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Design of Risk Management Strategies in Business Process Information Flow
Xue Bai
Operations and Information ManagementSchool of Business
University of Connecticut
Risk Workshop SAMSI 2
Outline
• Motivation and problem definition
• Methodology
• Experimental study
• Real world application
• Future research
Risk Workshop SAMSI 3
Motivation
• Impact of errors in corporate business processes – “10 percent to 30 percent of the data flowing through corporate
systems is bad…” (CFO magazine 2003)
• Impact of errors in healthcare processes– More than 8.8 million ADE’s occur each year in ambulatory care,
cost at least $5,000 per ADE. Medication errors account for 1 out of 131 ambulatory care deaths (Washington: eHealth Initiative 2004).
– Health care data quality: accuracy 67%, completeness: 30.7% (Stein et al. 2000)
• Legal mandates– Sarbanes Oxley Act (2002)– HIPAA (1996), Medical malpractice laws
Risk Workshop SAMSI 4
Physician Patient
Pharmacist
Insurer
Prescription
Prescription
Bill
Medication
Bill
An Example of BP with Errors and Risks
Call back and complain
Call back and complain
Call back and complain
Formulary mismatch
Wrong dosage
Adverse Drug Event
Call back efforts; Administrative cost; Patient satisfaction & loyalty &
litigation issues.
Patient ends up in
ER.
An example: a medication process
Bills for ER visit.
Manual check
E-prescribing systems
Performance review
E-order systems
Risk Workshop SAMSI 5
Physician Patient
Pharmacy
Insurer
Prescription
Prescription
Bill
Medication
Bill
An Example of BP with Errors and Risks
A medication process
Risk Workshop SAMSI 6
• A Business Process (BP)– Tasks– Information flow– Errors
• Accuracy• Completeness• Occurrence
– Risk exposure
– Design of Control structure for risk management
enter order info.
check alert info.
update medication info.
order database
inaccurate dosage
missing information
The order management process at the pharmacy
Manual check
E-order mgt.
check alert info.
update medication info.
databaseenter order info.
Elements of the Model
Risk Workshop SAMSI 7
Outline
• Motivation and problem definition
• Methodology
• Experimental study
• Real world application
• Future research
Risk Workshop SAMSI 8
Check alert info.
Update medication information
Enter order information
DatabaseCheck alert info.
Update medication information
Enter order information
Database
wrong dosage wrong dosage
A Simple Sequential Process
Process Structure Affects Error Impact
Risk Workshop SAMSI 9
A Simple Parallel Process
Order of medication
Shipping invoice
Payment voucher
Preparing voucher package
control
control
Process Structure Affects Control Function
Risk Workshop SAMSI 10
BP as a Graph
t1
t2
t3
The precedence matrix:
otherwise.,0
, precedesdirectly task if ,1][
jitT ijij
000
100
110
33T
Risk Workshop SAMSI 11
t1
t2
t3
The volume transition matrix:
p(T): the ratio between the volume output by task i and the volume fed to task j, given tij =1.
000
100
110
)( 33Tp
000
100
0
)(1312
33
rr
Tp
t1:Non-Condition node: t1:Condition node:
BP as a Graph
Risk Workshop SAMSI 12
• The propagation impact (PI) matrix:
– K: the length of the longest path in a process.
– p(T): the volume transition matrix
• The propagation potential:
kK
kTp
1
)(
jiji ][
000
100
210
000
100
110
T
000
100
110
)(Tpt1:Non-condition node:
000
100
0 23
21
000
100
110
T
000
100
10
)(21
Tpt1:Condition node:
Impact of Error
Risk Workshop SAMSI 13
Error Generation
• Error correlation structure• Models for error generation processes – hierarchical
sampling schema
• Controlling for dependence/independence due to the homogeneity/ heterogeneity of operations and resources involved
– Within a task
– Across tasks
,~,| Mi ormaldLogisticNGeneralizep
)( ~| imimim pBernoullipe Mm ,,1Ni ,,1
Risk Workshop SAMSI 14
• The number of errors of type m at task i:
– : number of errors of type m that show up at task i– : number of errors of type m that arrive at task i– : occurrence of errors of type m generated by task i– : average number of eim
im
N
j jmjiimimim eeeee ~~~1
ime
ime
imeime~
Error Propagation
Risk Workshop SAMSI 15
Loss and Risk Measurement
• Loss:cim: cost of an error of type m at task i.
