Allocation scheduling leads to optimum utilization of operation theater time

Abstract

Background

Cancellation of surgeries is a regular phenomenon in any hospital, and reasons may vary from clinical to managerial ones. The aim of the study is to suggest scheduling to address the problem of time over run related cancellations. This is an observational and descriptive study conducted in a tertiary care hospital with ophthalmology facilities. The sample size is calculated with 95% confidence interval using Epi Info 6 from the total surgeries performed in the last 5 years (n = 380). Simple random sampling technique was used.

Methods

Surgical time for all types of ophthalmic surgeries (n = 582) was observed. Allocation of listed cases to the available operating rooms (ORs) was carried out using the observed time using LEKIN software.

Results

The time over-run of 2 h and 6 h was noted for two units, whereas idle OR time was observed in other units. An average idle time of 19% was noted on each day. Reallocation of the cases to the ORs was carried out taking all the planned cases (of both the operating units of the day) as the number of jobs and all the available ORs as parallel machines using LEKIN software. All the planned cases could be accommodated; still, an average of 17% of the total available operation theater (OT) time was found idle on each day.

Conclusions

Planning of cases using procedure time and scheduling on a daily basis using allocation models with simple algorithms can provide optimal utilization of OTs and can address the time over-run and related cancellations.

Introduction

Health-care administrators have to be systematic for efficient allocation of material, humans, and financial resources needed for delivery of high-quality care.¹ The most expensive resources in a hospital are operating rooms (ORs), surgeons, and anesthesiologists. ORs in a hospital can be regarded as the hospital's engine.² Owing to highly specialized staff and large capital investments on equipment, a substantial degree of efficiency is required in the daily management of an operation theater (OT).³ This requires planning and scheduling of the OR for efficient use of resources in a cost-efficient way.⁴

The objectives in an operating theater are minimization of idle time of ORs and to minimize the surgeon's wait for availability of ORs. With these objectives and variation in the time of surgeries between surgeons and between cases, the scheduler faces the challenge of determining the sequence of surgeries and ensuring the minimal wastage of the surgeon's time.²

The operational research techniques provide optimal solutions for allocation of resources. The application of scheduling is highly effective for manpower and operation theaters in the hospital.⁴

Scheduling of the operation theater involves three levels of planning, i.e., strategic, tactical, and operational levels of planning. The strategic level deals with the distribution of OT time between the different medical specialties (or surgeons). This is often referred to as patient mix (or case mix). At the tactical level, a cyclic timetable called “master surgery schedule” is generated that divides OT time into different blocks for different specialties such as weekdays or shifts. At the operational level, the first step is the assignment of surgeries to ORs and days. The second step in operational scheduling is “Allocation scheduling,” which is scheduling the assigned surgeries with the respective rooms and days. This involves daily or weekly planning.^3,5, 6, 7 The scheduling of an operating theater (consisting of a number of ORs) is very similar to the parallel machine scheduling problem of a manufacturing industry. Here, an OR may be regarded as a machine, and a surgery may be regarded as a job.^1,2,5

Allocation scheduling

Allocation scheduling also known as intervention scheduling is the problem of scheduling previously assigned interventions within the respective rooms and days.^8,9

Overview of the hospital

The study hospital is a tertiary level public sector ophthalmology center which is also a teaching centre located in India. The hospital receives complicated eye cases from across the country and always faces a resource crunch. Time over-run has become a major cause of dissatisfaction to patients and surgeons and is the biggest cause of cancellation of surgeries in the hospital apart from patients' condition. However as an indicator of quality of care, a surgical cancellation rate of less than 5% is recommended.¹⁰ Being a public sector organization, the services provided are free of cost for the general ward patients; thus, the paying capacity of the patient has no role for the scheduling or cancellation of the case. The doctors (faculty) are the permanent employees on the hospital payroll. There are 6 units based on the clinical superspecialities. Each unit has been given fixed OPD and OT days, that is, 2 OPD and 2 OT days; two units operate on one day with an equal number of OTs. The sequencing of the cases in an OR is not fixed; the decision on which case is to be taken by the surgeon changes frequently during the day.

