Abstract: For the past few years, motor vehicle accidents and industrial accidents have occurred frequently, and pelvic fracture has become a common orthopaedic injury. Pelvic fracture is a severe trauma caused by the direct compression of the pelvis, often accompanied by other organ and system damage, with a disability rate of up to 50%~60%. Based on the stability of the pelvis, pelvic fracture can be classified into three categories: A, B, and C. Type B and C fractures are usually recommended for surgical treatment. Based on the patients’ life state at the time of admission, patients are divided into two types, convalescent patient and scheduled patient. Through examination, the fracture type of scheduled patient is determined and the surgical plan is made. Convalescent patients have random recovery time and receive surgery when they have a stable life state. When there are two types of patients in the system, the surgical allocation strategy is developed to maximize the expected benefit. In the context of sharing medical resources such as doctors, nurses and operating rooms, optimizing surgical arrangements and rational allocation of medical resources are crucial.
The Markov decision process model with the objective of maximizing the expected benefit is established. The backward iterative algorithm is used to get the optimal allocation strategy. The parameters of two types of patients are designed according to actual situation of the hospital. A case of 8-service-period is considered, then the optimal state path and decision path are obtained. The optimal allocation curve of different scenarios are drawn, and the structural properties of the optimal strategy are analyzed and proved. Changing the recovery time and the number of convalescent patients, the allocation strategies under different scenarios are got. Sensitivity analysis is also done by adjusting the parameters of two types of patients.
(1)With the quadratic penalty function, the optimal allocation curve takes the form of switching-curve. (2)There exists a critical index c^*_t(s), so that a convalescent patient will be selected when c≥c^*_t(s) and a scheduled patient is selected if c<c^*_t(s). Besides, critical index c^*_t(s) presents a monotonically increasing form, ifs₁≥s₂, then c^*_t(s₁)≥c^*_t(s₂). (3)Scenarios with the same ncp always share the same allocation policy, which means that they have the same critical values of each s. Exceptions exist when ncp=6 and ncp=7, both of which have two optimal allocation policies. (4)The difference of critical values between each scenario is no more than the difference ofncp between them. The more convalescent patients, the greater priority they will have.
However, limitations still exist and more work remains to be done in the future. First, we start the system with a random number of patients. In fact, patients who have not been served from the previous planning horizon may still wait in the system. Second, one request of each type of patient can arrive at every service period. Batch arrival is not considered, so the arrival patterns that we use have a discrepancy from the practical situation. Third, the time of surgery of each patient is assumed to be the same and equal to the length of the service period. However, due to the different types of pelvic fractures and the distinct condition of each person, the time of surgery may vary from patient to patient. The further research includes the following points: First, patients who are not served in the previous time period should be considered, and a reasonable initial value of the state should be set. Second, arrival patterns should be modified to consider more situations. Multi-facility and multi-patient-type problems should be modeled to further approach reality. Third, the planning horizon should be extended to make continuous and sequential decisions.

Key words: pelvic fracture, Markov decision process, stochastic recovery time

摘要： 骨盆骨折是一种高能量创伤且通常伴有多发伤,手术是主要的治疗方法,本文制定并优化创伤患者的手术分配计划。首先根据患者入院时的生命稳定状态,将手术患者分为恢复期和计划期两类;针对两类患者的不同特点,为恢复期患者设置随机恢复时间,以最大期望收益为目标建立马尔可夫决策过程模型;根据医院实际情况设计实验,采用后向迭代算法求解得到最优分配策略;改变惩罚函数形式和恢复期患者数量,制定不同场景的分配策略,提高医疗资源利用率。采用二次惩罚函数时,最优分配曲线呈现开关曲线形式;恢复期患者数量越多,其享有的优先权越高。

关键词: 骨盆骨折, 马尔可夫决策过程, 随机恢复时间