Jointly Appointment Scheduling in a Two-Phase Service System With Two Types of Patients Considering Multiple Servers and Stochastic Service Time

This article focuses on the appointment scheduling problem with stochastic service times in a two-phase healthcare service system. In this system, the two phases' services refer to medical test and physician consulting, respectively. And two types of patients with different service process exist on a specific day. One type of patient is the new-coming patient who only needs to be served by the physician (if a test is needed, it will be booked for another day due to resource limitation). The other type of patient is the "revisiting" patient who enters the system to get complex test followed by previous suggestions of physician, and he/she will visit the physician with the test results on the same day. All patients get their services through appointments. And the current policy of managing those appointments applied in hospitals is to schedule the appointments in two phases separately. However, as this policy does not take the interaction of two phases' service into consideration, lots of conflicts emerge in the operation process. To avoid the conflict of patients from different types and improve the system's efficiency, we innovatively proposed a jointly scheduling policy, which aims to make a joint scheduling decision for all the patients in two phases. To achieve this, we first formulate this problem as a stochastic program and conduct the sample average approximation approach to reformulate it as a deterministic problem. To solve it efficiently, a hybrid VNS_LSHAPE algorithm which combines the advantage of VNS (Variable Neighborhood Search) and L shape algorithm is subtly developed based on the properties of the problem. Finally, numerical experiments show that our proposed jointly scheduling policy has an overwhelming performance on the system's total cost compared with separately scheduling policy. Both types of patients' satisfaction and the utility of physicians are improved with this policy. Note to Practitioners -In many departments of hospitals, medical test and physician diagnose are two necessary service items provided to the patients. Such a department can be regarded as a two-phase service system. Generally, two types of patients usually exist in this system simultaneously on a work day. One type refers to the new-coming patients who come for an initial consulting of the physician. And the other type refers to the patients who revisit this system to take medical test and physician's further diagnosis sequentially. Since making appointments can