Stochastic Master Surgery Scheduling for the orthopaedic department at St. Olav's Hospital
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The regional health authority, Helse Midt-Norge (HMN), provides hospital services to the two counties Trøndelag and Møre og Romsdal. Forecasting estimates that the number of people living in these two counties that exceed 67 years old will increase by 42 % within 2030, yielding a massive increase of the demand for health care in the years to come (Helse-midt.no,2016) .St. Olav's Hospital is the largest hospital in HMN, and in this thesis we will consider the surgery scheduling at the orthopaedic department at St. Olav's Hospital. The orthopaedic department is responsible for treating all orthopaedic patients entering the hospital, both electives and emergencies. Treating the orthopaedic emergency patients within the dead lines proposed by the hospital has been an issue for many years. In addition to being unfortunate for the emergencies, delaying the emergencies also affects the elective patients. As the queue of emergencies grows, more emergency patients are scheduled for the elective ORs implying elective rescheduling. In addition, most of the emergency patients cover beds at the wards while waiting for surgery. In periods of many emergencies waiting for surgery, the bed capacity may become scarse, yielding rescheduling of elective inpatients. The least urgent of the emergency patients, the green emergencies, are the first ones to be displaced from the emergency ORs in periods of excessive emergency demand. In addition, only about 70 \% of these patients receive surgery within the dead line, and dedicating more OR capacity for the green emergency patients should be considered. The main problem faced in this report is the Master Surgery Scheduling Problem (MSSP). This problem consists of developing a cyclic Master Surgery Schedule (MSS), linking the surgical subspecialties to the different ORs through the cycle, which is typically set to one week. The majority of authors on the field focus exclusively on the elective patients, arguing that the emergencies are treated by dedicated resources. Although some authors address uncertain aspects relevant to surgery scheduling, the majority of optimization models provided on the field are deterministic. As a contribution to the existing literature, we propose a two-stage stochastic recourse formulation to address the stochastic arrival of emergency patients when solving the MSSP. In the first stage of the optimization model, we schedule the OR capacity available as either flexible or dedicated for electives, and we schedule elective patients for surgery in the elective OR slots. In addition, we schedule the amount of beds to be available at the wards on each day of the cycle. The stochastic parameters in the problem are the number of green emergencies that need to be scheduled in the cycle, and the daily number of emergency patients covering beds at the wards. The flexible OR capacity is dedicated to handle the weekly demand of green patients, and we require that all green patients should be scheduled for surgery in the second stage. If all the green emergency patients are scheduled and we still have excess capacity of flexible slots, more urgent emergencies are scheduled for these slots. If there are too few flexible slots available to treat all green emergencies present in the cycle, these patients need to be scheduled for the elective ORs, which may imply elective cancellations. In addition, if the bed capacity is reached and there are still elective inpatients left to be treated, these surgeries are cancelled. From running the optimization model on realistic size instances we find that applying a stochastic formulation provides additional value compared to the deterministic counterpart. Furthermore, we develop some general advises regarding the scheduling of flexible slots to elective ORs. If the OR capacity is regarded as better than the ward capacity, a relatively high share of the ORs should be made flexible. If however the bed capacity is good, and the OR capacity is scarse, less OR capacity should be scheduled as flexible. Applying a two-stage formulation to model the uncertainty means that we assume that all necessary information regarding the uncertainty will be made available to us at one specific point in time (before each cycle). This assumption, together with the fact that we generate a cyclical schedule to handle real life fluctuations over time calls for some way to test the robustness of the schedules proposed. To do this, we develop a discrete event simulation model that represents a real life hospital department. The entities considered in the system are the elective patients, the emergency patients, the wards, the elective ORs and the emergency ORs. There is yet another reason for developing the simulation model: We require a way of generating scenarios representing the stochastic parameters applied in the optimization model. The scenarios are generated from the simulation model, allowing us to generate scenarios that are dependent on the scheduling regime implemented in the simulation model. The main purpose of this thesis is to provide tactical decision support for the management at the orthopaedic department at St. Olav's Hospital, and we perform a case study of the department, applying both the models in a loop. By scheduling six flexible slots of four hours to the elective ORs we show that both the green and yellow emergencies receive surgery faster compared to the historical data. In addition, the flexible slot capacity makes the department better prepared for handling fluctuations in the demand for emergency surgeries. Because of this, far less elective rescheduling is needed. However, scheduling flexible slots yields a decrease in the number of electives scheduled, and there exist a trade-off between the number of electives scheduled versus the amount of elective rescheduling that need to be made when the system is exposed to emergency patients. Topics for further research include issues regarding symmetry in the optimization model formulation. If we can provide more efficient formulations, we may have the opportunity to impose more stages in the stochastic formulation.