## 1 Introduction  
With the enhanced demands of healthcare provision, many hospitals are facing intense pressure to improve efficiency and provide better medical services to more patients [1; 2; 3; 4]. According to a report from the National Bureau of Statistics of China, the number of yearly visits to all kinds of healthcare institutions increased from 4.9 billion in 2007 to 8.3 billion in 2018. The growing demand for healthcare services leads to increased demand upon new hospital buildings as well as the renovation and re-purposing of existing ones [4]. Many hospitals are considering reconstructing their old buildings and facilities to optimize the patient treatment process by significantly rearranging hospital layouts. An unprecedented healthcare facility construction boom in the United States has shown the importance of creating optimal physical environments to achieve the best possible outcomes for patients, families, and staff [5]. [PERSON] and [PERSON] [6] addressed the serious negative effects of suboptimal transport paths on patient outcomes and highlighted that it is necessary to improve the designs of hospitals in order to reduce patient transport distances and delays. Solving the facility layout problem (FLP) involves finding the most efficient arrangement of elements on the factory floor subject to different constraints in order to meet one or more objectives [7; 8]. An effective facility layout design can increase throughput, overall productivity, efficiency [9], and alleviates congestion [10]. The FLP has been studied for decades and applied to many diverse problems, such as printed circuit board design; the layout design of hospitals, schools, and airports; backboard wiring problems; typewriters; warehouses; and hydraulic turbine design [11]. One of the most important indicators of the efficiency of a layout in manufacturing industry is the material handling cost (MHC) [12],since 20-50% of the total operating costs of a manufacturing company and 15-70% of the total cost of manufacturing a product are attributed to MHC [13]. Thus, companies can improve productivity and reduce these costs by 10-30% if their facilities are arranged effectively [14]. Conversely, an ineffective layout may add as much as 36% to MHC [8]. Research indicates that more than 35% of system efficiency is likely to be lost due to incorrect layouts and location designs [15]. Hence, the issue of the FLP is one of the most important factors for resolution in the literature of production management and industrial engineering, attracting the attention of many researchers [16]. The term hospital facility layout problem (HFLP) refers to the application of facility layout theory and practice to a healthcare management context. From the perspective of management, the HFLP belongs to the strategic level of resource capacity planning and decision-making [17]. It aims to find the most efficient solutions to long-term efficiency and effectiveness decisions. The HFLP has a great impact on medical quality, job satisfaction for medical and other staff, and patient satisfaction [18; 19; 20; 21; 22; 23]. However, in practice, hospital buildings are often planned by architects based on their general experience and whatever legal regulations are extant at the time of commissioning [24; 25; 26; 27; 28], thus, without specific healthcare considerations being taken into account, re-design will be unable to guarantee whether the layout is optimal and fit for purpose. Therefore, considering the HFLP is an essential practice and the problem should be modelled through mathematics and address relevant holistic, applied, and specific factors. In the HFLP, total movement distance (or cost, by assigning unit cost to movement) of patients is the indicator most often used for evaluating layout. Long movement distances between departments waste time, are resource-inefficient, and reduce patient satisfaction, especially for people who are seriously ill [4] adding unnecessary burden to medical and ancillary staff.