Digital business model innovation reduces staffing costs with AIdriven division of labor based on ordinal activity times, generates full utilization, and prevents hospital insolvency.
Itable of contents
 Digital business model innovation was thought of early on – why did it permanently fail? Early digital aberrations are still present at present.
 First the ddigital business model innovation generates qualitatively new organizational structures. They solve the profitability problem with timeefficient staffing!
 A. Digitization goes through an algorithm that formalizes the facts.Digitization is not possible without mathematization.
 B. The source of value is timeefficient medical procedures. The two are mutually dependent. They are digitized in context. – Value creation and timeefficient organization have a reversibly clear relationship.
 Individual medical activity time (ΣmTZ) is calculated ordinal. Medical activity time cannot be calculated like production time.
 The specificity of ordinal activity time(s) in the organizational process – Arithmetric and ordinal times are quantitatively and qualitatively very different.
 Limiting ordinal activity times for arithmetic computations – Scaling differences: ordinal – arithmetic must be overcome by boundary value formation. This is the only way to create realistic time ratios.
 Combined ordinal activity times enable efficient organizational worksharing – Full utilization is made possible by multidimensional PARETO optimization.
 Design of fullload, multidimensional ordinal schedule optimization – Permutation optimization in the scattering event field
 Permanent time optimization of the PARETO front to compensate for real scattering single times – timing with conditional probabilities, applying BAYES’s theorem.
 Organizational and economic savings potential –
 Design of fullload, multidimensional ordinal schedule optimization – Permutation optimization in the scattering event field


 The staff requirement sinks permanently on ^{2}/3 of the current strength.
 Automatically adjust staffing levels to accommodate flexible caseloads.
 Z. B. Operating rooms: 8⇒ 5⇒ Staff cost reduction ≈ 1,2 Mio € / J.

 The Pull Time Strategy – Efficient “employee logistics” in the real organization – Practical use of conditional time probabilities
 Digital twin – process control of random times – The concept of time preview and active time control
 The (abstract) the overall concept
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1. Digital business model innovation was thought of early on – why did it permanently fail?
a. Unreal goals and false calculations always led to transformation of the business modelfailures – the failures are unresolved and ignored.
Digital solutions were already being developed for economic staffing to z. B. the …
“Causes regularly occurring overtime despite additional physician positions”, (Pragma) …
to be able to eliminate. But to do so, the Big Data concept (B D) was populated with existing inefficient data, in the hope that the concept would “find” the optimal time structures, without even suspecting that in this way analog time inefficiency would only become digital time inefficiency. Onefold reformatting was bound to lead to a negative result.
A viable concept has not yet been found, even at present:
α. The eone group is nihilistic and disillusioned, stating: …
“… z. Zt. doesn’t reach the doctor… Digitization is not worth it”
Youdoesn’t notice that in this review, the real (IT productivity paradox) appears to be operating in the inefficient structures they themselves initiate and that, for this reason alone, Digital Business Innovation is urgently needed.
β. The second group is euphoric, believing in the “economic healing powers” (virtually a “digitales drug”) emanating from digitization, despite failures. It is supposed to “cure” inefficiencies with “its own efficiency”. This delusion claims: it will …
“… later higherlevel software help solve economic problems” (Walker Project).
γ. Die third group beats “digitalNebengbusiness” for clinics, around the economic main problem: income < effort“mitigating” by mitigating. ..
“it is succeeding in reaching new customer groups… by combining fitness apps, Skype with… subscriptions“ (ZEQ)
This is based on examples of (businessmodelinnovations) from St. Gallen referred. This shows: Here, the economic impact of the digitization pprinciple not understood. Dthe examples from StGallen are because of theirzero marginal cost propertyeconomic – they own pure digital form. A hospital housebusiness model can be based on kembodied fullstaff, also never do without digital consulting. Bottom line: Am reducing medically unnecessarypersonalexpenses to reduce coststhere is no way around.
δ. The overwhelming majority maintains “loud silence” on Digital Business Model innovation to achieve sustainable value creation in hospitals because:
Where (supposedly) no problem is no solution needed.
But regardless of the (protective) stance, an economically “explosive” development is approaching: increasing risk of insolvency while sales are rising (Ø≈4%/y), growing staff shortages while workload ratios are poor (i. OP ≈ 62%). The enumeration can be continued. These contradictions force digitized solutions, even according to serious management consultants, because …
“Innovation and Digitizationare becoming the central lever,… Those who fail to… position itself witha newn business model, will… cease to exist. “ (Deloitte)
Positively worded: A Digital Business Model Innovation, relative to current levels of staffing costs, enables a permanent, real ..
Savings of ≈ Ø ⅓ dof personnel costs /Jyear.
Question: What digital means must be used for this?
2. Only a ddigital business model innovation generates qualitative new organizational structures that solve the problem of economic efficiency with time efficient personal use!
2. A. Every Digital Business Model innovation goes through a algorithm that first formalizes economic facts.
.
To take advantage of the productivity boost provided by the partially. impressive, patientoriented digitizations, for the hospital’s value creation, the worksharing processes that organize these efficient treatments must proportionally reduce effort. Patientoriented and organizational digitalization must both work efficiently. To be able to digitise organisational structures, the mathematical procedure for digitisation must be applied to valueadded structures. It goes through the following stages:
 Digitisation of a subject matter starts from knowledge about the subject matter. Value creation must first be understood rationally.
 The knowledge must be in theoretical form, so that it can be transformed into adequate, mathematical form (formula, algorithm).
