Shortening lead times in a business process is important for meetings service level agreements, decreasing inventories and working capital, keeping customers satis ed and in short: staying in business. Process mining methods make it possible to generate a large amount of transaction event data and case attributes that are useful for analysing lead times. However, nding root causes for long lead times is not so straightforward with current process mining methods. In this paper we extend our prevously presented in uence analysis methodology by providing alternative treatment for continuous target variables like lead times and making it possible to give weights for each process case. We extend our contribution measure by presenting the de nitions for binary/continuous as well as weighted/non-weighted needs. Using a publicly available reallife case study from Rabobank's service desk process we demonstrate the e ect of using either continuous or binary approach combined with possible weighting.
Every process owner and business leader in the world would be happy to hear that their own process or at least some part of it can be made faster. Reduced operational costs, better customer satisfaction and more sales are all potential bene ts from reducing the process lead times. Since real-life business processes are often very complex and produce a lot of data, we need to consider many potential root causes for lead time related problems, including for example customer speci c requirements, available resources, required competences for process workers, di erent business models, delivery options and products.
Our previously published in uence analysis methodology shows how the root
causes can be identi ed for generic process related problems [
In this paper we will present a methodology to systematically analyse and provide actionable root causes for lead times issues in current business processes. We identify the root causes why some cases have very long lead times and others are very short. Our method analyses each case attribute and value separately.
The rest of this paper is organized as follows: Section 2 introduces relevant background in process mining and data analysis. Section 3 presents our extension to the in uence analysis methodology introducing the contribution measures for continuous variables and case-speci c weights. Section 4 shows a real-life example followed by a section for Discussions and Summary. 2
This paper extends the in uence analysis methodology that we have published
earlier [
Even though business process performance has been studied a lot most of
the studies only cover the usage of binary conditions or decision tree approach
[
Basic idea of in uence analysis [
In this paper we extend the previous step 4. so that classi cation can be either binary as previously or we can use a continuous variable for representing the goodness or badness of a case. Regarding step 5. we only use the as-is average as the Change Type in this paper as that measure has proven to be most useful. However, it is also possible to use ideal and other average Change Types. Regarding step 6. we add new calculation formulas to cover also weighted versions of both binary and continuous contribution. 3
In this section we present four di erent formulas that are to be used as contribution measures for in uence analysis methodology. These measures are listed in Table 1. Depending on the performance indicator the contribution formula can be either binary or continuous. Depending on relative importance of cases the contribution formula can be weighted or not weighted. In typical business process analysis situations an actual business problem can often be formulated with any of these four formulas. Since the formulas give potentially di erent results it is important to understand that seemingly small di erences in formulating the problem may lead to large di erences in the analysis results. Thus it is often bene cial to use multiple contribution formulas for double-checking that suggested business process improvement areas are correct.
Our previous paper [
Our method and calculations start from understanding the initial size of the
business process problem. As presented in [
Sum of value of problematic Free-of-charge pizza if delivery takes more cases than 45 minutes. Problem size is equal to the monetary value of late pizza deliveries.
Sum of positive overtime Lead time from the customer calling a compared to average lead helpdesk to the moment the call is answered. time The shorter the lead time the better it is. Sum of overtime for each Lead time from the sending an invoice to the case compared to the moment the payment arrives. When this lead weighted average lead time time is multiplied by the value of the invoice multiplied by the weight we get the working capital, ie. using value of separately for each case invoice as the weight for each case.
In this paper we consider an actionable business process improvement in area X, which is a subset of the whole population, as an improvement that will change the performance of future cases in area X to be improved so that the performance of area X reaches the the current as-is average performance of whole population. For example a US company may have delivery challenges in Dallas region and the improvement project would then be to improve the performance in Dallas to the same level as other regions. For each measure we show the formula that we call Contribution% which gives result as a percentage gure between -100% and +100%. Positive Contribution% indicates how large part of the current lead time problem can be improved by making the selected business area to perform on the same level as the initial average for the whole business. Negative Contribution% tells how much bigger the lead time problem will become if performance in selected business area is weakened to the current average level.
