montecarlowith@risk
TRANSCRIPT
@Risk Demonstration8th December 2016
V1.0
Monte Carlo Simulation with @Risk
Risk Assessment to capture uncertainty due to variability in business.
Input derived from distribution fitted from historical dataOr Experience.
Average(“expected”) outcome does not capture the uncertainty in outcome.
OutputDistribution
• JarirBookstore buys 2017 Calendars for SAR 7.5 and sells them @ SAR 10 and gets refunded SAR 2.5 for all unsold calendar.
• Scenario 1: Demand follows a triangular distribution:Minimum: 100; Most Likely: 175; Maximum: 300
• Decision: What is the optimal quantity of calendar to order in Dec’16.
News Vendor Problem
• Two years of historical data of any new model introduced in market:-i. Actual Demandii. Early application ( Guests who booked), iii. Delivered to Guests who booked.
Fitting Distribution from Historical Data
Cash Balance Models
• All companies track their cash balance over time. • As specific payments come due, companies sometimes need to take out
short-term loans to keep a minimal cash balance.
• Objective: To simulate Entson’s cash flows and the loans the company must take out to meet a minimum cash balance.
• Solution: Entson Company believes that its monthly sales from November of the current year to July of next year are normally distributed with the means and standard deviations given in the table below.
• Each month Entson incurs fixed costs of $250,000.• In March, taxes of $150,000 and in June taxes of $50,000 must be paid.• Dividends of $50,000 must also be paid in June.• Entson estimates that its receipts in a given month are a weighted sum of sales from the current month,
the previous month, and two months ago, with weights 0.2, 0.6, and 0.2:
• Materials and labor needed to produce a month’s sales must be purchased one month in advance, and the cost of these averages to 80% of the product’s sales.
Cash Balance.xlsx (slide 1 of 3)
• At the beginning of January, Entson has $250,000 in cash, and the company wants to ensure that each month’s ending cash balance never falls below $250,000.
• This means that Entson might have to take out short-term (one-month) loans. The interest rate on a short-term loan is 1% per month.
• At the beginning of each month, Entson earns interest of 0.5% on its cash balance.
• The completed simulation model is shown to the right.
Cash Balance.xlsx (slide 2 of 3)
• Set the number of iterations to 1000 and the number of simulations to 1. Then run the simulation in the usual way.
• After running the simulation, obtain the summary results and the summary trend chart shown below.
Cash Balance.xlsx (slide 3 of 3)
Case: Maintaining Minimum Cash BalanceKnown:1. Monthly sales during the period from November’16 to July’17 is normally distributed with known means and SD.2. Fixed cost estimated at $250,000 monthly.3. Taxes-> March: $150,000 and June:$50,000.4. Dividend-> June: $50,0005. Raw Material Cost = 80 % of Product Sale and incurred one month lead before sales.6. Receipts in a given month(Rt) = Weighted Sum of Sales from the current and last two months ( St, St-1, St-2) Current month: Weight(Wt) = 0.2; previous month : Weight(Wt-1) = 0.6; two months ago : Weight(Wt-2) = 0.2
Rt = Wt * St + Wt-1 * St-1 + Wt-2* St-2
7. The company must maintain minimum Cash Balance of $250,000.8. If cash balance falls below minimum cash threshold, the company resorts to a cash revolver for deficit amount and returned
with in the following month with interest @ 1% per month.9. The company earns interest of 0.5% on its cash balance.
Estimate: i. Maximum Loan the company need to take out to meet its desired minimum cash balance. ii. How the loan will vary over time.iii. Total interest paid on the loan.
21%
22%
18%
17%
23%
Payment Week Distribution
0: Didn’t Pay within the month 1: Paid In First Week 2: Paid In Second Week3: Paid In Third Week 4: Paid In Fourth Week
Payment Week Distribution
W1W2
W3
W4 0
Payment week distribution can help in organizing our collection effort if we have a model to predict each Guests’ payment behavior.
Actionable insights from predicted Advance payer behavior.
Strategic Collection Effort helps us to identify advance Guests and are handled accordingly to maintain their payment behavior and avoid alienating these profitable customers.
Treatment of Advance Guests
العزيز عميلناأو فروعنا من بأي السيارة إيجار بسداد نذكركم
سجلكم جودة على حفاظاً سداد خدمة طريق عناالئتماني
للتمويل عبداللطيفجميل
(ii) After waiting for 2/3 days time to react on SMS, second SMS as reminder.(iii) After waiting for 2/3 days time to react on SMS, if still not paid, collector calls to remind.
At end of each week, we check Guest’s payment status whose maturity time to pay within that week has arrived. If not paid then (i) send SMS.
Actionable insights from predicted Due Guest’s payment behavior.
Strategic Collection Effort helps us to identify and intensify collection efforts early on, and call Guests only when necessary: Optimize calling effort.
العزيز عميلنامن بأي المستحق السيارة إيجار سداد نأملسرعة
جودة على حفاظاً سداد خدمة طريق عن أو فروعنااالئتماني سجلكم
للتمويل عبداللطيفجميل
Right Guest to call, at the Right Time, with Right Intensity.
• Priority list of calling: Overdue Customers from previous month. Guests are treated by calls coupled with SMS:-
• At end of each week, we check Guest’s payment status whose maturity time to pay within that week has arrived. If not paid then initiate collection effort.
• Guest are ranked in the calling list according to their paying behavior so that the collection agent can adapt their call tone/message.
If Guests are repeated delinquent, then following SMS is used instead of wasted calls, and delegate to legal.