 If it is in mathematical form, digitization is “just” the mathematical transformation of a given decimal structure into an equalvalue dual structure. The “tool” for the equalvalue transformation is the Boolean (algebra), because…
“…Every formula in Boolean algebra has a dual formula. Is the A FORMULA AllOWED, then it is also YOUR DUAL FORM,…”
The reverse: the currently common preferences (OP statutes), hierarchical practices, time estimates, Ø sizes, reference sizes (see. Staffing needs calculation), parascientific “art structures” (see decimal full staff), unreal ratios (see case numbers / full staff), etc. have no theoretical content. Such “subjectivisms” are not mathematizable and consequently not digitizable. They mathematically take the form of (Bayesian NASH equilibria). Equilibria are known to be the opposite of processes.
2. B. Digital business model innovation magnifies value creation by organizing medical operations in a timeefficient manner. Goal: Reduce staff costs.
1. Theoretical basis is valueadded accounting.
The term capitaloriented (success) is inappropriate because of its ownerorientation. It may be negative for him even without the risk of insolvency – but not for the hospital. If success is understood as value creation, insolvency risk is signaled early on, because value creation is never negative. The imminent digitisation target is about ordinary operational success = value creation of the KH. This is calculated from the realised ratio: origination – distribution.
“The relativized analysis has the advantage of the reference to the influence size (value creation) , characterises the operationalproductioneconomic activities. .. and resorts to traditional results source analysis… The hallmark of the concept is an origination account that allows statements about the sustainability of valueadded components and their distribution” (KH. Küting, CP. Weber: Die Bilanzanalyse, Verl: Schäffer/Pöschel, S 304, 324 ff)
Valueadded accounting is based on the requirements of the German Commercial Code (HGB § 275, para 2+5) (outline). The structural presentation is made according to: RD. Pfister; Valueoriented in Organizations, Basis of the Holistic Value Management Approach (n. European Standard 12973, vol 1; p 308) (value creation). Typically, their dichotomy: Creation = Consumption. Success here falls into consumption and is the consumable business share. The internal construction of the valueadding enterprise always builds on (selfconsumption), with selfconsumption not being allowed to be greater. It includes fixed payment obligations and the variable profit share (Ef > 0), because…
“Value creation is an integral part of any economic activity because only expected added value(Ef) induces economic agents to transact”
The value chain statement is also the factual basis of a Digital Business Model innovation in hospitals, by providing the theoretical, i.e. digitalisable knowledge. For the “internal control” of value creation several properties are significant:
Control over effort uses a “threshold” for personnel costs. It allows no unbridled growth. The valueadded structure is rearranged: WE = WV ⇒ (PW – VL) = (PK + tax + cap. Interest [Foreign+Own] + Ef) yields: ⇒ (WE) – (PF + tax + cap.interest) = Ef > 0. If taxes and interest are neglected because of lower, the 1st approximation yields a basic equation:
(WE) – (PK) = (EF) > 0.
Economic Strategy Approach for Digital Business Model Innovation: The level of personnel costs must always be managed to permanently stay below the size of the value creation. Then (Ef) > 0 and there is never any risk of insolvency. It follows: The most important task of a runoff digitization is: to provide the …
… quantitatively manage organizational efficiency so that the valueadded volume is not more than consumed at inception !
2. Mathematical relationship: value creation – organization
But Digital Business Model Innovation Fails on Pure Monetarian approach to the equityoriented notion of success that is exclusive to hospitals. It…
is being used by socalled profit and loss… affected. (They) always affect the income statement. Consequently, a profit increases equity, a loss decreases it. (equity)
Personnel costs are “only” a deduction and not an operating expense after that. This exclusive focus on monetary amounts prevents a look at their organizational sources. First, the valueadded account [according to (Schmalenbach) asks about the “causal” connection between organizational structure, the operational source, and its own consumption, the monetary operational effort.
A mathematical reference can be derived for the relationship between these two qualitatively differently structured enterprise levels, which follows the elemental idea of value creation:
“First something must be produced before it can be consumed”
The basic equation (WE)(PK) = (EF) > 0 is related to its turnovergenerating organizational source for this purpose: case count (FZ). Thus, the equation for economic (intensity) (action effectiveness; analogous to physical performance) ⇒ [(WE) / (FZ)] – [(PK) / (FZ)] = (Ef) / (FZ) > 0. Multiplying by 1 does not change the equation. The same is true for 1 = (PK)/(PK). The result is:
(VK) / (FZ) * [(WE) – (PK)] / (VK)= (VK) / (FZ) * (Ef) / (VK) = x > 0 D. i.e.: Organizational Efficacy depends on the factor: (VK) / (FZ).
In order to calculate at which quantities of (VK) and (FZ) which “efficacy” is achieved, both must be comparable across a common dimension. In organizational structure, this is time. If both dimensions are transformed according to their organizational time forms, the result is for: (FC): (mTZ) = medicine. Tätigkeitszeit and for (VK): tarifl.(AZ): (tBZ) = geplante Belegzeit (subset tarifl. AZ). (VK) / (FZ) becomes the time ratio: (tBZ) / (mTZ). Because in the medical process no full power (VK) has an interest in extending the (tBZ) at the individual patient longer than it is necessary for the execution of their medical activity (abuse not considered), a limit value is given:
(tBZ) ≥ (mTZ) → (tBZ) / (mTZ) ≥ 1 m. : lim (tBZ) / (mTZ) → 1
After transformation, organizational effectiveness (VK)/(FZ) = 1 gives temporalorganizational measure: 1 = 1 // [(∑tBZ) / (∑mTZ)]. If (VK) / (FZ) is replaced by this measure, a equation in which this measure expresses the effectiveness of organizational structures for value creation emerges. This factor: 1 // [(∑tBZ) / (∑mTZ)] is the “control variable”. The basic formula is:
[ 1 // (∑tBZ) / (∑mTZ) ] * [(WE) – (PK)] / (VK)] = (VK) / (FZ) * (EM) / (VK) > 0 with [lim: ∑(tBZ) / ∑(mTZ)→ 1]
Managing such hospital organizational structures timeefficiently requires consistent digital business model innovation.
