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Solving Patient's Scheduling Problems

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Today, due to technological advances and demographic changes, medical treatment costs are much faster. In order to control and reduce these costs and provide desirable services to patients, it is essential to plan and manage the resources and facilities of the treatment. In the meantime, surgery is considered as the largest consumer of resources available in hospitals. Since every surgery in the surgical ward requires a lot of resources, optimal management of this department is very difficult, despite the shortage of resources and increased demand. Also, taking into account the correlation between the other parts of the hospital and the surgical ward increases the importance and complexity of the problem.

On the other hand, since different parts of the health area are heavily influenced by random factors, it is very important to consider the uncertainty for modeling actual and applied issues, although it raises the complexity of the problem and the difficulty of solving it. Therefore, surgical planning is considered as the most basic element of each hospital. The most common procedure used in many hospitals for the planning and scheduling of the surgical department is the two main stages of assignment and sequencing. In the first stage, patients are assigned to one day and one part of the time of the surgical rooms, which are termed the block. In the sequencing phase, usually one day prior to surgery, the sequence of patients in each block is determined.

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The two general types of patients in the subject literature are patients of elective and non-elective patients. Selected patients are those that can already be planned for them. But the entry of non-elective patients is unexpected and requires emergency surgery. Selected patients can be divided into two types of Inpatient and outpatient care. Inpatients are admitted to those patients who need to spend the night at the hospital, while outpatients are usually treated one day and discharged the same day. The issue of determining the number of available rooms and allocating surgical blocks to rooms in a hospital with several rooms of the same operation (in terms of equipment), with the assumption of randomized surgical procedures, were modeled by Denton et al.

Batun et al. developed the Denton et al. model and its collaborators, and considered the sequencing of each room’s surgeries and the start time of surgeons. Mancilla & Storer [3], modeled the problem of sequencing and the time to start surgery in a health center with an operating room using the sample average approximation (SAA) in the form of a randomized numerical model. Saremi et al. modeled the issue of scheduling patients in a hospital by considering multiple resources (such as a recovery unit). To solve the problem, the authors developed a Tabu search-based meta-search algorithm. Dorgu and Melouk presented an adaptive appointment scheduling model for simulation optimization approach used to sequentially schedule appointments to yield desirable schedules for patients and clinical practices.

Also Srinivas and Ravindran developed prescriptive analytics framework to schedule patients in real-time. They proposed scheduling rules by simultaneously considering multiple design decisions and as a case study, with real data from a Family Medicine Clinic in Pennsylvania, is used to show the feasibility of the proposed framework. The results indicate that the proposed scheduling rules consistently outperform the benchmark rules for all the clinic settings tested. Deceunick et al. studied on Outpatient scheduling with unpunctual patients and no-shows. Their approach is based on a modified Lindley recursion in a discrete-time framework and obtains accurate predictions for the moments of the patient waiting times as well as the doctor’s idle times and overtime. It included in a local search algorithm to provide general insights into appointment scheduling under unpunctual patients.

The results obtains substantial cost reductions when patient classification is correctly exploited. Jiang et al. conduct descriptive analytics on MRI data of over 3.7 million patient records and determine the main factors affecting the waiting time and conduct predictive analytics to forecast the daily arrivals and the number of procedures performed at each hospital. The results show that hospitals can enhance their wait time management by delaying patient scheduling. Van de Vrugt et al. integrated scheduling of tasks and gynecologists to improve patient appointment scheduling of the Jeroen Bosch Hospital. They present a Mixed Integer Linear Programming (MIP) approach for this scheduling problem that has the objective to increase compliance of the soft constraints. Jiang et al. presented a stochastic programming model for outpatient appointment scheduling considering unpunctuality. They solved using Benders decomposition combined with the sample average approximation technique to determine the global optimal schedule. Harzi et al.[9] present a mixed integer linear programming approach to facilitate emergency department is a complex task. The main aim is to minimize the total waiting time of patient’s in the emergency department. The results show that the proposed approach could reduce the total waiting time of patients.

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