Review of the literature

The scheduling of an operating theatre (consisting of a number of ORs) is very similar to the parallel machine scheduling problem of a manufacturing industry. Here, an OR may be regarded as a machine, and a surgery may be regarded as a job.⁵

Scheduling helps us to generate mathematical solutions, calculate performance measures, and generate a schedule using spreadsheets or by scheduling software. LEKIN is a scheduling system developed at the Stern School of Business, New York University. The academic version of the software is available for download free of cost. It provides 6 basic workspace environments: single machine, parallel machines, flow shop, flexible flow shop, job shop, and flexible job shop. Using software, various schedules are derived with respect to various dispatching rules, such as shortest processing time, longest processing time, earliest due date, least slack, first come first serve, random selection, and so on. The obtained schedules are compared based on performance measures, such as make span, mean flow time, mean tardiness, maximum tardiness, mean lateness, and so on.²

Frame work and notation of scheduling

A scheduling problem is described by a triplet α/β/γ, where α describes the machine environment, β is the processing characteristics and constraints, and γ is the objective to be minimized. The number of jobs is denoted by n, and the number of machines is denoted by m.^2,6,11,12

The entries in the α field can be as follows: 1, Pm, Jm, and Fm.

• •1 is single machine.
• •P is the parallel machines.
• •J is the job shop machine environment.
• •F is the flow shop machine environment.
• •m is the number of machines.

The entries in the β field areas as follows:

• •r_j: “r” is the release date of job “j.” In service, this is the earliest possible starting time.
• •s_jk: “s” is the sequence dependent setup time between jobs j and k.
• •p_ij: “p” is the processing time of job j on machine i.
• •D_j: “D” denotes the due date of a job j.
• •p_rec: “p” denotes the priority constraints among the jobs.

The entries in the γ field are always a function of the completion times of the jobs. The completion time of job j is denoted by Cj. The possible objective functions are to be minimized:

• •Cmax is the make span, defined as maximum time (C1, …, Cn), which is equivalent to the completion time of the last job to leave the system.
• •Lmax is the maximum lateness, which is defined as maximum lateness of all the jobs (L1, … Ln).
• •Σ wjCj is the sum of the weighted completion times of the n jobs.
• •Σ wjTj is the sum of the weighted tardiness, where the tardiness of job j, Tj, is defined as max(Cj_dj,0).
• •Σ wjUj is the weighted number of tardy jobs, with Uj being 1 if Cj - dj and 0 if otherwise.

Measures for evaluating the schedule are as follows:

• •L_j is the amount of time by which the completion time of job j exceeds its due date: L_j = C_j−d_j.
• •Flow time (F_j) is the time job j spends in the system: F_j = C_j − r_j.

Aggregate performance measures

In a set of complete n jobs, aggregate performance measures are as follows:¹²

• •Total flow time: F = ⁿΣ_j=1 Fj
• •Mean flow time: F/n
• •Maximum flow time: F_max = max_1≤j≤n {F_j }
• •Maximum completion time: C_max = max_1≤j≤n {C_j}

Performance ratios

For the evaluation of the services, performance ratios are computed; this provides an insight into the system for planning the strategy for utilization efficiency.¹³ These ratios are as follows:

• •Overtime: defined as the number of periods outside regular hours when ORs are in service.
• •Occupation rate: defined as the number of periods when surgery rooms are in service including overtime over total availability in regular time.
• •Underutilization rate: defined as wasted time divided by the number of periods wherein ORs are in service (excluding overtime); it can be computed per surgeon, per day, or for the whole schedule.
• •Overutilization rate: defined as overtime divided by the number of periods wherein ORs are in service (excluding overtime); it can be computed per surgeon, per day or for the whole schedule.
• •Cancellation rate: defined as the number of cases canceled or delayed per day over the number of surgeons.
• •Usage: defined as the number of periods wherein surgery rooms are in service, including overtime; it can be computed per surgeon, per day, or for the whole schedule.

Materials and methods

Aim

The aim of the study was to suggest scheduling of cases for optimal utilization of operation theatre time.

Objectives

The objectives of the study were to quantify the operating time for surgeries, to assess the time over-run, and to suggest reallocation of cases for optimal utilization of OT time.

The study was undertaken by hospital administrators of the organization after obtaining clearance from the ethics committee of the institute (IESC/T-263). The study duration (including the pilot study, data collection, analysis, and preparation of the report) was eighteen months.