3. Data basis of digital business model innovation are real, individual activity hours in ordinary calculation
Note: A single value of: (tBZ) / (mTZ) must not be scaled. The single ratio is simply a quantity.
When time is spent on several medical activities (e.g., planning), the individual values are classified into relationships to others (mTZ). The problem: Because no single (mTZ) is the same as another, the ordinary class size of (∑mTZ???) must first be determined. It is not identical to the usual Ø time.
The unaccounted for difference of ordinal scaling of medical activity times and tariffed times (tBZ) is a main reason of the permanent failures in flow digitization ! !!
In order to have a sufficient understanding among medical professionals, the difference is explained by way of example. Because individual times are not calculated ordinally in HIS, the real OR times for the TuRP’s were taken from the Operation Protocols, which were originally intended to determine a correlation of prostate size and time duration – it was a failure, but it led down the right path.
Usual procedure calculates the (arithmetic) Ø time of 46.3 min from the individual times. But even a cursory look shows: the individual times don’t compress (as they should) in a Gaussian bell around the Ø. Even more drastically, not a single value is on the Ø. A metric scaling test would have to check whether a…
“additive change… indicates…change in actual size.” The following is an example of an additive…change in actual size. (size scaling)
The condition is not met. Reason: surgery times cannot be changed arbitrarily. I.e.: OR times are not arithmetic scaled.
3.1. The basis of a Digital Business Innovation must be real time data – and that is ordinary scaled.
One medical activity time(mTZ) is the INDIVIDUAL period of medical activity of a individual full force (FC) on individual patient (= case (FC)). It has the following (unusual) properties:

 (mTZ) can only be the measured time difference of the activity from its start to its end, because no (VK) can determine before the activity starts, in the sense of a mental experiment, what duration it will have. Manipulationfree time measurement is the basis. Typical for medical activities is that their duration is several similar never equal. The times differ in rank, but not in time interval – (hence ordinal scaling).
 Medical activity time has a special feature: the total activity is always a sequence of qualitatively different partial activities. These can be characterized in terms of time in the same way as the total activity. Consequence: in timeorganizational terms, total activity time is based on a noncausally related set of inherent parttimes, which determine a (preorder) for total activity time. Thus, the ordinal scaling of the total activity time is ordinally “underscaled” in its various subtimes.
 In single time, there is no scaling. Quantitatively, arithmic and ordinal single time are the same. The difference only becomes noticeable with class formation.
 Each individual time is unique. Consequence: there are no multiples of it and vice versa: it is not divisible.
forming ordinal time classes for the equal activity one full power.

 Ordinally scaled times are orderedas time events in time intervalst. The individual times fall as anonymous time events in one of the time intervals and appear in a frequency distribution in their entirety as ordinal dispersal. This can be calculated via rankdependent increase or decrease of the time event number (compute). To do this, each rank is compared to each in the event field compared. In the event field, the “most stable“ event range where there is no increase in time events at rank to either predecessor or successor – where: Δ=1 is. This is the mean rank distance of the time event from all others. It represents the ordinal time class for the set of singular (mTZ).
 After the mean rank distance is determined, the Δ=1 associated, mathematically unique time interval in the frequency distribution is derived. In their time interval sequence, this one interval represents the time center (Zz) of the distribution and serves as a plan variable in scheduling.
 All later individual times fall randomlydispersed in the frequency distribution, amplifying it and describing the charactoristic time behavior of these individual (VK) when repeating the activity increasingly more precisely (see: (simultaneous measurement) Heisenberg blurring), as shown by the TuRP times of the (CHA).
Class
Calculation yields: (Zz): 35 Min; Probable realization (p): 77%. In organizational planning, the tariff partial working time (tBZ) is applied in the factor: 1 // [(∑tBZ) / (Zz)] to the medical time centre (Zz) – this reverses the current state of affairs and is an essential part of Digital Business Model innovation for this reason alone. When the threshold value “1” is reached, “high efficiency in time” follows.
Spreading a medical activity time is not arbitrariness, but rests on differentially developed medical skills of a fulltime staff when dealing with the individual specifics of the patient.
The ordinal dispersion calculation (Zz) in the above distribution graph yields different frequency distributions for the 5 (VK) on the example: TuRP, whose ordinalstatistical properties account for the large deviations from the zth percentile. Currently common Ø time, both in time orgaisation (see Zz values) and in working time calculation (see tariff AZ). They will serve as demonstration examples in the remainder of this paper.
You can see from the analysis of the different full staff (FSC) that each of them solved the individual patient problems with their personal individuality timeindividual approach.
From the Practice: The evaluation of the times in the medical team caused considerable astonishment because there were large differences between the usual Ø time: 46.3 min / OP and the individual time centers (Zz), especially for the OP time planning.
Attention, this revealed a (solvable) problem
Even more astonishing were the differences between “felt” OR working time / mon. and measured monthly working time. It turned out: the monthly working time as the sum of all individual times / month correlates with the sum of the scatter values. It does not correlate with the nfold Ø times. These “distort” the actual workload.
⇒ Because the dispersion with its time center (Zz) for each medical activity time can be calculated mathematically, Boolean algebra is applicable. Consequently, the time base of medical activities is digitizable. The usable software already exists.
As of now, the “distorting subjectivisms” (estimates, benchmarks, reference numbers, revenueoriented staff sizes,. ..) that have prevented Digital Business Model innovation so far are no longer required.
The elimination of those parts of the business process that do not add sufficient value is part of the implementation of a Digital Business Model Innovation.
The concept of “timebias“.
It refers to the nonunique fact that a small part of the time used for planning almost or completely coincides with the reality. However, the vast majority of the times are simply wrong. Reason for this “confusion”: in practice one is forced to conform to the ordinal property of nondivisibility. In planning – without practical danger – arithmetic is used. This “arithmetic hermaphroditism” produces two types of illusory solutions in practice:
 Type 1: “shell planning” ⇒ (arithmetic over ordinal). It is necessary because it must “wrap” the real nondivisible ordinal time far enough. This “overscheduling” of activity time is one of the reasons for medically unjustified staffing requirements.