Weighting Weighted contributions can be used in contribution analysis. Simply we need Weight attribute for each case and we need to replace the 'amount of cases' values with 'sum of Weights of cases'. Now as an example we could have a total amount of 13 million EUR orders in the analysis and 2 million EUR orders are being delivered after the requested delivery date. So we will then run the contribution analysis to nd the case attributes and values that have the biggest contribution in terms of EUR to the 2 million that is being delivered late. If there is one single order of 1.99 million EUR that was delivered late, then obviously the characteristics of that single order will overrule all other possible ndings, even though if 100 other orders were delivered late. But that is de nitely just the wanted nding because in real life if situation is like that then the one order (almost) fully explains the orders being late and there may be no point in trying to nd more root causes for late deliveries. 3.1
Common De nitions Here we present the common de nitions used in all contribution formulas. De nition 1. Let C = fc1; : : : ; cN g be a set of cases in the process analysis. Each case represents a single business process execution instance. De nition 2. Let Cp = fcp1 ; : : : ; cpN g be a set of problematic cases. Cp C.
De nition 3. Let Ca = fca1 ; : : : ; caN g be a set of cases belonging to business process improvement segment A. Ca C.
De nition 4. Let dcj be the duration of the case cj .
De nition 5. Let wcj be the weight of the case cj . We consider linear weights so that double weight always means double importance. If wcj = 0 then case cj will have no e ect in the analysis when calculating weighted results. De nition 6. Let pr be the size of the problem in the original situation before any business process improvement: BiCo: amount of problem cases, wBiCo: sum of weights of problem cases, CoCo: sum of overtime compared to average duration, wCoCo: sum of overtime per case multiplied with weight of the case compared to the weighted average duration. 3.2
BiCo - Binary Contribution
For binary contribution the problem size is the amount of problematic cases.
Every case needs to be classi ed as problematic or successful as shown in [
Total problem size for BiCo is the amount of problematic cases prBiCo = Cp = P 1 as shown in equation 1 in Table 8 in Appendix A. Average cj2Cp P 1 function for BiCo is the average problem density rho = jCpj = cj2Cp jCj P 1 as shown cj2C in equation 2. Similarly the average problem density for BiCo of subset Ca is
P 1 a = jCjpC\aCj aj = cj2(CPp\C1a) as shown in equation 3. Finally theContribution% cj2Ca for BiCo of subset Ca is conBiCo =
P 1 cj2Ca
P 1 as shown in equation 4 cj2C ( a ) P 1
cj2Ca prBiCo
P = jCp\Caj jCaj = cj2(Cp\Ca) jCpj jCj cjP2Cp 1 1 3.3
wBiCo - Weighted Binary Contribution Weighted Binary Contribution extends the previous sigma-based formulas by replacing the static equal weight with case speci c weights wcj . Problem size as de ned in equation 5 in Table 8 in Appendix A is the sum of weights of all problem cases. Average problem density as de ned in equation 6 in Table 8 is the sum of weights of all problem cases divided by the sum of weights of all cases, and in a similar way the average problem density in equation 6 in Table 8 is the sum of weights of all problem cases in subset Ca divided by the sum of weights of all cases in subset Ca. 3.4
CoCo - Continuous Contribution Continuous Contribution allows analysing the lead time variables as continuous without the need for a xed separation of cases into long and short cases, ie. without the need of having a binary value for each case. For continuous analysis we consider a case as problematic if the value of continuous target variable is bigger than the average in the population as shown in equation 9 in Table 8. The bigger the positive di erence is the worse the behaviour. On the other hand, if the continuous target value is less than average then the case is a better-thanaverage. Using this approach the sum of positive deviations is always the same as the absolute value of the sum of negative deviations, meaning that the problem size for the whole population C is always zero. Problem size of any subset Ca may be nonzero meaning that the cases in subset Ca either have higher or smaller values for the target variable than the whole population. For analysing lead times the continuous target variable is any lead time variable of the business process cases, for example the total end-to-end lead time or any partial lead time from one activity to another. Average function for continuous analysis types is the average lead time, which is de ned for the whole population with equation 10 and subset using equation 11 in Table 8.
