Schdeduling

Anjomshoa et al.(2018) [2] described a mixed integer programming (MIP) model to an elective surgery scheduling. This model determined an allocation of blocks of time to surgical departments on each day of a four-week cycle. Similar pa- tients in each surgical department were treated as a group of identical patients, which allowed a simpler mathematical model than considering each patient in- dividually. Each surgery department had a list of patients with different groups of demand for resources. It was beneficial to use machine learning algorithms to group similar surgeries in terms of their resource demand.The patients were assigned into three categories according to the urgency of their surgery. Category 1 was classified as most urgent, with no delays allowed being implemented as a hard constraint. The other two categories were the second most urgent and the not urgent type respectively, which both allowed overdue surgeries. Each surgery group has a given resource demand including the urgency, surgery duration, length of post-operative hospital stay, probability of using the Intermediate Care Team (ICT), and hospital income earned for the patient.They constructed a number of individual objectives (size of the waiting list, number of overdue patients, tardy days, hospital performance, and funding) within one objective function by giving each different weights. Depending on a given hospital’s priorities, the weight of each objective can be modified. While this is one approach, the paper suggests there are various approaches to work with multi-objectives where the optimal decisions need to be taken in the pres- ence of trade-offs between objectives.The computational results of this paper showed that this model can generate a solution in a reasonable time with a reasonable optimality gap, even with complex multi-objectives for up to three months planning period. However, MIP has an exponential time performance. Hence, for modelling large data one should consider faster techniques such as heuristic algorithms.83.4 Ozkarahan (2000)Ozkarahan (2000) [5] modelled an elective surgery scheduling based on 10 day data from D.E.U hospital by minimising idle time and over time and increasing satisfaction of surgeons, nurses and patients. This model can be reused for other hospitals by modifying the constraints according to their conditions.In this paper, the problem Ozkarahan (2000) [5] described that the hospital used a full day block system for their operation rooms, which allows each department to use the day in any way their surgeons preferred. This was due to the staff satisfaction as working overtime can lead to employee turnover. Hospitals have difficulty in recruiting nurses. However, a day block system can frequently cause idle time between cases. Surgeons may spread their cases throughout the day. This leads to a low utilisation rate of using operation rooms. Ozkarhan (2000) [5] used block booking methods to reduce this idle time, which avoids making any unused time unavailable to other surgery departments.There were 8 operating rooms in this hospital, each of which was allocated to each surgery department due to special features of various types of surgeries. In this case, each department had all of the required equipment for its surgeries in that room which avoided any inconvenience of moving equipment. While this may limit the number of rooms can be used for each surgery department, when the demand for a certain type of surgery has increased, patients may need to wait longer to be scheduled.Ozkarahan (2000) [5] considered Block Scheduling Restrictions, Operation Room Utilisation, Operation Room Preference and Surgeons Preferences and Intensive Care Capabilities as the main objectives. These objectives balance the dura- tion of scheduled operations the length of blocks, minimise under utilisation and overtime for each operation room, allow surgical departments to choose the rooms they prefer, ensure the urgent surgeries of each department are sched- uled on the requested day and the number of patients need intensive care after surgery is no more than the number of spare beds in ICU. The mathematical model was comprehensive, but it did not explain how to solve the model in detail.

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