# Coupling Layout Optimization of Key Plant and Industrial Area

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Statement and Mathematical Model

- ➢
- Both plants and facilities are simplified as rectangles and placed orthogonally;
- ➢
- Plants cannot overlap each other, as with facilities;
- ➢
- Safety distance between facilities should meet the requirements in the regulations;
- ➢
- Multi-floor structure is applied. Facilities can be placed on the first floor or higher.

#### 2.1. Constraints

_{i}is set and specify that if r

_{i}= 0, the facility is placed horizontally, otherwise, if r

_{i}= 1, the facility is placed vertically. The relationship between the visual length and width of a facility in the region and its actual size can be described as follows:

_{i}and w

_{i}are the visual length and width after facility placement and l

_{ai}and w

_{ai}are the actual size of the facility. These constraints are also applicative for plant placement. They are also set as linking constraints between plant layout and area-wide layout. The length, width and aspect ratio of the key plant (explained in the next section) are determined through the results of the plant optimization and are regarded as known conditions in subsequent optimization. The sizes of other plants remain as original ones according to the case.

_{1i}and y

_{1i}are the coordinates of the lower left corner, and x

_{2i}and y

_{2i}are the coordinates of the upper right corner. Formulas (3)–(6) respectively represent that facility i is on the left, right, upper and lower side of facility j.

_{i}= 1 means facility i is placed at position K. Take a two-floor plant as an example, the constraint can be explained as follows:

_{1i}is the position of facility i on the first floor, and K

_{2i}is same position on the second floor; i is a high facility that needs to be placed across floors; and K

_{2j}is the position of facility j on the second floor. Equation (11) indicates that if the cross-floor facility is placed at position K, the other facilities cannot be arranged at position K on any floor.

_{pi}and y

_{pi}are the actual coordinates of pump i. x

_{p}and y

_{p}are the coordinates of the pump area. x

_{pri}and y

_{pri}are the coordinates of relative position of pump i inside the pump area.

_{Hi}and y

_{Hi}are the actual coordinates of heat exchanger i in the overall plant. x

_{H}and y

_{H}are the coordinates of the group, and w

_{Hi}is the width of heat exchanger i.

#### 2.2. Objective Function

_{m}is the Manhattan distance between the center coordinates of the two rectangular facilities, in the unit of m; and UIC

_{m}is the unit price of pipeline (USD/m), which is calculated by the method proposed by Stijepovic and Linke [38]:

_{i}and y

_{i}are the coordinates of the center point of facility i, and x

_{j}and y

_{j}belong to facility j; A

_{1}is the pipe cost per unit of quality, which is 0.82 USD/kg; wt

_{pip}

_{e}is the quality per meter of pipe, in the unit of kg/m; A

_{2}is the installation cost parameter, which is 185 USD/m

^{0.48}; D

_{out}is the outer pipe diameter in the unit of m; A

_{3}is the floor space cost of pipe, which is 6.8 USD/m; and A

_{4}is the insulation layer cost of pipe, which is 295 USD/m. The values of wt

_{pipe}, D

_{out}and related parameters are determined by Equations (20)–(22) [38]:

_{inner}is the inner diameter of pipe in the unit of m; Q is the material mass flow rate in the unit of kg/s; ρ is the material density in the unit of kg/m

^{3}; and u is the flow rate in the unit of m/s.

_{E}is the unit energy cost (USD/kW·h), H is the annual operating time (h/a), and P

_{m}is the pump work of transporting different materials (W), which is calculated by Equation (24):

_{f,m}is the energy consumed by overcoming the resistance along the way and gravity in the process of unit material transmission in the unit of J/kg, which is determined as:

_{m}is a binary variable which represents the material transportation in the vertical direction. If a material flow is transferred from a lower floor to a higher floor, the material handling cost includes the upward transfer cost, then α

_{m}= 1. Otherwise, α

_{m}= 0.

^{2}). x

_{1i}and y

_{1i}are the lower-left coordinates of facility i. l

_{i}and w

_{i}are the length and width.

_{1i}, y

_{1i}, l

_{i}, w

_{i}are parameters of the related plants.

