## Coupling Layout Optimization of Key Plant and Industrial Area

Read the introduction and sections 5 and 6. This article discusses a hybrid model for optimal layout planning, considering factors in plant layout design. What factors does the model not consider, and how important are these factors?

### Introduction

Facility layout problem (FLP) is an important branch of industrial engineering and has a great impact on production efficiency, operating safety and construction investment of a factory. It was firstly proposed by Koopmans and Beckmann in 1957, aiming to minimize the material handling cost by arranging given facilities reasonably. The research direction of early layout problems was the single-floor layout of equal-area facilities using a discrete QAP (Quadratic Assignment Problem) model. The area was divided into grids of the same size in one-to-one correspondence with the facilities. Since the facility shape and size have an obvious impact on the overall layout area, it is unreasonable to generalize the layout problem with equal size facilities. Therefore, some works tended to convert the direction into UA-FLPs (Unequal-Area Facility Layout Problems). Due to the shortage of land resources and limited horizontal space, a multi-floor layout has become one of the research hotspots. Various methods to assign facilities into floors have been implemented. Chang et al. classified the departments into groups according to the flow relationship, and the departments of a similar category are arranged on the same floor. Wang et al. divided facilities into different floors by stochastic algorithm, and obtained an optimal solution iteratively.

Many efforts have been made to rationalize the layout results. Safety factors were implemented by the TNT (Trinitrotoluene) explosion model or domino hazard index. Limitations on the area and aspect ratio of facilities were taken into account as well. The adjacent arrangement of special plants was implemented by arranging plants with upstream and downstream relationships jointly. The same objective was also achieved by maximizing the adjacent lengths of plants with frequent flow exchanges, or the total flow rate of departments next to each other. In order to make the mathematical models more accurate, a number of works have been done. Ahmadi and Jokar established a multiple-stage model in multi-floor layout research. Facilities were assigned to each floor using mixed integer programming (MIP), and the facility location on the floor and the final layout were determined by non-linear programming (NLP). Anjos and Vieira firstly optimized the relative location of departments in the region and then determined the inner precise layout. The model solved sequentially may lead to suboptimal solutions, so Leno et al. proposed a hybrid algorithm to optimize the internal and external layout at the same time. Various algorithms were adopted, such as GA and the simulated annealing algorithm, and both of these have obtained reasonable results. To improve the performance of each algorithm, many kinds of hybrid algorithms were often applied as well.

However, through the development of layout research in recent years, there are still some aspects left to be solved or improved. In order to solve such problems, some concepts need to be clarified. There are two main types of layout - namely, plant layout and area-wide layout (general layout). A plant is defined as a collection of multiple facilities, and the industrial area usually contains various plants. Plant layout is mainly devoted to the optimal arrangement of facilities with their original sizes in the plant area. Area-wide layout studies focus on the reasonable placement of plants with fixed or flexible sizes within the industrial area. The main purpose of both layouts is to reach the reasonable use of space and meet process requirements. However, the studied land scale of the area-wide layout is much larger than the plant layout, which results in more complicated factors that need to be considered, such as geographical factors and traffic conditions. Additionally, pipeline network design plays a more important role in the area-wide layout because of the long distance, which brings more solving difficulties as well. Therefore, at present, more attention is paid to the study of plant layout, and unfortunately, only a small number of researchers have focused on the area-wide layout due to its complexity. The coupling optimization of both is even rarer. However, it is quite essential because these two layouts are indivisible. Plant layout usually has an effect on the area-wide layout to some extent, especially in the aspect of the occupied area. If it is required to reach the best of both, plant layout must be considered in the design of the area-wide layout. To the best knowledge of the authors, few previous articles consider the impact of a single plant on the overall area, or whether a better scheme can be obtained if both layouts are taken into account at the same time. In addition, in previous studies, the number of facilities or plants was generally small due to the solving difficulty of layout problems. The number of facilities considered in the optimization was less than 10 in most of works. Even in some works with a larger problem size, there were around 20 facilities in total, which is still far from the actual situation.

Therefore, to deal with the above issues, a new idea to design an area-wide layout is put forward. The main contribution of this work lies in the development of the conventional single-layout studies, which means that the coupling optimization of the two layouts mentioned above is realized by several steps of optimization. The impact of plant layout on the area-wide layout is emphasized. This work focuses on improving the practicality of the layout optimization method and explores the internal relationships of different levels of layouts. The plant layout and area-wide layout are concerned at the same time and the coupling relationships between them are especially considered. The main purpose of this work is to figure out the impact of a special plant on the overall industrial area and the coupling relationships between a plant and the industrial area, so that some new construction ideas can be provided. This area has significant research value but has rarely been mentioned in previous studies. It is very beneficial if the cost of the industrial area can be greatly reduced by only modifying one certain plant. To achieve the above objectives, a method with multiple steps is proposed to solve the problem sequentially. Firstly, the key plant with the greatest impact on the overall layout is figured out and modified. It is then coupled with the industrial area. The whole layout with all the plants is optimized and compared with the original one to study the impact of changes in the key plant on the overall layout. Through the above steps, plant layout is well related to the area-wide layout. In addition, based on previous research, safety distance, multi-floor model and joint arrangement of special facilities are applied. A case with practical size is studied. A combined algorithm of the genetic algorithm (GA) and surplus rectangle fill algorithm (SRFA) is adopted to give rules for facility placement and optimize layout results effectively. As a conclusion, the point of this work is that a common problem which has not been studied before is raised and a set of approaches to address it is put forward. Through the case study, a better solution than the original one is certainly obtained due to the more comprehensive approach.

Source: Yan Wu, Siyu Xu, Huan Zhao, Yufei Wang, and Xiao Feng, https://www.mdpi.com/2227-9717/8/2/1Fhtm