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Feng H, Jia Y, Huang T, Zhou S, Chen H. An adaptive decision support system for outpatient appointment scheduling with heterogeneous service times. Sci Rep 2024; 14:27731. [PMID: 39532975 PMCID: PMC11557935 DOI: 10.1038/s41598-024-77873-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2024] [Accepted: 10/25/2024] [Indexed: 11/16/2024] Open
Abstract
Appointment scheduling (AS) plays a crucial role in outpatient clinic management. Traditional methods involve patient grouping using pre-defined rules and scheduling based on these groups. However, pre-defined rules may not adequately capture the heterogeneity in patients' service times (i.e., consultation duration). Advanced machine learning (ML) methods can address individual-level heterogeneity but pose challenges for practical scheduling. To strike a balance, we propose a data-driven AS decision support system, Cluster-Predict-Schedule (CPS), integrating both supervised and unsupervised ML for efficient patient grouping and scheduling. The novelty of CPS lies in its adaptability to service time heterogeneity through a data-driven approach, determining patient groups based on data rather than pre-defined rules. Additionally, CPS includes a generic and efficient algorithm for generating appointment templates adaptable to any number of patient groups. Our system's efficacy is demonstrated using a real-world dataset. Evaluated by the weighted sum of patient wait times, physician idle time, and overtime, CPS achieves up to 15.0% cost reduction compared to the FCFA (first-call, first-appointment) scheme and over 4.7% savings against the common New/Return classification with traditional sequencing candidate (TSC) rules. In addition, CPS enhances outpatient operational efficiency without compromising fairness.
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Affiliation(s)
- Haolin Feng
- School of Business, Sun Yat-sen University, Guangzhou, 510275, China
| | - Yiwu Jia
- Lingnan College, Sun Yat-sen University, Guangzhou, 510275, China
- School of Management, North Sichuan Medical College, Nanchong, 637100, China
| | - Teng Huang
- School of Business, Sun Yat-sen University, Guangzhou, 510275, China.
| | - Siyi Zhou
- Wechat Business Group, Tencent Technology Co., LTD, Guangzhou, 510433, China
| | - Hongyi Chen
- School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, 510006, China
- Hangu TCM Innovation and Research Institute, Guangzhou, 510655, China
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White SJ, Ho K, Maini K, Liang R. "Sorry for Holding You Up": Surgeons' Apologies for Lateness in Clinic Settings. HEALTH COMMUNICATION 2024; 39:2997-3008. [PMID: 38177980 DOI: 10.1080/10410236.2023.2299888] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/06/2024]
Abstract
Doctors running late may convey a lack of respect which can impair the therapeutic relationship. This study examines how surgeons address lateness in consultations with patients. We analyzed 52 consultation recordings from a range of surgical specialties in an Australian metropolitan setting. Conversation analysis was used to analyze interactional sequences where lateness was addressed. Six sequences were identified within four recordings. The two consultations with two apologies include a surgeon and registrar apologizing in a neurosurgical consultation and a surgeon apologizing twice within a colorectal consultation. Apologies were either accepted or responded to with an account for not accepting the apology. When these accounts were made, consultations could only progress when patients accepted an explanation for lateness or the degree of complainability about lateness was reduced. The infrequent occurrence of apologies for lateness, and the way in which these sequences unfolded when they did occur, suggest that there is greater acceptability of lateness for surgeons than in ordinary social situations.
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Affiliation(s)
- Sarah J White
- Centre for Social Impact, University of New South Wales
| | - Ken Ho
- Faculty of Health Sciences & Medicine, Bond University
| | | | - Rhea Liang
- Faculty of Health Sciences & Medicine, Bond University
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hua L, Dongmei M, Xinyu Y, Xinyue Z, Shutong W, Dongxuan W, Hao P, Ying W. Research on outpatient capacity planning combining lean thinking and integer linear programming. BMC Med Inform Decis Mak 2023; 23:32. [PMID: 36782168 PMCID: PMC9924205 DOI: 10.1186/s12911-023-02106-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Accepted: 01/09/2023] [Indexed: 02/15/2023] Open
Abstract
BACKGROUND The size and cost of outpatient capacity directly affect the operational efficiency of a whole hospital. Many scholars have faced the study of outpatient capacity planning from an operations management perspective. OBJECTIVE The outpatient service is refined, and the quantity allocation problem of each type of outpatient service is modeled as an integer linear programming problem. Thus, doctors' work efficiency can be improved, patients' waiting time can be effectively reduced, and patients can be provided with more satisfactory medical services. METHODS Outpatient service is divided into examination and diagnosis service according to lean thinking. CPLEX is used to solve the integer linear programming problem of outpatient service allocation, and the maximum working time is minimized by constraint solution. RESULTS A variety of values are taken for the relevant parameters of the outpatient service, using CPLEX to obtain the minimum and maximum working time corresponding to each situation. Compared with no refinement stratification, the work efficiency of senior doctors has increased by an average of 25%. In comparison, the patient flow of associate senior doctors has increased by an average of 50%. CONCLUSION In this paper, the method of outpatient capacity planning improves the work efficiency of senior doctors and provides outpatient services for more patients in need; At the same time, it indirectly reduces the waiting time of patients receiving outpatient services from senior doctors. And the patient flow of the associate senior doctors is improved, which helps to improve doctors' technical level and solve the problem of shortage of medical resources.
