ISyE 6203
Wrap Up
Exam Review
John H. Vande Vate
Fall 2011
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Summary
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Review of Probability & Regression
Forecasting
Building a distribution of demand
Safety Inventory/Lead time: Using inventory to
protect against demand variability
Pooling
Sourcing: Newsvendor and Extensions
Revenue Management
Make-to-stock & Make-to-Order
Alternative approach to managing variability
Distortions to the logic of logistics
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The Big Idea
• When combining random
variables, some of the
“noise” cancels. How much
cancels depends on the
correlation.
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Noise Canceling
• X1, X2 independent, identically
distributed rvs
• Var[2X1] = 4 2X
• Stdev[2X1] = 2X
• Var[X1 + X2] = 22X + 2*Cov(X,X)
• Stdev[X1 + X2] =
2  2Cov( X , X )  2 X
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X
• About 30% of the variability canceled
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How can we:
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Add across customers?
Add across products?
Add across time?
When do these conflict?
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The Big Idea
• Average Daily Sales: 1280.196
• Std Dev. In Daily Sales: 1546.472
• Average Weekly Sales: 6400.981
• Std Dev. In Weekly Sales: 5971.578
• Avg Weekly Sales = 5*Average Daily Sales
• What about the relationship between the variabilities?
• 5*Std Dev. In Daily Sales = 7732.361
What does the Big Idea say we should expect?
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Laws of Forecasting
• Law 1: Forecasts are wrong
• Law 2: Forecast Demand not Sales
• Law 3: It is generally easier to forecast
aggregate data than it is to forecast the details.
(Big Idea)
• Law 4: It is generally easier to forecast a short
time into the future that to forecast far into the
future
• Law 5: Simpler forecasts are generally better
forecasts
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Demand Distribution
• We know the forecast is WRONG
• But it does give us some information
• What Actual Sales will be is uncertain,
but we can develop a distribution for it
• What are the chances Actual Sales are
larger than X? Smaller than Y? …
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Actual to Forecast Ratios
Frequency
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Ratio < 1 Over
forecast
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Ratio > 1 Under
forecast
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2.
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1.
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•  the Avg is 1.1 (What does that mean?)
• σ the Std Dev is 0.87
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Context
• Forecasting to account for predictable
variability
• Managing the remaining variability
• Distribution for demand (given a forecast)
• Levers for managing
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Inventory
Time
Capacity
Influencing demand
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Lead Time Variability
Constant
Avg
Demand
Continuous
Review
If Lead Times are variable
• D = Average (daily) demand
• D = Std. Dev. in (daily) demand
• L = Average lead time (days)
• sL = Std. Dev. in lead time (days)
• Average lead time demand
– DL
• Std. Dev. in lead time demand
– L = L2D + D2 s2L
• Remember: Std. Dev. in lead time demand
drives safety stock
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Safety Stock in Periodic Review
Constant
Avg
Demand
Periodic
Review
• Probability of stock out is the probability demand
in T+L exceeds the order up to level, S
• Expected Demand in T + L
 D(T+E[L])
• Variance in Demand in T+L
Remember our
key fact
 (T+E[L]) D2 +D2 L2
• Order Up to Level: S= D(T+E[L]) + safety stock
• How to set the safety stock?
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With a Forecast
• Forecast of what?
Forecast of demand in T+L time periods –
that’s what we have to cover with our
Order-Up-To-Level S
• How far into the future? Do we make this
forecast one year in advance? One month in
advance? One week in advance?
A forecast of the demand over the T + L time
periods starting “now” – That’s what we need
to have to place the order – it goes into our
inventory POSITION immediately
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A/F ratios for the next T+L time
Distribution
of Error
Cumulative
Distribution
of Ratios
Error Ratios
35%
Ratio
100%
30%
90%
< 1 Over
forecast
Ratio > 1 Under
forecast
80%
25%
70%
20%
60%
15%
50%
10%
40%
5%
30%
V should be just
over 2.0 to
ensure a 90%
chance A/F ≤ v
0%
20%
0
0 to 0.5
0.5 to 1.0
1.0 to 1.5
1.5 to 2.0
2.0 to 2.5
2.5 to 3.0
10%
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 the Avg is 1.1
0%
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σ the Std Dev is 0.87
0.00 We0.25
0.50 week
0.75 and1.00
1.25is 41.50
2.00
2.25the 2.50
3.00
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Example:
order every
lead time
weeks,1.75
we want
to know
next 5 weeks
demand when we place this order. This order will determine S and so the inventory available to
cover the next T+L time periods
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Example
• If v = 2.1 and T+L = 5 weeks, that means
setting an order up to level of 10.5 = v*(T+L)
weeks of supply ensures a 90% chance we
won’t run short.
• In a perfect world, we would only need T+L
weeks of supply to cover T+L weeks of
demand so our Safety Stock in this setting is
(v-1)*(T+L) = 5.5 weeks of supply.
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Example
• Now we can re-insert the forecast:
If we forecast 10,000 units of sales over the next
5 weeks, then we should place an order up to
carry our inventory POSITION to 21,000 =
2.1*10,000 units
• 10,000 units over 5 weeks is a rate of r = 2,000
units per week. 21,000 units is 10.5 weeks of
demand
• Safety Stock rises and falls with the forecast but
Safety Lead Time remains 5.5 weeks.
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Pooling
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Collective Lead time demand N(n, n )
This is true if their demands and lead times are independent!
That’s our big idea at work.
Collective safety stock is n z
Total of individual safety stocks is nz
Typically demands are negatively or positively correlated
What happens to the collective safety stock if demands are
– positively correlated?