## 3. Optimization Algorithm

- ➢
- A series of random variables are generated in GA as the initial population, which determine the facility placement order and direction, the facility number in each floor and the length of the bottom edge of the plant area.
- ➢
- Since pumps, towers and reactors must be placed on the first floor and air coolers must be placed on the top floor, these special facilities are put aside. Other facilities are randomly sorted according to the variable values generated by GA, and the order is recorded in an array called P.
- ➢
- The value of the variable a determines the number of facilities placed on the first floor. In order P, the first a facilities are placed on the first floor, and the other facilities are placed on the second floor.
- ➢
- Add pump area, towers and reactors to the facilities of the first floor, and a new sort P1 of the facilities on the first floor is randomly generated. The layout of the first floor is optimized by SRFA, and the facility position coordinates are obtained and recorded in array A1. Since towers and reactors need to be placed across the floors, array B is used to record their locations.
- ➢
- Add air coolers to the facilities on the second floor, and a new sort P2 is generated randomly. Facilities on the second floor are also optimized by SRFA. Before the optimization, the positions recorded in array B are deleted from the available area on the second floor to ensure that the towers and reactors can be placed across the floors and do not overlap with other facilities on the second floor. The position coordinates of the facilities on the second floor are recorded in array A2.
- ➢
- The layout of the pump area on the first floor is optimized by SRFA, as well according to the order of pump placement. The coordinates of each pump are determined and added to array A1.
- ➢
- Calculate the total cost including pipe construction cost, material handling cost, land cost and floor cost, and obtain individual fitness values according to the position coordinates and sizes of each facility and material connection data in GA.
- ➢
- The current population in GA is judged. If it has reached the preset evolution number, the program will stop running; otherwise, a new generation of random variables will be generated through selection, crossover and mutation, and then step 2 will be carried out again to continue the operation.