Contribution measure for each possible subset Ca for CoCo is calculated as follows: subtract the average lead time of whole population C from the average lead time of the subset Ca, multiply this by the amount of cases in subset Ca. This gives an absolute value of how much more or less time is spent on the cases in subset Ca as a total compared to average of C. Final step is to divide this gure by the problem size, ie by the total sum of positive (or negative) cases in the population, giving the de nition for equation 12 in Table 8. 3.5
wCoCo - Weighted Continuous Contribution In this subsection we extend the previous de ned continuous contribution formulas to supports case speci c weights. It is good to note that weighted continuous contribution corresponds exactly to the working capital need in a business process. As an example lets consider the process of building houses where each case is one house. Working capital needed is proportional to the total cost of each house and the lead time from starting the constructions to selling the house. Weighted Continuous Contribution gives this measure when the cost of house is used as case speci c weight and building time is used as the lead time. The business improvement activity for reducing working capital for this construction company then corresponds to conducting in uence analysis using weighted continuous contribution analysis type to nd our the those subsets that should be the focus for process improvements.
Average weighted lead time using case speci c weights is calculated with equation 14 in Table 8. Di erence to the non-weighted formula is that the lead time of each case is multiplied by the case speci c weight and nally the result is divided by the total sum of weights. This weighted lead time is then used to calculate the total problem size according to equation 13 in Table 8 so that the absolute di erence of lead time for each case is multiplied by the case speci c weight and then summed up. In business terms this corresponds to calculating the extra working capital (positive) or unneeded working capital (negative) for each case and then summing them together. According to our approach if the lead time for every case is equally long then the problem size is zero and there is no extra working capital in the process.
Finally the contribution calculations for weighted continuous analysis are done similarly than in non-weighted analysis, ie subtract the weighted average duration of subset Ca from the total weighted average and multiply this by the sum of weights in subset Ca. When this is divided by the total problem size we get the amount of working capital that would be freed if the lead times for cases Ca could be reduced to the average weighted lead time in the whole population C as shown in equation 16 in Table 8. 3.6
Strengths and Weaknesses of Analysis Types It is not trivial to decide which analysis type should be used in a particular business process analysis situation. Table 3 shows the strengths and weaknesses for binary and continuous analysis types and Table 4 respectively for weights. Often it is desirable to select one analysis type as the primary type for a particular analysis and then use the other analyses for reviewing, double-checking and con rming results from a perspective. { Does not need any separate { Is sensitive for outliers. If one case cut-of threshold. Continuous takes million times longer than the variable like lead time is other cases then the whole analysis is used directly by the algo- likely to suggest improvement in all rithm and overtime is calcu- the subsets Ca containing that particlated from the average dura- ular case. tion. Type Equal weights Di erent weights
In this section we show a real life example of using the presented analysis types
with a publicly available data from Rabobank Group ICT from BPI Challenge
2014 [
As the weighting for cases we use a formula wcj = (6 Impactcj )(6 U rgencycj )(6 P rioritycj ) where Impact, Urgency and Priority all have values in (1,2,3,4,5) where 1 means highest importance and 6 is the lowest importance. With this formula the highest possible weight is whigh = (6 1)(6 1)(6 1) = 125 and lowest possible weight is wlow = (6 5)(6 5)(6 5) = 1. Using these weights the weighted average lead time drops to 3.97 days. This means that on average the lead time is shorter for more important cases than for less important cases. Same nding can also be made from the binary results since the average problem density is 15.9% and weighted average problem density is 11.1%.
