Reason: Schedules and processes are not coordinated. Planning increases demand. Time measurement changes the schedule.
A chain of arguments:
Thesis: It is not individual activities, but systematically organised complexes of activities that are typical of hospitals. This complex structure is the benchmark for time optimisation.
The goal: ‘Optimising processes in hospitals in terms of time.’(1) Optimisation is not a pro-cess that follows a law of nature. Optimisation requires active control.
The logical question arising from this goal is whether the right resources are available for implementation. These begin with the basic data, the times and their structures.
The answer is clearly no!
Unlike in the past, hospitals today must not only ensure that the right medical specialties are available in sufficient numbers for operations. Operations are becoming increasingly specialised medically. Quality requirements are rising, which on the one hand increases the number of cooperating specialists, but on the other hand shortens their attendance time, as it is limited to specific tasks. This parcelled the time structures for staffing requirements. To this end, an adequate, multidimensional time system must be developed, be-cause for the operating theatre manager or the chief physician conference, the need for specialist knowledge among operating theatre staff is increasing with…
"Process optimisation in the operating theatre (through)… minimally invasive procedures, intraoperative imaging,… the need for specialist knowledge among operating theatre staff. An operating theatre is not (only) managed by a large operating theatre team, but also by staff who specialise in specific procedures… This results in new requirements for the functional planning of capacities and operating theatre times." (2)
The usual formula: [(number of activities * average activity time) : (annual working time)] cannot be used to calculate performance units (x) for staffing requirements. It is unusable because it:
- is based on an average arithmetic activity time and
- refers to total working time close to the balance sheet.
- does not calculate staffing requirements, but rather workplace financing with cases. (y)
The formula is known to produce arbitrary, ambiguous and imprecise results. In the ab-sence of anything better, it is used as an approximation method for planning. However, due to its dubious nature, it is…
‘… unclear whether staffing plans are even in line with requir-ements …’ (3)
The Solution Steps
Step 1
‘Personal sovereignty’ over the desired use of operating theatre time must be ended. Currently, the organisational principle of individual benefit maximisation for full-time employees dominates, leading to subjective standards regarding the overall use of operating theatres. At present, an agreement is usually concluded. It consists of the…
‘service levels agreed between the management and the chief physician’ (4)
This ‘subjectivism’ must (and can) be eliminated – especially in view of the increasing prevalence of computer-assisted and minimally invasive surgery. Medically, these pro-cedures are based on real-time digital structures, but organisationally they are linked to subjective, manual organisational structures. This structural disharmony prevents the growing efficiency of real-time medical structures from having a positive impact on the eco-nomic performance of hospitals. When TuR-P was still performed according to the ‘Millin’ method, two doctors were required. With the current laparoscopic TuR-P, only one doctor is needed. Nevertheless, personnel costs are rising.
Only when organisational time structures are available in digital form can they be integrat-ed into digital medical structures, and only then can the potential for medical efficiency be fully exploited economically. This is possible because:
- Every medical activity has a temporal sequence that forms the inherent basis for the organisational time structure.
- Every division of medical labour is cooperative in terms of time, so that all basic times can be integrated.
The strategic premise is to maximise the collective benefit for the hospital. The organi-sational basis is the tamper-proof measurement of activity times, which are digitally pro-cessed and incorporated into the planning of full utilisation of the operating theatres. This is calculated using the current, time-dependent activity density function across all oper-ating theatre shifts. What is new about this is that…
‘if real optimisation is to be achieved, then optimisation must actually be planned’.
This schedule optimisation does not serve the purpose of formalised ‘preferred scheduling’, which becomes meaningless in view of the actual workflow in the operating theatre and leads to a de facto unplanned workflow, but rather serves to optimise the real-time control of the actual workflow in the operating theatre.
Example: The request from the management of the University Hospital in Prešov (Slovakia) is: Is it possible to optimise the merger of a small operating theatre wing with a larger one? Currently, both are operated separately.
The monthly schedule contains all the necessary data total operating room capacity 100%
The calculation using the activity density function yielded the following result:
The time-dependent use of the operating theatre is very uneven and inefficiently distributed throughout the entire standard working time (1.5 shifts).
Consequence: At 48% (+52%=100%), the planned staffing requirements exceed the medically necessary requirements.
Because only a few actual operating times (according to protocol) were available, time op-timisation could only be estimated. However, if the actual operating times (as is often the case) are ≈1/3 below the current planned times, then the following estimate applies in the first approximation (blue): Optimisation is possible!
Full operating theatre utilisation in Prešov is just one example – but —
It is best for you to have your own time utilisation tested.
Request the test in the calculation module.