## 4. Optimization Process

## 5. Case Study and Result Discussion

#### 5.1. Process of Finding the Key Plant

#### 5.2. Internal Layout Optimization of the Key Plant

#### 5.3. Coupling of the Key Plant and Industrial Area

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Koopmans, T.C.; Beckmann, M. Assignment Problems and the Location of Economic Activities. Econometrica
**1957**, 25, 53–76. [Google Scholar] [CrossRef] - Zhou, J.Y.; Love, P.E.D.; Teo, K.L.; Luo, H.B. An exact penalty function method for optimising QAP formulation in facility layout problem. Int. J. Prod. Res.
**2017**, 55, 2913–2929. [Google Scholar] [CrossRef] - Kim, J.-G.; Kim, Y.-D. Layout planning for facilities with fixed shapes and input and output points. Int. J. Prod. Res.
**2000**, 38, 4635–4653. [Google Scholar] [CrossRef] - Lee, G.-C.; Kim, Y.-D. Algorithms for adjusting shapes of departments in block layouts on the grid-based plane. Omega
**2000**, 28, 111–122. [Google Scholar] [CrossRef] - Liu, J.; Liu, J. Applying multi-objective ant colony optimization algorithm for solving the unequal area facility layout problems. Appl. Soft. Comput.
**2019**, 74, 167–189. [Google Scholar] [CrossRef] - Kalita, Z.; Datta, D. Multi-Objective Optimization of the Multi-Floor Facility Layout Problem; IEEE: New York, NY, USA, 2017; pp. 64–68. [Google Scholar]
- Chang, C.-H.; Lin, J.-g.; Lin, H.-J. Multiple-Floor Facility Layout Design with Aisle Construction. Ind. Eng. Manag. Syst. Int. J.
**2006**, 5, 1–10. [Google Scholar] - Wang, R.Q.; Zhao, H.; Wu, Y.; Wang, Y.F.; Feng, X.; Liu, M.X. An industrial facility layout design method considering energy saving based on surplus rectangle fill algorithm. Energy
**2018**, 158, 1038–1051. [Google Scholar] [CrossRef] - Wang, R.Q.; Wu, Y.; Wang, Y.F.; Feng, X. An industrial area layout optimization method based on dow’s Fire Explosion Index Method. Chem. Eng. Trans.
**2017**, 61, 493–498. [Google Scholar] [CrossRef] - Wang, R.Q.; Wu, Y.; Wang, Y.F.; Feng, X.; Liu, M.X. An layout optimization method for industrial facilities based in domino hazard index. In Proceedings of the 9th International Conference on Foundations of Computer-Aided Process Design; Munoz, S.G., Laird, C.D., Realff, M.J., Eds.; Elsevier Science Bv: Amsterdam, The Netherlands, 2019; Volume 47, pp. 89–94. [Google Scholar]
- Xiao, Y.J.; Zheng, Y.; Zhang, L.M.; Kuo, Y.H. A combined zone-LP and simulated annealing algorithm for unequal-area facility layout problem. Adv. Prod. Eng. Manag.
**2016**, 11, 259–270. [Google Scholar] [CrossRef] [Green Version] - Hou, S.W.; Wen, H.J.; Feng, S.X.; Wang, H.; Li, Z.B. Application of Layered Coding Genetic Algorithm in Optimization of Unequal Area Production Facilities Layout. Comput. Intell. Neurosci.
**2019**, 2019, 3650923. [Google Scholar] [CrossRef] [Green Version] - Hu, M.H.; Wang, M.J. Using genetic algorithms on facilities layout problems. Int. J. Adv. Manuf. Technol.
**2004**, 23, 301–310. [Google Scholar] [CrossRef] - Zhao, H.; Wang, Y.; Feng, X. Optimization of area-wide layout in petrochemical plant with multiple sets of facilities. Petrochem. Technol.
**2017**, 46, 938–943. [Google Scholar] - Tari, F.G.; Neghabi, H. Constructing an optimal facility layout to maximize adjacency as a function of common boundary length. Eng. Optimiz.
**2018**, 50, 499–515. [Google Scholar] [CrossRef] - Liu, J.F.; Zhang, H.Y.; He, K.; Jiang, S.Y. Multi-objective particle swarm optimization algorithm based on objective space division for the unequal-area facility layout problem. Expert Syst. Appl.
**2018**, 102, 179–192. [Google Scholar] [CrossRef] - Feng, J.G.; Che, A. Novel integer linear programming models for the facility layout problem with fixed-size rectangular departments. Comput. Oper. Res.
**2018**, 95, 163–171. [Google Scholar] [CrossRef] - Ahmadi, A.; Jokar, M.R.A. An efficient multiple-stage mathematical programming method for advanced single and multi-floor facility layout problems. Appl. Math. Model.
**2016**, 40, 5605–5620. [Google Scholar] [CrossRef] - Anjos, M.F.; Vieira, M.V.C. An improved two-stage optimization-based framework for unequal-areas facility layout. Optim. Lett.
**2016**, 10, 1379–1392. [Google Scholar] [CrossRef] [Green Version] - Leno, I.J.; Sankar, S.S.; Ponnambalam, S.G. An elitist strategy genetic algorithm using simulated annealing algorithm as local search for facility layout design. Int. J. Adv. Manuf. Technol.
**2016**, 84, 787–799. [Google Scholar] [CrossRef] - Ebrahimi, A.; Kia, R.; Komijan, A.R. Solving a mathematical model integrating unequal-area facilities layout and part scheduling in a cellular manufacturing system by a genetic algorithm. SpringerPlus
**2016**, 5, 1254. [Google Scholar] [CrossRef] [Green Version] - Vazquez-Roman, R.; Diaz-Ovalle, C.O.; Jung, S.; Castillo-Borja, F. A reformulated nonlinear model to solve the facility layout problem. Chem. Eng. Commun.
**2019**, 206, 476–487. [Google Scholar] [CrossRef] - Kulturel-Konak, S. The zone-based dynamic facility layout problem. INFOR
**2019**, 57, 1–31. [Google Scholar] [CrossRef] - Grobelny, J.; Michalski, R. A novel version of simulated annealing based on linguistic patterns for solving facility layout problems. Knowl. Based Syst.
**2017**, 124, 55–69. [Google Scholar] [CrossRef] - Paes, F.G.; Pessoa, A.A.; Vidal, T. A hybrid genetic algorithm with decomposition phases for the Unequal Area Facility Layout Problem. Eur. J. Oper. Res.
**2017**, 256, 742–756. [Google Scholar] [CrossRef] - Turanoglu, B.; Akkaya, G. A new hybrid heuristic algorithm based on bacterial foraging optimization for the dynamic facility layout problem. Expert Syst. Appl.
**2018**, 98, 93–104. [Google Scholar] [CrossRef] - CCPS. Guidelines for Siting and Layout of Facilities, 2nd ed.; Wiley: New York, NU, USA, 2018; pp. 17–26. [Google Scholar]
- Ejeh, J.O.; Liu, S.S.; Papageorgiou, L.G. Optimal layout of multi-floor process plants using MILP. Comput. Chem. Eng.
**2019**, 131, 106573. [Google Scholar] [CrossRef] - Latifi, S.E.; Mohammadi, E.; Khakzad, N. Process plant layout optimization with uncertainty and considering risk. Comput. Chem. Eng.
**2017**, 106, 224–242. [Google Scholar] [CrossRef] - Lee, D.H.; Lee, C.J. The Plant Layout Optimization Considering the Operating Conditions. J. Chem. Eng. Jpn.
**2017**, 50, 568–576. [Google Scholar] [CrossRef] - Elbeltagi, E.; Hegazy, T.; Eldosouky, A. Dynamic layout of construction temporary facilities considering safety. J. Constr. Eng. Manag.
**2004**, 130, 534–541. [Google Scholar] [CrossRef] - Song, X.L.; Xu, J.P.; Zhang, Z.; Shen, C.; Xie, H.P.; Pena-Mora, F.; Wu, Y.M. Reconciling strategy towards construction site selection-layout for coal-fired power plants. Appl. Energy
**2017**, 204, 846–865. [Google Scholar] [CrossRef] - Alves, D.T.S.; de Medeiros, J.L.; Araujo, O.D.F. Optimal determination of chemical plant layout via minimization of risk to general public using Monte Carlo and Simulated Annealing techniques. J. Loss Prev. Process Ind.
**2016**, 41, 202–214. [Google Scholar] [CrossRef] - Dunker, T.; Radons, G.; Westkamper, E. A coevolutionary algorithm for a facility layout problem. Int. J. Prod. Res.
**2003**, 41, 3479–3500. [Google Scholar] [CrossRef] - Jeong, D.; Seo, Y. Golden section search and hybrid tabu search-simulated anneling for layout design of unequal-sized facilities with fixed input and output points. Int. J. Ind. Eng. Theory Appl. Pract.
**2018**, 25, 297–315. [Google Scholar] - Tavakkoli-Moghaddam, R. LADEGA: Unequal Facilities Layout Design Using a Genetic Algorithm for Large-Scale Problems; Stankin Publishing House: Moscow, Russia, 2000; pp. 237–243. [Google Scholar]
- Atta, S.; Mahapatra, P.R.S. Population-based improvement heuristic with local search for single-row facility layout problem. Sadhana Acad. Proc. Eng. Sci.
**2019**, 44, 222. [Google Scholar] [CrossRef] [Green Version] - Stijepovic, M.Z.; Linke, P. Optimal waste heat recovery and reuse in industrial zones. Energy
**2011**, 36, 4019–4031. [Google Scholar] [CrossRef] - Holland, J.H. Adaptation in Natural and Artificial Systems; University of Michigan Press: Ann Arbor, MI, USA, 1975. [Google Scholar]
- Pierreval, H.; Caux, C.; Paris, J.L.; Viguier, F. Evolutionary approaches to the design and organization of manufacturing systems. Comput. Ind. Eng.
**2003**, 44, 339–364. [Google Scholar] [CrossRef] - Tao, W.; Wang, H.; Li, Z. Optimal Solution of Rectangular Part Layout Based on Rectangle-Filling Algorithm. China Mech. Eng.
**2003**, 14, 1104–1107. [Google Scholar]

