Application of Operational Research Techniques in Operating Room Scheduling Problems: Literature Overview

Şeyda Gür; Tamer Eren

doi:10.1155/2018/5341394

Application of Operational Research Techniques in Operating Room Scheduling Problems: Literature Overview

Gür, Şeyda;Eren, Tamer 2018-06-13 00:00:00 Hindawi Journal of Healthcare Engineering Volume 2018, Article ID 5341394, 15 pages https://doi.org/10.1155/2018/5341394 Review Article Application of Operational Research Techniques in Operating Room Scheduling Problems: Literature Overview S¸eyda Gu¨r and Tamer Eren Department of Industrial Engineering, Faculty of Engineering, Kırıkkale University, 71450 Kırıkkale, Turkey Correspondence should be addressed to Tamer Eren; teren@kku.edu.tr Received 3 November 2017; Revised 27 March 2018; Accepted 13 May 2018; Published 13 June 2018 Academic Editor: John S. Katsanis Copyright©2018S¸eydaGu¨randTamerEren.-isisanopenaccessarticledistributedundertheCreativeCommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Increased healthcare costs are pushing hospitals to reduce costs and increase the quality of care. Operating rooms are the most important source of income and expense for hospitals. -erefore, the hospital management focuses on the eﬀectiveness of schedules and plans. -is study includes analyses of recent research on operating room scheduling and planning. Most studies in the literature, from 2000 to the present day, were evaluated according to patient characteristics, performance measures, solution techniquesusedintheresearch,theuncertaintyoftheproblem,applicabilityoftheresearch,andtheplanningstrategytobedealt within the solution. One hundred seventy studies were examined in detail, after scanning the Emerald, Science Direct, JSTOR, Springer, Taylor and Francis, and Google Scholar databases. To facilitate the identiﬁcation of these studies, they are grouped according to the diﬀerent criteria of concern and then, a detailed overview is presented. literature, researchers have developed a wide range of ap- 1. Introduction proaches to the solution process by identifying the problem. Hospitals, whose production output is service, have begun to Solutions have been oﬀered to these problems by consid- take strategic steps for the services they provide due to in- ering diﬀerent performance criteria. creased health requirements and the competitive environ- -is study aims at analyzing in detail the studies in the ment. -erefore, hospital management needs to reduce costs literature related to the operating room scheduling problem and improve ﬁnancial assets. Operating rooms earn two- in hospitals. It also shows the criteria that are based on thirds of hospital incomes and also constitute for about healthcare plans. In addition, this work provides up-to-date 40% of hospital expenses [1]. From this point of view, op- and general information about the planning and scheduling erating rooms account for the largest share in terms of both of health service systems. It explores how services systems income and expenditure. For this reason, the increase in the have taken steps against the increasingly high costs of productivity of operating rooms has an important inﬂuence medical technology and how they use their resources eﬃ- ciently. We present work that explicitly includes this in- ontheﬁnancialandultimateethicalperformanceofhospitals. As a result, operating rooms constitute the most interesting formation and contributions made to this area. Moreover, and attractive areas in hospitals [2]. With these performance with the contributions obtained from the research carried improvements, service quality and patient satisfaction are out,thisareaisreﬂectedsuchthatitcanbeeasilyunderstood increasing in direct proportion. by readers who want to do further research. In addition, -e operating room scheduling problem is treated as bringing together thoroughly the literature examined in a special branch in optimization problems. For the past detail provides a better deﬁnition of the studied subject. four decades, researchers have been cautiously focused on When the literature review was conducted, operating room planning and scheduling studies to achieve goals such as scheduling and planning keywords were searched for in the performance and productivity in the operating room. In the Emerald, Science Direct, JSTOR, Springer, Taylor and 2 Journal of Healthcare Engineering the patient’s elective (inpatient or outpatient) or nonelective Francis, and Google Scholar databases. -e results of the examination allowed 170 studies to be compiled. (urgency) status. Section 3 examines performance criteria, waiting times, postponed operations, utilization of the op- Whentheliteratureisexamined,itisseenﬁrstthatthere are limited number of literature review studies related to erating room, ﬁnancial assets, and preferences. In Section 4, operating room scheduling and planning. Cayirli et al. [3] the research methodology is based on the analytical method reviewed the literature on the problem of scheduling out- employed and the evaluation techniques applied in the so- patienttreatmentinhospitalsandexamined70studies.-ey lution process. In Section 5, the state of uncertainty is ex- aimed atpresenting themodelingapproachesin detail.-ey amined according to the stochastic or deterministic states of narrowed the broad scope of health services according to the studies examined. In Section 6, the applicability of the research,thedatausedinthestudies,andtheapplicationsare search criteria and purposes. Cardoen et al. [4] presented a detailed analysis of 115 studies by reviewing the literature examined.InSection7,theplannedstrategicstepstobetaken in the operating room are reported. Each section that is on operating room scheduling. -ey categorized their work according to these features, drawing attention to certain identiﬁed for analysis includes the detailed structure of the worksandthelistofworksdone,aswellasbrieﬂymentioning features encountered during the scheduling phase. -us, they prepared a study that makes it easy to access more the related terminology. sophisticated and frequently searched for search criteria. Guerriero and Guido [5] analyzed 130 research works re- 2. Patient Features lated to the application of operational research in surgical planningandschedulingstudiesandexaminedtheresultsof Existingstudiesonoperatingroomschedulingandplanning the problem types encountered in the solution approaches. in the literature are divided into two major groups, as Detailedinformationisgivenrelatedtothestepstakeninthe elective and nonelective patients. -e elective patient group management of the operating room and management in is able to preplan and does not involve any ambiguity and hospitals more widely, and relevant optimization studies on variability. -e nonelective patient group is also known as this topic are evaluated. emergency patients. -is is a group of patients who need Unlike other studies in the literature, all of the studies urgent intervention because they face life-threatening risks. reviewedinthisstudydatefromtheyear2000andlater.-is -is phrase is used to show the urgency and priority of the isbecauseoftheincreaseintheannualbudgetthatoperating clinical interventions. Due to the uncertainty of this group’s rooms were consuming at the end of the 1990s, which has structure, they do not form part of the planning of surgeons become the focus of both hospital administrators and re- beforehand,butinsteadariseunexpectedly.-eﬁrstpriority searchers. Besides ﬁnancial assets, various performance is given to this emergency group of patients, and then, the measures and approaches have been developed by consid- other patient groups are included in the planning process ering the problem dimension that they deal with from [3]. -e nonelective patient group constitutes a large part of diﬀerent angles. When all of the research done is taken into the surgical demand and takes priority. Scheduling and consideration, it appears that the vast majority was carried planning for this type of patient group in hospitals is out after 2000. Moreover, since the development of tech- considered a diﬃcult task. Accepting such operations in nology has also caused changes in the working structures of hospitals requires them to consider both reserving existing organizations,currentstudiesarefocusingonmorecomplex capacity and taking into account uncertainty at the same problems. For these reasons, in this study, we limited the time. -e other group of patients relates to previously research dimension to both analyzing the contributions of planned operations [6]. In the literature, the elective patient the new approaches developed and increasing accessibility. group has a greater share of scheduling and planning than However, the studies that have been investigated have been thenonelectivepatientgroup.Inthevastmajorityofstudies, examined according to diﬀerent perspectives and are pre- researchersdistinguishbetweenthetwogroupsofpatientsin sented to the reader. Considering that hospitals are one of which their work is located, although they do not fully thekeyareasofoperationresearch,wefocusthisresearchon describe the elective patient group. Even though in most of the scheduling and planning of operating rooms. In- the studies on scheduling and planning of the operating formation on the eﬃcient and eﬀective use of operating room, the ﬁnancial assets of the hospital are reduced, and rooms has been given by conveying the strategic situations revenues are increased, Nouaouri et al. [7] did research on consideredinplanningandschedulingstudies.-ediﬀerent how hospitals should use their existing resources in areas perspectives discussed in the study provide the reader with where unusual conditions such as disasters or catastrophic immediate access to the information they seek. -is study, damage could occur. In such cases, victims need to be re- which facilitates direct access to information and includes ferredtohospitalsinnearbyregionsforurgenttreatment.In up-to-date research, is signiﬁcant in diﬀerent ways, exam- the face of such urgency, hospitals have developed a reactive iningoperatingroomsfrombothmanagerialandprocedural approach that focuses on maximizing human survival by perspectives. ignoring ﬁnancial assets. -ey recommend reorganizing the -e review structure of this study includes subject operation plan if necessary. -e problem of operating room headings according to the criteria speciﬁed. -is study, scheduling involves many uncertainties due to its structure. structured according to more speciﬁc and descriptive char- Becauseofthis,moststudiesmakecertainassumptionsinthe acteristics, is divided into 7 sections. Section 2, on patient solution process, without considering these uncertainties. characteristics,includesexaminingtheliterature accordingto When these uncertainties arise, some researchers favor Journal of Healthcare Engineering 3 Table 1: Patient features. rescheduling. van Essen etal. [8] considered the uncertainties insurgicaltimesandalsoplansthatareinterruptedduetothe Elective patient group [1, 6, 8–100] arrival of emergency operations. -ey developed a decision [6, 7, 9, 13, 21, 35, 48, 52, 74, Nonelective patient group support system for this problem and determined the best- 90, 97, 99, 101–110] corrected plan for the operating room. Looking at the results, they observed that fewer operations were canceled with this with the expected ﬁnancial assets in the scheduling process. decision support system. -e studies in Table 1 divide the patient group into two. If the nonelective patient group is considered, the hospital Unlike these studies, the study by Zonderland et al. [111] should respond to this emergency as soon as possible. Erdem focuses on the semiurgent group of patients. Semiurgent et al. [9] presented an approach with a mixed integer linear patient groups, besides the other emergency groups, are programming method for rescheduling elective patients in the deﬁned as patient groups whose symptoms include such event of emergency operations. As a distinguishing feature cases as spinal fractures with or without minimal neuro- from similar studies, the cost of rejecting urgent health con- logical symptoms. -is patient group was considered with ditions, which has a critical impact on the hospital in an the Markov decision chain. Many other authors, on the emergency, is included in the model structure. -ey gained contrary, in their work, see as a source of motivation the a broad perspective through the use of a genetic algorithm degree of uncertainty resulting from the nonelective patient which allows the model to provide the most appropriate so- group and indicate that they privatize their work. At the lutionsunderdiﬃcultscenarios.