. Before this research, the impacts of machine automation levels on the energy consumption reductions have seldom been discussed in energy-efficient production scheduling optimizations.
- There are two types of MILP models for the IPPS problem, and the Type-2 MILP model can realize a true integration of process planning and scheduling [2]. Based on our previous Type-2 MILP model [2], this research reports a novel multi-objective MILP model for the energy-efficient IPPS problem for the first time where the energy consumption criterion together with the makespan criterion is optimized simultaneously.
- Due to the complexity in solving the MILP model, a multi-objective memetic algorithm is developed to accommodate multi-objective optimization of the IPPS problem. In the proposed algorithm, the variable neighborhood search (VNS) is adopted to enhance the search ability of the algorithm. Instead of the abusive weighted sum method, the Pareto-based method [51] is adopted in the proposed memetic algorithm; this multi-objective optimization paradigm allows a set of non-dominated solutions for the decision maker. To determine the most promising scheduling scheme from the Pareto front, the TOPSIS decision method is adopted.

## 4. Mathematical Modelling

#### Subscripts and notations

$i,{i}^{\prime}$ | jobs, 1 $\le i\le \left|n\right|$, |

$j,{j}^{\prime}$ | operations, $1\le i\le |{n}_{i}|$, |

$k,{k}^{\prime}$ | machines, |

h | combinations, |

${O}_{ij}$ | the j-th operation of job i, |

${O}_{ihj}$ | the j-th operation of job i using the h-th combination of that job. |

#### Sets and parameters

A | a very large positive integer, |

${p}_{ijk}$ | the processing time of ${O}_{ij}$ on machine k, |

${R}_{ih}$ | the set that contains the operations belonging to the h-th combination of job i, |

${K}_{i}$ | the set of combinations of job i, |

n | the set of all the jobs, |

${n}_{i}$ | the set of all the operations in the network graph of job i, |

${M}_{ij}$ | the set of available machines for ${O}_{ij}$, |

${V}_{ij{j}^{\prime}}$ | 1, if ${O}_{ij}$ is to be processed before ${O}_{i{j}^{\prime}}$ represented directly by the network graph; 0, otherwise, |

${Q}_{ij{j}^{\prime}}$ | 1, ${O}_{ij}$ should be processed directly or indirectly before ${O}_{ij}$; 0, otherwise, |

${P}_{k}$ | the rated power of machine k, |

$Pcu{t}_{k}$ | the cutting power of machine k, $Pcu{t}_{k}=Pidl{e}_{k}+(1-\alpha )\beta {P}_{k}$, |

$Pidl{e}_{k}$ | the idle power of machine k, $Pidl{e}_{k}=\alpha {P}_{k}$. |

#### Variables

${C}_{max}$ | makespan, |

$EC$ | total energy consumption, |

${Y}_{ih}$ | 1, if the h-th combination of job i is selected; 0, otherwise, |

${X}_{ihjk}$ | 1, if operation ${O}_{ihj}$ is processed on machine k; 0, otherwise, |

${Z}_{ij{j}^{\prime}}$ | 1, if operation ${O}_{ij}$ is processed directly or indirectly before ${O}_{i{j}^{\prime}}$; 0, otherwise, |

${C}_{ihj}$ | the completion time of ${O}_{ihj}$, |

${W}_{ij{i}^{\prime}{j}^{\prime}}$ | 1, if ${O}_{ij}$ is processed before ${O}_{{i}^{\prime}{j}^{\prime}}$ on a machine; 0, otherwise, |

$M{C}_{k}$ | the completion time of the last operation on machine k, |

$MC{T}_{k}$ | the total production time of the operations on machine k (the time in cutting on machine k). |

#### Objectives

#### Constraints

#### Constraints

## 5. Multi-Objective Memetic Algorithm

#### 5.1. Encoding & Decoding

#### 5.2. Crossover & Local Search

#### 5.3. Multi-Objective Optimization

## 6. Experiments with Discussions

#### 6.1. Experiment 1

- Assign operations to the machines with low powers as much as possible. For example, the power values of machines 1, 3, 4, 6, 9, 10, 12, and 15 are larger than 15kw and only few operations are assigned to machines 1, 6, 9, and 10 according to Figure 8. In this way, the machine with low constant energy use will be assigned more operations to save energy; the negative effect is that the makespan criterion will deteriorate because more operations will accumulate and wait to be processed.
- Finish operation processing as early as possible on the machines with large powers. For example, operations processed by machines 1, 9, and 10 are sequenced compactly according to Figure 8 and the machines will be shut down once the machining procedures of the operations are finished; in this way, the idle energy consumptions on these machines can be reduced.
- From Figure 8, energy-efficient scheduling can also be realized by tight arrangements of operations on machines because this can edge out the idle time intervals on machines and therefore the idle energy consumption can be reduced.