Number | Name | Length (m) | Width (m) | Area (m^{2}) |
---|---|---|---|---|

1 | PS | 205 | 234 | 47,970 |

2 | COF | 95 | 190 | 18,050 |

3 | GS | 37 | 59 | 2183 |

4 | HU | 176 | 190 | 33,440 |

5 | RWH | 165 | 190 | 31,350 |

6 | FCC | 74 | 186 | 13,764 |

7 | LHR | 59 | 44 | 2596 |

8 | LPGDD | 59 | 146 | 8614 |

9 | SR | 80 | 190 | 15,200 |

10 | AC | 196 | 88 | 17,248 |

11 | HP | 91 | 190 | 17,290 |

12 | CR | 88 | 146 | 12,848 |

13 | NH | 88 | 59 | 5192 |

14 | PP | 73 | 146 | 10,658 |

15 | DC | 124 | 205 | 25,420 |

16 | ACS | 99 | 80 | 7920 |

17 | CCR | 92 | 69 | 6348 |

18 | RTD | 117 | 439 | 51,363 |

19 | TF | 731 | 434 | 317,254 |

20 | STA | 176 | 322 | 56,672 |

Number | Name | Area Changes Aspect Ratio Stays the Same | Area Changes Aspect Ratio Changes | ||||||
---|---|---|---|---|---|---|---|---|---|