Step 2
Time optimisation planning must always be based on individual operating times. This means that the individual times must already be optimised. However, they are ‘inflated’. Currently, each full-time employee selects a strategy duration when planning their individual operation. The full-time employee must plan an arithmetic activity duration, even though they cannot know this objectively. This fictitious time is determined by subjective rationality. It is based on their own ‘personal experience … [on]’ <sup>(5)</sup> This is based on empirical values, reference values, performance units, guidelines, etc. It is in their nature to plan with the help of “time capsules,” whose function is to be large enough to include the “outliers.” As a result, the planned times are excessive.
Average times are only seemingly scientific. Their disadvantage: they generate systematic overtime. The overtime does not differ from the empirical value.
Despite this strategy, this does not mean that the formal planning of all individual times is wrong. This results from the dispersion. In the frequency distribution, ≈ 5–8% of the indivi-dual times (almost) correspond to the “inflated” planned operating time. But ≈ 92–95% of the individual times are significantly oversized = idle times of the first order.
The graph illustrates this using the operating times from the TuR-P example.(6) The “exper-iential time” of 60 min is much too long for the other 4 TuR-P times; only the individual time of 55 min is (almost) correct. The average time of 44 min is close to the individual time of 40 min. Conclusion: 80% of the times are also “inflated” here, while 20% are close to reality with only an 8% deviation.
Three sub-steps are required for error correction:
Step 2.a
Actual times become (real) planned times
The actual individual operating times are measured without manipulation using sensors. This raw data is operationalised to generate time information that forms the basis for the real operating theatre schedule. A time centre is defined in which >50% of the statistically distributed individual times fall. The time centre is usually left-skewed in the frequency distribution – i.e. it does not exhibit average characteristics.
Example: A hospital wanted to know: Is there a correlation between the weight of a gland and the operating time? Answer: No
However, the analysis yielded a completely unexpected result. The most probable operat-ing time (frequency table) could be calculated for each individual urologist. Conclusion: The planned time is the time with the highest probability, not the ‘time capsule’.
Step 2.b
Integrated working time
When calculating requirements using the standard formula: [[(number * average time) : an-nual working time] using the easily calculable average time, each full-time employee is separately ‘assigned’ individual operating theatre time. This calculation does not allow for flexible influence (integration) of the members of the surgical team in terms of time.
The accuracy of this ‘rigid’ calculation is very low.
Medically demanding surgical activities require the systematic cooperation of specific medical specialists. This creates interfaces, but also an organisational structure that integrates the individual activities at a higher, holistic level. This situation must be adequately reflected by a ‘consolidated’, integrated activity time. For this purpose, the currently measured individual duration of the ‘n’ different specialist activities is assigned to their n time dimensions in an n-dimensional time volume, and the integrated activity time is calcu-lated from this. This is entered as a time event in an ordinal frequency table.
The integrated activity time is dynamic, as the cooperating activities never take place at the same time due to the individuality of the patients and the full-time staff. In addition, there are time anomalies due to unplanned complications that the specialists have to deal with. Anaesthesia, for example, depends on widely varying ASA scores. With an ASA score of 4, the time deviation is significantly greater than with an ASA score of 1. This prevents a permanently consistent, identical time synchronisation with the other specialists. Radiology also sometimes has reason to take multiple images. A linear time calculation is completely unsuitable here.
When a specific activity time changes, the measured time changes on its time dimension, which affects the integrated activity time. This creates a ‘time cloud’. The core interval is formed from >50% of the individual times. This is the planned time for an operation with division of labour. It cannot be compared with the ‘unrealistic’, subjective experience of a full-time employee.
Time integration has a particularly positive effect on the hospital’s economic efficiency. The calculation of integrated activity time replaces the…
‘…criterion: sum of individual benefits… as an addable quantity… (new quantity) ordinal values (better/equal/worse). Marginal pro-ductivity must be equal. This condition ensures that the greatest possible quantity of goods is produced.’ (7)
Full utilisation ensures the same organisational conditions in all operating theatres, so that the marginal productivity of the surgical teams grows at the same rate. Collective benefit maximisation for the hospital can therefore be implemented consistently (no interfaces) from the overall operating theatre resource down to the individual basic activity. There are no separate stages of value creation, which makes economic control possible.
Step 2.c
Checking the time required for individual activities to verify implementation of the operating theatre plan – the path to a digital twin
The optimisation goal is to achieve full utilisation of the operating theatre. This was planned using PARETO optimisation based on time centres (confidence intervals). However, due to significant differences between individual patients, the confidence intervals may be exceeded in real life. This is measured and a targeted time adjustment is made.
This is possible because medical activity as a whole consists of a sequence of qualitatively different sub-activities, each of which has its own time. The time centres of the sub-times are calculated in the same way as the total activity time, which leads to a consistent, conditional relationship (no cause) between the sub-times and the total time. This can be calculated using Bayes’ theorem. Since this applies to all evidence-based operations per day, a permanently calculable time structure is created for the continuously implemented overall operating programme, so that the overall process in all operating theatres is also permanently PARETO-optimised. In principle, the plan and reality are almost identical. The result is a consistent ‘network of times’.