-us,theyachievedasuperior sametime,asigniﬁcantnumberofstudiesdonotspecifythe solutionqualityforproblemsetscontaininghighpatientloads. patientgroupduringtheschedulingandplanningprocesses. -ere is a signiﬁcant impact on the hospital’s policy- From a general point of view, the lack of clear deﬁnition of setting capacity from the need to allow emergency surgical operating room scheduling and planning problems in terms situations while planning and scheduling elective patients. ofpatientfeaturessuggeststhatmanystudiesareinadequate. Marques et al. [10] pointed out two conﬂicting goals when In the literature examined for the two groups of patients, scheduling an elective patient group. -ey used a meta- the elective patient group is frequently preferred by re- heuristic approach with integer linear programming with the searchers for convenience in the solution process. In these aim of reducing waiting lists by rationalizing resources. studies, surgeons identify the operations and they will per- Khanna et al. [11] noted the diﬃculties experienced in the form at the beginning of the week and plan the timing for surgical scheduling of the elective patient group. -ey de- theseselectedpatientgroups.Often,inthesestudies,theyaim veloped a predictive-based methodology for planning pro- at balancing the utilization of the operating room and re- cesses in order to gain a general viewpoint. -ey created ducingwaitingtimesforpatientsonthewaitinglist.-ereare a template that represents the utilization of the operating many assumptions for planning in this patient group. -e room by conducting a retrospective analysis of estimated uncertainty of patients’ arrival times is ignored by most workload information and waiting lists. ShahabiKargar et al. studies, such as 1, 9, 10, 15–20, and 70–72. In addition, no [12] used regression analysis to estimate the duration of studies that planned simultaneously for these two groups of operation procedures for elective patient groups. Putting the patients were found [4]. Future studies can take these situ- focus on the utilization of the operating room oﬀered an ations into account by developing new algorithms to address algorithm for making more accurate predictions for the this deﬁciency in the literature. Because of the priorities with manager. Jung et al. [13] proposed an integrated approach to which emergency cases are regarded, they must be operated help to make a balanced plan with the need to react to needs on the day of admission. When these cases arrive at the arising during operating room planning. -is approach, hospital,anoperationintheelectivepatientgroupiscanceled whichconsistsofathree-stepprocess,allowsreschedulingfor when there is no appropriate operating room. After these emergency patients after elective patients have been allocated cancellations, surgeons are then working overtime. In further totheoperatingroomandresources.Intheirwork,Neyshabouri studies by researchers, with new models or algorithms, they and Berg [14] developed a formulation that considers the in- may consider extra costs due to overtime and cancellations, tensive care unit (ICU), which is one of the other departments overtime capacity constraints, and the inclusion of both related to the operating room. -ey also combined a simu- elective and nonelective patient groups without cancellations. lationmodelandaformulationtounderstandthelevelofrisk Planning can be done to reduce assumptions along with associated with the proposed surgical plans. -ey relieved the variousuncertaintiessuchasthetimeofarrivalofthepatients, obstaclesthatcouldbeexperiencedintheoperatingroomwith thedurationofthesurgicalprocedure,andconsideringallthe a robust two-step optimization method to avoid the uncer- organizational and technical constraints. When evaluating taintiesofthedurationofsurgery.Table1presentsthestudies bothelectiveandnonelective patientgroups,thewaitingtime according to patient features. ofpatients,aswellastheeﬀectontheworkloadofthestaﬀand From Table 1, it is seen that researchers focus more on hospital, should be considered. the elective group of patients. -e nonelective patient group isoverlookedmorebecauseofthediﬃcultyoftransferringit to the models created. When this situation is examined, it is 3. Performance Criteria stated by researchers that it is diﬃcult to plan the operating room as the degree of uncertainty in the problem increases. Various performance measures are used in evaluating op- However, it is easier to associate the elective patient group erating room planning and scheduling problems in the 4 Journal of Healthcare Engineering Table 2: Performance criteria. [6, 16, 17, 19, 20, 25, 30–33, 37, 46, 54, 57, 67, 74, 77, 78, 82, 83, 90, Patient Waiting time 91, 93, 97, 98, 100–102, 104, 112–119] Surgeon [77, 114, 120, 121] [1, 8, 11, 15, 17, 20, 22, 25, 26, 28, 32, 36, 37, 38, 42, 46, 48, 54, 60, Operating room 62, 65, 66, 68, 70, 73, 76, 78, 82, 84–87, 89, 92, 95, 98–100, 102, 103, 105, Utilization 106, 109, 110, 112, 114, 117, 118, 120, 122–135, 136–142] [14, 22, 24, 38, 41, 42, 48, 51, 60, 61, 65, 69, 70, 75, 78, 80, 82, 85, 110, ICU (intensive care unit) 122, 124, 143, 144] [6, 15, 20, 21, 26, 27, 29, 34, 43, 46, 53, 60, 62, 69, 73, 76, 84, 95, 96, Operating room 101, 104, 117, 120, 124, 125, 145, 146, 137] Overtime ICU [6] PACU (postanesthesia care unit) [117] Completion time [21, 65, 66, 86, 91, 143, 147, 148] Patient postponement/rejection [33, 67, 90, 94–96, 111, 118, 119, 146] [1, 21, 23, 25, 35, 36, 40, 44, 45, 52, 61–63, 69, 79, 80, 81, 87, 92, 93, 98, Financial asset 111, 112, 114, 117, 121, 126, 139, 149–156] Preferences [15, 39, 72, 78, 87, 144, 145, 157] Humanitarian goals [7, 15, 43–45, 55, 83, 84, 104, 106, 108, 152–154, 158] [7, 9, 11–13, 18, 22, 23, 27, 29, 31, 34, 35, 42, 49, 50, 51, 55, 56, 58, Others 59, 63, 64, 67, 71, 72, 74, 88, 97, 99, 103, 105, 107, 113, 116, 120, 129, 130–132, 136, 144, 148, 150, 151, 158, 159, 160–170] literature. While these performance measures customize the the planning they have done, they should evaluate the performance of the given data, whether this is actual data or structure of the problem, they also limit the size. As the number of evaluated criteria increases, the problem struc- speciﬁc probability distributions. -e degree of satisfaction of patients on long waiting lists in hospitals directly aﬀects ture becomes more diﬃcult and complicated. Individual performance measures have been distinguished, including themotivationofthehealthcareinstitutionsintermsofboth waiting time, utilization, patient postponement, cost, and so material and morale [16]. -e group on the waiting list is on. -e studies examined in Table 2 are classiﬁed according divided by researchers into two groups, namely, surgeons to these performance criteria. and patients. -e importance of the satisfaction of the Table 2 contains several studies that include other surgeonsisemphasizedasmuchasthedegreeofsatisfaction performance measures. Looking at these studies from of the patients. During the planning of the operating room, a broad perspective, it is actually seen that researchers have theyoﬀeracombinationthatallowssurgeonstoreducetheir taken diﬀerent approaches for planning of hospital orga- waiting times. -ey touch on the relationship between the durationofoperationsandthewaitingtimesofthesurgeons. nizations. In the studies reviewed, researchers often con- sidered the balanced utilization of operating rooms and the -e accuracy of the time estimates of these operations de- reduction of costs. -e complexity and interactions of all scribes the quality of operating room scheduling. thesefactorsareasourceofproblemsforhospitalmanagers, Utilization, which is shown as another performance who are looking for eﬃcient and eﬀective utilization of criterion,hasbeensetastheobjectivebymanystudiesinthe operating rooms and want to keep the patient/staﬀ satis- literature. In addition, researchers handled the utilization faction level high. Within this context, they are searching criterion separately in terms of operating room sections. A for the most appropriate operating room scheduling and large majority focus is in particular on the utilization rate of planning. Researchers should increase the criterion level operating rooms. Because of the large ﬁnancial asset rep- they consider for future studies. Although not particularly resented by operating room utilization rates, even small emphasized, there should be a focus on the balanced op- changes in the schedules have eﬀects on various overheads such as overtime pay at the hospital. Many studies in the eration of the other parts of the operating room that are integrated. -e compatibility between actual situations and literature have developed diﬀerent approaches to the ef- schedules that are made without considering these units can fectiveness of the utilization of operating rooms and have be examined. In addition, patient postponement or re- noted the impact of both overuse and underuse. From this jection, which is among the performance criteria, can result pointofview,theyemphasizethattheeﬃciencyofoperating in serious damage to the hospital both materially and roomuseshouldbekeptatthemaximumlevelinthebalance reputationally. However, this measure has not been adopted of these two cases. -ey propose a hierarchical approach as very much in the literature. Researchers should analyze the an alternative to the diﬃculty of computation [17], which relationshipbetweenthesecriteriaforfuturestudies.Sinceit relates to the utilization of operating rooms because of the is very diﬃcult to evaluate all these criteria at the same time, distributionofoperationsbalancedbetweensurgeongroups. they should make a plan that takes these criteria into One important factor that can make hospital organi- zations more eﬀective is the increase in costs in the health consideration, as the outcome of the relationship is most likely to contribute to the hospital. -en, as a result of services. -e beneﬁt of utilizing the most eﬃcient operating Journal of Healthcare Engineering 5 Table 3: Status of the operating room. [1, 6, 7, 10, 11–19, 21, 22, 24, 26–29, 31–33, 35–37, 39, 42–47, 50, 52–57, 59, 60, 62–64, 66–68, 70–74, 76–79, 82, 83, 87, 89, 90, 92–94, 99, 101–103, 105–107, Only the operating room 109, 111–116, 120–123, 125–130, 132–135, 137, 138, 142, 143, 145–147, 149–155, 159–163, 165, 167, 168] PACU [9, 49, 84, 85, 117, 131] Integrated operating room ICU [25, 30, 38, 41, 48, 49, 51, 61, 65, 69, 75, 80, 81, 124, 144] Others [20, 23, 34, 40, 58, 86, 88, 104, 108, 110, 136, 148, 157, 158, 164, 166, 169] room capacity cannot be ignored. Planning processes in- et al. [158] created a formulation that relieves both surgical volvingbasicobjectivessuchastheeﬀectivenessofresources and nonsurgical constraints. In planning that considers the surgeon’s preferences, the eﬀects of these preferences are in hospital organizations are dimensioned as strategic, op- erational, and tactical. van Oostrum et al. [22] developed examined. Xiang et al. [145] considered surgeons’ experi- ences of scheduling problems in their work. -ey developed a model that meets the requirements for utilization of the operating room by addressing planning at the tactical level a balanced planning and scheduling approach based on the with the solution approach they oﬀer. Augusto et al. [65] inclusion of certain surgeons in some operation groups. focusedtheirworkonthedailyplanningofoperatingrooms, -ey analyzed the eﬀectiveness of their algorithm with this where various constraints were reﬂected in the model they preference option for the surgeons. set up. -ey helped management by improving the utili- zation of operating rooms. Tan et al. [60] reached goals in 4. Techniques Used in Solution Processes their solution approach to reduce variability in bed occu- pancy rates, as well as in the operating room eﬀectiveness, Operating room planning and scheduling processes aﬀect which varies with over- and underuse. the entire hospital organization. -ese processes are in- Another criterion that is as important as the utilization creasingly complicated by the inclusion of areas such as the of the operating room is the utilization of intensive care intensive care unit (ICU), or the PACU, which are other units. -e intensive care unit capacity, measured by the parts of the operating room. But it is considered beneﬁcial number of beds on these units, is a source of concern for fromastrategicpointofviewtoimprovetheoverallprocess. hospitals. Kim et