Why hold Safety Inventory

1
Why hold Safety Inventory?

• Demand uncertainty
• Supply uncertainty
• Measures of product availability
• Product fill rate (fr)
• Order fill rate
• Cycle service level (CSL)

2
Normal Probability Distribution
f
P
x
Pprob(ltx) normdist(x,mean,s.d.,1)
F(x) x
norminv(P,mean,s.d.) F-1(x) flikelihood(x)
normdist(x,mean,s.d.,0) f(x)
3
Normal Distribution Examples

• Demand D has mean460, standard deviation180.
• What is the probability that Dlt300?
  normdist(300, 460, 180, 1) 0.187031
• What is the probability that Dgt400? Prob(Dlt400)
  normdist(400, 460, 180, 1) 0.369441, so
  Prob(Dgt400) 1 - 0.369441 0.630559.
• How much inventory is needed to have a 95 chance
  of not running out? norminv(0.95, 460,180)
  756

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Replenishment policies

• When to reorder?
• How much to reorder?
• Continuous Review Order fixed quantity when
  total inventory drops below Reorder Point (ROP)
• Periodic Review Order at fixed time intervals to
  raise total inventory to Order up to Level (OUL)

5
Product Fill Rate

• fr fraction of product demand that is satisfied
  from inventory
• Equivalent to probability that demand is supplied
  from available inventory

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Order Fill Rate

• Fraction of (possibly multi-product) orders are
  satisfied from inventory
• If one product is missing from a multi-product
  order (due to not being in available inventory),
  the order is not satisfied.
• Will be lower than Product fill rate.

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Cycle Service Level

• CSL fraction of replenishment cycles that do
  not result in stockouts
• Replenishment cycle time between receipt of
  successive lots.
• Equivalent to probability that new shipment
  arrives before demand exhausts inventory
• Does not measure amount of unmet demand, just how
  many cycles have stockouts of any size.

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Safety Inventory Terminology for Continuous
Review

• ss (avg) safety inventory
• R mean demand per period
• sR standard deviation of R
• L lead time (periods)
• RL mean demand during lead time RL
• sL standard deviation of RL
• ROP Re-order point

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Calculating Service Levels for Continuous Review
Policy

• ROP, Q are specified. What is the ss, CSL, fr?
• Average safety inventory is whats left over from
  the ROP after demand during the lead time
• ss ROP RL.
• Average inventory (safety cycle) is Q/2 ss
• CSL is the probability that the ROP inventory
  outlasts the lead time demand

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Fill Rate

• Proportion of customer demand satisfied from
  stock
• ESC is the expected shortage per cycle
• ss is the safety inventory
• Q is the order quantity

ESC -ss1-NORMDIST(ss/?L, 0, 1, 1) ?L
NORMDIST(ss/??L, 0, 1, 0)
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Example 8.1 (Continuous Review Policy)

• R 2,500 /week ?R 500
• L 2 weeks Q 10,000 ROP 6,000
• ss ROP - RL
• Average Inventory
• Average Flow Time
• Cycle service level, CSL F(RL ss, RL, ?L)

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Example 8.2 Evaluating Fill Rate

• ss 1,000, Q 10,000, Fill Rate (fr) ?
• ESC -ss1-NORMDIST(ss/?L, 0, 1, 1)
• ??L NORMDIST(ss/?L, 0, 1, 0)
• -1,0001-NORMDIST(1,000/707, 0, 1, 1)
• 707 NORMDIST(1,000/707, 0, 1, 0)
• 25.13
• fr (Q - ESC)/Q (10,000 - 25.13)/10,000
  0.9975.

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Calculating Safety Inventory to meet Desired
Service Levels Continuous Review

• CSL or fr is specified. What is the ss, ROP?
• Recall that CSL F(ROP)
• As before, ROP ssRL

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Calculating Safety Inventory to meet Desired
Service Levels Continuous Review

• The formulas for fr are too complex to be
  directly inverted.
• Set up Excel formulas to calculate fr given ss,
  and adjust ss until the desired fr is achieved.
• Can use Excel tool Goalseek to automate this
  process.
• Goalseek might not be accurate enough to match a
  small fr A few alternatives
• Calculate ESC (1 - fr)Q, and let goalseek
  manipulate ss to match the appropriate ESC.
• Calculate 100 or 1000 times fr to give goalseek a
  larger target

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Example 8.2 Evaluating Safety Inventory Given CSL

• R 2,500/week ?R 500
• L 2 weeks Q 10,000 CSL 0.90
• ss FS-1(CSL)?L
• ROP ss RL
• Factors driving safety inventory
• Replenishment lead time
• demand uncertainty

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Evaluating Safety Inventory Given Desired Fill
Rate

• If desired fill rate is fr 0.975, how much
  safety inventory should be held?
• ESC (1 - fr)Q 250
• Solve

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Evaluating Safety Inventory Given Fill Rate
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Factors Affecting Fill Rate

• Safety inventory Fill rate increases if safety
  inventory is increased. This also increases the
  cycle service level.
• Lot size Fill rate increases on increasing the
  lot size even though cycle service level does
  not change.

