Management Science

1
Management Science

• Term 1, 2003/2004
• Class 6Risk Analysis Using Simulation 2
• Raf Jans Moritz Fleischmann
• Rotterdam School of Management / Erasmus
  University Rotterdam

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Simulation Key Concepts

• Uncertain input gt model gt uncertain output
• Define probability distribution for your inputs
• Take one sample for each of the uncertain inputs
  according to their probability distributions
• Record the output
• Repeat this many times, to obtain a
  distributionof outcomes for your output.

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Simulation Key Concepts
OUTPUT?
INPUT
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Simulation Key Concepts
OUTPUT?
INPUT
OUTPUT
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Simulation Key Concepts
INPUT 1
INPUT 2

OUTPUT?
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Simulation Key Concepts
OUTPUT
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Simulation Remarks

• The outcome of a simulation depends on the random
  samples generated in each iteration
• gt Repeating a simulation in general does not
  yield exactly the same results (in contrast
  with repeatedly running solver or Precision
  Tree)
• However, the distribution of the outcome across a
  large number of iterations is approximately the
  same
• gt A large enough number of iterations is crucial
  to assure reliable results!

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Simulation Remarks

• Simulation is relatively costly in terms of
  computational effort because of
• need for many iterations
• lack of optimization capabilities
• gt Do not use simulation just for convenience
  if more direct optimization / modeling approaches
  are available
• Simulation may provide a last resort if other
  approaches are not feasible (because of too many
  / too complex uncertainties)

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Wellyntoy Products The Dynatron

• Danny Keepstone, Marketing Manager
• How many Dynatrons to produce for 2000?
• Standard-model versus Super-model
• Dynatron History 1998-1999
• September 1998 contract
• Early 1999 product development
• April 1999 production quantity set at 52,000
  units byDanny Keepstone Saul Gassman
• 33,000 standard and 19,000 super
• Machine capacity 150,000 units (cost 50,000)
• Production delays led to sales of only 35,000
  units
• 21,000 standard (12,000 still on inventory)
• 14,000 super (5,000 still on inventory)

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Dynatron History 2000

• higher sales forecasts
• uncertainty about total demand and mix
• expected 150,000 sales, 60 standard - 40 super
• production capacity
• existing capacity 150,000 units at no additional
  cost
• up to 200,000 at 15,000 cost
• up to 500,000 at 70,000 cost
• price fixed
• 4.30 for Standard model
• 5.50 for Super model
• costs
• direct costs 2.50 for Standard model, 3.20
  for Super model
• additional costs equal to 12 of gross margin
• inventory costs 2 of direct costs per month,
  for 6 months

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News Vendor Decision

• The setting at Wellintoys is an example of a
  so-called news vendor decision
• production/purchase decision long before selling
  seasongt high uncertainty
• short selling season / limited replenishment
  opportunities
• gt make trade-off between risk of ordering too
  much (overage) and risk of ordering too little
  (underage) by comparing cost effects of both
  cases
• Typical, challenging decision problem for short
  lifecycle products (toys, fashion, electronics,)
• See Operations Management class for detailed
  analysis

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What to do with leftover stock?

• Assumption 1
• Overproduction is left in stock for an averageof
  6 months
• All the stock can be set off against production
  quantities in the next period
• gt No influence of direct cost
• Assumption 2
• Leftover stock is lost
• Overproduction is not kept in inventory
• gt Take into account production cost for lost
  stock

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Optimal Decision No Uncertainty

• Expected total demand
• 150,000
• Expected Mix
• 60 Standard
• 40 Super
• Optimal Decision
• produce 78,000 standard
• produce 55,000 super
• production exactlyequal to demand
• profit 264,000

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Recognizing uncertainty

• Total Demand
• base 150,000
• minimum 50,000
• maximum 300,000
• Mix
• base 40 super
• minimum 30 super
• maximum 60 super

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Scenario Analysis

• Worst-case Scenario
• demand 50,000
• mix 30 super
• profit 52,020
• Best-case Scenario
• demand 300,000
• mix of no importance
• (as for any mix
• demand gt available)
• profit 264,000(identical to base case)

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One-way sensitivity analysis
Demand
264,000
50,000
54,640
75,000
106,980
100,000
159,320
125,000
211,660
150,000
264,000
175,000
264,000
200,000
264,000
225,000
264,000
250,000
264,000
275,000
264,000
300,000
264,000
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One-way sensitivity analysis
Proportion
Super
264,000
30
227,880
35
245,940
40
264,000
45
249,870
50
235,740
55
221,610
60
207,480
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Two-Way Sensitivity Analysis
264,000
30
35
40
45
50
55
60
50,000
52,020
53,330
54,640
55,950
57,260
58,570
59,880
75,000
103,050
105,015
106,980
108,945
110,910
112,875
114,840
100,000
154,080
156,700
159,320
161,940
164,560
167,180
169,800
125,000
205,110
208,385
211,660
214,935
212,190
200,415
188,640
150,000
227,880
245,940
264,000
249,870
235,740
221,610
207,480
175,000
245,940
264,000
264,000
264,000
259,290
242,805
226,320
200,000
264,000
264,000
264,000
264,000
264,000
264,000
245,160
225,000
264,000
264,000
264,000
264,000
264,000
264,000
264,000
250,000
264,000
264,000
264,000
264,000
264,000
264,000
264,000
275,000
264,000
264,000
264,000
264,000
264,000
264,000
264,000
300,000
264,000
264,000
264,000
264,000
264,000
264,000
264,000
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Alternative Decisions