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Affiliation(s)
- Li hua
- grid.430605.40000 0004 1758 4110Abdominal Ultrasound Department, Diagnostic Ultrasound Center, First Hospital of Jilin University, Changchun, Jilin China ,grid.64924.3d0000 0004 1760 5735School of Public Health, Jilin University, Changchun, Jilin China
| | - Mu Dongmei
- Department of Clinical Research, First Hospital of Jilin University, Changchun, Jilin, China. .,School of Public Health, Jilin University, Changchun, Jilin, China.
| | - Yang Xinyu
- grid.64924.3d0000 0004 1760 5735School of Public Health, Jilin University, Changchun, Jilin China
| | - Zhang Xinyue
- grid.64924.3d0000 0004 1760 5735School of Public Health, Jilin University, Changchun, Jilin China
| | - Wang Shutong
- grid.64924.3d0000 0004 1760 5735School of Public Health, Jilin University, Changchun, Jilin China
| | - Wang Dongxuan
- Abdominal Ultrasound Department, Diagnostic Ultrasound Center, First Hospital of Jilin University, Changchun, Jilin, China.
| | - Peng Hao
- grid.64924.3d0000 0004 1760 5735School of Public Health, Jilin University, Changchun, Jilin China
| | - Wang Ying
- grid.64924.3d0000 0004 1760 5735School of Public Health, Jilin University, Changchun, Jilin China
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Hadid M, Elomri A, Padmanabhan R, Kerbache L, Jouini O, El Omri A, Nounou A, Hamad A. Clustering and Stochastic Simulation Optimization for Outpatient Chemotherapy Appointment Planning and Scheduling. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2022; 19:15539. [PMID: 36497611 PMCID: PMC9736607 DOI: 10.3390/ijerph192315539] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Revised: 11/06/2022] [Accepted: 11/09/2022] [Indexed: 06/17/2023]
Abstract
Outpatient Chemotherapy Appointment (OCA) planning and scheduling is a process of distributing appointments to available days and times to be handled by various resources through a multi-stage process. Proper OCAs planning and scheduling results in minimizing the length of stay of patients and staff overtime. The integrated consideration of the available capacity, resources planning, scheduling policy, drug preparation requirements, and resources-to-patients assignment can improve the Outpatient Chemotherapy Process's (OCP's) overall performance due to interdependencies. However, developing a comprehensive and stochastic decision support system in the OCP environment is complex. Thus, the multi-stages of OCP, stochastic durations, probability of uncertain events occurrence, patterns of patient arrivals, acuity levels of nurses, demand variety, and complex patient pathways are rarely addressed together. Therefore, this paper proposes a clustering and stochastic optimization methodology to handle the various challenges of OCA planning and scheduling. A Stochastic Discrete Simulation-Based Multi-Objective Optimization (SDSMO) model is developed and linked to clustering algorithms using an iterative sequential approach. The experimental results indicate the positive effect of clustering similar appointments on the performance measures and the computational time. The developed cluster-based stochastic optimization approaches showed superior performance compared with baseline and sequencing heuristics using data from a real Outpatient Chemotherapy Center (OCC).