 Type 2: “ParallelZiteration“ ⇒ (computing in “stretching” time units produces “juxtaposition” instead of complex cooperation). The medical division of labour, typical of hospitals, is implemented in a linear way in terms of time organisation and leads to parallel structures instead of multidimensionality in the use of resources (personnel, technical resources).
Type 1 : The “shell planning” or the “shop opening principle”
Such frequency distributions per (VK) are currently uncommon. There are many hospitals that have practice resigned to the fact that planning with arithmetic Ø time (here: 46.3 min) does not correspond to reality (“By chance, that’s just the way it is”). Staff planning is nevertheless calculated with it, even if in organisational practice it has to be dispensed with. For this, the sham solution: “practical experience” has been developed.
But it only superficially dispenses with the theory, without suspecting that it will nevertheless make the ordinary properties of nondivisibility of ordinal time when it uses “maximum time”, even though Øtime is formally a divisible time. It “normalises” the schedule of staff deployment by “abundantly” expecting activity duration by setting precisely the schedule time which, in its experience, is the longest at present. This reallongest single time is now used as a “blueprint” and applied to the other, shorter times for class formation. Except for the 5th OR, 4 ORs are overplanned with 80 min. This assures the 4 OPs that their real times undivided “fit” into the time envelope – the result is an indissoluble contradiction. It does not allow innovation of the business structure through digitalisation.
With this “overplanning” (27%), the remaining 4 (UK) formally as “busy”, even though they are really 80 min not “really” busy.
In the example hospital, they go a step further and forgo using laborsharing resources by “reserving” an operating room all day long. It is scheduling according to the “shutteropening principle“. The “store opening” generates 182 min = 45% idle time (utilization 55%). The Ausrede: the OR team needs preparation time.
Conclusion: The timing is in line with reality at < 20%. At > 80% it is overscheduled. 1 // [(tBZ) / (mTZ)]is not computable, because (mTZ) is falsified. Suchoverschedulingare only qualitativeevident.
On type 2: division of labor as “uncooperative parallel use” of capacity
.
The “bogus solution” for division of labor attempts to solve resource utilization with the divisibility of arithmetic Ø times of activities. A typical, technically complex example is calculated by: T. Klöss, Capacity planning; (OPManagement), Ch: E.1.; pp: 154 ff. He is of the irreverent opinion:
“The OR time requirement consists of the medium CutNath Times. .” (ibid. p 162)
In the simpler but equally structured model calculation for the (TuRP), 5 (VK) with the Ø time: 46.3 min must then be divided between 2 ORs. Formal arithmetic would result in the following division: 2.5 (VK) to each 2 OP with 115.75 min OP time. If the approach were implemented in practice, it leads to strange oddities:
1. As long as (tBZ)level scheduling is not confronted with (mTZ)level reality, there are no conflicts. Anyway, it doesn’t bother any manager when their calculations give strange “decimal (VK)” – here 2.5 (VK) – even though human parts are not medically considered to be unfit for life. The problem is: staffing needs are calculated from (strange) plan figures and not from practice – although that is exactly what is needed.
2. Yetnever has the collective of (VCs) of a clinic operated on a patient collectively – but this is precisely the (supposed) fact that Øtime depicts. But if only individual, integer full forces do this in real life, then the mathematics must be adequate. The arithmetic is not.
As soon as arithmetic times have to be implemented in reality, a “cloak structure” acts on Ø times. Halving the Ø time (23.2 min) means that a real (VK) would have to become a half – 0.5(VK) – so that 1 half in each operating room would “halfoperate” on each patient ⇒ What nonsense! It is unfortunate that mathematics is not physics. Anyone who connects 2 live wires incorrectly there will burn their fingers. True, the “mock planning” has to accept that one (VK) cannot be divided, but thereupon again only a “halfsolution” is developed by linearly updating the Ø time. In the 1st operating room, 3 ORs must now be performed, and in the 2nd operating room, only 2 ORs must be performed. In this mathematically rigid “corset” two effects meet: 1. the additive updating of times and 2. the use of fixed, unreal Ø times. This creates empty time = medically unnecessary staff time. Flexible, cooperative use by adjusting to current, random times does not allow for this “rigid time corset.”
Again, the “time corset” not only doesn’t allow for Digital Business Model innovation. Because such a form of division of labour is not rational, it must be “administratively instructed”. I.e.: This form of worksharing generates in addition to the quantitatively “inflated” time spent on medical activities, time spent on (not calculated here) administrative activities (drafting of OR statutes, allocation of usage rights for ressources, scheduling in chief physician meetings, controls by OR managers,. ..). In contrast, Digital Business Model Innovation realizes the transition from “ownership” to use of resources.
Conclusion: Analogous to α. there is a Overscheduling. Again, 1 // [(∑tBZ) / (∑mTZ)] is quantitatively uncomputable, so it cannot be digitized.
The planning with the (TuRP) is intentionally simple, but typical model calculations. The monthly analysis of the real process in the example hospital, as in 42 other KH’s, shows the same problems. The calculation real time structures was performed using a timedependent activity density function.
The 61.8% occupancy rate results 38.2% medically unnecessary Personnel. This “fate” is not inevitable. Continuing the TuRP model bill, to build full capacity with Digital Business Model Innovation, a Paradigm Shift has been made. The inefficient time structure is changing to digitally controlled, cooperativesdivision of labor:
Placed in the real process results in a fullload (≈ 98%) im Beispielkrankenhaus. The effects of a Digital Business Model Innovation are:
 By (Zz)usage, 3 medically unnecessary operating rooms reduced.
 Because of 1.5 shifts, 4.5 OP teams [16 (UK)] deployed.
 The economic personnel cost saving is ≈ 1.1 M / y.
.