Top-3 positive and negative contributions for each Analysis Type are shown in Table 5. For BiCo the highest contribution% is 4.2% for case attribute value WBS000091 and lowest contribution% is -9.3% for case attribute value WBS000091. When considering the most bene cial focus are for process improvement reducing the lead time most we see that BiCo results in WBS000091 and all other Contribution Formulas result in WBS000088. According to the gures the best performing area regarding lead time is WBS000073 in all Contibution Formulas except that in Weighted Binary Contribution the best practice area is #N/B.
Some interesting results include the behaviour of cases whose attribute ServiceComp WBS(CBy) has the value WBS000091 which contributes to 4.2% (Top 1) of the total problem in BiCo, 3.4% (Top 2) in wBiCo, but only 1.7% (Top 8) in CoCo and only 1.2% (Top 7) for wCoCo. Reason for higher contribution in BiCo and lower in CoCo is that average lead time for area WBS000091 is only 6.14 which is only little longer than the average for the whole process 5.07. This means that there are many WBS000091 -cases that have lead time a little bit longer than 7 days. On the other hand the behaviour of area WBS000088 is the opposite, since it only contributes 2.4% (Top 3 value) of the total problem in BiCo, 3.7% (Top 1) in wBiCo, much more 10.4% (Top 1) in CoCo and even more 12.7% (Top 7) in wCoCo. Reason for this behaviour is that the average lead time for cases in area WBS000088 is 39.2 days which is much longer than the average lead time 5.07
Very interesting results include the behaviour of area #N/B which is listed as best practice area with negative contribution -1.7% in BiCo (Top -2), -8.3% in wBiCo (Top -1) and -5.9% in wCoCo (Top -2). However it is listed as problem area with positive contribution 2.6% in CoCo (Top 5 Problem Area!). There are at least two reasons for this result: rst the high weight cases in #N/B perform much better than the low weight cases, ie. BiCo contribution gets 6.6 percentage points better with weighting than without and CoCo contribution gets 8.5 percentage points better. Second reason is that area #N/B performs consistently worse in Continuous analysis compared to binary analysis, which is caused by the higher than average lead time of 6.2% in CoCo, which again is caused by certain amount of very long lead time cases.
Activity occurrences. In this subsection we show the Rabobank root cause analysis for long lasting cases using activity occurrence data. As a preprosessing step we add a new case attribute for each di erent activity name and use the amount of activity occurrences as the value for that case attribute in each case. For example if activity Status Change occurs twice for a certain case, then the value of case attribute Status Change will 2 for that particular case.
Table 6 shows the top-5 positive and negative root causes for binary analysis types and 7 for the continuous analysis types. From these tables we make following observations: { Lack of reassignments is the most important negative root cause for a case to exceed 7 day SLA (BiCo analyses) or generally take a long time (CoCo analysis). In other words, having zero reassignments makes a case very fast. { Contribution values for activity occurrence amounts are much higher than they are for the case attribute ServiceComp WBS(CBy), which means that these activity amounts correlate more with the total duration than the case attribute ServiceComp WBS(CBy). { Update from customer(1) is most important positive root cause for long case duration as can be seen in continuous contributions in table 7. However for binary contributions in table 6 the Status Change(2) is more important positive root cause which means that having two occurences of Status Change is a bigger risk for failing SLA than getting an update from customer. In this paper we have presented a method for focusing business process improvement to reduce lead times. We have de ned four di erent analysis types and shown how they can be used with actual data. Summary of our key ndings is: 1. In uence analysis methodology is able to nd root causes for long lead times. 2. Root causes for long lead times may be substantially di erent when using a prede ned lead time limit for problematic/successful cases (binary) compared to when using continuous lead time values. 3. Case speci c weighting can be easily used when analysing both binary and continuous contribution. 4. When weighting is used together with continuous contribution the analysis can be directly used as working capital analysis solution.
Acknowledgements. We thank QPR Software Plc for the practical experiences from a wide variety of customer cases and for funding our research. The algorithms presented in this paper have been implemented in a commercial process mining tool QPR ProcessAnalyzer.
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