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Affiliation(s)
- Majed Hadid
- College of Science and Engineering, Hamad bin Khalifa University, Doha 34110, Qatar
| | - Adel Elomri
- College of Science and Engineering, Hamad bin Khalifa University, Doha 34110, Qatar
| | - Regina Padmanabhan
- College of Science and Engineering, Hamad bin Khalifa University, Doha 34110, Qatar
| | - Laoucine Kerbache
- College of Science and Engineering, Hamad bin Khalifa University, Doha 34110, Qatar
| | - Oualid Jouini
- Laboratoire Génie Industriel, Université Paris-Saclay, Centrale Supélec, Gif-sur-Yvette, 91190 Paris, France
| | - Abdelfatteh El Omri
- Surgical Research Section, Department of Surgery, Hamad Medical Corporation, Doha 3050, Qatar
| | - Amir Nounou
- Pharmacy Department, National Center for Cancer Care & Research, Hamad Medical Corporation, Doha 3050, Qatar
| | - Anas Hamad
- Pharmacy Department, National Center for Cancer Care & Research, Hamad Medical Corporation, Doha 3050, Qatar
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Appointment Scheduling Problem in Complexity Systems of the Healthcare Services: A Comprehensive Review. JOURNAL OF HEALTHCARE ENGINEERING 2022; 2022:5819813. [PMID: 35281532 PMCID: PMC8913063 DOI: 10.1155/2022/5819813] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Revised: 01/14/2022] [Accepted: 01/25/2022] [Indexed: 12/29/2022]
Abstract
This paper provides a comprehensive review of Appointment Scheduling (AS) in healthcare service while we propose appointment scheduling problems and various applications and solution approaches in healthcare systems. For this purpose, more than 150 scientific papers are critically reviewed. The literature and the articles are categorized based on several problem specifications, i.e., the flow of patients, patient preferences, and random arrival time and service. Several methods have been proposed to shorten the patient waiting time resulting in the shortest idle times in healthcare centers. Among existing modeling such as simulation models, mathematical optimization techniques, Markov chain, and artificial intelligence are the most practical approaches to optimizing or improving patient satisfaction in healthcare centers. In this study, various criteria are selected for structuring the recent literature dealing with outpatient scheduling problems at the strategic, tactical, or operational levels. Based on the review papers, some new overviews, problem settings, and hybrid modeling approaches are highlighted.
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Al-Hawari T, Alrejjal A, Mumani AA, Momani A, Alhawari H. A Framework for Multi-response Optimization of Healthcare Systems Using Discrete Event Simulation and Response Surface Methodology. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2022. [DOI: 10.1007/s13369-022-06633-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Paré G, Raymond L, Castonguay A, Grenier Ouimet A, Trudel MC. Assimilation of Medical Appointment Scheduling Systems and Their Impact on the Accessibility of Primary Care: Mixed Methods Study. JMIR Med Inform 2021; 9:e30485. [PMID: 34783670 PMCID: PMC8663712 DOI: 10.2196/30485] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Revised: 07/14/2021] [Accepted: 10/09/2021] [Indexed: 01/20/2023] Open
Abstract
BACKGROUND The COVID-19 pandemic has prompted the adoption of digital health technologies to maximize the accessibility of medical care in primary care settings. Medical appointment scheduling (MAS) systems are among the most essential technologies. Prior studies on MAS systems have taken either a user-oriented perspective, focusing on perceived outcomes such as patient satisfaction, or a technical perspective, focusing on optimizing medical scheduling algorithms. Less attention has been given to the extent to which family medicine practices have assimilated these systems into their daily operations and achieved impacts. OBJECTIVE This study aimed to fill this gap and provide answers to the following questions: (1) to what extent have primary care practices assimilated MAS systems into their daily operations? (2) what are the impacts of assimilating MAS systems on the accessibility and availability of primary care? and (3) what are the organizational and managerial factors associated with greater assimilation of MAS systems in family medicine clinics? METHODS A survey study targeting all family medicine clinics in Quebec, Canada, was conducted. The questionnaire was addressed to the individual responsible for managing medical schedules and appointments at these clinics. Following basic descriptive statistics, component-based structural equation modeling was used to empirically explore the causal paths implied in the conceptual framework. A cluster analysis was also performed to complement the causal analysis. As a final step, 6 experts in MAS systems were interviewed. Qualitative data were then coded and extracted using standard content analysis methods. RESULTS A total of 70 valid questionnaires were collected and analyzed. A large majority of the surveyed clinics had implemented MAS systems, with an average use of 1 or 2 functionalities, mainly "automated appointment confirmation and reminders" and "online appointment confirmation, modification, or cancellation by the patient." More extensive use of MAS systems appears to contribute to improved availability of medical care in these clinics, notwithstanding the effect of their application of advanced access principles. Also, greater integration of MAS systems into the clinic's electronic medical record system led to more extensive use. Our study further indicated that smaller clinics were less likely to undertake such integration and therefore showed less availability of medical care for their patients. Finally, our findings indicated that those clinics that showed a greater adoption rate and that used the provincial MAS system tended to be the highest-performing ones in terms of accessibility and availability of care. CONCLUSIONS The main contribution of this study lies in the empirical demonstration that greater integration and assimilation of MAS systems in family medicine clinics lead to greater accessibility and availability of care for their patients and the general population. Valuable insight has also been provided on how to identify the clinics that would benefit most from such digital health solutions.