al. [75] focused on improving the per- Given the work involved in these facilities, the researchers’ formance of intensive care units eﬀectively and eﬃciently to resultshighlighttheextenttowhichtheperformancequality make a positive contribution to healthcare in their model. increases. At the same time, when the uncertainties of these -is criterion, which is included in the performance facilities are not overlooked, it seems that the long-term criteria as patients postponed, indicates the quality of the eﬀect for the hospital is in the positive direction. Table 3 service given to the patient. Addis et al. [67] guaranteed the contains the structure of studies in the literature in terms of quality of service provided at a certain level of performance. solutiontechniques.Whilemoststudiesaddresstheoperating -ey developed a punishment function to prevent deferrals room on its own, other studies are available that incorporate and delays due to postponements. Likewise, they presented simultaneous solution approaches integrated with these fa- an optimization approach with a block scheduling strategy cilities.Inadditiontothese,recentlyreportedoperatingroom [33], which provides a penalty function to avoid as many schedulingstudiesarealsorelatedtohealthservices,although patient postponements as possible. In order to assess the they are seen to be integrated with diﬀerent ﬁelds. models in terms of solution quality, the number of patients Looking at Table 3, it is observed that improvements operated on, the waiting times, and the delays experienced have been made in the planning and scheduling processes were examined. through the integrated studies carried out in recent periods, One of the most common goals in operating room although a great majority of studies have shifted to practice schedulingproblemsistheexpectedperformanceintermsof where the operating room is considered alone. -e analysis ﬁnancial assets. In general, an operating room planning and of the consequences of these integrations is also an im- scheduling problem is indirectly aﬀected by the cost crite- portant gateway to the work to be undertaken in the coming rion, even when other goals are considered. -at is why, in years. In the real world, the operating room is integrated fact, this criterion is among the cornerstones of healthcare with rest of the hospital such as the PACU and ICU. -is units. Meskens et al. [152] developed a model that considers makes the planning process very diﬃcult. Often there are constraints on material resources encountered in real life. disruptions from planning that is not done correctly or that With an eﬃcient algorithm, they created a schedule that does not balance these integrated parts correctly. -ese allows for the eﬃcient utilization of the operating room and disruptions have negative consequences, such as post- the surgeon. Baesler et al. [143] focused on a scheduling ponement or rejection of patients, an increase in surgeons’ approach aimed at maximizing hospital revenues by waiting time, or prolonged preparation and cleaning time. addressing the plans in the organizational structure at -is gives the hospital both extra costs and patient/staﬀ strategic and tactical levels. dissatisfaction. Researchers can conduct studies that ana- Another performance criterion is the preference crite- lyze the impact of these negative outcomes on the pa- rionwhichisadoptedasanaimbyresearchersintheprocess tient, as opposed to planning work in general. -e overall of scheduling and planning the operating room. Van Huele performance of the operating room can be evaluated. Later, 6 Journal of Healthcare Engineering Table 4: Solution techniques. Mathematical Programming [17, 33, 34, 47, 60, 90, 92, 125, 136, 142, 164] Integer programming [8, 10, 23, 25, 28, 32, 41, 49, 52–54, 95, 110, 113, 114, 122, 140, 149, 156, 159] [1, 9, 13, 21, 24, 27, 30, 36, 40, 44, 56, 58, 62, 66, 68, 70, 71, 78, 84, 85, 86, 93, 100, 102, 104, 126, Mixed integer programming 128, 134, 138, 144, 152, 157, 162] Goal programming [15, 16, 42] Dynamic programming [23, 149, 160] Constraint programming [87, 137, 152, 166] [6, 14, 20, 21, 30, 31, 35, 38, 49, 51, 55, 58, 61, 73, 76, 77, 83, 91, 95, 96, 97, 102, 105, 106, 116, 118, Simulation 119, 131, 133, 143, 145, 153, 158, 161, 163, 167] Branch bounding algorithm [61, 121] Lagrangian relaxation approach [45, 65, 148] [7, 13, 18, 26, 37, 54, 57, 59, 73, 85, 103, 109, 112, 113, 115, 123, 128, 147, 162, 118, 94, 156, Heuristic algorithm 140, 98, 141] Genetic algorithm [9, 19, 62, 82, 89, 124, 131, 135, 154] Ant colony algorithm [29, 46, 145, 164] Annealing simulation [24, 51, 77, 143] [6, 11, 12, 22, 38, 39, 43, 46, 48, 50, 63, 64, 67, 69, 72, 74, 79, 80, 81, 88, 92, 99, 101, 107, 108, 111, Other methods 117, 120, 127, 129, 130, 132, 139, 146, 150, 151, 155, 161, 165, 168, 169, 170] as a result of this study, the most important factor aﬀecting helpreducethediﬃcultyofcalculationwhenthereareslight hospitalsinthenegativedirectioncanbeinvestigated.Ifthis changes in the structure of the problems. In the use of solution methodologies where performance measures are factor is most relevant to a certain department, plans can be madetoimprovethatdepartment.Focusingonthedetailsof eﬀective, many researchers are discussing how to approach uncertainty as the amount of uncertainty increases and the the studies, it is seen that some of the criteria such as uti- lization of the operating room, reduction of patient waiting resulting eﬀectiveness of the established model structure. lists, cost, and similar criteria are taken together. Problems From the work done, it is seen that researchers go to the thatareintegratedwithdiﬀerentunitsfocusmoreonspeciﬁc solution process by using the advantages of each method. In functions. fact, these solution methods require various assumptions to -emainobjectivewastoimprovetheutilizationratesof be made in the problem. Every algorithm or model that has the units that they integrate within these special functions. been developed gives very eﬀective results day-by-day in the -e studies under the other heading in Table 3 are mostly process of operating room scheduling and planning. studies where nurse units are considered together. -e However eﬀective they are, these results are not enough and must be continuously improved, and the solution area ex- special situations of the nurse units and their relations with the operating room are reﬂected. Martinelly et al. [34] de- panded. Researchers can leverage the power of constraint veloped a model proposal that shows the relationship be- programming to create mathematical or logical represen- tween the operating room and nurse management, and the tations of existing constraints in the problem. With con- numberofoperatingrooms,numberofnurses,andovertime straint programming, many solution areas can be found in concepts. When the main purpose of the study is examined, the deﬁnition cluster and the most suitable one can be se- an integration that represents two diﬀerent management lected within the solution area. -is allows the evaluation of areas is seen with a ﬂexible model understanding. -ey diﬀerent values in the solution process. Moreover, in order established an operating room scheduling model that both toobtainsatisfactoryresultsinashorttime,heuristicmethods plans for nurses and at the same time considers resource can be used, and a solution approach can be developed for constraints. -e model incorporates nurse restrictions that queuing models to nonelective patient groups. Belie¨n et al. [24]optimizedthebedoccupancyrateswiththeoptimization make the process even more diﬃcult for already complex operating room processes. However, the results show that systemtheyhavesetup,allowingthesamespecialistsurgeons there is no relation between the number of operating rooms toconcentrateonthesame operatingroom.Itis seenthatthe andthe number of nurses. It is stated that thereis aninverse results of the calculations produced successful plans based on relationship between the number of nurses and the amount these two objectives. Figure 1 expresses the location of the of overtime work. -is,in fact, means that the validity of the solution techniques in the literature visually. nurses in theintegration of both management areas is small. From Figure 1, it can be seen that more simulation and In the operating room scheduling and planning literature, mathematical models are used in the solution process of the there are methodologies that use a speciﬁc analysis and problem studied. -ere is also diversity under the headings mentioned as other methods in the solution process. Re- solution technique. Table 4 lists these methodologies and what they focus on. searchers have brought diﬀerent perspectives to the solu- tions of problems through diﬀerent techniques. It is diﬃcult Table 4 presents a perspective on the analysis of prob- lems. It seems that there are diﬀerent suggestions that can to produce alternative solutions to the challenge of the Journal of Healthcare Engineering 7 Figure 1: Solution techniques. operating room scheduling problem and to obtain high sudden occurrences in planning have a negative eﬀect for quality results from these solutions. -ey have helped to bothsurgeonsandpatients.Atthesametime,uncertainties improve the functioning of the operating room [87], which in the duration of surgical operations are critical for op- successfully reﬂects the expression power of the solution erating room planning. Operations that exceed the pre- approachtheyhaveproposedtosolvethesediﬃculties.-ey dicted duration aﬀect not only the start time of the next arefocusedonthedailyplanningoftheoperatingroomwith operation in the program but also all the day’s other op- the constraint programming method. In addition, human erations. -ese late start-ups aﬀect the shift times in the and material constraints that reﬂect the surgeon’s prefer- planning, right up to the last working hour of the day, and ences are included in the model. When the results are ex- resultin staﬀovertimecosts. Table5 lists thestochastic and amined, it appears that the solution method they use is an deterministic approaches. ideal tool for competing goals. Meskens [152] compared When detailed analyses of the studies are carried out, it their constraint programming method with a mixed integer canbeseenindetailinTable5thattheuncertaintiesintimes programming model, another optimization tool, to examine and arrival times aﬀect waiting lists and the utilization of their eﬀectiveness in real-life problems. -ey considered resources. In addition,the uncertainties in the margin of the various constraints in their work and presented the ad- contribution to the hospital structure, which will keep the vantages and disadvantages of both models. expected high ﬁnancial cost, also indicate that operating When we look at the work done recently, we prefer rooms aﬀect the utilization capacity. However, attention should also be paid to the diﬃculties that may arise from integrated methods rather than using a single solution technique,duetothediﬀerentexternalfactorsthatmakethe failure of the hospital’s medical equipment. In the literature, problem structure more diﬃcult. Researchers have aimed at future studies should give more importance to this source of increasing the quality of the solution by using integrated uncertainty, so that improvements in the quality of the methods.Furthermore,theanalysisofthescenarioswithtest solution can be realized by researchers, because this is an dataisperformedwiththepresentedsimulationapproaches. important problem that needs attention when it aﬀects the If it is emphasized that these analyses support the imple- starting times of operations. By increasing the number of mentation results, this can be interpreted as indicating that studiestoreducethenegativeeﬀectsofsuchuncertaintiesin the approaches are successful. thecomingyears,researcherswillbeabletomakesigniﬁcant contributions to both real-life practices and the literature. Due to the diﬃculties in the solution process of these un- 5. Uncertainty Status certaintiesintermsoftheirstructure,itseemsthatstochastic studies are not very useful. Also, in the literature, the ca- One of the biggest problems encountered in the planning pacity requirements in emergency situations, the arrival andschedulingofoperatingroomsisthatthereistoomuch times of these emergencies, and the duration of operations ambiguity due to the structure of these problems. Many are usually neglected. -ese neglected situations should be researchers have considered various assumptions for the addressed through stochastic studies