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Safety Inventory Terminology for Periodic Review

• ss (avg) safety inventory
• R mean demand per period
• sR standard deviation of R
• L lead time (periods)
• T reorder interval (periods)
• RTL mean demand until next shipment R(TL)
• sTL standard deviation of RTL
• OUL Order Up-to Level

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Calculating Service Levels for Periodic Review
Policy

• T, OUL are specified. What are the ss, CSL, fr?
• Average safety inventory is whats left over by
  the time a shipment arrives
• avg ss OUL RTL
• Average lot size is the same as average demand
  between reviews avg QRTRT
• Average inventory (safety cycle) is Q/2 ss
• CSL is the probability that OUL inventory will
  last until the next shipment arrives, after LT
  periods.

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Example Periodic Review Policy

• R 2,500/week ?R 500
• L 2 weeks T 4 weeks OUL 16,000
• ss OUL RLT
• Average Inventory
• Average Flow Time
• Cycle service level, CSL F(RL ss, RL, ?L)

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Calculating Safety Inventory to meet Desired
Service Levels Periodic Review

• CSL is specified. What is the ss, OUL?
• Recall that CSL F(OUL)
• As before, ROP ssRLT

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Example Periodic Review Policy

• R 2,500/week ?R 500
• L 2 weeks T 4 weeks CSL 0.90
• What is the required safety inventory?
• Factors driving safety inventory
• Demand uncertainty
• Replenishment lead time
• Reorder interval

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Impact of Supply Uncertainty

• R Average demand per period
• ?R Standard deviation of demand per period
• L Average lead time
• ?sL Standard deviation of lead time

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Impact of Supply Uncertainty

• R 2,500/day ?R 500
• L 7 days Q 10,000 CSL 0.90
• Safety inventory when sL 0 is 1,695
• Safety inventory when sL 1 is 3,625
• Safety inventory when sL 2 is 6,628
• Safety inventory when sL 3 is 9,760
• Safety inventory when sL 4 is 12,927
• Safety inventory when sL 5 is 16,109
• Safety inventory when sL 6 is 19,298

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Basic Quick Response Initiatives

• Reduce information uncertainty in demand
• Reduce replenishment lead time
• Reduce supply uncertainty or replenishment lead
  time uncertainty
• Increase reorder frequency or go to continuous
  review

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Accurate Response The Impact of Inventory Pooling
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Example of Aggregation with Correlation

• Four car dealerships, each with
• R25 cars/wk
• sR5 cars/wk
• L2 wks
• So sL7.07 for each dealership
• To meet a CSL of 90 requires avg. safety
  inventory of 9.06 for each dealership
• Total average safety inventory 36.24

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Example of Aggregation with Correlation (contd)

• Consider replacing the four dealerships with a
  single dealership.
• RC 100 cars/wk
• ss normsinv(CSL)sLC
• What happens for different values of r?

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Example of Aggregation with Correlation (contd)
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Impact of Correlation on Benefit From Aggregation
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Factors Affecting Value of Aggregation

• Demand Correlation
• Coefficient of Variation of demand
• Value of product

33
Impact of cv and Product Value on Benefit From
Aggregation
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Methods of Accurate Response

• Physical Centralization
• Information centralization
• Specialization
• Product substitution
• Raw material commonality (postponement)

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Example 8.9 Value of Component Commonality
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Mass Customization I Customize Services Around
Standardized Products
Source B. Joseph Pine
Deliver customized services as well as
standardized products and services
Market customized services with
standardized products or services
Continue producing standardized products or
services
Continue developing standardized products or
services
37
Mass Customization II Create Customizable
Products and Services
Deliver standard (but customizable) products or
services
Market customizable products or services
Produce standard (but customizable) products or
services
Develop customizable products or services
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Mass Customization III Provide Quick Response
Throughout Value Chain
Reduce Delivery Cycle Times
Reduce selection and order processing cycle
times
Reduce Production cycle time
Reduce development cycle time
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Mass Customization IV Provide Point of Delivery
Customization
Point of delivery customization
Deliver standardize portion
Market customized products or services
Produce standardized portion centrally
Develop products where point of delivery
customization is feasible
40
Mass Customization V Modularize Components to
Customize End Products
Deliver customized product
Market customized products or services
Produce modularized components
Develop modularized products
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Types of Modularity for Mass Customization
Component Sharing Modularity
Cut-to-Fit Modularity
Bus Modularity
Mix Modularity
Sectional Modularity
42
Cautions in Implementing Postponement and
Modularity

• End products must look suitably different to the
  consumer
• Design and production costs can only be justified
  over a family of products
• Performance and cost of a product can be
  optimized by eliminating modularity. Do a small
  set of products provide most of the sales?

43
Summary of Learning Objectives
44
Continuous Review Policy Safety Inventory and
Cycle Service Level

• L Lead time for replenishment
• R Average demand per unit time
• ?RStandard deviation of demand per period
• RL Mean demand during lead time
• ?L Standard deviation of demand during lead time
• CSL Cycle service level
• ss Safety inventory
• ROP Reorder point

Average Inventory Q/2 ss
45
Periodic Review Policy Safety Inventory

• L Lead time
• T Reorder interval
• R Average demand per unit time
• ?R Standard deviation of demand per unit time
• ?LT Standard deviation of demand during LT
  periods
• CSL Cycle service level
• ss Safety inventory
• OUL Order up to level