Study population

All cases of elective surgical procedures carried out at the center were included in the study population.

Pilot study

A pilot study was carried out to understand the processes of OT and to refine the methodology for data collection. The surgeries were grouped in accordance with descriptions from standard text books of ophthalmology.

Sample size

The sample size was calculated with 95% confidence interval (CI) using Epi Info 6 from the total surgeries performed in the last 5 years (n = 380). To cover all types of surgeries, the sample size was kept at 582. Stratified random sampling technique was used for selection of cases.

Observations of procedure time

The name of the surgery, name of the surgeon, start time, and end time were noted on a sheet. The start time was taken from the time the patient was positioned on the operation table, and the end time was taken as the time when patient was shifted out of the operating table. The observer remained in the OT with access to all the ORs so that the timing of all cases could be noted. The setup and cleanup times of the OR were noted separately for fifty cases.^3,14,15

Preparation of OT schedules using LEKIN software

A parallel machine environment was chosen for generating the schedules. One planned OT list per unit was taken randomly for three units, the list of their sister unit (unit operating on the same day) for that day was taken, and the schedules were generated to access the time over-run/underutilizations in the planned lists.^2,12

Input parameters in LEKIN software

• 1.A machine framework was constructed separately for general anesthesia (GA) and local anesthesia (LA) cases for each unit each day.
• 2.No weightage or priority was allotted (all were planned cases).
• 3.The average setup and cleanup time was added to the calculated average operation time for calculation of processing time for each surgery.
• 4.The due date (time at which all operations should finish) is 540 min for each OT table.
• 5.Owing to software limitation, the same jobs were clubbed, and the processing time was increased accordingly.
• 6.The algorithms used for generating the schedules were shortest processing time (SPT) first and longest processing time (LPT) first.

Performance measures and schedules

The performance measures considered for the scope of the study were make span time, number of late jobs, and total flow time.

Assessment of utilization of ORs

From the schedules prepared and the performance measure, idle time and time over-run for each OR was assessed.

Optimization

Rescheduling of the planned cases was carried out for optimal utilization.

Limitation of the study

The schedules were prepared considering the operating time; the general norms followed in the OTs, such as children, patients with comorbidity and clean cases first and infected cases, HBsAg-positive/HIV-positive cases in the end, availability of the adequate number of instruments for the surgery, and so on.

This was taken care of by ‘assigning priority to cases’: a function available in the software.

Results

Overview of the OT of the hospital

• 1.There were 14 operation tables placed in 10 ORs. ORs are divided into the GA side, with five ORs (5 OT tables), and LA side, with five ORs (9 OT tables).
• 2.All the OT tables were equipped to take GA cases.
• 3.OT timings were from Monday to Saturday from 0800 h to 1700 h.
• 4.There were six clinical units. Each unit was allotted for two OT days, so that every day, two units were allocated to a fixed number of operation tables. The division of the OT rooms and tables were carried out as per the policy of the center.
• 5.The type of anesthesia depended on the profile of the patient, with special reference to the age of the patient rather than to the type of surgery.
• 6.The cleanup and setup time of the OR was same for all the cases, that is, independent of the type of anesthesia or type of surgery.

Surgical operation time

The time taken for surgeries was found to be highly variable among faculty members and residents. To overcome the variations, the average time taken for a surgery was taken into consideration for further scheduling. Table 1 shows the average time of operation as per group and subgroup classification.

Table 1.

Time taken for various eye surgeries.

Subgroup of surgery		Average operation time (minimum)	SD (minimum)
Cornea, sclera, uvea, conjunctiva
Corneal transplant		92.67	1.53
DCR		94.50	27.58
K Pro		33.67	2.31
PK		91.50	8.82
Symblepheron release and graft		45.85	28.37
Scleral graft		78.5	02.12
Corneal surgery using laser		37.80	16.60
Extraocular, orbital, and ocular tumors
Entropion surgery		51.83	27.64
Enucleation, exenteration, evisceration		73.06	25.33
Extraocular excision		69.29	26.04
LPS plication		68.67	32.81
Orbitotomy		105.00	7.07
Sling surgery		51.00	–
Tarsal surgery		43.67	16.68
Glaucoma
DLCP		14.33	33.08
TRAB and MMC		51.4	31.27
Lens
Cataract surgery		38.95	22.78
Lens aspiration cataract surgery		46.76	18.46
Phacoemulsification surgery		34.22	16.15
Squint
Divergent squint surgery		41.08	22.28
Eso and exo squint surgery		28.12	17.90
Convergent squint surgery		46.63	24.97
R and VR
VR and SOI		114.69	34.92
SOR		52.19	25.98
PPV		81.31	29.46
Laser		26.25	3.50
Membranectomy		73.50	49.88
Buckling		108.63	13.35
Minor surgeries
GA	EUA and eye evaluation	20.125	5.696
LA/GA	Ocular injections	15.667	2.797
	ICL	15.304	1.05
	Pterygium; suture removal; AC wash; resuturing, chalazion removal	23.118	12.309

