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ISyE 6203 Wrap Up Exam Review

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ISyE 6203 Wrap Up Exam Review John H. Vande Vate Fall 2011 – PowerPoint PPT presentation

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Title: ISyE 6203 Wrap Up Exam Review


1
ISyE 6203Wrap UpExam Review
  • John H. Vande Vate
  • Fall 2011

2
Summary
  • 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

3
The Big Idea
  • When combining random variables, some of the
    noise cancels. How much cancels depends on the
    correlation.

4
Noise Canceling
  • X1, X2 independent, identically distributed rvs
  • Var2X1 4 ?2X
  • Stdev2X1 2?X
  • VarX1 X2
  • StdevX1 X2
  • About 30 of the variability canceled

2?2X 2Cov(X,X)
5
How can we
  • Add across customers?
  • Add across products?
  • Add across time?
  • When do these conflict?

6
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 5Average Daily Sales
  • What about the relationship between the
    variabilities?
  • 5Std Dev. In Daily Sales 7732.361
  • What does the Big Idea say we should expect?

7
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

8
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?

9
Actual to Forecast Ratios
Ratio lt 1 Over forecast
Ratio gt 1 Under forecast
  • ? the Avg is 1.1 (What does that mean?)
  • s the Std Dev is 0.87

10
Context
  • Forecasting to account for predictable
    variability
  • Managing the remaining variability
  • Distribution for demand (given a forecast)
  • Levers for managing
  • Inventory
  • Time
  • Capacity
  • Influencing demand

11
Lead Time Variability
Constant Avg Demand
  • If Lead Times are variable
  • D Average (daily) demand
  • sD 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
  • sL ?Ls2D D2 s2L
  • Remember Std. Dev. in lead time demand drives
    safety stock

Continuous Review
12
Safety Stock in Periodic Review
  • Probability of stock out is the probability
    demand in TL exceeds the order up to level, S
  • Expected Demand in T L
  • D(TEL)
  • Variance in Demand in TL
  • (TEL) sD2 D2 sL2
  • Order Up to Level S D(TEL) safety stock
  • How to set the safety stock?

Constant Avg Demand
Remember our key fact
Periodic Review
13
With a Forecast
  • Forecast of what?
  • How far into the future? Do we make this forecast
    one year in advance? One month in advance? One
    week in advance?

Forecast of demand in TL time periods thats
what we have to cover with our Order-Up-To-Level S
A forecast of the demand over the T L time
periods starting now Thats what we need to
have to place the order it goes into our
inventory POSITION immediately
14
A/F ratios for the next TL time
Ratio lt 1 Over forecast
Ratio gt 1 Under forecast
V should be just over 2.0 to ensure a 90 chance
A/F v
  • ? the Avg is 1.1
  • s the Std Dev is 0.87
  • Example We order every week and lead time is 4
    weeks, we want to know the next 5 weeks demand
    when we place this order. This order will
    determine S and so the inventory available to
    cover the next TL time periods

15
Example
  • If v 2.1 and TL 5 weeks, that means setting
    an order up to level of 10.5 v(TL) weeks of
    supply ensures a 90 chance we wont run short.
  • In a perfect world, we would only need TL weeks
    of supply to cover TL weeks of demand so our
    Safety Stock in this setting is (v-1)(TL) 5.5
    weeks of supply.

16
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
    2.110,000 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.

17
Pooling
  • Collective Lead time demand N(nm, s)
  • This is true if their demands and lead times are
    independent!
  • Collective safety stock is zs
  • 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?
  • spooled2 2s2 2Covariance
  • 2s2 - 2s2 spooled2 2s2 2s2
  • So spooled 2s, the unpooled standard deviation

Thats our big idea at work.
Pooling always reduces inventory, but how much
varies
18
Newsvendor
If Salvage Value is gt Cost?
  • Balance the Risks and Rewards
  • Reward (Selling Price Cost)(1-P)
  • Risk (Cost Salvage)P
  • (Selling Price Cost)(1-P) (Cost Salvage)P
  • P

19
Objective for the first 10K
  • Return on Investment
  • 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?

Expected Profit Invested Capital
20
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?

21
Different View
  • Use Lagrange
  • Maximize S Expected Profit(Qi)
  • - 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

22
Relative Sales Rates
23
Two Constraints
  • P Average Sales Rate at Full Price
  • xprice Weeks we sell at price
  • S Units we salvage
  • max P(60x60 541.31x54 481.73x48
    362.81x36
  • ) 25S
  • s.t. x60 x54 x48 x36 ? 15
  • s.t. P(x60 1.31x54 1.73x48
    2.81x36) S 2000
  • s.t. x60 ? 1 (This is a bound. Like x54
    ? 0)
  • non-negativity

24
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.

25
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

26
KOVPThe Push-Pull Interface
Production System before KOVP
Early Order Assignment
Start Order Assignment
Sort
Sort
Bodyshell work Paint shop Assembly
Production System with KOVP
Make-to-Order
Late Order Assignment
Frozen Horizon
Start order assignment
Sort
OSM
Bodyshell work Paint shop Assembly
27
DELL BRH1 Manufacturing
Manufacturing Layout
Manufacturing Flow
Servers
INBOUND
Shipping
Notebooks
New Lean Lines
Desktops
OUTBOUND
Finished Goods RAM Cabinets
Lean Lines
28
Ship-to-Average Forecasts
29
Ship to Average
Deflate shipments Avg. forecast (x weeks)
deflation factor
Max. Inventory Position
Inventory Position
(almost) constant shipment quantities !
Time
Inflate shipments Avg. forecast (x weeks)
inflation factor
30
Shipment Comparison
ship-to-forecast
(shipment adjustment 66)
ship-to-average
(shipment adjustment 14)
DefinitionShipment Adjustment shipment
quantity changes more than 10 compared to
previous one
31
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

32
Two Contradictory Facts
  • Companies generally will not allow taxes and the
    like to influence logistics decisions
  • Supply Chain Engineers are Tax ( Duty Tolls
    ) Engineers

33
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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