3.2. Limits of ordinal times in economic efficiency calculations
Hospital structures also require the analysis of contexts in which arithmetic and ordinal times occur in common (s: personalternative calculations). Because the two types of time are scaled differently, ordinal time (Zz) must first be transformed into a “quasiarithmetic” limit (aaG) so that temporal quantities of an organizational as well as a managerial nature are comparable. The TuRP times (1→8) of the (CHA) show that this is not possible in the ordinary “raw state”:
t1 < t2 < t3 = t4 = t5 < t6 < t7 < t8 ⇒ (t_{1} ≠ t_{8})
With these quantity differences, the 4 basic arithmetic operations v. the division: (1/tn) cannot be performed. There is no link between tn and tm . It must exist. Quasiarithmetic computation with ordinal quantities is only possible if the axioms of (Abelian group theory), in particular: (tn*tm = tm*tn); t*t^{1} = e and t*e = t are satisfied because of divisibility. The quasiarithmetic transformation must be equal in value.
The mathematical task now is to regroup data. Only those allow for multiple successive iterations until the 8 individual times have been transformed into narithmetically approximated limits (aaG). Individual times (t_{1}≠t_{n}) become: n*(aaG)times. Value equality of (aaG) with the different individual times represents the ordinal modified (HERON)transformation processher.
Important: The nfold (aaG) gives only the actuallyconsumed tariffed working time/mon. The sum: Σ(aaG) also removes the sometimes significant time distortions (especially for highly dispersive activities). Two (CHA) examples:
1. TuRP times: (aaG) = 33,2 Min. For 8 OP/M. = 265.6 min / M = 4.4 hrs tarifl. AZ / M. Sham solution: Ø: 46.3 * 8 ≈ 6.2 hrs / M. I.e.: The (CHA) is 1.8 hr / M tariff overvalued.
2. RPE times: (aaG) = 159.5 min. For 15 OP/M = 2,325 min / M = 39 hrs tarifl. AZ / M. Sham + the values of 3 OA: Ø: 183.4 * 15 ≈ 45.9 hrs / M. I.e.: The (CHA) is 6.9 hr / M tariff overvalued.
The greater the dispersion, the greater the time bias, e.g. ureteral stone, testicular carcinoma, kidney stone,……………………………………………………………………. . The same applies in reverse. The AZ of the STA is real by 1 hr longer than calculated.
After the Heron transformation of the OP’s of one (VK), for example, because of care other (VK), or because of advanced training, etc., these (aaG) can then also be inserted into the usual business calculation. The ΣaaG for all (VK) of urology is:
ΣaaG(CHA) + ΣaaG(OÄ) + ΣaaG(OA1) + ΣaaG(OA2) + ΣaaG(STA) = Total OR time of the Urology Clinic per month
Although this is just the theoretical consideration for a Digital Business Model innovation: 1.8 * 12 = 21.6 hrs/yr ≈ 1,296 min/yr. If more TuRP’s of 35 min each were operated during this time, this would yield ≈ 11,000 € /yr. This should trigger considerations because the OR wing where TuRP’s take place is on the balance sheet, which has to be depreciated annually. Realistic TuPP times with other realistic OR times could help in real terms to ease the balance sheet financial situation of the KH.
The ΣaaG corresponds to the tariff working hours and must be related to the total of all medical activity hours to determine staffing needs. Only here is the factor: 1 // [(∑tBZ) / (∑Zz)] correctly calculable. This has 2 important consequences:
 Long, sometimes very long stretches of activities for medical reasons. But: such activity hours are now not overtime. They are not related to fixed work hours. The calculation is reversed, because the averaged working time is calculated from flexible individual times. The overtime problem is eliminated because (aaG) long and short OR times are “offset” against each other. This results in an “average time load” per (VK). If hospital management practically implements this time flexibility, no unpaid overtime is incurred. Digital business model innovation eliminates this current “coarse grid” of working time calculation.
 The approach of (Pragma): “Causes of regularly occurring overtime despite additional physician positions” becomes moot.
 Because the (aaG) is multiplied by the real, nfold number of activities, a change in the number of cases (FC) is systematically taken into account. As a result, unbridled growth in personnel costs due to decoupling of (AC) numbers from (FC) numbers is eliminated. A rationalization strategy through Digital Business Model innovation becomes possible. The lament of P. Magunia [UB (R. Berger)], the…
financial situation has never been so tight as it is today. … the 600 hospital executives surveyed are more pessimistic than ever about the future.
… Is “fuzzy” and no approach to a Digital Business Model innovation Quantitatively accurate is the Insolvency Monitor from “Creditsafe” to the (hospitalinsolvencies). The geometric average increase in KH insolvencies from 2018 was x° = 16.31% /year. Pessimism no longer suffices. Reality can change. The structures of the Federal Statistical Office (case numbers, employee numbers) Subject Series 12 Series 6.1.1 (2020), can now be a thing of the past:
The annual rates of increase are the geometric average of the annual individual values.



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4. Digital business model innovation generates timeefficient division of labor through Kcombination of ordinal activity times.
The timeorganizational division of labor would have to be the inherent attribute of medical division of labor in order to achieve the economically desired efficiency effect. But: Ø times cannot objectively achieve this. Mathematically, the failed experiment mutates to (Bayesian Nash equilibrium). This does not produce efficiency in the division of labor, because it is in the nature of any equilibrium to respond to change by returning quickly to its initial position.
The task is reapproached. Now real timebaseline data are available. From these, intelligent information for AI control will be generated, providing a solution for medical Organizational specificity finds:
Unlike production, medical activities, because of their ordinal nature, it is not possible to determine their duration in advance of their commencement or even during their course in a predictable manner.