LA, local anesthesia; GA, general anesthesia; SD, standard deviation.

Dacryocystorhinostomy (DCR); Keratoprosthesis (K Pro); Penetrating Keratoplasty (PK); Levator Palpebrae Superioris (LPS) plication; Diode Laser Cyclophotocoagulation (DLCP); Trabeculectomy and Mitomycin C (TRAB & MMC); Retinal & Vitro-retinal (VR) Surgeries; VR & Silicone Oil Injection (SOI); Silicone Oil Removal (SOR); Pars Plana Vitrectomy (PPV); Implantable Contact Lens (ICL); Anterior Chamber (AC).

Input parameters

Parallel machine environment was constructed separately for GA and LA cases for each unit each day in the software. The input parameters for the schedules are as below:

• Day 1: For Unit A 06 GA cases (jobs) were assigned for 2 tables (machines) and 44 LA cases (jobs) were assigned for 4 tables (machines).

• For Unit B 13 GA cases (jobs) were assigned for 2 tables (machines) and 53 LA cases (jobs) were assigned for 6 tables (machines).

• Day 2: For Unit A 13 GA cases (jobs) were assigned for 2 tables (machines) and 49 LA cases (jobs) were assigned for 5 tables (machines).

• For Unit B 24 GA cases (jobs) were assigned for 2 tables (machines) and 21 LA cases (jobs) were assigned for 5 tables (machines).

• Day 3: For Unit A 10 GA cases (jobs) were assigned for 1 table (machines) and 33 LA cases (jobs) were assigned for 6 tables (machines).

• For Unit B 23 GA cases (jobs) were assigned for 3 tables (machines) and 39 LA cases (jobs) were assigned for 4 tables (machines).

Performance measures

Table 2 shows the performance measures with LPT and SPT algorithms (schedules attached in supplementary file).

Table 2.

Performance measures for operation tables.

Day	Operating unit	Algorithms	GA cases			LA cases
			Make span time	No. of late jobs	Total flow time	Make span time	No. of late jobs	Total flow time
Day 1	Unit A	LPT	206	0	919	403	0	11,464
		SPT	206	0	685	421	0	7678
	Unit B	LPT	528	0	4992	468	0	17,049
		SPT	534	0	2830	534	0	8928
Day 2	Unit A	LPT	445	0	3687	371	0	10,336
		SPT	490	0	2974	425	0	8962
	Unit B	LPT	700	12	11,396	183	0	2134
		SPT	728	4	6752	190	0	1959
Day 3	Unit A	LPT	929	6	5846	487	0	10,632
		SPT	929	4	4373	511	0	7921
	Unit B	LPT	347	0	5295	343	0	8188
		SPT	360	0	3638	352	0	6240

LA, local anesthesia; GA, general anesthesia; LPT, longest processing time first; SPT, shortest processing time first.

Assessment of utilization of the ORs

Table 3 and Fig. 1 shows the day-wise available idle time for each operating unit and total idle time in a day.

Table 3.

Idle operation theatre (OT) time observed.