20% | 40% | 60% | 80% | 20% | 40% | 60% | 80% | ||

1 | PS | 1.10 | 1.46 | 1.76 | 1.89 | 1.20 | 1.18 | 1.76 | 1.71 |

2 | COF | 2.13 | 1.80 | 2.13 | 1.14 | 1.56 | 1.80 | 2.13 | 1.14 |

3 | HU | 1.26 | 1.53 | 2.22 | 2.15 | 1.26 | 1.69 | 1.41 | 2.45 |

4 | RWH | 1.35 | 1.14 | 1.55 | 2.94 | 1.27 | 1.36 | 1.55 | 2.94 |

5 | FCC | 2.70 | 3.23 | 4.28 | 5.21 | 2.70 | 3.48 | 4.84 | 7.07 |

6 | LPGDD | 2.68 | 3.17 | 4.16 | 2.38 | 2.08 | 2.38 | 3.57 | 2.38 |

7 | SR | 2.19 | 1.80 | 2.19 | 2.70 | 1.35 | 1.80 | 2.28 | 3.62 |

8 | AC | 1.41 | 1.88 | 2.23 | 4.46 | 2.08 | 1.58 | 2.23 | 2.08 |

9 | HP | 1.93 | 1.38 | 1.63 | 2.98 | 1.41 | 1.78 | 2.22 | 4.15 |

10 | CR | 2.69 | 3.06 | 2.79 | 3.19 | 2.59 | 3.06 | 3.19 | 3.44 |

11 | NH | 2.96 | 3.95 | 1.97 | 3.95 | 4.44 | 3.29 | 1.97 | 3.95 |

12 | PP | 3.25 | 3.05 | 1.90 | 1.92 | 3.13 | 3.05 | 4.33 | 5.29 |

13 | DC | 1.66 | 1.55 | 1.81 | 2.82 | 1.86 | 1.95 | 2.82 | 3.63 |

14 | ACS | 3.07 | 2.59 | 2.59 | 2.59 | 3.07 | 4.10 | 4.53 | 4.53 |

15 | CCR | 4.24 | 3.77 | 2.83 | 3.23 | 3.63 | 3.77 | 3.63 | 3.23 |

16 | TF | 1.05 | 1.10 | 1.15 | 1.16 | 1.03 | 1.07 | 1.05 | 1.11 |

17 | STA | 1.06 | 1.24 | 1.49 | 1.72 | 1.29 | 1.18 | 1.49 | 1.27 |

Original Layout | Reconstruction Layout | |
---|---|---|

Length (m) | 34 | 42 |

Width (m) | 146 | 76 |

LC (10^{4} ¥/a) | 49.57 | 32.15 |

PIC (10^{4} ¥/a) | 30.26 | 34.99 |

POC (10^{4} ¥/a) | 22.28 | 29.82 |

FC (10^{4} ¥/a) | 0 | 19.29 |

TC (10^{4} ¥/a) | 102.11 | 116.25 |

Original Layout | Modified Layout | Difference between the Modified and Original Layout | Coupling Result | |
---|---|---|---|---|

FCC plant total annual cost (10^{4} ¥/a) | 102.11 | 116.25 | 14.14 | −180.61 |

Industrial annual cost (10^{4} ¥/a) | 7492.75 | 7298.00 | −194.75 |

© 2020 by the authors. 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**

Wu, Y.; Xu, S.; Zhao, H.; Wang, Y.; Feng, X.
Coupling Layout Optimization of Key Plant and Industrial Area. *Processes* **2020**, *8*, 185.
https://doi.org/10.3390/pr8020185

**AMA Style**

Wu Y, Xu S, Zhao H, Wang Y, Feng X.
Coupling Layout Optimization of Key Plant and Industrial Area. *Processes*. 2020; 8(2):185.
https://doi.org/10.3390/pr8020185

**Chicago/Turabian Style**

Wu, Yan, Siyu Xu, Huan Zhao, Yufei Wang, and Xiao Feng.
2020. "Coupling Layout Optimization of Key Plant and Industrial Area" *Processes* 8, no. 2: 185.
https://doi.org/10.3390/pr8020185