Ffor the organizational structures, 2 tasks need to be solved:
 Design the optimal schedule, with the goal of worksharing fullutilization. Mathematically, it has the effect that in the factor: 1 // [(ΣtBZ) / (ΣZz) the planned occupancy times (ΣtBZ) become almost identical to the medical time centers (ΣZz). The factor takes the total value “1”: ⇒ I.e.: there is (almost) no medically unnecessary staffing.
 Permanent time optimization of the real procedure, so that partial deviations of real individual times from the plan can be corrected for. For its realization, the factor: 1 // [(ΣtBZ) / (ΣZz) = 1 automatically and permanently must strive for its limit: [lim: ∑(tBZ) / ∑(mTZ)→ 1]. This is the “mathematical core” of Digital Business Model innovation in hospitals.
To α: Timeoptimal planning of the workflow
The mathematical basis of Digital Business Model innovation also requires new computational structures. Ordinal activity times (mTZ) are no longer additive numbers, but they are interpreted as time sets with rankordered elements. The “summation” becomes the union of elements of a time set – properties that are well suited for the organizational division of labor.
In organizational division of labor,“n”full forces (FCs) in “m”parallel ordered resources (spatial dimension) over the “t”time ((clock)time dimension) are used. In addition, there are subdimensions for the time nesting of the dependent (VK) (see surgeon⇔anesthetist). Timestructurally, this is a data cube (ndimensional matrix w. pvectors). Activity always consists of ideationalplanning and materialpractical elements. This requires 2 data dimensions each: Time planning / Time realization. Their interaction is possible through optimization. The mathematics for this is ordinal, dynamic, multicriterial (Paretoefficiency). In terms of value creation, it has the
“…Property that no one can be made better off without another being made worse off…. Pareto efficiency can thus be considered absence of wastefulness“
A sophisticated mathematical account can be found in the dissertation: (computation) Pareto efficiency is the systematization of the core of a
Digital Business Model Innovation. ⇒ Because the timeoptimal organization can be computed mathematically from many medical activity times, the Boolsche algebra is applicable. Consequently, optimal time organization of medical activity times is digitizable. The usable software already exists.
To understand the principle of Pareto efficiency, the demonstration calculation continues with the TuRP times. They are intended to explain the digitally controlled structure of a multidimensional scheduling (special structures: emergencies, deferred urgency, high sterile and/or septic space planning, curfews, etc. require complex permutation structures. They follow the same principles as elementary permutations, with appropriate adaptations. For simplicity, the complex representation is omitted).
Note: Ordinal arithmetic dispenses with the 4 basic arithmetic types and is toosoon unfamiliar:
 Step: generate an event space (= theoretical total number of all possible combinations). The possible rankings of the 5 ORs are calculated: Ψ = 5x5x5x5 = 5^{5} = 3.125 equivalent arrangements.
 Step: Activity dimension: Within the 3.125, permutations of the concrete individual combinations are considered: For the 1st TurP we get: 1,2,3,4,5⇒ 2,1,3,4,5⇒ 2,3,1,4,5⇒ 2,3,4,1,5.⇒ 2,3,4,5,1. Analogous combinations also apply to the 2. 3. 4. and 5. TuRP.
 Step Space Dimension: The 5 TuRP should be performed in 2 OP’s. This will decompose the activity dimension 1 – 5 into 2 subsets each. For example, (1,2,3) (4,5) are created… so 3,125 x 2 = 6,230 activity subsets. For them, (1,2,3) is equal to (2,1,3), (2,3,1) and (4,5), (5,4) Important: There are no singular, but only plural solutions in the multidimensionalworkstep sequence.
 Step time dimension: activities 15 are given associated times: 1=35; 2=40; 3=50; 4=35; 5=60 min (Σ= 220 min). According to the activity subsets of the space dimension, 3,125 time pairs are now created. This results in different time sets per OR room (regardless of the order in which the subactivities are performed within the OR), from which their time difference (Δ) is calculated. The pairs are ordered by size. The mathematical analysis looks for the pairing with the smallest time difference. The minimum ensures that neither of the two surgical teams has to work idle time or overtime. This is the Vfull workload that the Digital Business Model innovation realizes.
 target value for fullutilization TuRP: 220/2= 110 min. From the pairs, the ones corresponding to the target value 110 min are chosen. The pair: (1,2,3) (4,5)⇒⇒ (125)(95) = Δ 30 is unsuitable. It generates 27.3% idle time+overtime. This combination is just short of the currently typical underutilization – in (very) many operating rooms, ≈ 33% is considered “normal”. Optimal: Ranking: (1,4,2) (3,5) ⇒ (35, 35, 40) (50, 60) = (110) (110) ⇒ ⇒ Δ+/0 = Full load factor.
Flexibility: The quantitative structure can be optimized within its framework according to practical needs. Because it is a quantity of time, (VK) can use it as variablesvolume of time by swapping among themselves according to their arrangements. In the OR example, 6 swaps occur without violating the principle of full utilization. This also makes it possible to take into account special requirements (see above).
The 1st stage of a Digital Business Model Innovation in hospitals has been completed with timeoptimal planning. In the 2nd stage, an algorithmmus must now implement the planning in a process governed by predictable time contingencies.



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To β: realizing the timeoptimal, divisionoflabor flow
In full operation of a hospital with more than one shift and in an OR wing with more than 3 OR rooms, the plain model calculation for the optimal time flow is mathematically insufficient. Following the same principle, complex models for complex flow structures have been developed – modified ordinally – to evolutionary algorithms suitable for multiobjective optimization in hospitals. Underlying them is a maththematic algorithm that can be implemented via a (Pareto front) a structured complex of single times can control the optimization of twodimensional spacetime.
In multiobjective optimization, the Pareto front (also called Pareto frontier or Pareto set) is the set of all Pareto efficient solutions. The concept is widely used in engieering. It allows the designer to restrict attention to the set of efficient choices, and to make tradeoffs within this set, rather than considering the full range of every parameter.