Day	Unit	Type of OR	No. of ORs available (a)	No of cases planned	Available OR time (540 × a) (b), minutes	Total make span time (Cmax) (c), minutes	Available idle OT time (b–c), minutes
Day 1	Unit A	GA	2	6	1080	412	668
		LA	4	44	2160	1684	476
		Total	6	50	3240	2096	1144
	Unit B	GA	2	13	1080	1068	12
		LA	6	53	3240	3204	36
		Total	8	66	4320	4272	48
	Total		14	116	7560	6368	1192
Day 2	Unit A	GA	2	13	1080	980	100
		LA	5	49	2700	2125	575
		Total	7	62	3780	3105	675
	Unit B	GA	2	24	1080	1456	−376
		LA	5	21	2700	950	1750
		Total	7	45	3780	2406	1374
	Total		14	107	7560	5511	2049
Day 3	Unit A	GA	1	10	540	929	−389
		LA	6	33	3240	3066	174
		Total	7	43	3780	3995	−215
	Unit B	GA	3	23	1620	1080	540
		LA	4	39	2160	1408	752
		Total	7	62	3780	2488	1292
	Total		14	105	7560	6483	1077

LA, local anesthesia; GA, general anesthesia; OR, operating room.

Fig. 1.

Operation theatre (OT) time utilization. The figure shows idle time on day 1 in unit A for both LA and GA cases, on day 2 in unit A for both LA and GA cases and unit B for LA cases, and on day 3 in unit A for LA cases and unit B for both GA and LA cases. Time over-run is noted for GA cases of unit B on day 2 and for GA cases of unit A on day 3. OR, operating room; LA, local anesthesia; GA, general anesthesia.

Optimization

For optimization, rescheduling was performed on day 2 and day 3 when time over-run/underutilization was found. As it has been brought out, all the OTs are equipped to take both GA and LA cases, schedules were prepared with 3 GA tables and 4 LA tables for unit B for day 2. For day 3, schedules were prepared combining the GA and LA cases of both the units and taking 5 GA tables and 9 LA tables.

Revised parameters for input

• For day 2, Redistribution of OT tables was done within the unit, that is out of total 7 tables for the unit, 3 tables were used for GA cases (initially 2) and 4 were used for LA cases as against (initially 5).

• For Day 3, All the GA cases of both the units were considered together as one parallel machine environment constructed and all the LA cases of both the units were considered together as one parallel machine environment constructed in the software.

• The following are the revised parameters for input:

• Day 2: For Unit B 24 GA cases (jobs) were assigned for 3 tables (machines) and 21 LA cases(jobs) were assigned for 4 tables (machines).

• Day 3: 33 GA cases (jobs) were assigned for 5 tables (machines) and 72 LA cases (jobs) were assigned for 09 tables (machines).

• The result is shown in Table 4.

Table 4.

Performance measures with optimization.

Day and Unit	Algorithms	Make span time	No. of late jobs	Total flow time	Make span time	No. of late jobs	Total flow time
		GA cases			LA cases
Day 2, unit B (with 3 GA and 4 LA tables)	LPT	471	0	7798	218	0	2570
	SPT	516	0	4753	224	0	2340
Day 3, unit A and B (with no unit-wise demarcation of ORs)	LPT	400	0	9182	485	0	15,670
	SPT	441	0	5722	519	0	11,872

LA, local anesthesia; GA, general anesthesia; OR, operating room; LPT, longest processing time first; SPT, shortest processing time first.

Discussion

In the study hospital, the strategic and tactical scheduling was in place with block scheduling (distribution of two operating days to each of the six units); however, the operational scheduling was not carried out on a daily basis, that is, the sequencing of the cases to each OR was carried out and fixed and changes many times as per the instructions of the surgeon.

Our study focused on operational scheduling, that is, allocation and sequencing of cases to the ORs on a daily basis, so that the idle OT time and time over-run can be effectively addressed.

In our study, the average procedure time of surgeries ranged from 16 min to 114 min, with an average of 59 min.

Mpyet¹⁶ in his study conducted in the ophthalmology department of Jos Teaching Hospital, Nigeria, noted an average time of 25.7 min per case.

Joustra et al¹⁷ in their study conducted in the ophthalmology department of the Academic Medical Center at Amsterdam observed the average surgical case duration of 80 min.

Van Houdenhoven et al¹⁸ in their study conducted at Erasmus MC, Rotterdam, the Netherlands, noted that the operation time for ophthalmology operations ranged from 46 min to 127 min.

Because the types of ophthalmic surgeries have not been elaborated by the authors, a comparison cannot be made with the aforementioned studies.

Using the average procedure time, the allocation scheduling of the planned OT list for the day, the cases were sequenced using LPT and SPT algorithm/rules.