• Field Sales Representative
• Standard 130,000 units
• Super 95,000 units
• Production Manager
• Standard 80,000 units
• Super 70,000 units
• Product Manager (Gassman)
• Standard 115,000 units
• Super 85,000 units

Total 225,000 units Profit in base case
of 163,040
Total 150,000 units Profit in base case
of 257,640
Total 200,000 units Profit in base case of
226,380
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Comparative Sensitivity Analysis
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Total Demand Forecast

• Total Demand Forecast
• median 150,000
• minimum 50,000
• 3 chances in 4 of demand being higher than
  125,000
• 1 chance in 4 of demand being higher than 190,000
• maximum 300,000
• Cumulative Probability Distribution
• minimum (0) 50,000
• 25 percentile 125,000
• median (50) 150,000
• 75 percentile 190,000
• maximum (100) 300,000

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Demand Distribution
RiskCumul(50,300,125,150,190,0.25,0.5,0.75)
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Demand Distribution
RiskCumul(50,300,125,150,190,0.25,0.5,0.75)
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Mix Forecast

• Mix Forecast
• 50-50 chance of 40 demand for Super model
• maximum 60
• minimum 30
• 75 chance less than 45
• 25 chance less than 36
• Cumulative Probability Distribution
• minimum (0) 30
• 25 percentile 36
• median (50) 40
• 75 percentile 45
• maximum (100) 60

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Mix Distribution
RiskCumul(0.3,0.6,0.36,0.4,0.45,0.25,0.5,0.75)
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Mix Distribution
RiskCumul(0.3,0.6,0.36,0.4,0.45,0.25,0.5,0.75)
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Simulation
DYNATRON
RiskCumul(50000,300000, 125000,150000,190000,
0.25,0.5,0.75)
Standard
Super
Total
Production
78,000
55,000
133,000


Inventory
12,000
5,000
17,000
Available
90,000
60,000
150,000
Demand
76,868
48,653
125,521
Proportion
61
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100
RiskCumul(0.3,0.6, 0.36,0.4,0.45,0.25,0.5,0.75
)
Sales
76,868
48,653
125,521
Inventory
13,132
11,347
24,479
Price
4.30
5.50
Direct Costs
2.50
3.20
Gross Margin
138,363
111,902
Add. costs
16,604
13,428
Inventory costs
3,939.47
4,357.25
Net Margin
117,820
94,116
Total earnings
211,937
Capacity Costs
0
Add Output
Net Result
211,937
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Simulationof Base Policy

• Minimum 56,000
• Expected 220,000
• Maximum 264,000
• Stand. Deviation 57,000
• gt Substantially different from estimate
  without uncertainty!

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Field Sales Representative

• Minimum -45,000
• Expected 174,000
• Maximum 360,000
• Stand. Deviation 109,000
• P(loss) 7 (downside risk)
• P(gt 300,000) 17 (upside potential)

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Production Manager

• Minimum 48,000
• Expected 231,000
• Maximum 298,000
• Stand. Deviation 70,000
• P(loss) 0 (downside risk)
• P(gt 300,000) 0 (upside potential)

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Gassman

• Minimum 16,000
• Expected 229,000
• Maximum 368,000
• Stand. Deviation 98,000
• P(loss) 0 (downside risk)
• P(gt 300,000) 26 (upside potential)

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How about our Original Suggestion?

• Optimal solution with no uncertainty is not
  necessarily also optimal solution when
  uncertainty is taken into account !

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What to do with stock?

• Assumption 2
• All the stock is lost
• Take into account the production cost for the
  lost stock
• No cost for royalties, discounts, advertising,
  promotion
• Over production is not kept in inventory
• Very easy to model as well

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Field Sales Representative

• Minimum -520,000
• Expected -40,000
• Maximum 357,000
• Stand. Deviation 236,000
• P(loss) 59 (downside risk)
• P(gt 300,000) 10 (upside potential)

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Production Manager

• Minimum -245,000
• Expected 154,000
• Maximum 297,000
• Stand. Deviation 150,000
• P(loss) 18 (downside risk)
• P(gt 300,000) 0 (upside potential)

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Gassman

• Minimum -396,000
• Expected 66,000
• Maximum 368,000
• Stand. Deviation 212,000
• P(loss) 36 (downside risk)
• P(gt 300,000) 19 (upside potential)

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What to do with stock?
The assumption regarding the overproduction has a
huge impact on the results
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Key Insights

• We simulate one policy (strategy, decision) at
  the time and analyse the outcome. (see Risk is
  associated with a decision, not a problem)
• As a result of the simulation, we obtain a
  distribution of results.
• Combining simulation and optimization is
  difficult
• When we compare various policies, we typically
  see the trade-off between expected value and
  risk.

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Key Insights

• The flaw of average do not make decision based
  on average values!The average value of the
  output is not equal to the output of the average
  input values!
• Understanding basic statistic concepts is
  crucial.

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Next class

• Class 7 Performance analysis using DEA
• Wednesday, December 10
• Preparation Case Modells DEA
• Workshop on Decision Analysis
• Thursday, December 11
• Assignment 2 will be available Friday, December 5
• Deadline Monday, December 15

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Think it over

• All models are wrong, but some are useful.
• - W. E. Deming,
• the father of modern quality control