# A Novel Hybrid Simulated Annealing for No-Wait Open-Shop Surgical Case Scheduling Problems
## 2 Literature Review  
The constant increase in patients and surgeries requires additional unconventional techniques to develop efficiency, particularly in creating ORs [1; 2]. ORs are one of the most significant customer services that require high-cost resources, including human resources, equipment, and medicine [3]. The surgery takes place in a setting of challenging advancements such as vital expenditure on health care [4; 5], growing fees in health care costs [6], rising surgery demand caused by aging people, and industrial developments that have increased the range of surgical interventions [7]. OR surgery scheduling deals with characterizing the operation start times of surgeries and allocating the proposed sources to the scheduled surgeries. This allows for several constraints to secure a comprehensive surgery flow, source availability, and specialty supplies of human sources [8; 9]. The suggested mission plays an essential role in maintaining timely medications for the patients by maintaining the stability of the hospital's source operation [10]. Current patient scheduling is necessary for operation research, such as multi-objective optimization. Several operation research methods [11; 12; 13], such as a discrete-event simulation model [14] and an optimization-based scheduling tool [15], are used to decrease the size of the patient wait list significantly [16]. To simplify the scheduling process, a general method is used to schedule the venesection and clinic visit one day and the infusion the following day [17]. Sequencing and scheduling are critical decision-making processes in developing efficiency in manufacturing and services industries such as healthcare. Scheduling is a decision-making process that allocates resources to activities in given time intervals and optimizes one or more objects [18]. Some researchers detected any scheduling problem as having one of three characteristics: the machine environment, problem conditions, and the objective function of a problem [19; 20; 21; 22]. In the first field, the background of the problem is stated [23; 24]; in the second field, the acronyms suggest the condition of the problem; and in the third field, the objective function of the scheduling problem is resolved. The second and third fields have numerous modes [25]. A scheduling problem is illustrated with the triple \(\alpha|\beta|\gamma\). Field \(\alpha\) defines the machine environment and only contains one input. Field \(\beta\) includes details of process types and constraints without input or with one or more inputs. Field \(\gamma\) defines the object which should be minimized and often has one input [26; 27]. The initial study [28], which offered a solving algorithm for the open-shop problem, recommended a linear time algorithm to solve open-shop problems with two machines. The objective function is minimizing the makespan. They also created a polynomial algorithm for the case where the shop has more than two machines. Preemptions are not allowed to minimize the makespan, which has been applied in several studies [29; 30; 31; 32; 33; 34; 35]. Optimal finish time (OFT) is used in different scheduling problems to find the OFT of open-shop problems and offers a linear time algorithm to see the OFT of open-shop problems with two machines [36; 37; 38; 39]. Preemptions were permitted to find the OFT of open-shop problems with more than two machines [40; 41; 42]. In these problems, it is believed that the number of operations with a non-zero processing time is more than the number of machines and jobs [43]. Some methods offered a heuristic algorithm for solving the open-shop problem with two machines and transportation times [44; 45; 46; 47; 48; 49; 50]. In another suggested model, the transportation time between machines, as a fixed one, was described and associated with a delay time between the completion time of one operation and the start time of the following operation on the same job [51]. The problem of an open shop with two machines and different transportation times was suggested.