Of the 3 proven types of evolutionary alorithms, the ordinal modified method of the goal attainment function was selected for Digital Business Model Innovation in Hospitals.
“The method of target achievement function estimates the probability of achieving the target in the target space and looks for significant differences between these probability density functions for different optimizers. “ (goal attainment function)
It’s mathematical generality allows it to be used to optimize time for other medical activities as well (e.g.: differential diagnosis process) to achieve endtoend Digital Business Model innovation.
Specifics of time organisation:
Ordinal singleztime falls in the real sequence not only “into” but also “beside” the time center (Zz) but into the time pattern. They deviate from their (Zz) depending on the activity constancy of the full force (VK). When which specific case occurs is a matter of chance. Reason:
 In optimal scheduling, the “stable” time center (Zz) is explicitly defined as a plan size.
 In real time, individual times scatter over the interval [0→(Zz)→1]. For the most part, they generate time differences with respect to (Zz).
H. h.: In pt 2, the difference is: single time⇔scheduled time in (computable) context. The real “time gap” can and must be closed computationally because of the compliance with the limit: lim∑(tBZ)/∑(mTZ)→1 computationally. With partial scattering optimization, the real time course is automatically “dense”. This ensures real organizational full capacity (≈ 100%) and is the organizational version of avoiding administrative overhead through Digital Business Model innovation.
The temporal structure data in the realization of medical activities.
His total volume consists of 3 distinct, mutually modifying time types, in which the evolutionary Pareto front transforms planned times into real times. The Vchanging occurs according to the principle of minitimes spatial time volume. The 3 types of time have the following character:
 Fixer, but shrinking schedule. Its volume is increasingly entering and being “consumed” by the Pareto front.
 The Pareto front permanently absorbs new, partial volumes of time from the schedule and permanently gives up just as many completed fixed times. This is the specificity of the evolutionary AI algorithm. For this purpose, the minimum of the spacetime volume is checked every 5 min for each single activity and the (conditional) probability density for this time clock per OR is calculated. Depending on deviation from the schedule, the planned time is added that can compensate for the deviation at most. Since probability density tests are continuous and the adjustment is thus ongoing, it is assured that the AI algorithm reaches the target of (full utilization) real (threshold >> 95%).
The terminated in the process but growing fixed activity time volume. The result of the process manifests itself in a fixed time volume of terminated activities across all OR rooms.
Linking ordinal times with conditional time probabilities possible loadable time forecastsfor time optimization in the Pareto front
At real timing there are mathematical differences to timing:
1. In medical overall activities, there is a organizational Nnet of subactivities (= sequence+set+parallel) that is not reducible to additive row of partial activities(cut⇒ seam) and consequently not, as it e. Currently, on addition of their times. Their complex structure also includes timeshifted (e.g., anesthesia) and parallel activities (e.g., measurement).
2. The single partial activity performs a typical medical procedure. This operation is primary for the sequence. The partial operation time is measured against it. The measurement domain can capture duration both (directly) (see glandquantity/time), it can capture it rankordered (indirectly) as sequences of intervals (see shorterlonger), and it can capture it as (indirectly) dual facts (see visual controls), from which time for subsequent activities is derived. This shows: already the activity types produce measurements that belong to different scale levels and are therefore incompatible with each other. The 4 basic types of arithmetic cannot represent the unity of such structures.
3. The concrete partial activity time is the time of a medical matter that it needs to create with its completion the condition for the time completion of the overall activity. In terms of time organization, the partial activity times (across different)scale levels are in conditional relationship with the total activity time. A partial activity time “generates” the total activity time not by multiplying it, but by “transferring” its time to the total activity time in unity with other partial activity times. Each partial activity time corresponds in time to the total activity time.
4. Because when the same partial activity is repeated, the medical facts act at different rates due to the individuality of the patient, the times are not the same. Consequently, differently structured “time correspondences“ between partial and total activity time form in the multiplicity of </span style=”textdecoration: underline;”>differently structured “time correspondences“ between partial and total activity time. Over a frequently occurring partial activity time, therefore, not only do a number of times (time events) build up, the directly corresponding to the most frequent total activity time (Zz), but also time events corresponding to scattering times, i.e. adjacent to the time center (Zz).
The concrete calculation:
a. Within a partial activity, there is a time interval that contains the most frequent ordinary time events. For these, the time ratio(a/b) must be determined in that all times (a) have the property of corresponding directly to the most frequent times of the total activity time (Zz). It is set in the same interval in relation to the times (b) that do not correspond.
b. The most frequent ordinal total activity time in the interval (Zz) forms with the residual times of the scatter a time ratio (x/y) in which (x) represents the number of all time events in (Zz) and (y) represents the number of times not in (Zz) (scattering).
c. The quatitative time influence (α) of partial activity time (I) on total activity time (Zz) is obtained when the conditional total activity time ratio (x/y) [i. Denominator] is the proportions of the conditional partial activity time ratio (a/b) [i. Numerator] in the dual time ratio: (α) = [(a/b) // (x/y)] “counts“. This is true for all subactivities (I)…(N).
d. The quantitative time impact of all partial activity times (I)…(N) on the paid activity time (Zz) is given by the product of all time ratios:. [(a/b) // (x/y)] * [(c/d) // (x/y)] *…… * [(n/m) // (x/y)] * (x/y) and expressed as %probability after appropriate transformation.
e. A time estimate for the end of a current overall activityis created successively (increasingly better) by calculating its time ratio (a/b) after the end of a subactivity and forming the product with previous time ratios formed for subactivities that have already ended. The loadable probable time tendency for (Zz) = 100% arises:

 : [(a/b) // (x/y)] = (α) (α %) <<< (Zz %)
 : [(a/b) // (x/y)] * [(c/d) // (x/y)] = (β) (β %) << (Zz %)
 : [(a/b) // (x/y)] * [(c/d) // (x/y)] * [(e/f) // (x/y)] = (γ) (γ %) < (Zz %)
 : …. etc.