Hans et al¹⁹ in their study conducted at Erasmus University Medical Center used the LPT rule for scheduling surgeries.

Testi et al¹³ in their study in Genova (Genoa), Italy, applied a simulation method to analyze different rules of surgical case sequencing such as LWT, LPT, and SPT.

We noted that SPT algorithms had less total flow time than LPT. The study hospital faced a space constraint in the OT waiting area; to overcome this, it was recommended that the cases that took shorter time should be taken up first (SPT rule) as with this rule, the total time spent by patients in the system is less. However, this benefit has to be weighted against fatigue caused to surgeons during later hours of the day.

In our study, the OR time in certain units remained underused, and in other units, there was time over-run. On each day, idle OR time was observed, which was 16%, 27%, and 14% of the total available time for day 1, 2, and 3, respectively (average = 19%). Both the units were noted to have idle time for GA and LA cases on day 1; on day 2, idle time was observed for both cases in one unit; time over-run for GA cases and idle time for LA cases were observed in other units; therefore, for optimization, one of its LA OT table was used for GA cases.

On day 3, in one unit, there was time over-run for GA cases, which was higher than the available idle time for LA cases of the same unit; therefore, for optimization, all the GA cases of both units were scheduled on five GA tables, and all the LA cases of both units were scheduled on nine LA tables; with this, the time over-run could be effectively managed with sharing of OT time between the operating units of the same day, as shown in Table 4.

In our study, the idle time noted for day 1 was approximately 20 h, for day 2 was 34 h, and for day 3 was 18 h. The optimization was carried out for day 2 and day 3 after which the idle time reduced from 34 h to 33 h for day 2 and from 18 h to 6 h for day 3.

With the rescheduling, the idle time was reduced as shown in Table 5 and Fig. 2. For day 3, idle time was reduced to 9% from 14%; however, for day 2, the idle time reduced only by 1%, that is, from 27% to 26% (average idle time to 17%).

Table 5.

Idle Operation theater (OT) time after rescheduling.

Day	Unit	Type of OR	No. of ORs available (a)	No. of cases planned	Available OR Time (540 × a) (b), minutes	Total make span time (Cmax) (c), minutes	Available idle OT time, (b-c), minutes
Day 2	Unit B	GA	3	24	1620	1548	72
		LA	4	21	2160	896	1264
		Total	7	45	3780	2444	1336
Total, both units			14	107	7560	5549	2011
	Unit A and unit B	GA	5	33	2700	2205	495
		LA	9	72	4860	4671	189
	Total		14	105	7560	6483	684

LA, local anesthesia; GA, general anesthesia; OR, operating room.

Fig. 2.

Comparison of idle Operation Theater (OT) time before and after scheduling, The figure shows reduction in idle time on day 2 and 3 when rescheduling was performed; in unit 1, no rescheduling was performed (no change) as there was no time over-run.

The study brings out that the division of ORs between the units of the allotted block (as seen for day 3) and further division of ORs within the unit based on the type of anesthesia to be given, despite the fact that all the tables are equipped to take both types of cases (as seen for day 2), reduce, the overall OT utilization. Recommendations were made to reconsider the assigning of the OT tables based on the type of anesthesia.

The study has provided the procedure time estimates; this if used to plan cases can further reduce the idle time, that is, the number of cases planned can be increased, and more number of surgeries can be undertaken on a day, thus reducing the surgery waiting list.

Our study shows that with allocation scheduling for the day, the planned cases can be managed within the resources with no overtime or cancellations due to lack of time.

Conclusion

We conclude with the recommendations that planning of cases for a day should be based on procedure time estimates and allocation scheduling for the cases to the ORs on a daily basis.

The use of software by the OT manager for the day-to-day allocation of cases to the ORs using the procedure time can bring operational efficiency; it can reduce time over-run and idle OT time. The software-based allocation if carried out at the planning level, while preparing the OT list, can reduce cancellation of cases due to time over-run. Planning the cases based on the time estimates of the surgeries and using allocation scheduling can benefit the hospital by increasing per day number of surgeries.

Disclosure of competing interest

The authors have none to declare.

Appendix A. Supplementary data

The following is the Supplementary data to this article:

Multimedia component 1