– Negatively correlated?
Pooling always reduces
inventory, but how much
varies
• pooled2 = 22 + 2*Covariance
• 22 - 2*2 ≤ pooled2 ≤ 22 + 2*2
• So pooled ≤ 2, the unpooled standard deviation
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Newsvendor
• Balance the Risks and Rewards
Reward: (Selling Price – Cost)*(1-P)
Risk: (Cost – Salvage)*P
If Salvage
Value is >
Cost?
(Selling Price – Cost)*(1-P) = (Cost – Salvage)*P
P=
(Selling Price – Cost)
(Selling Price – Cost)
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(Selling Price – Cost  Cost – Salvage) (Selling Price – Salvage)
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Objective for the “first 10K”
• Return on Investment:
Expected Profit
Invested Capital
• Questions:
– What happens to Expected Profit per unit as the order
quantity increases?
– What happens to the Invested Capital per unit as the order
quantity increases?
– What happens to Return on Investment as the order quantity
increases?
– Which styles will show the higher return on investment?
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Different View
• Maximize S Expected Profit(Qi)
• S.t. S ci Qi = Invested Capital Target
• That maximizes the ROIC for the
“portfolio”
• How to do it?
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Different View
• Use Lagrange
• Maximize S Expected Profit(Qi)
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- Tax Rate* S ci Qi
• At a given Tax Rate, the answer maximizes
the ROIC over all portfolios with that amount
of Invested Capital.
• Increasing the Tax Rate reduces the Invested
Capital
• So, we can carve out the frontier of high
ROIC portfolios vs Invested Capital
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Relative Sales Rates
Item
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Full Price
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Full Price
Mean
Std Dev
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Ratio of Sales Rates
10%
20%
1.30
1.34
1.39
1.27
1.23
1.83
1.77
1.83
1.79
1.44
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10%
1.31
0.06
40%
2.63
2.94
3.00
2.67
2.81
20%
1.73
0.16
40%
2.81
0.16
A discount of 10% lifts weekly sales by 31%
Mean
Std Dev
1
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1.31
0.06
1.73
0.16
2.81
0.16
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Two Constraints
• P = Average Sales Rate at Full Price
• x[price] = Weeks we sell at price
• S = Units we salvage
max P*(60x[60] + 54*1.31x[54] + 48*1.73x[48] + 36*2.81x[36]
) + 25S
s.t. x[60] + x[54] + x[48] + x[36]  15
s.t. P*(x[60] + 1.31x[54] + 1.73x[48] + 2.81x[36]) + S = 2000
s.t. x[60]  1 (This is a bound. Like x[54]  0)
non-negativity
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The 3 Levers
• Manage variability with
– Inventory:
• The classic buffer against changes in and uncertainty
about demand.
• The cost is working capital and risk of obsolescence and
damage, extra handling, etc.
– Capacity:
• Changes in production rate, overtime, extra shifts,
furloughs, shutdowns, etc.
• The cost is fixed capital invested in idle capacity,
disruptions to workforce, suppliers, carriers, …
– Time:
• Making the customer wait either via longer delivery
commitments or backordering or
• The cost is in customer satisfaction, competitiveness, lost
sales, etc.
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Priorities
• Make-to-Stock
– Protect capacity
– Balance between
• availability (the time buffer) and
• inventory
• Make-to-Order
– No (finished goods) inventory
– Balance between
• Order-to-delivery time
• Capacity
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KOVP
The Push-Pull Interface
Production System before KOVP
Early
Order Assignment
Start Order Assignment
Bodyshell work
Sort
Sort
Paint shop
Assembly
Production System with KOVP
Make to Stock Late
Make-to-Order
Frozen
Horizon
Order Assignment
Sort
Start order assignment
OSM
Bodyshell work
Paint shop
Assembly
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DELL BRH1 – Manufacturing
Manufacturing Flow
Manufacturing Layout
Servers
Notebooks
Shipping
INBOUND
New Lean Lines
Desktops
Finished Goods
RAM Cabinets
Lean Lines
OUTBOUND
Entrada fábrica
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Ship-to-Average & Forecasts
Percent Error
80%
60%
40%
20%
0%
Daily
Weekly
Monthly
Quarterly
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Forecast quantity
120
100
daily
weekly
monthly
quarterly
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60
40
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Ship to Average
Deflate shipments:
Avg. forecast (x weeks)
* deflation factor
Inventory Position
Max. Inventory
Position
(almost) constant
shipment quantities !
Time
Inflate shipments:
Avg. forecast (x weeks)
* inflation factor
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Shipment Comparison
ship-to-forecast
700
shipments
(shipment adjustment: 66%)
800
600
500
400
300
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weeks
ship-to-average
700
shipments
(shipment adjustment: 14%)
800
600
500
400
300
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weeks
Definition:
Shipment Adjustment: shipment quantity changes more than 10% compared to previous
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The Point
• The message of supply chain management is
that supply chain competes against supply
chain.
• Look to reduce cost, improve performance in
the supply chain, not just your company
• Variability costs money so manage the
variability you transmit to suppliers
• …
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Two Contradictory “Facts”
• Companies generally will not allow
taxes and the like to influence logistics
decisions
• Supply Chain Engineers are Tax (&
Duty & Tolls &…) Engineers
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Final Exam
• Four questions
– Short answer questions on the course
lectures since mid-term
• 1 Question on: The Big Idea, A/F ratios, safety
inventory, safety lead time
• 1 Question on: Obermeyer
• 1 Question on: Retail Pricing
• 1 Question on Projects
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