Lecture7-QuantitativeAnalysis2.pptx
- 1. MTAT.03.231 Business Process Management Lecture 7 – Quantitative Process Analysis II Marlon Dumas marlon.dumas ät ut . ee 1
- 2. Process Analysis Process identification Conformance and performance insights Conformance and performance insights Process monitoring and controlling Executable process model Executable process model Process implementation To-be process model To-be process model Process analysis As-is process model As-is process model Process discovery Process architecture Process architecture Process redesign Insights on weaknesses and their impact Insights on weaknesses and their impact 2
- 3. Process Analysis Techniques Qualitative analysis • Value-Added & Waste Analysis • Root-Cause Analysis • Pareto Analysis • Issue Register Quantitative Analysis • Flow analysis • Queuing analysis • Simulation 3
- 4. 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 4
- 5. Flow analysis does not consider waiting times due to resource contention Queuing analysis and simulation address these limitations and have a broader applicability Why flow analysis is not enough? 5
- 6. • 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 Question: Should another MD position be instated? Queuing Analysis © Laguna & Marklund 6
- 7. 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 © Dimitri P. Bertsekas 7
- 8. Burstiness Causes Interference Queuing results from variability in processing times and/or interarrival intervals © Dimitri P. Bertsekas 8
- 9. • Deterministic arrivals, variable job sizes Job Size Variation Causes Interference © Dimitri P. Bertsekas 9
- 10. • The queuing probability increases as the load increases • Utilization close to 100% is unsustainable too long queuing times High Utilization Exacerbates Interference © Dimitri P. Bertsekas 10
- 11. • 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 11
- 13. Basic characteristics: • l (mean arrival rate) = average number of arrivals per time unit • m (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 l m c © Wil van der Aalst 13
- 14. Given l , m and c, we can calculate : • r = resource utilization • Wq = average time a job spends in queue (i.e. waiting time) • W = average time in the “system” (i.e. cycle time) • Lq = average number of jobs in queue (i.e. length of queue) • L = average number of jobs in system (i.e. Work-in- Progress) Queuing theory concepts (cont.) l m c Wq,Lq W,L © Wil van der Aalst 14
- 15. M/M/1 queue l m 1 Assumptions: • time between arrivals and processing time follow a negative exponential distribution • 1 server (c = 1) • FIFO L=r/(1- r) Lq= r2/(1- r) = L-r W=L/l=1/(m- l) Wq=Lq/l= l /( m(m- l)) μ λ Capacity Available Demand Capacity ρ = = © Laguna & Marklund 15
- 16. m l = = r * c Capacity Available Demand Capacity • Now there are c servers in parallel, so the expected capacity per time unit is then c*m W=Wq+(1/m) Little’s Formula Wq=Lq/l Little’s Formula L=lW © Laguna & Marklund M/M/c queue 16
- 17. • For M/M/c systems, the exact computation of Lq is rather complex… • Consider using a tool, e.g. • http://www.supositorio.com/rcalc/rcalclite.htm (very simple) • http://queueingtoolpak.org/ (more sophisticated, Excel add-on) Tool Support 0 2 c c n n q P ) 1 ( ! c ) / ( ... P ) c n ( L r r m l = = = = 1 c 1 c 0 n n 0 ) c /( ( 1 1 ! c ) / ( ! n ) / ( P = m l m l m l = 17
- 18. Situation • Patients arrive according to a Poisson process with intensity l ( the time between arrivals is exp(l) distributed. • The service time (the doctor’s examination and treatment time of a patient) follows an exponential distribution with mean 1/m (=exp(m) distributed) The ER can be modeled as an M/M/c system where c = the number of doctors Data gathering l = 2 patients per hour m = 3 patients per hour Question – Should the capacity be increased from 1 to 2 doctors? Example – ER at County Hospital © Laguna & Marklund 18
- 19. • 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) r 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 19
- 20. • Textbook, Chapter 7, exercise 7.12 We consider a Level-2 IT service desk with two staff members. Each staff member can handle one service request in 4 working hours on average. Service times are exponentially distributed. Requests arrive at a mean rate of one request every 3 hours according to a Poisson process. What is the average time between the moment a service request arrives at this desk and the moment it is fulfilled? …Now consider the scenario where the number of requests becomes one per hour. How many level-2 staff are required to be able to start serving a request on average within two working hours of it being received? Your turn 20