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Affiliation(s)
- Guy Paré
- Department of Information Technologies, HEC Montréal, Montréal, QC, Canada
| | - Louis Raymond
- École de gestion, Université du Québec à Trois-Rivières, Trois-Rivières, QC, Canada
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Safdar KA, Emrouznejad A, Dey PK. An optimized queue management system to improve patient flow in the absence of appointment system. Int J Health Care Qual Assur 2021; ahead-of-print. [PMID: 33179461 DOI: 10.1108/ijhcqa-03-2020-0052] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
PURPOSE The aim of this research study is to develop a queue assessment model to evaluate the inflow of walk-in outpatients in a busy public hospital of an emerging economy, in the absence of appointment systems, and construct a dynamic framework dedicated towards the practical implementation of the proposed model, for continuous monitoring of the queue system. DESIGN/METHODOLOGY/APPROACH The current study utilizes data envelopment analysis (DEA) to develop a combined queuing-DEA model as applied to evaluate the wait times of patients, within different stages of the outpatients' department at the Combined Military Hospital (CMH) in Lahore, Pakistan, over a period of seven weeks (23rd April to 28th May 2014). The number of doctors/personnel and consultation time were considered as outputs, where consultation time was the non-discretionary output. The two inputs were wait time and length of queue. Additionally, VBA programming in Excel has been utilized to develop the dynamic framework for continuous queue monitoring. FINDINGS The inadequate availability of personnel was observed as the critical issue for long wait times, along with overcrowding and variable arrival pattern of walk-in patients. The DEA model displayed the "required" number of personnel, corresponding to different wait times, indicating queue build-up. ORIGINALITY/VALUE The current study develops a queue evaluation model for a busy outpatients' department in a public hospital, where "all" patients are walk-in and no appointment systems. This model provides vital information in the form of "required" number of personnel which allows the administrators to control the queue pre-emptively minimizing wait times, with optimal yet dynamic staff allocation. Additionally, the dynamic framework specifically targets practical implementation in resource-poor public hospitals of emerging economies for continuous queue monitoring.
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Diamant A. Dynamic multistage scheduling for patient-centered care plans. Health Care Manag Sci 2021; 24:827-844. [PMID: 34374889 DOI: 10.1007/s10729-021-09566-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Accepted: 04/12/2021] [Indexed: 11/24/2022]
Abstract
We investigate the scheduling practices of multistage outpatient health programs that offer care plans customized to the needs of their patients. We formulate the scheduling problem as a Markov decision process (MDP) where patients can reschedule their appointment, may fail to show up, and may become ineligible. The MDP has an exponentially large state space and thus, we introduce a linear approximation to the value function. We then formulate an approximate dynamic program (ADP) and implement a dual variable aggregation procedure. This reduces the size of the ADP while still producing dual cost estimates that can be used to identify favorable scheduling actions. We use our scheduling model to study the effectiveness of customized-care plans for a heterogeneous patient population and find that system performance is better than clinics that do not offer such plans. We also demonstrate that our scheduling approach improves clinic profitability, increases throughput, and decreases practitioner idleness as compared to a policy that mimics human schedulers and a policy derived from a deep neural network. Finally, we show that our approach is fairly robust to errors introduced when practitioners inadvertently assign patients to the wrong care plan.
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Affiliation(s)
- Adam Diamant
- Schulich School of Business, York University, 111 Ian Macdonald Boulevard, Toronto, Ontario, M3J 1P3, Canada.