 : [(a/b) // (x/y)] = (α) (α %) <<< (Zz %)
Probably means in the sense of (von Mises) objectively to assume the fact …
. ..that for future events only calculation is possible, as a circumstance conditioned by the objective setup of reality.
This probability here always uses real measured times (not thought experiments), which allow the application of the limit theorems of stochastics (laws of large numbers). The more times, the more precise the statements.
5. Prior to this algorithm system, a loadable time prediction can be made on the er expectable time completion of a new, still ongoing medical activity. If the new subactivities are physically (chemically. ) approximately comparable to those that occurred in a similar manner in the same activity, it is (highly)likely that the new activity will also end with a similar total activity time. If this does not apply, the divergent probabilities must be calculated. The product of matching and deviating individual probabilities gives the +/ time delay of the total activity (x < Zz or Zz < y).
The logistic regression
The algorithm that can map these conditional relationships is the (logistic regression, p. 232) (per UK). Their goal is…
the dependent variable to the highest possible degree statistically (too) explain, and quantify the directed influence of each independent variable on the dependent variable and.
For this purpose, a digital timeperforce activitydependent system is constructed, within which the total activity time is the dependent variable (target time) and the complex of the previous partial activity times are the independent (conditional) variables (partial times). From the point of view of the individual activity of a (VC), it generates a kind of formal “timeline”, (the conditional time) towards the overall activity, at each of its activity to the subactivities across the board. For many activities, the time coincidences from the timeline create a nonparallel temporal “line mesh” – the data basis of a mathematical (Preorder), which is based on (conditionalprobabilities), their multiplication sets and the (Bayes theorem)is calculated on nondichotomous intervals. This “underlays” each subactivity with an ordinal time structure representing it. It is then determined with high probability whether or not the schedule will be met. The Pareto front algorithm thus receives time data for its “decision” whether it can continue in compliance with the planned time course or whether it has to reoptimize due to time deviations [e.g. bleeding, staff absence, material breakage …].
This theory is demonstrated on the TuRP example (for simplicity without staggered/parallel times). The five subactivities are said to be: I. wash, II. insert lap, III. Planing, IV. Stopping bleeding, V. Disinfection. The times of pts: IV are shown below in the respective frequency distribution of the individual times. They are all associated with a single time in the frequency distribution of TuRP. Dark colored times of the subactivities are directly related to the time center of the TuRP. The gray colored times are related to times next to the (Zz). The conditional probability was calculated for both sets of times per subactivity. The multiplicative concatenation of the values yields the cumulatively increasing probability sequence, which, depending on the real progress of the subactivities, quantifies the probability of achieving the target time (TuRP; 35 min) in %: e.g.: I:78.1< II:83.3< III:91.6< IV:89.7< V:92.6; goal achievement from III certain (> 85 %).
Where are standard times e.g. due to severe bleeding (IV) not met, a regression order of the probabilities results as a warning. This would be in case (IV): 78.1→ 83.3→ 91.6→ 41.7→ 92.6. Target achievement is below (< 77.5%). The Pareto front processes these “insight” by calculating whether it can still realize full utilization with the subsequently planned medical activity or whether it needs to avoid idle time by temporal and/or spatial regrouping. In this case this would lead to plan corrections for the activity of subsequent full staff, who would be informed about it in time (10 min before the end of the TuRP).
Video
In order to assess the need for change, there is a timebased monitoring for the overall workpart process.
The blue page boundaries denote the time limits up to which actual, random individual values can scatter without jeopardizing the implementation of the optimal schedule. Green is the current realtime trend around the plan values (0 line).
To be able to realize the objective function optimal with the Pareto Front, the BAYES probability calculus is available in statistics To this mathematics Boolean algebra is applicable. Consequently, the Pareto front is digitizable. The usable software already exists.
5. The economic results of digital business model innovation.
For the first time, the result follows the strategy: Maximizing the collective benefit f. d. hospital. OOrganizational and economic savings potentials: Personnel cost reduction, measured at current level: ≈ Ø ¹/3 /J. E.g.: 8 operating theatres reduced to 5 operating theatres (= full utilisation). Consequence:


 Savings in personnel costs per year ≈ 1.2 million € (permanent).
 Capital value (Co) of investment (8% Z.); Co = €3.409m
 Internal interest ro = 42.7%
 Capital value rate k (over 5 yrs) = 503%
 annual excess return K^{* }= 43.26%
 Return d. total investment. kg = 51.26%
 Permanent savings of 18 fulltime employees (out of 48)

The project will continue with the differential diagnostic process.



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6. Digital business model innovation enables pull logistics for timeoptimized fullstaffing.
The forecasting function determines not only the likely end of a task, but also the possible start of the subsequent task. This can be used as an organisational strategy for working without idle time in subsequent activities. For this purpose, the (Pull principle) is digitized.
This principle is a control of consumption by “pulling“.
No longer will activity start at a significantly earlier time prognostically fixed (see OP scheduling the day before). Similarly, the activity is not called after the previous activity has already ended (push strategy). The current new attendance time is determined by the activity preceding it by timely retrieval . The prediction function of conditional probabilities not only enables a pull strategy, it can also digitally control its realization. The control effort of organizational processes is significantly reduced.
7th Digital Gemini
The Digital Business Model Innovation presented above can be seen as the basis for a series of higher levels of Digital Business Innovation. The property under point 2 is expandable on a daily basis for the overall organisation over time. Then a (Digital Twin) is created. This is the…
virtual representation of a… process used to predict the performance characteristics of its physical counterpart .
The Digital Twin for Total Activity Time is a software that contains (per day) the scheduled time process. As a simulation model it serves to calculate and represent timerelated impacts and/or organisational impact assessments that occur in case of unpredictable situational changes (e.g. emergencies, staff absences, supply problems,…) that require quantitative or qualitative new planning.