• Risk Measures– Expected Loss (EL), Value-at-Risk (VaR), Conditional Value-at-
Risk (CVaR)
imim
N
j jmjiim ceel ~~
1
EL CVaR VaR
loss
β
Risk Workshop SAMSI 16
Risk Measures
– Expected Loss
– Value-at-Risk
– Conditional Value-at-Risk
),(:min )(l
lxlxr
dlxlfxxr
)(),(
-1
1 )(
dlxlfx
0
),()(E
EL CVaR VaR
loss
β
)(xr )(x)(E x
Risk Workshop SAMSI 17
• Control allocation factor
• Effectiveness of control
–the probability of a control catching an error:• Deterministic control
• Stochastic control
• Cost of control (per period)
Risk Management: Control Model
NixxN
iii ,,1,1,10
1
.0,1
,))(()( 1
1
ii
bii
N
jjiii
db
xdtpx i
.10,10 ,)( iia
iii gaxgx i
.10,10
)Bernoulli(~)(
ii
aiii
ga
xgx i
Risk Workshop SAMSI 18
Model Formulation I, II, and III
– Design problem: Given a budget B,
– Model I: “Expected-Loss-Optimal” Control Structure
– Model II: “β-VaR-Optimal” Control Structure
– Model III: “β-CVaR-Optimal” Control Structure
.,...,1,10,1,)(..
)(min
11
1
NixxBxts
x
i
N
ii
N
iii
N
iii
)(xL
,),(:min )(l
lxlxr
)()( xrlx
Risk Workshop SAMSI 19
Outline
• Motivation and problem definition
• Methodology
• Experimental study
• Real world application
• Future research
Risk Workshop SAMSI 20
Experimental Study
• Experimental design– Topological variation
• Sequential, parallel, arbitrary
– Process size• Small (4 tasks), medium (10 tasks), large (25 tasks)
– Cost of control vs. Loss per error ( )• Expensive: (500, 1000, 2000, 4000, 10000), inexpensive: (25, 50,
100)
– Tolerance level of risks (β)• β = 0.90, 0.95, 0.99
– Error correlation• Independent, dependent
ii cd /
Risk Workshop SAMSI 21
Experimental Results• As the process size increases, (Table 113, 115, 117, 119, 121,
and 123)– The optimal amount of control allocation in total increases– The optimal amount of control allocation at each task decreases– For sequential structure, the objective function value increases
exponentially; for parallel structure, the magnitude remains the same. • As the tolerance level of risks (β) changes (Table 2 and 10;
Table 22 and 30), – The optimal amount of control allocation in total increases– The impact of β at the task level depends on characteristics of the loss
distributions• In the range of β value and loss distributions tested, the impact is
insignificant.
• As the ratio cost of control / loss per error ( ) increases (Table 153-159)– The optimal amount of control allocation at each task decreases– The optimal amount of control allocation in total decreases
ii cd /
Risk Workshop SAMSI 22
Experimental Results (continue)
• Optimal control allocations depend on risk objectives.– The relative importance of each task location changes accordingly– Tradeoffs when consider multi-risk objectives
• For processes with sequential structure, holding other factors constant, – The highest control allocations occur at tasks towards the center of the
process.
• For processes with parallel structure, holding other factors constant, – The highest control allocations occur at the merging tasks of the
process.
Risk Workshop SAMSI 23
Outline
• Motivation and problem definition
• Methodology
• Experimental study
• Real world application
• Future research
Risk Workshop SAMSI 24
• An Order Fulfillment Process The Data: 15 tasks, 13 internal tasks, 46 errors that occur in different tasks, costs
per error per type, frequencies of error occurrences, cost factors of controls, based 1200 orders per month.
Case Study
Risk Workshop SAMSI 25
The tasks:0) Clients place order, 1) Enter order information, 2) Check payer and insurance info. 3)
Create/update contracts, 4) Prove prescription, 5) Prepare prescribed items, 6) Dispense from alternative source, 7) Submit drug orders to wholesaler, 8) Deliver medication, 9) Prepare and send claims to an insurance company or 10) to the responsible party, 11) Collect payments, 12) Post payments and prepare vouchers, 13) Update ledgers, 14) insurer/clients pay bills.
Results: Optimal Allocation of Control Resource
Risk Workshop SAMSI 26
The tasks:0) Clients place order, 1) Enter order information, 2) Check payer and insurance info. 3)
Create/update contracts, 4) Prove prescription, 5) Prepare prescribed items, 6) Dispense from alternative source, 7) Submit drug orders to wholesaler, 8) Deliver medication, 9) Prepare and send claims to an insurance company or 10) to the responsible party, 11) Collect payments, 12) Post payments and prepare vouchers, 13) Update ledgers, 14) insurer/clients pay bills.
Results: Optimal Objective Function Values
Risk Workshop SAMSI 27
Outline
• Motivation and problem definition
• Methodology
• Experimental study
• Real world application
• Future research
Risk Workshop SAMSI 28
• Summary– Risk management models for error associated risks in business process
information flow
• Future research– Sensitivity analysis of the effect of other factors on optimal
control allocations and risk objectives• Loss per error, Control effectiveness, Cost structure of controls,
Topological redesign, Analytic solution for CVaR
– Managerial problems• Multi-Objective Optimization• Find the maximum confidence level β for a given value-at-risk • Given the output errors, identify the most probable error sources • Many others.
Future research