by researchers. productionofcorrectprogramsandforthedevelopmentof contributions to hospital organizations. When the litera- ture is examined, it focuses on the uncertainties in patient 6. Applicability of the Study arrivalsandoperationtimes.Whenwelookattheliterature on stochastic studies, unpredictable arrivals, especially of When the literature is examined, a comprehensive test is nonelective patient groups, have various eﬀects. -ese appliedtoanalyzetheperformanceofthedevelopedmodels. Mathematical programming Integer programming Mixed integer programming Goal programming Dynamic programming Constraint programming Simulation Branch bounding algorithm Lagrangian relaxation approach Heuristic algorithm Genetic algorithm Ant colony algorithm Annealing simulation Other methods 8 Journal of Healthcare Engineering Table 5: Uncertainty status. [1, 9, 10, 13, 15, 16, 17, 18, 19, 20, 23, 25, 26, 28, 29, 31, 32, 34, 36, 37, 41, 42, 44, 47, 49, 50, 53–60, 62, 64–72, Deterministic 78, 79, 82, 83, 85–89, 100, 102, 112, 115, 124, 125, 127, 129, 137, 144, 145, 147, 150, 152, 157, 159, 170] [6, 13, 14, 20, 21, 22, 24, 27, 33, 35, 38, 40, 48, 51, 52, 61, 63, 73, 76, 77, 80, 84, 90, 92, 95, 104–110, 114, 117, Stochastic 126, 130, 131, 138, 143, 155, 160, 162] Table 6: Application of studies. Not tested [35, 50, 57, 70, 75, 87, 144, 152] [1, 6, 7, 9, 14, 19, 21, 23, 25, 26, 28, 29, 32, 34, 36, 39, 41, 44–49, 51, 52, 58, 61, 63, 65, 67, 71, 72, -eoretical data 74, 79, 80, 83, 85, 86, 91, 94, 103, 105, 107, 109, 112, 114, 116, 117, 120, 127, 129, 131, 133, 135, 136, 139, 145, 147, 153, 157, 158, 160, 161, 166] Test data [10, 11–13, 15–18, 20, 22, 24, 27, 29–31, 33, 37, 38, 40, 42, 43, 53–56, 59, 60, 62, 64, 66, 68, 69, Real data 73, 76–78, 82, 84, 88, 93, 95, 97, 100, 102, 104, 106, 110, 113, 115, 121–126, 128, 130, 132, 134, 138, 141–143, 146, 149, 150, 151, 154, 156, 159, 162–165, 168, 170] Fortheseexperimentalteststhatdemonstratetowhatextent increase hospital eﬃciency with the performance values goals can be reached, a signiﬁcant amount of data entry is obtained as a result of these plans. In addition, researchers required. Looking at Table 6, in the studies listed, it is seen cancommentonwhichpointsintheschedulestheytestwith that performance analysis of most of the studies is done actualdataneedtobedevelopedorwhichpointstheyshould using theoretical data. -e data used in these studies are concentrateon.Withtheactualdataused,theycanshowthe robustness of the model they have built and the extent to divided into two groups; the actual data/set of theoretical data is obtained either at random or with a certain proba- which it can be put into real practice. Since the studies bility distribution. However, even if data sets from real-life prepared under various assumptions neglect many sources, problems are used in studies, most of the developed ap- it is diﬃcult for managers to perceive the positive potential proachesarenotreﬂectedintherealapplication.Inthiscase, ofrealapplications.Onthecontrary,ifitisjudgedtobevery researchersshouldconcentrateonthereasonsforconﬂicting diﬃcult or even impossible to take all the assumptions into ideas between the application phase and the model they are consideration, hospital organizations need to take strategic developing. stepstosupportsuchwork,becauseinrealitynohospitalcan Table 6 gives an analysis of studies of the use of real make all these assumptions. solution data and the diﬀerent solution techniques in Table 4. -e results obtained from the experimental tests on the 7. Planning Strategies developed models show that the operating rooms need to be more balanced according to the current utilization condi- In hospitals that provide healthcare, managers want to tionsandhelptocreateproposalsfor ﬂexibleuseatlesscost. maximize the yield from the utilization of the operating In hospitals, which are regarded as service units, the plan- rooms through a variety of strategic steps. -is has led to ning that is prepared for the operating room may include diﬀerent strategic plans. Hospital administrators have severalpossiblemishaps.-erefore,itisseenasbeneﬁcialby planned strategic steps in operating rooms, including open researchers to perform short-term real applications of the planning strategy, block planning strategy, and modiﬁed studies. However, the point of view of hospital adminis- block planning strategy. -e studies in Table 7 are listed trators, in hospital organizations that already have a diﬃcult according to these strategic steps. In Figure 2, the distri- and complicated structure, is that the sudden application of butions of the studies are shown visually. these studies may complicate problem. Banditori et al. [30] When we look at Table 7 and Figure 2 together, it is seen focused on reducing the number of patients on the waiting that the open planning strategy is most common. -e block list by considering a plan for each day of the month. At the planning strategy is divided into two parts: block planning sametime,theaimwastoavoidcostincreasescausedbythis with Master Surgical Scheduling (MSS) and block planning waitingandthenegativeeﬀectsthatmightbeexperiencedon strategy only. It appears that this distinction has emerged satisfaction levels. Accordingly, a set of solutions was pro- from the diﬀerent situations in which researchers handle duced. As with every study, these studies have limits. -e their work from a managerial point of view. When the authors who conducted experimental simulation tests using sections under the block planning strategy are examined the real-life data mention the diﬃculties that models can together,itisseeninmanystudiesthatresearchersthinkthat experience in the planning process due to the 1-month it is time and space that should be reserved for surgical planning horizon. specialties. Researchers commonly choose one of two parts Researchers should use more of the experimental sets reserved for planning strategies in the scheduling process. obtained from real data to assess the performance of the However, unlike most studies, Liu et al. [118] addressed the planning and schedules. Planning and schedules need to be open planning and block planning strategy together. -ey applied in real life to allow the healthiest performance also developed a metaheuristic algorithm to solve this measurement. Hospital administrators who allow this can problem. -e open planning strategy allows surgeons to be Journal of Healthcare Engineering 9 Table 7: Planning strategies. [1, 6, 9, 10, 12, 13, 16–18, 21, 23, 26, 28, 29, 32, 34, 35, 37, 38, 43, 44, 46, 48, 52, 54, 55, 58, 59, 62, 63, 65, Open planning strategy 66, 68, 69, 73–77, 80, 81, 83–87, 101, 104, 106–110, 112, 118, 124–127, 130, 139, 147, 149, 152, 157, 161] [15, 19, 20, 22, 24, 25, 27, 30, 31, 33, 36, 40, 41, 49–51, 53, 56, 60, 61, 67, 78, 88, 89, 95, 102, 103, 105, 114, Block planning strategy 116, 118, 129, 145, 150, 151, 159, 170] approachestohelpuserswithstrategicplanning.Addisetal. [33] aimed at reducing waiting times for patients by as- Open planning strategy suming a block planning strategy. In the study, particular attention was paid to ensure that the operating room ca- Block planning strategy pacity is balanced in terms of surgical expertise. In this article, which is also integrated with the master surgical schedules,thewaitingpatientsetisallocatedtotheoperating Block planning strategy (MSS) rooms. 0 10203040506070 While studies of open planning strategies were popular during the 1960s, today diﬀerent strategies for increasing Figure 2: Planning strategies. productivity continue to be developed. But nowadays, too, there are many studies that use open planning strategy in ordertoavoidthediﬃcultyandcomplexityofcalculation.In assigned to appropriate operating rooms with appropriate [26], no speciﬁc time is reserved for any particular surgeon time. When an empty schedule is considered, it is assumed with the open planning strategy. As is the case in most thatpatientswillbereceivedonaﬁrst-come-ﬁrst-servebasis, studies, the main point of this study was to increase the taking into consideration their arrival times. For schedules eﬃciency of the utilization of the operating room. created in the block planning strategy, the same day of the week, the same time zone, and the same operating room are stored in the service of a particular surgeon or specialist. 8. Conclusion With this strategy, it is necessary to adjust the appropriate operating room at the hours when the operating rooms are -is study examined 170 planning and scheduling studies open. related to operating rooms scanned in the databases of the -e modiﬁed block planning strategy is a process of Emerald, Science Direct, JSTOR, Springer, Taylor and reconﬁguring operations that are not in the previously Francis, and Google Scholar. -e contributions of these constructed blocks for unused time. -is is described as studies tothe literatureandthereader were assessedandthe ﬂexible planning because it requires the reorganization of pointstheyemphasizedwereidentiﬁed.Whileevaluatingthe the initial construction schedules. In future studies, using goals that the studies want to accomplish, the technical block planning strategy, the preferences of surgeons can be structure was examined. For the analysis of the studies, given more importance and the eﬃciency of these plans can a systematic structure was established in this study so as to be increased. Also, with block scheduling, certain times make it easy to focus on what readers want speciﬁcally to within the surgeons’ working hours can be left empty. -us, investigate. In addition, by comparing the studies, it can be it is both separate from the surgeons’ rest time and makes it easily seenwhich pointof study thework hastaken forward. easiertoallocateasuitableoperatingroomintheeventofan Clear lists were created with the tables presented to improve emergency. -is can reduce the delays that can be experi- the accessibility of the ﬁndings. enced during the preparation and cleaning periods between It is seen that optimization methods are generally pre- operations as well as the patient waiting time that is caused ferred in the studies about the planning and scheduling of by these conditions. theoperatingroom,withtheaimofprovidingthebestresult When these studies are examined, it is seen that they withinthesolutionprocess.Atthesametime,eﬀortsarealso allow better use of the surgeon’s time, and at the same time, made to avoid complicating the model due to the various prevent delays that may occur due to extra preparation time constraints encountered in real life, and the solution area is for operations requiring diﬀerent surgical expertise in the created within these frameworks to improve the process. operatingroom.-is hasmadeblock planningstrategiesthe Researchers have emphasized the need to balance the re- focus of researchers. -e block planning strategy, which is sources available and improve the eﬀectiveness of staﬀ in associated with the main surgical scheduling problem, de- order to optimize the utilization of operating rooms, which ﬁned as the allocation of operational resources to surgical hospitaladministratorsseeasthemostcriticalpart.Optimal groups,isbeingconsideredinmanystudies.Intheliterature utilizationofoperatingroomsispossiblewhenassessedwith examined, there are 16 main surgical scheduling studies diﬀerentperformancemeasures.Eventhoughindirectly,itis [20, 22, 24, 25, 27, 30, 31, 40, 49, 53, 56, 60, 61, 88, 150, 151]. diﬃcult to reﬂect these interrelated criteria together, so the Mannino et al. [27] considered the problem of estimating solutions are proposed under many assumptions. demand levels in creating the main surgical schedules and Another problem that complicates the solution process then aimed at stabilizing patient tail lengths and reducing of the problems is that there is too much uncertainty. In the the maximum overtime. In their work, they introduced new studies, patients were separated into two groups, ignoring 10 Journal of Healthcare Engineering the uncertainty of their arrival times. In studies dealing with Conflicts of Interest a nonelective group of patients, it was noticed that other -e authors declare that there are no conﬂicts of interest operations were postponed or canceled when an unplanned regarding the publication of this paper. case occurred in the created schedules. Delayed operations cause both surgeons and other staﬀ to work overtime and Acknowledgments reduce the level of satisfaction by increasing patient com- plaints. 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Publisher: Hindawi Publishing Corporation
