Three-Phase Simulation

Simulation Narrative: Federal Insurance Company is a national multi-lines insurance carrier based in the Mid-Atlantic. The company has hired a consultant to design and build a computer simulation model of their current personal automobile physical damage insurance claim handling process. The company’s auto claims are all handled via 24 hour national claims processing center staffed with 60 claim adjusters. Each claim adjuster is currently required to the handle up to 20 separate claims at time. Claims can be reported by policy holders through an online process via a phone call to the claim center.

Simulation Objectives: Federal Insurance hopes that by simulating the current auto physical damage claim adjustment system they will be able to gain insights into the system that will enable the company to improve the current process performance. The company is interested in evaluating the following aspects of the current process:

Average processing time for claims Resource utilization Though put capability at various resource levels

Simulation Methodology: A three-phase simulation approach will be utilized for the model. An analysis of historical claim data for the company was utilized to develop some of the model parameters (see appendix for analysis of claims data).

The inversion random sampling method was used for estimating the mean inter-arrival times for new loss notices into the system. The Box-Mueller polar variation transform was used to estimate the process durations for evaluating and for settling claims.

The presentation of this model will focus on the design of the simulation algorithm which is written in pseudo code rather than a formal programming language.

Model Validation and Testing: The following steps were used in the model verification and testing process:

1. Validation of pseudo-random number generator to insure that pseudo-random numbersare uniformly distributed in (0,1) and that they satisfy statistical criteria of independence.

2. Similar validation of the stochastic variate generators.

3. Validation of the simulation program logic by printing out status variables, future event list, and other relevant data structures each time an event takes place in the simulation and check by hand whether the data structures are updated appropriately.

4. Validation of model relationships by engaging company management in checking that model’s assumptions about the actual system processes are credible.

5. Validation of model output by comparing actual data, where available with the output obtained from the simulation model.

1

Declaration of Variables

Constant MaxEnt = 15,000

Constant MaxC = 15,000

Type EntDetails ‘Info for each entity

Name as string ‘For output

Avail as integer ‘Boolean for scheduling

TimeCell as integer ‘Next event time if scheduled

NextAct as integer ‘Next B if scheduled

Util as integer ‘Total busy time so far

End Type

RunDuration as integer ‘Length of simulation

Clock as integer ‘Current simulation time

PrevClock as Integer ‘Previous simulation time

CurrEnt as integer ‘Current entity

NumCurrEnts as integer ‘Number of current entities

CStarted as integer ‘Boolean check for C phase

NumCs as integer ‘Number of Cs

Adjust as integer ‘Number of adjuster resources

NewClaim as integer ‘Number of new claims started

NewClaimQ ‘Number of claims in NewClaimQ

EvaluatedClaimQ ‘Number of claims in EvaluateClaimsQ

ClosedClaim as integer ‘Number of claims closed

Details (MaxEnt) as EntDetails ‘Array of entity info

CurrentEntArray (MaxEnt) as integer ‘Array of entities found by A Phase

2

Sub Main

Initialize variables

Set RunDuration = 0 ‘Initialize RunDuration

Set Clock = 0 ‘Initialize simulation time

Set PrevClock = 0 ‘Initialize previous simulation time

Set NumCs = 0 ‘Initialize number of Cs

Set NewClaim = 0 ‘Initialize number of new claims started

Set NewClaimQ = 0 ‘Initialize number of claims in NewClaimQ

Set EvaluatedClaimQ = 0 ‘Initialize number of claims in EvaluateClaimsQ

Set ClosedClaim = 0 ‘Initialize number of closed claim

Set Parameters

Set Simulation run length = 60,000 ‘Initialize simulation run length to 60,000 minutes

Set Observation interval = 60 ‘Initialize model observation interval to 60 minutes

Set Adjust = 60 ‘Initialize number of resources to 60

Set LossNotice mean inter-arrival time = 12 ‘Initialized mean inter-arrival time for claims to 12 minutes

Set Mean ClaimEval time = 180 ‘Initialize mean claim evaluation duration to 180 minutes

Set mean ClaimSettle time = 60 ‘Initialize mean claim settlement duration to 60 minutes