- 21. • 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 21
- 22. Process Simulation Model the process Define a simulation scenario Run the simulation Analyze the simulation outputs Repeat for alternative scenarios 22
- 23. Example 23
- 24. Elements of a simulation scenario 1. Processing times of activities • Fixed value • Probability distribution 24
- 27. • Fixed • Rare, can be used to approximate case where the activity processing time varies very little • Example: a task performed by a software application • Normal • Repetitive activities • Example: “Check completeness of an application” • Exponential • Complex activities that may involve analysis or decisions • Example: “Assess an application” Choice of probability distribution 27
- 28. Simulation Example Exp(20m) Normal(20m, 4m) Normal(10m, 2m) Normal(10m, 2m) Normal(10m, 2m) 0m 28
- 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 29
- 30. 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 30
- 31. 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 31
- 32. 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 32
- 33. 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 33
- 34. Resource pool assignment Officer Clerk Clerk Officer Officer Syste m 34
- 35. Process Simulation Model the process Define a simulation scenario Run the simulation Analyze the simulation outputs Repeat for alternative scenarios ✔ ✔ ✔ 35
- 36. Output: Performance measures & histograms 36
- 37. Process Simulation Model the process Define a simulation scenario Run the simulation Analyze the simulation outputs Repeat for alternative scenarios ✔ ✔ ✔ ✔ 37
- 38. Tools for Process Simulation • ARIS • ITP Commerce Process Modeler for Visio • Logizian • Oracle BPA • Progress Savvion Process Modeler • ProSim • Bizagi Process Modeler • Check tutorial at http://tinyurl.com/bizagisimulation • Signavio + BIMP • http://bimp.cs.ut.ee/ 38
- 39. BIMP – bimp.cs.ut.ee • Accepts standard BPMN 2.0 as input • Simple form-based interface to enter simulation scenario • Produces KPIs + simulation logs in MXML format • Simulation logs can be imported into a process mining tool 39
- 40. BIMP Demo 40
- 41. • Textbook, Chapter 7, exercise 7.8 (page 240) Your turn 41
- 42. • Stochasticity • Data quality • Simplifying assumptions Pitfalls of simulation 42
- 43. • Problem • Simulation results may differ from one run to another • Solutions 1. Make the simulation timeframe long enough to cover weekly and seasonal variability, where applicable 2. Use multiple simulation runs, average results of multiple runs, compute confidence intervals Stochasticity 43 Multiple simulation runs Average results of multiple runs Compute confidence intervals
- 44. • Problem • Simulation results are only as trustworthy as the input data • Solutions: 1. Rely as little as possible on “guesstimates”. Use input analysis where possible: • Derive simulation scenario parameters from numbers in the scenario • Use statistical tools to check fit the probability distributions 2. Simulate the “as is” scenario and cross-check results against actual observations Data quality 44
- 45. • That the process model is always followed to the letter • No deviations • No workarounds • That a resource only works on one task • No multitasking • That if a resource becomes available and a work item (task) is enabled, the resource will start it right away • No batching • That resources work constantly (no interruptions) • Every day is the same! • No tiredness effects • No distractions beyond “stochastic” ones Simulation assumptions 45
- 46. Next week Process identification Conformance and performance insights Conformance and performance insights Process monitoring and controlling Executable process model Executable process model Process implementation To-be process model To-be process model Process analysis As-is process model As-is process model Process discovery Process architecture Process architecture Process redesign Insights on weaknesses and their impact Insights on weaknesses and their impact 46