Copyright: Copyright © 2018 Şeyda Gür and Tamer Eren. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ISSN: 2040-2295
eISSN: 2040-2309
DOI: 10.1155/2018/5341394
Publisher site: See Article on Publisher Site

Abstract

Hindawi Journal of Healthcare Engineering Volume 2018, Article ID 5341394, 15 pages https://doi.org/10.1155/2018/5341394 Review Article Application of Operational Research Techniques in Operating Room Scheduling Problems: Literature Overview S¸eyda Gu¨r and Tamer Eren Department of Industrial Engineering, Faculty of Engineering, Kırıkkale University, 71450 Kırıkkale, Turkey Correspondence should be addressed to Tamer Eren; teren@kku.edu.tr Received 3 November 2017; Revised 27 March 2018; Accepted 13 May 2018; Published 13 June 2018 Academic Editor: John S. Katsanis Copyright©2018S¸eydaGu¨randTamerEren.-isisanopenaccessarticledistributedundertheCreativeCommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Increased healthcare costs are pushing hospitals to reduce costs and increase the quality of care. Operating rooms are the most important source of income and expense for hospitals. -erefore, the hospital management focuses on the eﬀectiveness of schedules and plans. -is study includes analyses of recent research on operating room scheduling and planning. Most studies in the literature, from 2000 to the present day, were evaluated according to patient characteristics, performance measures, solution techniquesusedintheresearch,theuncertaintyoftheproblem,applicabilityoftheresearch,andtheplanningstrategytobedealt within the solution. One hundred seventy studies were examined in detail, after scanning the Emerald, Science Direct, JSTOR, Springer, Taylor and Francis, and Google Scholar databases. To facilitate the identiﬁcation of these studies, they are grouped according to the diﬀerent criteria of concern and then, a detailed overview is presented. literature, researchers have developed a wide range of ap- 1. Introduction proaches to the solution process by identifying the problem. Hospitals, whose production output is service, have begun to Solutions have been oﬀered to these problems by consid- take strategic steps for the services they provide due to in- ering diﬀerent performance criteria. creased health requirements and the competitive environ- -is study aims at analyzing in detail the studies in the ment. -erefore, hospital management needs to reduce costs literature related to the operating room scheduling problem and improve ﬁnancial assets. Operating rooms earn two- in hospitals. It also shows the criteria that are based on thirds of hospital incomes and also constitute for about healthcare plans. In addition, this work provides up-to-date 40% of hospital expenses [1]. From this point of view, op- and general information about the planning and scheduling erating rooms account for the largest share in terms of both of health service systems. It explores how services systems income and expenditure. For this reason, the increase in the have taken steps against the increasingly high costs of productivity of operating rooms has an important inﬂuence medical technology and how they use their resources eﬃ- ciently. We present work that explicitly includes this in- ontheﬁnancialandultimateethicalperformanceofhospitals. As a result, operating rooms constitute the most interesting formation and contributions made to this area. Moreover, and attractive areas in hospitals [2]. With these performance with the contributions obtained from the research carried improvements, service quality and patient satisfaction are out,thisareaisreﬂectedsuchthatitcanbeeasilyunderstood increasing in direct proportion. by readers who want to do further research. In addition, -e operating room scheduling problem is treated as bringing together thoroughly the literature examined in a special branch in optimization problems. For the past detail provides a better deﬁnition of the studied subject. four decades, researchers have been cautiously focused on When the literature review was conducted, operating room planning and scheduling studies to achieve goals such as scheduling and planning keywords were searched for in the performance and productivity in the operating room. In the Emerald, Science Direct, JSTOR, Springer, Taylor and 2 Journal of Healthcare Engineering the patient’s elective (inpatient or outpatient) or nonelective Francis, and Google Scholar databases. -e results of the examination allowed 170 studies to be compiled. (urgency) status. Section 3 examines performance criteria, waiting times, postponed operations, utilization of the op- Whentheliteratureisexamined,itisseenﬁrstthatthere are limited number of literature review studies related to erating room, ﬁnancial assets, and preferences. In Section 4, operating room scheduling and planning. Cayirli et al. [3] the research methodology is based on the analytical method reviewed the literature on the problem of scheduling out- employed and the evaluation techniques applied in the so- patienttreatmentinhospitalsandexamined70studies.-ey lution process. In Section 5, the state of uncertainty is ex- aimed atpresenting themodelingapproachesin detail.-ey amined according to the stochastic or deterministic states of narrowed the broad scope of health services according to the studies examined. In Section 6, the applicability of the research,thedatausedinthestudies,andtheapplicationsare search criteria and purposes. Cardoen et al. [4] presented a detailed analysis of 115 studies by reviewing the literature examined.InSection7,theplannedstrategicstepstobetaken in the operating room are reported. Each section that is on operating room scheduling. -ey categorized their work according to these features, drawing attention to certain identiﬁed for analysis includes the detailed structure of the worksandthelistofworksdone,aswellasbrieﬂymentioning features encountered during the scheduling phase. -us, they prepared a study that makes it easy to access more the related terminology. sophisticated and frequently searched for search criteria. Guerriero and Guido [5] analyzed 130 research works re- 2. Patient Features lated to the application of operational research in surgical planningandschedulingstudiesandexaminedtheresultsof Existingstudiesonoperatingroomschedulingandplanning the problem types encountered in the solution approaches. in the literature are divided into two major groups, as Detailedinformationisgivenrelatedtothestepstakeninthe elective and nonelective patients. -e elective patient group management of the operating room and management in is able to preplan and does not involve any ambiguity and hospitals more widely, and relevant optimization studies on variability. -e nonelective patient group is also known as this topic are evaluated. emergency patients. -is is a group of patients who need Unlike other studies in the literature, all of the studies urgent intervention because they face life-threatening risks. reviewedinthisstudydatefromtheyear2000andlater.-is -is phrase is used to show the urgency and priority of the isbecauseoftheincreaseintheannualbudgetthatoperating clinical interventions. Due to the uncertainty of this group’s rooms were consuming at the end of the 1990s, which has structure, they do not form part of the planning of surgeons become the focus of both hospital administrators and re- beforehand,butinsteadariseunexpectedly.-eﬁrstpriority searchers. Besides ﬁnancial assets, various performance is given to this emergency group of patients, and then, the measures and approaches have been developed by consid- other patient groups are included in the planning process ering the problem dimension that they deal with from [3]. -e nonelective patient group constitutes a large part of diﬀerent angles. When all of the research done is taken into the surgical demand and takes priority. Scheduling and consideration, it appears that the vast majority was carried planning for this type of patient group in hospitals is out after 2000. Moreover, since the development of tech- considered a diﬃcult task. Accepting such operations in nology has also caused changes in the working structures of hospitals requires them to consider both reserving existing organizations,currentstudiesarefocusingonmorecomplex capacity and taking into account uncertainty at the same problems. For these reasons, in this study, we limited the time. -e other group of patients relates to previously research dimension to both analyzing the contributions of planned operations [6]. In the literature, the elective patient the new approaches developed and increasing accessibility. group has a greater share of scheduling and planning than However, the studies that have been investigated have been thenonelectivepatientgroup.Inthevastmajorityofstudies, examined according to diﬀerent perspectives and are pre- researchersdistinguishbetweenthetwogroupsofpatientsin sented to the reader. Considering that hospitals are one of which their work is located, although they do not fully thekeyareasofoperationresearch,wefocusthisresearchon describe the elective patient group. Even though in most of the scheduling and planning of operating rooms. In- the studies on scheduling and planning of the operating formation on the eﬃcient and eﬀective use of operating room, the ﬁnancial assets of the hospital are reduced, and rooms has been given by conveying the strategic situations revenues are increased, Nouaouri et al. [7] did research on consideredinplanningandschedulingstudies.-ediﬀerent how hospitals should use their existing resources in areas perspectives discussed in the study provide the reader with where unusual conditions such as disasters or catastrophic immediate access to the information they seek. -is study, damage could occur. In such cases, victims need to be re- which facilitates direct access to information and includes ferredtohospitalsinnearbyregionsforurgenttreatment.In up-to-date research, is signiﬁcant in diﬀerent ways, exam- the face of such urgency, hospitals have developed a reactive iningoperatingroomsfrombothmanagerialandprocedural approach that focuses on maximizing human survival by perspectives. ignoring ﬁnancial assets. -ey recommend reorganizing the -e review structure of this study includes subject operation plan if necessary. -e problem of operating room headings according to the criteria speciﬁed. -is study, scheduling involves many uncertainties due to its structure. structured according to more speciﬁc and descriptive char- Becauseofthis,moststudiesmakecertainassumptionsinthe acteristics, is divided into 7 sections. Section 2, on patient solution process, without considering these uncertainties. characteristics,includesexaminingtheliterature accordingto When these uncertainties arise, some researchers favor Journal of Healthcare Engineering 3 Table 1: Patient features. rescheduling. van Essen etal. [8] considered the uncertainties insurgicaltimesandalsoplansthatareinterruptedduetothe Elective patient group [1, 6, 8–100] arrival of emergency operations. -ey developed a decision [6, 7, 9, 13, 21, 35, 48, 52, 74, Nonelective patient group support system for this problem and determined the best- 90, 97, 99, 101–110] corrected plan for the operating room. Looking at the results, they observed that fewer operations were canceled with this with the expected ﬁnancial assets in the scheduling process. decision support system. -e studies in Table 1 divide the patient group into two. If the nonelective patient group is considered, the hospital Unlike these studies, the study by Zonderland et al. [111] should respond to this emergency as soon as possible. Erdem focuses on the semiurgent group of patients. Semiurgent et al. [9] presented an approach with a mixed integer linear patient groups, besides the other emergency groups, are programming method for rescheduling elective patients in the deﬁned as patient groups whose symptoms include such event of emergency operations. As a distinguishing feature cases as spinal fractures with or without minimal neuro- from similar studies, the cost of rejecting urgent health con- logical symptoms. -is patient group was considered with ditions, which has a critical impact on the hospital in an the Markov decision chain. Many other authors, on the emergency, is included in the model structure. -ey gained contrary, in their work, see as a source of motivation the a broad perspective through the use of a genetic algorithm degree of uncertainty resulting from the nonelective patient which allows the model to provide the most appropriate so- group and indicate that they privatize their work. At the lutionsunderdiﬃcultscenarios.