The creation of the ‘network of times’ marks a qualitative change in time management.
The medical process itself drives its own time management process.
Time management has been separated from the subjective abilities of full-time staff.
The benefit: The mathematically digitizable basis of the digital twin has been created.
‘…criterion: sum of individual benefits… as an addable quantity… (new quantity) ordinal values (better/equal/worse). Marginal pro-ductivity must be equal. This condition ensures that the greatest possible quantity of goods is produced.’ (7)
Full utilisation ensures the same organisational conditions in all operating theatres, so that the marginal productivity of the surgical teams grows at the same rate. Collective benefit maximisation for the hospital can therefore be implemented consistently (no interfaces) from the overall operating theatre resource down to the individual basic activity. There are no separate stages of value creation, which makes economic control possible.
A digital twin is a..
‘…virtual model of a physical process that reflects its properties… in real time. The digital replica enables: real-time monitoring; scenario planning; fault diagnosis; performance optimisat-ion;…’(8)
Demonstration of the basis of the digital twin: The times of the sub-activities of the (TuR-P) and the total operation time show how the times are related. Blue times are directly related, grey times are indirectly related. Their integration creates a conditional relationship.
The advantage: even before the end of haemostasis, it is known whether the TuR-P will be completed on schedule in 45 minutes or whether there will be a delay. The next patient, their surgeon and the transport service can be informed (pull management). There are no idle times for the subsequent operation.
This is technically possible by measuring real time with sensors.
Step 3
All full-time employees in an operating theatre currently plan for tactically extended times compared to actual times (‘time capsule’). Everyone must make this time capsule as ‘unassailable’ as possible in comparison to the others. However, since no one can be sure that there will be no ‘time outliers’, the best strategy is to additionally secure the time capsule with a ‘time buffer’ to avoid collisions with the times of predecessors and successors. Everyone behaves in the same way. This leads to an inefficient, uncooperative time structure (= NASH equilibrium) in the operating theatre = second-order idle time.
(See also: Original operating theatre plan for the orthopaedic clinic (9)) – This can be calculated mathematically.
Internationally, operating room utilization is around ≈62%. It varies between EU countries, ranging from 49% (Italy) to 67% (Netherlands).
Solution:
Distribution of the ordinal medical activity times of all planned operations using ordinal PARETO equilibrium optimisation across the number of operating theatres.
Demonstration: 5 TuR-P: 35, 35, 40, 50, 60 = 220 min (Ø 44 min) are to be distributed across 2 operating theatres without idle times. A NASH equilibrium based on 44 min Ø cannot achieve this. However, this is possible with ordinal times.
An event field with 55 = 3,125 occupancy possibilities is generated and divided into 2 sub-sets for 2 operating theatres. Each rank is assigned an operating time and the 3,125 per-mutations are executed. The 5 partition series with the smallest time difference are optimal. The demonstration shows the
Large surgical facilities that operate in multiple shifts, have more than four operating theat-res and therefore perform more than 15 operations per day would have to calculate significantly more than 1515 = 4.3789×1017 permutations for optimal planning. As operating theat-res grow in size, the number of permutations also grows exponentially, but at the same time, savings in staffing requirements and opportunities to deploy the full-time staff saved for other purposes also grow exponentially.
A standard PC processor can handle the task in a very short time. Furthermore, there are no quantitative limitations for AI algorithms. Digital time optimisation therefore pays off both organisationally and economically, because…
The more digital permutations, the greater the savings in:
a. digitally controlled, organisational time sequences and
b. the reduction of medically unnecessary personnel.
The difference:
There is also potential for savings in manual time management – but only ‘virtually’, be-cause even if the operating theatre manager tried to create an ordinally optimised operating theatre occupancy, the number of permutations required would be beyond human capacity.
Conclusion:
Non-digital operating theatre scheduling ‘manages’ existing time-saving potential.
However, it cannot exploit this potential without digitalisation.
TuR-P served only as an example – but —
– Having your own digital operating theatre scheduling tested is best for you.
Request the test in the calculation module!
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(1) (https://www.air-log.com/de/newsartikel/prozessoptimierung-im-krankenhaus.html)
(2) (https://www.kma-online.de/aktuelles/medizintechnik/detail/der-zwang-zur-effizienz-und-prozessoptimierung-im-op-a-34389)
(3) (https://www.arbeitszeitberatung.de/fileadmin/pdf-publikationen/pub96.pdf)
(4) (ibid.)
(5) (https://www.fraecermed.de/idle-times-2nd-type/)
(6) (Staff shortages and staffing requirements in hospitals)
(7) (https://www.welt-der-bwl.de/Pareto-Effizienz)
(8) (https://leverage-robotics.com/glossar/digitaler-zwilling/)
(9) (https://www.fraecermed.de/original-op-plan/)