Actionable insights from predicted Overdue Guest’s payment behavior.
Strategic Collection Effort helps us to identify fruitless calls and replace with other effective treatment strategy like starting with SMS and followed by actual legal handling.
المحترم عميلناأمام لمطالبتكم القانونية للشؤون ملفكم بتحويل نفيدكم
منكم الموقعة ألمر بالرياضبموجبسندات التنفيذ محكمةللتمويل عبداللطيفجميل
Week1 onwards
Treatment of Potential Overdue GuestsSince most Guest pay their due in later part of the month, the first week is utilized by collectors to call those who are predicted to default within the month window ( potential overdue).
• Guest likelihood to “survive” steadily decreases, till it reaches 0, implying, the Guest should have paid by then.
• Potential Delinquent customers’ probability to “survive” will not reach 0, within an identified window (beyond which Guest is Overdue).
Survival Analytics to predict Guest payment behavior.
Survival Model helps us to predicts:- i. Which Guest will pay; ii. When will they pay; iii. Ranking of bad defaulter
Footprints of Customer Data
Guest MaritalStatusId
NationalityId
WorkPlaceId JobId
GuestGovernmentId Age
NoOfDependents Income
GuestGenderId
NoOfContracts
Opening DueSAR
OpeningAdvance
U/C* Predicted
1008783530 1 1 600 130 2 38 0 19000 1 1…. ….
0.854 0
How two extreme Guests are predicted( Defaulter):-Best rated Guest in August 2016.
*U/C=Used Period/Contract Period
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
4 4 4 3 4 4 4 4 3 3 0 2 3 3 3 2 3 2 2 2 1 2 1 1 1 1 1 0 0 0 0 0 0 0 0
Used Period
Paid in Week
Guest MaritalStatusId
NationalityId
WorkPlaceId JobId
GuestGovernmentId Age
NoOfDependents Income
GuestGenderId
NoOfContracts
Opening DueSAR
OpeningAdvance
U/C* Predicted
2344026428 1 40 430 105 1 52 0 50000 1 1…. ….
0.812 1
How two extreme Guests are predicted( Week 1 Payer):-Best rated Guest in August 2016.
*U/C=Used Period/Contract Period
Used Period
Paid in Week
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
1 0 4 1 3 4 4 2 2 2 1 1 0 4 1 3 1 4 1 4 1 1 4 4 1 3 1 1 1 1 1 1 1 2 1 1 1 1 1
Results Oct 2015.
661 Guests Total
Paid 508 19 527
Not Paid 40 94 134
Total 548 113 661
Pay Not PayActualPredicted
Model Accuracy= (508+94)/661=
Model Misclassification Rate= (40+19)/661=
96.39%Paid Prediction Rate=508/527=
91.07%
70.15%
8.92%
Unpaid Prediction Rate=94/134=
Total Due reported = SAR 159,517Average Due of Predicted cases who indeed did not pay = SAR 1,697.Assuming 30% chances of recovery from these cases, Overdue recovery= 0.3*1697*94=47,855Overdue reduction = 45,855 SAR
Month Year Week1 Week2 Week3 Week4 till end DefaulterOctober 2015 66.26% 69.14% 85.02% 59.91% 91.07%November 2015 84.37% 66.28% 73.08% 73.95% 93.78%December 2015 75.64% 67.28% 65.16% 75.21% 93.48%January 2016 62.92% 79.25% 88.35% 73.49% 91.57%February 2016 61.51% 78.80% 87.91% 76.20% 81.14%March 2016 60.12% 69.19% 89.56% 76.89% 70.81%April 2016 60.62% 70.62% 88.12% 80.75% 92.62%May 2016 60.12% 69.19% 89.56% 76.89% 70.80%June 2016 69.86% 63.59% 79.55% 80.85% 87.94%July 2016 64.50% 83.25% 86.20% 77.95% 86.44%August 2016 68.08% 64.43% 78.33% 71.73% 89.28%September 2016 75.21% 74.15% 84.61% 68.74% 70.86%October 2016 72.59% 88.08% 89.51%
Collection Optimization Model Accuracy Results.
The accuracy matters most in the defaulter prediction, where average accuracy is 85%.Weekly Prediction helps in load balancing calls for collectors.
Month Year
Paid Prediction Rate
UnPaid Prediction Rate Quality
October 2015 96.39% 70.15%
November 2015 97.61% 79.45%
December 2015 98.59% 72.46%
January 2016 97.27% 75.63%
February 2016 77.80% 92.94%
March 2016 93.12% 71.64%
April 2016 97.83% 70.39%
May 2016 85.05% 22.40%*
June 2016 89.91% 81.68%
July 2016 85.65% 87.40%
August 2016 92.15% 10.38%*
September 2016 62.95% 89.96%
Prediction Accuracy Affecting Revenue from Collection Effort
The blips in Unpaid Prediction rate in May’16 and Aug’16 is explained by the sudden change in trend of overdue. However as the trend restores, the accuracy is restored.
1. This results is under testing at Amir Soultan Branch with two collectors level for November.
2. Starting December’2016, the solution should be extended to the entire Amir Soultan Branch to halt the rising overdue.
Above steps can be implemented with “0” cost.3. After gaining the confidence and improvement in the model, the scope
will be extended to allJan’2017 onwards this solution will be extended to sub-region with 1 SAS license and 1 server, dispatching weekly lists to each collector.
4. Mar’2017, after review of result, SAS consultants will be required to architect this solution for entire region. License cost will remain same, server cost will increase.
Way Forward:-