End Sub

3

Sub Simulate

‘Calls A, B and C Phases after initialization

Do While Clock < RunDuration

A Phase

B Phase

C Phase

Do Events

Loop

End Sub

4

Sub A Phase

‘Performs time scan by examining the Details array

‘Checks all entities for which Avail is False, looks for the smallest time cells

‘Min time cell entities stored in CurrEntArraay

Initialize NumCurrEnts = 0 ‘Set CurrEnt counter

Initialize Minm = 50,000 ‘Set Minm value

For Entity = 1 to NumEnts ‘Go through Details Array

If Details(Entity) Avail = False Then ‘Skip if Avail

If Details (Entity) TimeCell <= Minm Then ‘Find if Minm > TimeCell

NumCurrEnt = 1 ‘Reset NumCurrEnts

Else: NumCurrEnts = NumCurrEnts + 1 ‘or Increment NumCurrEnts

End If

End If

Next

If Minm = 50,000 Then

Debug

Stop

Else If Minm < 0

Debug

Stop

Else Set Clock = Minm ‘Found next Clock value

5

End If

End Sub

Sub B Phase

‘Works through the CurrEnt Array and executes the correct Bs

Display EntDetails

For Entity = 1 to NumCurrEnts ‘Work through CurrEntArray

CurrEnt = CurrEntArray (Entity) ‘Take CurrEnt number

Details (CurrEnt) Avail = True ‘Set CurrEnt as Avail

Select Case Details (CurrEnt) NextAct ‘Now do the correct B activity

Case 1

B1

Case 2

B2

Case 3

B3

Case 4

B4

Case 5

B5

Case Else

Debug

6

End Select

Next

End Sub

Sub C Phase

‘Attempt each C

CStarted = True

Repeat Until CStarted = False

C1

C2

C3

C4

C5

Loop

End Sub

7

Sub Schedule

‘Schedules an entity for a B activity

With Details (ThisEnt)

If Avail = False Then

Debug

Stop

End If

Avail = False

NextAct = NextB

If GetClock + ThisDuration > GetRunDuration Then

ThisDuration = GetRunDuration – GetClock

End If

TimeCell = GetClock + ThisDuration

Util = Details(ThisEnt) Util + ThisDuration

Update Adjust = Adjust - .05 ‘Decrement Adjuster resource by .05

End

End Sub

8

Sub B1 Arrival of a Loss Notice (claim)

NewClaim = NewClaim +1

NewClamQ = NewClaimQ + 1

Schedule PresentLossNotice

Set x=0 ‘Initialize x

Set λ = 5 ‘Set parameter rate to 5 arrivals per hour

Set u=Rand() ‘Take random number

Compute x = log(1-u)/(-λ) ‘Compute value x using Box-Muller polar variation

Return x ‘The required sample value from the negative exponential function

End

‘Data structures

‘x = integer which will be the required sample

‘u = a real variable which will hold a uniform [0,1) random number

‘λ = parameter rate

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End Sub

Sub B2 End of Claim Evaluation

EvaluatedClmQ = EvaluateClmQ +1

End Sub

Sub B3 End of Claim Settlement

ClosedClaim = ClosedClaim +1

End Sub

10

Sub C1 Begin Claim Evaluation

Set ThisAdjust as integer

ThisAdjust = FirstAdjust - .05

Do While NewClaimQ > 0 And ThisAdjust < LastAdjust

ThisAdjust = ThisAdjust + .05

If ThisAdjust >= >.05 Then

Set CStarted

NewClaimQ = NewClaimQ – 1

Schedule ThisAdjust

Repeat ‘Run Box-Mueller polar variation transform

v1 = 2 * Rand() ‘Compute v1

v2 = 2 * Rand () ‘Compute v2

w = v1 * v1+v2 ‘Form w

Until (w<= 1) ‘Reject if w too large

z1 = v1 * Sqrt (-2 *LOG (w)/w) ‘Form z1 and z2

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z1 = v1 * Sqrt (-2 *LOG (w)/w)

Return z1 and z2 ‘Return with standard normal variates

If z1 or z2 < 0

Repeat

End Sub

Sub B4 Observation of Queue Lengths

NewClmRec = NewClaimQ

ClaimsEval = EvaluatedClaimQ

Obs = Obs +1

Schedule Observer, 60, ObsInterval

End Sub

12

Appendix A Claim Adjustment Process Flow Chart

13

Notice of Claim Received

Start

New Claim Queue

Claim is Evaluated

Appendix B Analysis of claim occurrence

Year Claims Reported Total Paid Claims Avg. Claim Size Average Claims Per Day Average Claims per hour 2008 43,840 135,771,000 3,097 120 52009 46,118 133,844,000 2,902 126 52010 45,104 129,989,000 2,882 124 52011 47,372 140,089,000 2,957 130 52012 41,458 152,345,000 3,675 114 5

Average: 44,778 138,407,600 3,103 123 5

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Settle Claim

End

Evaluated Claim Queue

Claim data is from company Annual Statement Schedule P.

Appendix C

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1-7 days 8 - 14 days 15-21 days 22 -30 days 31 - 60 days

Over 60 days

0%

10%

20%

30%

40%

50%

60%

70%

Claim Processing Time

Note: Above exhibit based on estimated processing times.

Appendix D

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Appendix F

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Appendix G

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