-us,theyachievedasuperior sametime,asigniﬁcantnumberofstudiesdonotspecifythe solutionqualityforproblemsetscontaininghighpatientloads. patientgroupduringtheschedulingandplanningprocesses. -ere is a signiﬁcant impact on the hospital’s policy- From a general point of view, the lack of clear deﬁnition of setting capacity from the need to allow emergency surgical operating room scheduling and planning problems in terms situations while planning and scheduling elective patients. ofpatientfeaturessuggeststhatmanystudiesareinadequate. Marques et al. [10] pointed out two conﬂicting goals when In the literature examined for the two groups of patients, scheduling an elective patient group. -ey used a meta- the elective patient group is frequently preferred by re- heuristic approach with integer linear programming with the searchers for convenience in the solution process. In these aim of reducing waiting lists by rationalizing resources. studies, surgeons identify the operations and they will per- Khanna et al. [11] noted the diﬃculties experienced in the form at the beginning of the week and plan the timing for surgical scheduling of the elective patient group. -ey de- theseselectedpatientgroups.Often,inthesestudies,theyaim veloped a predictive-based methodology for planning pro- at balancing the utilization of the operating room and re- cesses in order to gain a general viewpoint. -ey created ducingwaitingtimesforpatientsonthewaitinglist.-ereare a template that represents the utilization of the operating many assumptions for planning in this patient group. -e room by conducting a retrospective analysis of estimated uncertainty of patients’ arrival times is ignored by most workload information and waiting lists. ShahabiKargar et al. studies, such as 1, 9, 10, 15–20, and 70–72. In addition, no [12] used regression analysis to estimate the duration of studies that planned simultaneously for these two groups of operation procedures for elective patient groups. Putting the patients were found [4]. Future studies can take these situ- focus on the utilization of the operating room oﬀered an ations into account by developing new algorithms to address algorithm for making more accurate predictions for the this deﬁciency in the literature. Because of the priorities with manager. Jung et al. [13] proposed an integrated approach to which emergency cases are regarded, they must be operated help to make a balanced plan with the need to react to needs on the day of admission. When these cases arrive at the arising during operating room planning. -is approach, hospital,anoperationintheelectivepatientgroupiscanceled whichconsistsofathree-stepprocess,allowsreschedulingfor when there is no appropriate operating room. After these emergency patients after elective patients have been allocated cancellations, surgeons are then working overtime. In further totheoperatingroomandresources.Intheirwork,Neyshabouri studies by researchers, with new models or algorithms, they and Berg [14] developed a formulation that considers the in- may consider extra costs due to overtime and cancellations, tensive care unit (ICU), which is one of the other departments overtime capacity constraints, and the inclusion of both related to the operating room. -ey also combined a simu- elective and nonelective patient groups without cancellations. lationmodelandaformulationtounderstandthelevelofrisk Planning can be done to reduce assumptions along with associated with the proposed surgical plans. -ey relieved the variousuncertaintiessuchasthetimeofarrivalofthepatients, obstaclesthatcouldbeexperiencedintheoperatingroomwith thedurationofthesurgicalprocedure,andconsideringallthe a robust two-step optimization method to avoid the uncer- organizational and technical constraints. When evaluating taintiesofthedurationofsurgery.Table1presentsthestudies bothelectiveandnonelective patientgroups,thewaitingtime according to patient features. ofpatients,aswellastheeﬀectontheworkloadofthestaﬀand From Table 1, it is seen that researchers focus more on hospital, should be considered. the elective group of patients. -e nonelective patient group isoverlookedmorebecauseofthediﬃcultyoftransferringit to the models created. When this situation is examined, it is 3. Performance Criteria stated by researchers that it is diﬃcult to plan the operating room as the degree of uncertainty in the problem increases. Various performance measures are used in evaluating op- However, it is easier to associate the elective patient group erating room planning and scheduling problems in the 4 Journal of Healthcare Engineering Table 2: Performance criteria. [6, 16, 17, 19, 20, 25, 30–33, 37, 46, 54, 57, 67, 74, 77, 78, 82, 83, 90, Patient Waiting time 91, 93, 97, 98, 100–102, 104, 112–119] Surgeon [77, 114, 120, 121] [1, 8, 11, 15, 17, 20, 22, 25, 26, 28, 32, 36, 37, 38, 42, 46, 48, 54, 60, Operating room 62, 65, 66, 68, 70, 73, 76, 78, 82, 84–87, 89, 92, 95, 98–100, 102, 103, 105, Utilization 106, 109, 110, 112, 114, 117, 118, 120, 122–135, 136–142] [14, 22, 24, 38, 41, 42, 48, 51, 60, 61, 65, 69, 70, 75, 78, 80, 82, 85, 110, ICU (intensive care unit) 122, 124, 143, 144] [6, 15, 20, 21, 26, 27, 29, 34, 43, 46, 53, 60, 62, 69, 73, 76, 84, 95, 96, Operating room 101, 104, 117, 120, 124, 125, 145, 146, 137] Overtime ICU [6] PACU (postanesthesia care unit) [117] Completion time [21, 65, 66, 86, 91, 143, 147, 148] Patient postponement/rejection [33, 67, 90, 94–96, 111, 118, 119, 146] [1, 21, 23, 25, 35, 36, 40, 44, 45, 52, 61–63, 69, 79, 80, 81, 87, 92, 93, 98, Financial asset 111, 112, 114, 117, 121, 126, 139, 149–156] Preferences [15, 39, 72, 78, 87, 144, 145, 157] Humanitarian goals [7, 15, 43–45, 55, 83, 84, 104, 106, 108, 152–154, 158] [7, 9, 11–13, 18, 22, 23, 27, 29, 31, 34, 35, 42, 49, 50, 51, 55, 56, 58, Others 59, 63, 64, 67, 71, 72, 74, 88, 97, 99, 103, 105, 107, 113, 116, 120, 129, 130–132, 136, 144, 148, 150, 151, 158, 159, 160–170] literature. While these performance measures customize the the planning they have done, they should evaluate the performance of the given data, whether this is actual data or structure of the problem, they also limit the size. As the number of evaluated criteria increases, the problem struc- speciﬁc probability distributions. -e degree of satisfaction of patients on long waiting lists in hospitals directly aﬀects ture becomes more diﬃcult and complicated. Individual performance measures have been distinguished, including themotivationofthehealthcareinstitutionsintermsofboth waiting time, utilization, patient postponement, cost, and so material and morale [16]. -e group on the waiting list is on. -e studies examined in Table 2 are classiﬁed according divided by researchers into two groups, namely, surgeons to these performance criteria. and patients. -e importance of the satisfaction of the Table 2 contains several studies that include other surgeonsisemphasizedasmuchasthedegreeofsatisfaction performance measures. Looking at these studies from of the patients. During the planning of the operating room, a broad perspective, it is actually seen that researchers have theyoﬀeracombinationthatallowssurgeonstoreducetheir taken diﬀerent approaches for planning of hospital orga- waiting times. -ey touch on the relationship between the durationofoperationsandthewaitingtimesofthesurgeons. nizations. In the studies reviewed, researchers often con- sidered the balanced utilization of operating rooms and the -e accuracy of the time estimates of these operations de- reduction of costs. -e complexity and interactions of all scribes the quality of operating room scheduling. thesefactorsareasourceofproblemsforhospitalmanagers, Utilization, which is shown as another performance who are looking for eﬃcient and eﬀective utilization of criterion,hasbeensetastheobjectivebymanystudiesinthe operating rooms and want to keep the patient/staﬀ satis- literature. In addition, researchers handled the utilization faction level high. Within this context, they are searching criterion separately in terms of operating room sections. A for the most appropriate operating room scheduling and large majority focus is in particular on the utilization rate of planning. Researchers should increase the criterion level operating rooms. Because of the large ﬁnancial asset rep- they consider for future studies. Although not particularly resented by operating room utilization rates, even small emphasized, there should be a focus on the balanced op- changes in the schedules have eﬀects on various overheads such as overtime pay at the hospital. Many studies in the eration of the other parts of the operating room that are integrated. -e compatibility between actual situations and literature have developed diﬀerent approaches to the ef- schedules that are made without considering these units can fectiveness of the utilization of operating rooms and have be examined. In addition, patient postponement or re- noted the impact of both overuse and underuse. From this jection, which is among the performance criteria, can result pointofview,theyemphasizethattheeﬃciencyofoperating in serious damage to the hospital both materially and roomuseshouldbekeptatthemaximumlevelinthebalance reputationally. However, this measure has not been adopted of these two cases. -ey propose a hierarchical approach as very much in the literature. Researchers should analyze the an alternative to the diﬃculty of computation [17], which relationshipbetweenthesecriteriaforfuturestudies.Sinceit relates to the utilization of operating rooms because of the is very diﬃcult to evaluate all these criteria at the same time, distributionofoperationsbalancedbetweensurgeongroups. they should make a plan that takes these criteria into One important factor that can make hospital organi- zations more eﬀective is the increase in costs in the health consideration, as the outcome of the relationship is most likely to contribute to the hospital. -en, as a result of services. -e beneﬁt of utilizing the most eﬃcient operating Journal of Healthcare Engineering 5 Table 3: Status of the operating room. [1, 6, 7, 10, 11–19, 21, 22, 24, 26–29, 31–33, 35–37, 39, 42–47, 50, 52–57, 59, 60, 62–64, 66–68, 70–74, 76–79, 82, 83, 87, 89, 90, 92–94, 99, 101–103, 105–107, Only the operating room 109, 111–116, 120–123, 125–130, 132–135, 137, 138, 142, 143, 145–147, 149–155, 159–163, 165, 167, 168] PACU [9, 49, 84, 85, 117, 131] Integrated operating room ICU [25, 30, 38, 41, 48, 49, 51, 61, 65, 69, 75, 80, 81, 124, 144] Others [20, 23, 34, 40, 58, 86, 88, 104, 108, 110, 136, 148, 157, 158, 164, 166, 169] room capacity cannot be ignored. Planning processes in- et al. [158] created a formulation that relieves both surgical volvingbasicobjectivessuchastheeﬀectivenessofresources and nonsurgical constraints. In planning that considers the surgeon’s preferences, the eﬀects of these preferences are in hospital organizations are dimensioned as strategic, op- erational, and tactical. van Oostrum et al. [22] developed examined. Xiang et al. [145] considered surgeons’ experi- ences of scheduling problems in their work. -ey developed a model that meets the requirements for utilization of the operating room by addressing planning at the tactical level a balanced planning and scheduling approach based on the with the solution approach they oﬀer. Augusto et al. [65] inclusion of certain surgeons in some operation groups. focusedtheirworkonthedailyplanningofoperatingrooms, -ey analyzed the eﬀectiveness of their algorithm with this where various constraints were reﬂected in the model they preference option for the surgeons. set up. -ey helped management by improving the utili- zation of operating rooms. Tan et al. [60] reached goals in 4. Techniques Used in Solution Processes their solution approach to reduce variability in bed occu- pancy rates, as well as in the operating room eﬀectiveness, Operating room planning and scheduling processes aﬀect which varies with over- and underuse. the entire hospital organization. -ese processes are in- Another criterion that is as important as the utilization creasingly complicated by the inclusion of areas such as the of the operating room is the utilization of intensive care intensive care unit (ICU), or the PACU, which are other units. -e intensive care unit capacity, measured by the parts of the operating room. But it is considered beneﬁcial number of beds on these units, is a source of concern for fromastrategicpointofviewtoimprovetheoverallprocess. hospitals. Kim et al. [75] focused on improving the per- Given the work involved in these facilities, the researchers’ formance of intensive care units eﬀectively and eﬃciently to resultshighlighttheextenttowhichtheperformancequality make a positive contribution to healthcare in their model. increases. At the same time, when the uncertainties of these -is criterion, which is included in the performance facilities are not overlooked, it seems that the long-term criteria as patients postponed, indicates the quality of the eﬀect for the hospital is in the positive direction. Table 3 service given to the patient. Addis et al. [67] guaranteed the contains the structure of studies in the literature in terms of quality of service provided at a certain level of performance. solutiontechniques.Whilemoststudiesaddresstheoperating -ey developed a punishment function to prevent deferrals room on its own, other studies are available that incorporate and delays due to postponements. Likewise, they presented simultaneous solution approaches integrated with these fa- an optimization approach with a block scheduling strategy cilities.Inadditiontothese,recentlyreportedoperatingroom [33], which provides a penalty function to avoid as many schedulingstudiesarealsorelatedtohealthservices,although patient postponements as possible. In order to assess the they are seen to be integrated with diﬀerent ﬁelds. models in terms of solution quality, the number of patients Looking at Table 3, it is observed that improvements operated on, the waiting times, and the delays experienced have been made in the planning and scheduling processes were examined. through the integrated studies carried out in recent periods, One of the most common goals in operating room although a great majority of studies have shifted to practice schedulingproblemsistheexpectedperformanceintermsof where the operating room is considered alone. -e analysis ﬁnancial assets. In general, an operating room planning and of the consequences of these integrations is also an im- scheduling problem is indirectly aﬀected by the cost crite- portant gateway to the work to be undertaken in the coming rion, even when other goals are considered. -at is why, in years. In the real world, the operating room is integrated fact, this criterion is among the cornerstones of healthcare with rest of the hospital such as the PACU and ICU. -is units. Meskens et al. [152] developed a model that considers makes the planning process very diﬃcult. Often there are constraints on material resources encountered in real life. disruptions from planning that is not done correctly or that With an eﬃcient algorithm, they created a schedule that does not balance these integrated parts correctly. -ese allows for the eﬃcient utilization of the operating room and disruptions have negative consequences, such as post- the surgeon. Baesler et al. [143] focused on a scheduling ponement or rejection of patients, an increase in surgeons’ approach aimed at maximizing hospital revenues by waiting time, or prolonged preparation and cleaning time. addressing the plans in the organizational structure at -is gives the hospital both extra costs and patient/staﬀ strategic and tactical levels. dissatisfaction. Researchers can conduct studies that ana- Another performance criterion is the preference crite- lyze the impact of these negative outcomes on the pa- rionwhichisadoptedasanaimbyresearchersintheprocess tient, as opposed to planning work in general. -e overall of scheduling and planning the operating room. Van Huele performance of the operating room can be evaluated. Later, 6 Journal of Healthcare Engineering Table 4: Solution techniques. Mathematical Programming [17, 33, 34, 47, 60, 90, 92, 125, 136, 142, 164] Integer programming [8, 10, 23, 25, 28, 32, 41, 49, 52–54, 95, 110, 113, 114, 122, 140, 149, 156, 159] [1, 9, 13, 21, 24, 27, 30, 36, 40, 44, 56, 58, 62, 66, 68, 70, 71, 78, 84, 85, 86, 93, 100, 102, 104, 126, Mixed integer programming 128, 134, 138, 144, 152, 157, 162] Goal programming [15, 16, 42] Dynamic programming [23, 149, 160] Constraint programming [87, 137, 152, 166] [6, 14, 20, 21, 30, 31, 35, 38, 49, 51, 55, 58, 61, 73, 76, 77, 83, 91, 95, 96, 97, 102, 105, 106, 116, 118, Simulation 119, 131, 133, 143, 145, 153, 158, 161, 163, 167] Branch bounding algorithm [61, 121] Lagrangian relaxation approach [45, 65, 148] [7, 13, 18, 26, 37, 54, 57, 59, 73, 85, 103, 109, 112, 113, 115, 123, 128, 147, 162, 118, 94, 156, Heuristic algorithm 140, 98, 141] Genetic algorithm [9, 19, 62, 82, 89, 124, 131, 135, 154] Ant colony algorithm [29, 46, 145, 164] Annealing simulation [24, 51, 77, 143] [6, 11, 12, 22, 38, 39, 43, 46, 48, 50, 63, 64, 67, 69, 72, 74, 79, 80, 81, 88, 92, 99, 101, 107, 108, 111, Other methods 117, 120, 127, 129, 130, 132, 139, 146, 150, 151, 155, 161, 165, 168, 169, 170] as a result of this study, the most important factor aﬀecting helpreducethediﬃcultyofcalculationwhenthereareslight hospitalsinthenegativedirectioncanbeinvestigated.Ifthis changes in the structure of the problems. In the use of solution methodologies where performance measures are factor is most relevant to a certain department, plans can be madetoimprovethatdepartment.Focusingonthedetailsof eﬀective, many researchers are discussing how to approach uncertainty as the amount of uncertainty increases and the the studies, it is seen that some of the criteria such as uti- lization of the operating room, reduction of patient waiting resulting eﬀectiveness of the established model structure. lists, cost, and similar criteria are taken together. Problems From the work done, it is seen that researchers go to the thatareintegratedwithdiﬀerentunitsfocusmoreonspeciﬁc solution process by using the advantages of each method. In functions. fact, these solution methods require various assumptions to -emainobjectivewastoimprovetheutilizationratesof be made in the problem. Every algorithm or model that has the units that they integrate within these special functions. been developed gives very eﬀective results day-by-day in the -e studies under the other heading in Table 3 are mostly process of operating room scheduling and planning. studies where nurse units are considered together. -e However eﬀective they are, these results are not enough and must be continuously improved, and the solution area ex- special situations of the nurse units and their relations with the operating room are reﬂected. Martinelly et al. [34] de- panded. Researchers can leverage the power of constraint veloped a model proposal that shows the relationship be- programming to create mathematical or logical represen- tween the operating room and nurse management, and the tations of existing constraints in the problem. With con- numberofoperatingrooms,numberofnurses,andovertime straint programming, many solution areas can be found in concepts. When the main purpose of the study is examined, the deﬁnition cluster and the most suitable one can be se- an integration that represents two diﬀerent management lected within the solution area. -is allows the evaluation of areas is seen with a ﬂexible model understanding. -ey diﬀerent values in the solution process. Moreover, in order established an operating room scheduling model that both toobtainsatisfactoryresultsinashorttime,heuristicmethods plans for nurses and at the same time considers resource can be used, and a solution approach can be developed for constraints. -e model incorporates nurse restrictions that queuing models to nonelective patient groups. Belie¨n et al. [24]optimizedthebedoccupancyrateswiththeoptimization make the process even more diﬃcult for already complex operating room processes. However, the results show that systemtheyhavesetup,allowingthesamespecialistsurgeons there is no relation between the number of operating rooms toconcentrateonthesame operatingroom.Itis seenthatthe andthe number of nurses. It is stated that thereis aninverse results of the calculations produced successful plans based on relationship between the number of nurses and the amount these two objectives. Figure 1 expresses the location of the of overtime work. -is,in fact, means that the validity of the solution techniques in the literature visually. nurses in theintegration of both management areas is small. From Figure 1, it can be seen that more simulation and In the operating room scheduling and planning literature, mathematical models are used in the solution process of the there are methodologies that use a speciﬁc analysis and problem studied. -ere is also diversity under the headings mentioned as other methods in the solution process. Re- solution technique. Table 4 lists these methodologies and what they focus on. searchers have brought diﬀerent perspectives to the solu- tions of problems through diﬀerent techniques. It is diﬃcult Table 4 presents a perspective on the analysis of prob- lems. It seems that there are diﬀerent suggestions that can to produce alternative solutions to the challenge of the Journal of Healthcare Engineering 7 Figure 1: Solution techniques. operating room scheduling problem and to obtain high sudden occurrences in planning have a negative eﬀect for quality results from these solutions. -ey have helped to bothsurgeonsandpatients.Atthesametime,uncertainties improve the functioning of the operating room [87], which in the duration of surgical operations are critical for op- successfully reﬂects the expression power of the solution erating room planning. Operations that exceed the pre- approachtheyhaveproposedtosolvethesediﬃculties.-ey dicted duration aﬀect not only the start time of the next arefocusedonthedailyplanningoftheoperatingroomwith operation in the program but also all the day’s other op- the constraint programming method. In addition, human erations. -ese late start-ups aﬀect the shift times in the and material constraints that reﬂect the surgeon’s prefer- planning, right up to the last working hour of the day, and ences are included in the model. When the results are ex- resultin staﬀovertimecosts. Table5 lists thestochastic and amined, it appears that the solution method they use is an deterministic approaches. ideal tool for competing goals. Meskens [152] compared When detailed analyses of the studies are carried out, it their constraint programming method with a mixed integer canbeseenindetailinTable5thattheuncertaintiesintimes programming model, another optimization tool, to examine and arrival times aﬀect waiting lists and the utilization of their eﬀectiveness in real-life problems. -ey considered resources. In addition,the uncertainties in the margin of the various constraints in their work and presented the ad- contribution to the hospital structure, which will keep the vantages and disadvantages of both models. expected high ﬁnancial cost, also indicate that operating When we look at the work done recently, we prefer rooms aﬀect the utilization capacity. However, attention should also be paid to the diﬃculties that may arise from integrated methods rather than using a single solution technique,duetothediﬀerentexternalfactorsthatmakethe failure of the hospital’s medical equipment. In the literature, problem structure more diﬃcult. Researchers have aimed at future studies should give more importance to this source of increasing the quality of the solution by using integrated uncertainty, so that improvements in the quality of the methods.Furthermore,theanalysisofthescenarioswithtest solution can be realized by researchers, because this is an dataisperformedwiththepresentedsimulationapproaches. important problem that needs attention when it aﬀects the If it is emphasized that these analyses support the imple- starting times of operations. By increasing the number of mentation results, this can be interpreted as indicating that studiestoreducethenegativeeﬀectsofsuchuncertaintiesin the approaches are successful. thecomingyears,researcherswillbeabletomakesigniﬁcant contributions to both real-life practices and the literature. Due to the diﬃculties in the solution process of these un- 5. Uncertainty Status certaintiesintermsoftheirstructure,itseemsthatstochastic studies are not very useful. Also, in the literature, the ca- One of the biggest problems encountered in the planning pacity requirements in emergency situations, the arrival andschedulingofoperatingroomsisthatthereistoomuch times of these emergencies, and the duration of operations ambiguity due to the structure of these problems. Many are usually neglected. -ese neglected situations should be researchers have considered various assumptions for the addressed through stochastic studies by researchers. productionofcorrectprogramsandforthedevelopmentof contributions to hospital organizations. When