#### 6.2. Experiment 2

## 7. Conclusions

- Due to low constant energy use of machines with low automation levels, operations are suggested to be processed by machines with low automation levels. In such a case, the idle energy consumption can be reduced. This strategy can be applied to the cases where only few operations to be processed because there will be many idle time intervals.
- Increasing the number of operations or jobs is another way to improve energy use rate; there will be no idle time intervals between two operations on a machine and therefore, the idle energy consumption can be reduced.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Names | Number of Positions | Purpose |
---|---|---|

Scheduling string | ${\sum}_{i}{\left|{R}_{ih}\right|}_{max}$ at most | Operations belonging to different jobs will be processed sequentially according to the sequence in this string. |

Process plan string | $\left|n\right|$ | Indicate which operation combination will be adopted for each job. |

Operation string | There are $\left|n\right|$ operation strings; each has ${\left|{R}_{ih}\right|}_{max}$ positions at most | The operation IDs and machine IDs of the corresponding operations are specified in each position; each operation string stands for an operation combination. |

Number | Jobs | Job ID | Operations |
---|---|---|---|

1 | 6 | 1, 2, 3, 10, 11, 12 | 79 |

2 | 6 | 4, 5, 6, 13, 14, 15 | 100 |

3 | 6 | 7, 8, 9, 16, 17, 18 | 121 |

4 | 6 | 1, 4, 7, 10, 13, 16 | 95 |

5 | 6 | 2, 5, 8, 11, 14, 17 | 96 |

6 | 6 | 3, 6, 9, 12, 15, 18 | 109 |

7 | 6 | 1, 4, 8, 12, 15, 17 | 99 |

8 | 6 | 2, 6, 7, 10, 14, 18 | 96 |

9 | 6 | 3, 5, 9, 11, 13, 16 | 105 |

10 | 9 | 1, 2, 3, 5, 6, 10, 11, 12, 15 | 132 |

11 | 9 | 4, 7, 8, 9, 13, 14, 16, 17, 18 | 168 |

12 | 9 | 1, 4, 5, 7, 8, 10, 13, 14, 16 | 146 |

13 | 9 | 2, 3, 6, 9, 11, 12, 15, 17, 18 | 154 |

14 | 9 | 1, 2, 4, 7, 8, 12, 15, 17, 18 | 151 |

15 | 9 | 3, 5, 6, 9, 10, 11, 13, 14, 16 | 149 |

16 | 12 | 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15 | 179 |

17 | 12 | 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18 | 221 |

18 | 12 | 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17 | 191 |

19 | 12 | 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18 | 205 |

20 | 12 | 1, 2, 4, 6, 7, 8, 10, 12, 14, 15, 17, 18 | 195 |

21 | 12 | 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 16, 18 | 201 |

22 | 15 | 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18 | 256 |

23 | 15 | 1, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18 | 256 |

24 | 18 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 | 300 |

Machine ID | Power (kW) | Machine ID | Power (kW) | Machine ID | Power (kW) |
---|---|---|---|---|---|

1 | 25 | 6 | 19 | 11 | 7 |

2 | 12 | 7 | 7 | 12 | 21 |

3 | 17 | 8 | 5 | 13 | 9 |

4 | 18 | 9 | 23 | 14 | 13 |

5 | 12 | 10 | 16 | 15 | 28 |

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**MDPI and ACS Style**

Jin, L.; Zhang, C.; Fei, X.
Realizing Energy Savings in Integrated Process Planning and Scheduling. *Processes* **2019**, *7*, 120.
https://doi.org/10.3390/pr7030120

**AMA Style**

Jin L, Zhang C, Fei X.
Realizing Energy Savings in Integrated Process Planning and Scheduling. *Processes*. 2019; 7(3):120.
https://doi.org/10.3390/pr7030120

**Chicago/Turabian Style**

Jin, Liangliang, Chaoyong Zhang, and Xinjiang Fei.
2019. "Realizing Energy Savings in Integrated Process Planning and Scheduling" *Processes* 7, no. 3: 120.
https://doi.org/10.3390/pr7030120