关键词: 手术病例分配, 松鼠搜索算法, 模糊手术时间, 调度优化

Abstract: As the core of medical institutions, operating room department involves the most extensive personnel, and occupies a large amount of funds. According to incomplete statistics, the surgery involves 70% of hospital departments, accounting for 9% of the annual budget and 40% of the total revenue. Due to the rapid growth of population and the worsening aging problem, residents' medical needs continue to expand. The demand for surgery often exceeds that for the medical load, which causes a long waiting time.
Surgical case assignment problem (SCAP) is an important part of operating room planning and has been proved to be NP-hard. It can be simply described as a set of surgical cases that are assigned to the appropriate operating rooms within the planning period and meet the constraints of the corresponding deadlines and durations. In SCAP, the surgery duration is predetermined. Due to the influence of doctors' skills and intraoperative emergencies, the duration usually fluctuates within a certain range which could affect the efficiency of operating room circulation.
In this paper, an extended model of SCAP which considers the fuzzy surgery duration is proposed (FSCAP), and an improved squirrel search algorithm is designed to address this problem. The contributions of this paper can be concluded as follows: (1)we extend the model of SCAP to the fuzzy environment, which considers the uncertain surgery duration; (2)we modify the squirrel search algorithm and apply it to solve the proposed FSCAP. Generally, this study could optimize the surgery sequence of patients and improve the utilization efficiency of operating room resources.
Combined with the actual surgery situation of hospital, the uncertainty of surgery duration is considered in SCAP, where the triangular fuzzy number is introduced to establish the surgical case assignment model with the objective of minimizing fuzzy operating cost.
In this paper, an improved squirrel search algorithm (ISSA) is developed to address the problem. First, a single list encoding scheme and a corresponding decoding method are proposed. Second, several effective heuristics are employed to improve the quality of initial population. Third, the path relinking technology and the reverse operator are embedded into the algorithm to simulate the foraging behaviors of flying squirrels. Based on the datasets proposed by RIZK and ARNAOUT(2012), 10 instances for the surgical case assignment problem with fuzzy surgery duration are developed to evaluate the effectiveness of the proposed algorithm.
To further evaluate the effectiveness and superiority of ISSA, several existing methods including CPLEX, discrete particle swarm optimization (DPSO), hybrid biogeography optimization (HBBO) and memetic algorithm with novel semi-constructive evolution operators (MASC) are employed for comparisons. For each instance, the proposed algorithm is performed 30 times independently.
Table 2 presents the comparison results between ISSA and CPLEX for the small-scale instance. From the table, it can be seen that the ISSA can always obtain the optimal solution for each instance at each run, where the values of the best, average and worst are the same. In comparison with the value found by CPLEX, the relative error of the average value is 0.00%. Hence, it can be concluded that the ISSA demonstrates great accuracy and stability in addressing small-scale instances. The comparison results between ISSA and other meta-heuristics for bigger scale instances are shown in Table 3. From the table, it can be seen that the ISSA could obtain feasible solutions for all the instances, while other algorithms fail with an increase in the instance scale. The reason lies in the fact that several effective heuristics are embedded into the ISSA, which improves the quality of initial population. Therefore, ISSA demonstrates a greater superiority than other algorithms in solving FSCAP.
However, there are still a few limitations of this study. The FSCAP is an ideal mathematical model, which is an extension of classic SCAP. In the process of actual surgical planning, medical institutions should not pay attention to the operating cost merely. More indicators such as doctor-patient satisfaction, surgical resources utilization and patient waiting time ought to be taken into consideration. Additionally, the classic SCAP simplifies the constraints of human resources and surgical equipment. These resources constraints affect the operating room planning critically. Therefore, subsequent studies will further consider the extension of objective functions and realistic constraints. To test the performance of the proposed ISSA, the benchmarks generated by random are conducted. In future, the authors would apply the proposed algorithm to the datasets collected from medical institutions.

Key words: surgical cases assignment, squirrel search algorithm, fuzzy surgery duration, scheduling optimization