lecture 6 – quantitative process analysis ii
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MTAT.03.231 Business Process Management
Lecture 6 – Quantitative Process
Analysis II
Marlon Dumas
marlon.dumas ät ut . ee
1
Process Analysis Process
identification
Conformance and performance insightsConformance and
performance insights
Processmonitoring and controlling
Executable processmodel
Executable processmodel
Processimplementation To-‐be process
modelTo-‐be process
model
Processanalysis
As-‐is processmodel
As-‐is processmodel
Process discovery
Process architectureProcess architecture
Processredesign
Insights onweaknesses and their impact
Insights onweaknesses and their impact
Process Analysis Techniques
Qualitative analysis • Value-Added & Waste Analysis • Root-Cause Analysis • Pareto Analysis • Issue Register
Quantitative Analysis • Flow analysis • Queuing analysis • Simulation
1. Introduction 2. Process Identification 3. Essential Process Modeling 4. Advanced Process Modeling 5. Process Discovery 6. Qualitative Process Analysis 7. Quantitative Process Analysis 8. Process Redesign 9. Process Automation 10. Process Intelligence
Flow analysis does not consider
wai0ng 0mes due to resource conten0on
Queuing analysis and simula0on address these limita0ons and have a broader applicability
Why flow analysis is not enough?
• Capacity problems are common and a key driver of process redesign • Need to balance the cost of increased capacity against the gains of
increased productivity and service • Queuing and waiting time analysis is particularly
important in service systems • Large costs of waiting and/or lost sales due to waiting
Prototype Example – ER at a Hospital • Patients arrive by ambulance or by their own accord • One doctor is always on duty • More patients seeks help ⇒ longer waiting times Ø Question: Should another MD position be instated?
Queuing Analysis
© Laguna & Marklund
If arrivals are regular or sufficiently spaced apart, no queuing delay occurs
Delay is Caused by Job Interference
Deterministic traffic
Variable but spaced apart traffic
Time
Arrival Times
Departure Times
1 3 42
1 3 42
Time
Arrival Times
Departure Times
1 3 42
1 3 42
© Dimitri P. Bertsekas
Burstiness Causes Interference
Time
Queuing Delays
Bursty Traffic
1 2 3 4
1 2 3 4
* Queuing results from variability in processing times and/or interarrival intervals
© Dimitri P. Bertsekas
• Deterministic arrivals, variable job sizes
Job Size Variation Causes Interference
Time
Queuing Delays
© Dimitri P. Bertsekas
• The queuing probability increases as the load increases • Utilization close to 100% is unsustainable à too long
queuing times
High Utilization Exacerbates Interference
Time
Queuing Delays
© Dimitri P. Bertsekas
• Common arrival assumption in many queuing and simulation models
• The times between arrivals are independent, identically distributed and exponential • P (arrival < t) = 1 – e-λt
• Key property: The fact that a certain event has not happened tells us nothing about how long it will take before it happens • e.g., P(X > 40 | X >= 30) = P (X > 10)
The Poisson Process
© Laguna & Marklund
Basic characteristics: • λ (mean arrival rate) = average number of arrivals per
time unit • µ (mean service rate) = average number of jobs that can
be handled by one server per time unit: • c = number of servers
Queuing theory: basic concepts
arrivals waiting service
λ µ c
© Wil van der Aalst
Given λ , µ and c, we can calculate : • occupation rate: ρ • Wq = average time in queue • W = average system in system (i.e. cycle time) • Lq = average number in queue (i.e. length of queue) • L = average number in system average (i.e. Work-in-Progress)
Queuing theory concepts (cont.)
λ µ c
Wq,Lq
W,L
© Wil van der Aalst
M/M/1 queue
λ µ 1
Assumptions: • time between arrivals and
processing time follow a negative exponential distribution
• 1 server (c = 1) • FIFO
L=ρ/(1- ρ) Lq= ρ2/(1- ρ) = L-ρ W=L/λ=1/(µ- λ) Wq=Lq/λ= λ /( µ(µ- λ))
µλ
CapacityAvailableDemandCapacityρ ==
© Laguna & Marklund
µλ
==ρ*cCapacityAvailable
DemandCapacity
• Now there are c servers in parallel, so the expected capacity per time unit is then c*µ
W=Wq+(1/µ)
Little’s Formula ⇒ Wq=Lq/λ
Little’s Formula ⇒ L=λW
© Laguna & Marklund
M/M/c queue
• For M/M/c systems, the exact computation of Lq is rather complex…
• Consider using a tool, e.g.
• http://queueingtoolpak.org/ (for Excel) http://www.stat.auckland.ac.nz/~stats255/qsim/qsim.html
Tool Support
02
c
cnnq P
)1(!c)/(...P)cn(Lρ−
ρµλ==−= ∑
∞
=
1c1c
0n
n
0 )c/((11
!c)/(
!n)/(P
−−
=⎟⎟⎠
⎞⎜⎜⎝
⎛
µλ−⋅
µλ+
µλ= ∑
Ø Situation • Patients arrive according to a Poisson process with intensity λ
(⇔ the time between arrivals is exp(λ) distributed. • The service time (the doctor’s examination and treatment time
of a patient) follows an exponential distribution with mean 1/µ (=exp(µ) distributed)
⇒ The ER can be modeled as an M/M/c system where c = the number of doctors
Ø Data gathering ⇒ λ = 2 pa0ents per hour ⇒ µ = 3 pa0ents per hour
v Ques0on – Should the capacity be increased from 1 to 2 doctors?