the litera- ture is examined, it focuses on the uncertainties in patient 6. Applicability of the Study arrivalsandoperationtimes.Whenwelookattheliterature on stochastic studies, unpredictable arrivals, especially of When the literature is examined, a comprehensive test is nonelective patient groups, have various eﬀects. -ese appliedtoanalyzetheperformanceofthedevelopedmodels. Mathematical programming Integer programming Mixed integer programming Goal programming Dynamic programming Constraint programming Simulation Branch bounding algorithm Lagrangian relaxation approach Heuristic algorithm Genetic algorithm Ant colony algorithm Annealing simulation Other methods 8 Journal of Healthcare Engineering Table 5: Uncertainty status. [1, 9, 10, 13, 15, 16, 17, 18, 19, 20, 23, 25, 26, 28, 29, 31, 32, 34, 36, 37, 41, 42, 44, 47, 49, 50, 53–60, 62, 64–72, Deterministic 78, 79, 82, 83, 85–89, 100, 102, 112, 115, 124, 125, 127, 129, 137, 144, 145, 147, 150, 152, 157, 159, 170] [6, 13, 14, 20, 21, 22, 24, 27, 33, 35, 38, 40, 48, 51, 52, 61, 63, 73, 76, 77, 80, 84, 90, 92, 95, 104–110, 114, 117, Stochastic 126, 130, 131, 138, 143, 155, 160, 162] Table 6: Application of studies. Not tested [35, 50, 57, 70, 75, 87, 144, 152] [1, 6, 7, 9, 14, 19, 21, 23, 25, 26, 28, 29, 32, 34, 36, 39, 41, 44–49, 51, 52, 58, 61, 63, 65, 67, 71, 72, -eoretical data 74, 79, 80, 83, 85, 86, 91, 94, 103, 105, 107, 109, 112, 114, 116, 117, 120, 127, 129, 131, 133, 135, 136, 139, 145, 147, 153, 157, 158, 160, 161, 166] Test data [10, 11–13, 15–18, 20, 22, 24, 27, 29–31, 33, 37, 38, 40, 42, 43, 53–56, 59, 60, 62, 64, 66, 68, 69, Real data 73, 76–78, 82, 84, 88, 93, 95, 97, 100, 102, 104, 106, 110, 113, 115, 121–126, 128, 130, 132, 134, 138, 141–143, 146, 149, 150, 151, 154, 156, 159, 162–165, 168, 170] Fortheseexperimentalteststhatdemonstratetowhatextent increase hospital eﬃciency with the performance values goals can be reached, a signiﬁcant amount of data entry is obtained as a result of these plans. In addition, researchers required. Looking at Table 6, in the studies listed, it is seen cancommentonwhichpointsintheschedulestheytestwith that performance analysis of most of the studies is done actualdataneedtobedevelopedorwhichpointstheyshould using theoretical data. -e data used in these studies are concentrateon.Withtheactualdataused,theycanshowthe robustness of the model they have built and the extent to divided into two groups; the actual data/set of theoretical data is obtained either at random or with a certain proba- which it can be put into real practice. Since the studies bility distribution. However, even if data sets from real-life prepared under various assumptions neglect many sources, problems are used in studies, most of the developed ap- it is diﬃcult for managers to perceive the positive potential proachesarenotreﬂectedintherealapplication.Inthiscase, ofrealapplications.Onthecontrary,ifitisjudgedtobevery researchersshouldconcentrateonthereasonsforconﬂicting diﬃcult or even impossible to take all the assumptions into ideas between the application phase and the model they are consideration, hospital organizations need to take strategic developing. stepstosupportsuchwork,becauseinrealitynohospitalcan Table 6 gives an analysis of studies of the use of real make all these assumptions. solution data and the diﬀerent solution techniques in Table 4. -e results obtained from the experimental tests on the 7. Planning Strategies developed models show that the operating rooms need to be more balanced according to the current utilization condi- In hospitals that provide healthcare, managers want to tionsandhelptocreateproposalsfor ﬂexibleuseatlesscost. maximize the yield from the utilization of the operating In hospitals, which are regarded as service units, the plan- rooms through a variety of strategic steps. -is has led to ning that is prepared for the operating room may include diﬀerent strategic plans. Hospital administrators have severalpossiblemishaps.-erefore,itisseenasbeneﬁcialby planned strategic steps in operating rooms, including open researchers to perform short-term real applications of the planning strategy, block planning strategy, and modiﬁed studies. However, the point of view of hospital adminis- block planning strategy. -e studies in Table 7 are listed trators, in hospital organizations that already have a diﬃcult according to these strategic steps. In Figure 2, the distri- and complicated structure, is that the sudden application of butions of the studies are shown visually. these studies may complicate problem. Banditori et al. [30] When we look at Table 7 and Figure 2 together, it is seen focused on reducing the number of patients on the waiting that the open planning strategy is most common. -e block list by considering a plan for each day of the month. At the planning strategy is divided into two parts: block planning sametime,theaimwastoavoidcostincreasescausedbythis with Master Surgical Scheduling (MSS) and block planning waitingandthenegativeeﬀectsthatmightbeexperiencedon strategy only. It appears that this distinction has emerged satisfaction levels. Accordingly, a set of solutions was pro- from the diﬀerent situations in which researchers handle duced. As with every study, these studies have limits. -e their work from a managerial point of view. When the authors who conducted experimental simulation tests using sections under the block planning strategy are examined the real-life data mention the diﬃculties that models can together,itisseeninmanystudiesthatresearchersthinkthat experience in the planning process due to the 1-month it is time and space that should be reserved for surgical planning horizon. specialties. Researchers commonly choose one of two parts Researchers should use more of the experimental sets reserved for planning strategies in the scheduling process. obtained from real data to assess the performance of the However, unlike most studies, Liu et al. [118] addressed the planning and schedules. Planning and schedules need to be open planning and block planning strategy together. -ey applied in real life to allow the healthiest performance also developed a metaheuristic algorithm to solve this measurement. Hospital administrators who allow this can problem. -e open planning strategy allows surgeons to be Journal of Healthcare Engineering 9 Table 7: Planning strategies. [1, 6, 9, 10, 12, 13, 16–18, 21, 23, 26, 28, 29, 32, 34, 35, 37, 38, 43, 44, 46, 48, 52, 54, 55, 58, 59, 62, 63, 65, Open planning strategy 66, 68, 69, 73–77, 80, 81, 83–87, 101, 104, 106–110, 112, 118, 124–127, 130, 139, 147, 149, 152, 157, 161] [15, 19, 20, 22, 24, 25, 27, 30, 31, 33, 36, 40, 41, 49–51, 53, 56, 60, 61, 67, 78, 88, 89, 95, 102, 103, 105, 114, Block planning strategy 116, 118, 129, 145, 150, 151, 159, 170] approachestohelpuserswithstrategicplanning.Addisetal. [33] aimed at reducing waiting times for patients by as- Open planning strategy suming a block planning strategy. In the study, particular attention was paid to ensure that the operating room ca- Block planning strategy pacity is balanced in terms of surgical expertise. In this article, which is also integrated with the master surgical schedules,thewaitingpatientsetisallocatedtotheoperating Block planning strategy (MSS) rooms. 0 10203040506070 While studies of open planning strategies were popular during the 1960s, today diﬀerent strategies for increasing Figure 2: Planning strategies. productivity continue to be developed. But nowadays, too, there are many studies that use open planning strategy in ordertoavoidthediﬃcultyandcomplexityofcalculation.In assigned to appropriate operating rooms with appropriate [26], no speciﬁc time is reserved for any particular surgeon time. When an empty schedule is considered, it is assumed with the open planning strategy. As is the case in most thatpatientswillbereceivedonaﬁrst-come-ﬁrst-servebasis, studies, the main point of this study was to increase the taking into consideration their arrival times. For schedules eﬃciency of the utilization of the operating room. created in the block planning strategy, the same day of the week, the same time zone, and the same operating room are stored in the service of a particular surgeon or specialist. 8. Conclusion With this strategy, it is necessary to adjust the appropriate operating room at the hours when the operating rooms are -is study examined 170 planning and scheduling studies open. related to operating rooms scanned in the databases of the -e modiﬁed block planning strategy is a process of Emerald, Science Direct, JSTOR, Springer, Taylor and reconﬁguring operations that are not in the previously Francis, and Google Scholar. -e contributions of these constructed blocks for unused time. -is is described as studies tothe literatureandthereader were assessedandthe ﬂexible planning because it requires the reorganization of pointstheyemphasizedwereidentiﬁed.Whileevaluatingthe the initial construction schedules. In future studies, using goals that the studies want to accomplish, the technical block planning strategy, the preferences of surgeons can be structure was examined. For the analysis of the studies, given more importance and the eﬃciency of these plans can a systematic structure was established in this study so as to be increased. Also, with block scheduling, certain times make it easy to focus on what readers want speciﬁcally to within the surgeons’ working hours can be left empty. -us, investigate. In addition, by comparing the studies, it can be it is both separate from the surgeons’ rest time and makes it easily seenwhich pointof study thework hastaken forward. easiertoallocateasuitableoperatingroomintheeventofan Clear lists were created with the tables presented to improve emergency. -is can reduce the delays that can be experi- the accessibility of the ﬁndings. enced during the preparation and cleaning periods between It is seen that optimization methods are generally pre- operations as well as the patient waiting time that is caused ferred in the studies about the planning and scheduling of by these conditions. theoperatingroom,withtheaimofprovidingthebestresult When these studies are examined, it is seen that they withinthesolutionprocess.Atthesametime,eﬀortsarealso allow better use of the surgeon’s time, and at the same time, made to avoid complicating the model due to the various prevent delays that may occur due to extra preparation time constraints encountered in real life, and the solution area is for operations requiring diﬀerent surgical expertise in the created within these frameworks to improve the process. operatingroom.-is hasmadeblock planningstrategiesthe Researchers have emphasized the need to balance the re- focus of researchers. -e block planning strategy, which is sources available and improve the eﬀectiveness of staﬀ in associated with the main surgical scheduling problem, de- order to optimize the utilization of operating rooms, which ﬁned as the allocation of operational resources to surgical hospitaladministratorsseeasthemostcriticalpart.Optimal groups,isbeingconsideredinmanystudies.Intheliterature utilizationofoperatingroomsispossiblewhenassessedwith examined, there are 16 main surgical scheduling studies diﬀerentperformancemeasures.Eventhoughindirectly,itis [20, 22, 24, 25, 27, 30, 31, 40, 49, 53, 56, 60, 61, 88, 150, 151]. diﬃcult to reﬂect these interrelated criteria together, so the Mannino et al. [27] considered the problem of estimating solutions are proposed under many assumptions. demand levels in creating the main surgical schedules and Another problem that complicates the solution process then aimed at stabilizing patient tail lengths and reducing of the problems is that there is too much uncertainty. In the the maximum overtime. In their work, they introduced new studies, patients were separated into two groups, ignoring 10 Journal of Healthcare Engineering the uncertainty of their arrival times. In studies dealing with Conflicts of Interest a nonelective group of patients, it was noticed that other -e authors declare that there are no conﬂicts of interest operations were postponed or canceled when an unplanned regarding the publication of this paper. case occurred in the created schedules. Delayed operations cause both surgeons and other staﬀ to work overtime and Acknowledgments reduce the level of satisfaction by increasing patient com- plaints. 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Application of Operational Research Techniques in Operating Room Scheduling Problems: Literature Overview

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