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Sun Y, Raghavan UN, Vaze V, Hall CS, Doyle P, Richard SS, Wald C. Stochastic programming for outpatient scheduling with flexible inpatient exam accommodation. Health Care Manag Sci 2021; 24:460-481. [PMID: 33394213 DOI: 10.1007/s10729-020-09527-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Accepted: 10/21/2020] [Indexed: 10/22/2022]
Abstract
This study is concerned with the determination of an optimal appointment schedule in an outpatient-inpatient hospital system where the inpatient exams can be cancelled based on certain rules while the outpatient exams cannot be cancelled. Stochastic programming models were formulated and solved to tackle the stochasticity in the procedure durations and patient arrival patterns. The first model, a two-stage stochastic programming model, is formulated to optimize the slot size. The second model further optimizes the inpatient block (IPB) placement and slot size simultaneously. A computational method is developed to solve the second optimization problem. A case study is conducted using the data from Magnetic Resonance Imaging (MRI) centers of Lahey Hospital and Medical Center (LHMC). The current schedule and the schedules obtained from the optimization models are evaluated and compared using simulation based on FlexSim Healthcare. Results indicate that the overall weighted cost can be reduced by 11.6% by optimizing the slot size and can be further reduced by an additional 12.6% by optimizing slot size and IPB placement simultaneously. Three commonly used sequencing rules (IPBEG, OPBEG, and a variant of ALTER rule) were also evaluated. The results showed that when optimization tools are not available, ALTER variant which evenly distributes the IPBs across the day has the best performance. Sensitivity analysis of weights for patient waiting time, machine idle time and exam cancellations further supports the superiority of ALTER variant sequencing rules compared to the other sequencing methods. A Pareto frontier was also developed and presented between patient waiting time and machine idle time to enable medical centers with different priorities to obtain solutions that accurately reflect their respective optimal tradeoffs. An extended optimization model was also developed to incorporate the emergency patient arrivals. The optimal schedules from the extended model show only minor differences compared to those from the original model, thus proving the robustness of the scheduling solutions obtained from our optimal models against the impacts of emergency patient arrivals.
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Affiliation(s)
- Yifei Sun
- Thayer School of Engineering, Dartmouth College, College, 14 Engineering Dr, Hanover, NH, 03755, USA.
| | | | - Vikrant Vaze
- Thayer School of Engineering, Dartmouth College, College, 14 Engineering Dr, Hanover, NH, 03755, USA
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The Effects of Session Standardization and Template Optimization on Improving Access to High-Demand Pediatric Subspecialty Care. J Ambul Care Manage 2019; 43:81-88. [PMID: 31644507 PMCID: PMC7329233 DOI: 10.1097/jac.0000000000000312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
A major focus of US health care systems is ensuring timely patient access to subspecialty care. This article describes the experiences of a large children's hospital after implementation of clinic session standardization and template optimization. Outpatient specialty clinic sessions were standardized to 4-hour periods, and all unfilled complex appointment slots were made available for any appointment type within 72 hours of the clinic date. Three high-demand outpatient clinical services achieved increased aggregate potential and completed outpatient appointments over a 2-year period. These improvements were mostly due to an increase in providers and were not always coupled to shorter patient lag times.
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Ansarifar J, Tavakkoli-Moghaddam R, Akhavizadegan F, Hassanzadeh Amin S. Multi-objective integrated planning and scheduling model for operating rooms under uncertainty. Proc Inst Mech Eng H 2018; 232:930-948. [PMID: 30238862 DOI: 10.1177/0954411918794721] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This article formulates the operating rooms considering several constraints of the real world, such as decision-making styles, multiple stages for surgeries, time windows for resources, and specialty and complexity of surgery. Based on planning, surgeries are assigned to the working days. Then, the scheduling part determines the sequence of surgeries per day. Moreover, an integrated fuzzy possibilistic-stochastic mathematical programming approach is applied to consider some sources of uncertainty, simultaneously. Net revenues of operating rooms are maximized through the first objective function. Minimizing a decision-making style inconsistency among human resources and maximizing utilization of operating rooms are considered as the second and third objectives, respectively. Two popular multi-objective meta-heuristic algorithms including Non-dominated Sorting Genetic Algorithm and Multi-Objective Particle Swarm Optimization are utilized for solving the developed model. Moreover, different comparison metrics are applied to compare the two proposed meta-heuristics. Several test problems based on the data obtained from a public hospital located in Iran are used to display the performance of the model. According to the results, Non-dominated Sorting Genetic Algorithm-II outperforms the Multi-Objective Particle Swarm Optimization algorithm in most of the utilized metrics. Moreover, the results indicate that our proposed model is more effective and efficient to schedule and plan surgeries and assign resources than manual scheduling.
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Affiliation(s)
- Javad Ansarifar
- 1 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
| | - Reza Tavakkoli-Moghaddam
- 1 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran.,2 Arts et Métiers Paris Tech, Metz, France
| | - Faezeh Akhavizadegan
- 1 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
| | - Saman Hassanzadeh Amin
- 3 Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, Canada
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