Example – ER at County Hospital
© Laguna & Marklund
• Interpretation • To be in the queue = to be in the waiting room • To be in the system = to be in the ER (waiting or under treatment)
• Is it warranted to hire a second doctor ?
Queuing Analysis – Hospital Scenario
Characteristic One doctor (c=1) Two Doctors (c=2) ρ 2/3 1/3 Lq 4/3 patients 1/12 patients L 2 patients 3/4 patients
Wq 2/3 h = 40 minutes 1/24 h = 2.5 minutes W 1 h 3/8 h = 22.5 minutes
© Laguna & Marklund
• Versatile quantitative analysis method for • As-is analysis • What-if analysis
• In a nutshell: • Run a large number of process instances • Gather performance data (cost, time, resource usage) • Calculate statistics from the collected data
Process Simulation
Process Simulation
Model the process
Define a simula0on scenario
Run the simula0on
Analyze the simula0on outputs
Repeat for alterna0ve scenarios
Elements of a simulation scenario
1. Processing times of activities • Fixed value • Probability distribution
• Fixed • Rare, can be used to approximate case where the ac0vity processing 0me varies very liWle
• Example: a task performed by a soYware applica0on • Normal
• Repe00ve ac0vi0es • Example: “Check completeness of an applica0on”
• Exponen0al • Complex ac0vi0es that may involve analysis or decisions • Example: “Assess an applica0on”
Choice of probability distribu0on
29
Elements of a simulation model
1. Processing times of activities • Fixed value • Probability distribution
2. Conditional branching probabilities 3. Arrival rate of process instances and probability distribution
• Typically exponential distribution with a given mean inter-arrival time • Arrival calendar, e.g. Monday-Friday, 9am-5pm, or 24/7
Branching probability and arrival rate Arrival rate = 2 applications per hour
Inter-arrival time = 0.5 hour Negative exponential distribution From Monday-Friday, 9am-5pm
0.3
0.7
0.3
9:00 10:00 11:00 12:00 13:00 13:00
35m 55m
Elements of a simulation model
1. Processing times of activities • Fixed value • Probability distribution
2. Conditional branching probabilities 3. Arrival rate of process instances
• Typically exponential distribution with a given mean inter-arrival time • Arrival calendar, e.g. Monday-Friday, 9am-5pm, or 24/7
4. Resource pools
Resource pools
• Name • Size of the resource pool • Cost per time unit of a resource in the pool • Availability of the pool (working calendar) • Examples
• Clerk Credit Officer • € 25 per hour € 25 per hour • Monday-Friday, 9am-5pm Monday-Friday, 9am-5pm
• In some tools, it is possible to define cost and calendar per resource, rather than for entire resource pool
Elements of a simulation model
1. Processing times of activities • Fixed value • Probability distribution
2. Conditional branching probabilities 3. Arrival rate of process instances and probability distribution
• Typically exponential distribution with a given mean inter-arrival time • Arrival calendar, e.g. Monday-Friday, 9am-5pm, or 24/7
4. Resource pools 5. Assignment of tasks to resource pools
Process Simulation
Model the process
Define a simula0on scenario
Run the simula0on
Analyze the simula0on outputs
Repeat for alterna0ve scenarios
✔ ✔ ✔
Process Simulation
Model the process
Define a simula0on scenario
Run the simula0on
Analyze the simula0on outputs
Repeat for alterna0ve scenarios
✔ ✔ ✔
✔
Tools for Process Simula0on
• ARIS • Bizagi Process Modeler • ITP Commerce Process Modeler for Visio • Logizian • Oracle BPA • Progress Savvion Process Modeler • ProSim • Signavio + BIMP
BIMP – bimp.cs.ut.ee
• Accepts standard BPMN 2.0 as input • Simple form-‐based interface to enter simula0on scenario • Produces KPIs + simula0on logs in MXML format
• Simula0on logs can be imported to the ProM process mining tool
• Simula0on results may differ from one run to another • Make the simula0on 0emframe long enough to cover weekly and seasonal variability, where applicable
• Use mul0ple simula0on runs • Average results of mul0ple runs, compute confidence intervals
Stochas0city
45
• Simula0on results are only as trustworthy as the input data • Rely as liWle as possible on “guess0mates” • Use input analysis
• Deriver simula0on scenario parameters from numbers in the scenario • Use sta0s0cal tools to check fit the probability distribu0ons
• Simulate the “as is” scenario and cross-‐check results against actual observa0ons
Data quality piialls
46
• That the process model is always followed to the leWer • No devia0ons • No workarounds
• That resources work constantly and non-‐stop • Every day is the same! • No 0redness effects • No distrac0ons beyond “stochas0c” ones
Simula0on assump0ons
47
Next week
Process identification
Conformance and performance insightsConformance and
performance insights
Processmonitoring and controlling
Executable processmodel
Executable processmodel
Processimplementation To-‐be process
modelTo-‐be process
model
Processanalysis
As-‐is processmodel
As-‐is processmodel
Process discovery
Process architectureProcess architecture
Processredesign
Insights onweaknesses and their impact
Insights onweaknesses and their impact
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