Inventory%20Management:%20Safety%20Inventory%20(%20I%20)

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Inventory Management Safety Inventory ( I )
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Safety Inventory

• Safety Inventory is inventory carried for the
  purpose of satisfying demand that exceeds the
  amount forecasted for a given period.
• Purposes of holding safety inventory

• Demand uncertainty
• Supply uncertainty

Inventory
Cycle Inventory
Average Inventory
Safety Inventory
Time
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Planning Safety Inventory

• Appropriate level of safety inventory is
  determined by

• Uncertainty of both demand and supply
• Uncertainty increases, then safety inventory
  increases.

• Desired level of product availability Desired
  level of product availability
• increases, then safety inventory increases.

• Actions to improve product availability while
  reducing safety inventory

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Measuring Demand Uncertainty

• Uncertainty within lead time

• Assume that demand for each period i, i1,.,k
  is normally distributed with a mean Di and
  standard deviation si .

• The total demand during k period is normally
  distributed with a mean of P and a standard
  deviation of W

• If demand in each period is independent and
  normally distributed with a mean of D and a
  standard deviation of sD , then

k
åsi2
PKD
i1

• Coefficient of variation

CV s/m
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Measuring Product Availability

• Product fill rate ( fr )

• The fraction of product demand that is satisfied
  from product in inventory
• It is equivalent to the probability that product
  demand is supplied from available inventory

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• Order fill rate

• The fraction of orders that are filled from
  available inventory
• Order fill rates tend to be lower than product
  fill rates because all products must be in stock
  for an order to be filled

• Cycle service level (CSL)

• The fraction of replenishment cycles that end
  with all the customer demand being met
• The CSL is equal to the probability of not having
  a stockout in a replenishment cycle
• A CSL of 60 percent will typically result in a
  fill rate higher than 60

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Measuring Product Availability -- Page 5

• Product fill rate ( fr )
• Order fill rate
• Cycle service level (CSL)

• An order for a total of 100 palms and has 90 in
  inventory

? fill rate of 90

• Customer may order a palm along with a
  calculator. The order is filled only if both
  products are available.

Order received

• Don't run out of inventory in 6 out of 10
• replenishment cycles

? CSL 60
On-hand inventory

• In the 40 of the cycles where a stockout
• does occur, most of the customer demand
• is satisfied from inventory

Unfilled demand
Filled demand
0
? fill rate gt 60
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Replenishment Policies

• A replenishment policy consists of decisions
  regarding
• When to reorder
• How much to reorder.

• Continuous review
• Inventory is continuously tracked and an order
  for a lot size Q is placed when the inventory
  declines to the reorder point (ROP).

• Periodic review
• Inventory status is checked at regular periodic
  intervals and an order is placed to raise the
  inventory level to a specified threshold, i.e.
  order up to level (OUL) .

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Replenishment Policies

• A replenishment policy consists of decisions
  regarding
• When to reorder
• How much to reorder.

• Continuous review
• Inventory is continuously tracked and an order
  for a lot size Q is placed when the inventory
  declines to the reorder point (ROP).

• Periodic review
• Inventory status is checked at regular periodic
  intervals and an order is placed to raise the
  inventory level to a specified threshold.

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Continuous Review System

• The remaining quantity of an item is reviewed
  each time a withdrawal is
• made from inventory, to determine whether it
  is time to reorder.

• Other names are Reorder point system, fixed
  order quantity system

• Inventory position

IP OHSR-BO

• IP inventory position
• OH on-hand inventory
• SR scheduled receipts (open orders)
• BO units backordered or allocated

• Decision rule

• Whenever a withdrawal brings IP down to the
  reorder point (ROP), place
• an order for Q (fixed) units.

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Continuous Review System
ROP average demand during lead time safety
stock
IP
IP
Order received
On-hand inventory
Order received
Q
OH
OH
ROP
ROP
Order placed
Order placed
Time
L3
L2
L1
TBO2
TBO3
TBO1
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Continuous Review System
ROP average demand during lead time safety
stock
IP
IP
Order received
On-hand inventory
Order received
Q
OH
OH
ROP
Order placed
Order placed
Time
L3
L2
L1
TBO2
TBO3
TBO1
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Continuous Review System
ROP average demand during lead time safety
stock
IP
IP
Order received
On-hand inventory
Order received
Q
OH
OH
ROP
Order placed
Order placed
Time
L3
L2
L1
TBO2
TBO3
TBO1
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Example
Given the following data

• Average demand per week, D 2,500
• Standard deviation of weekly demand, sD 500
• Average lead time for replacement, L 2 weeks
• Reorder point, ROP 6,000
• Average lot size, Q 10,000

ROP-DL6,000-5,0001,000

• Safety inventory,ss
• Cycle inventory
• Average inventory
• Average flow time

Q/210,000/25,000
5,0001,0006,000
Average inventory / Throughput6,000/2,500 2.4w
eeks
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Evaluating Cycle Service Level and Safety
Inventory
CSL Prob (Demand during lead time of L weeks
ROP)
Demand during lead time is normally distributed
with a mean of DL and a standard deviation of sL

• CSLFunction ( ROP,DL,sL )

ROPDLZ LsD
zFs-1(CSL)
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Finding Safety Stock with a Normal Probability
Distribution for an 85 Percent CSL
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Average demand during lead time
4-gtROP
ROP
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2
z sL
Safety stock z sL
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Evaluating Cycle Service Level and Safety
Inventory
CSL Prob (Demand during lead time of L weeks
ROP)
Demand during lead time is normally distributed
with a mean of DL and a standard deviation of sL

• CSLFunction ( ROP,DL,sL )

ROPDLZ LsD
zFs-1(CSL)
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Example
Given the following data

• Q 10,000
• ROP 6,000
• L 2 weeks
• D2,500/week, sD500

2x2,5005,000

• DLDL

• CSLProability of not stocking out in a cycle

F(ROP, DL, sL )F(6000,5000,707) NORMDIST(6000,5
000,707,1)0.92
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Normal Distribution in Excel Commands (Page 12)

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Normal Distribution in Excel (Demo)
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Example
Given the following data

• Q 10,000
• ROP 6,000
• L 2 weeks
• D2,500/week, sD500
• CSL0.9

2x2,5005,000

• DLDL

• ssFs-1(CSL)

F(ROP, DL, sL )F(6000,5000,707) NORMDIST(6000,5
000,707,1)0.92
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Example
Given the following data

• D2,500/week
• sD500
• L 2 weeks
• Q 10,000,
• CSL0.9

2x2,5005,000

• DLDL

• ssFs-1(CSL)xsLNORMDIST(CSL)xsL

1.282x707906

• ROP

2x2,5009065,906
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Example
Given the following data

• D2,500/week
• sD500
• L 2 weeks
• Q 10,000,
• CSL0.9

2x2,5005,000

• DLDL

• ssFs-1(CSL)xsLNORMDIST(CSL)xsL

1.282x707906

• ROP

2x2,5009065,906
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Periodic Review System

• Other names are
• fixed interval reorder system or periodic
  reorder system.
• Decision Rule
• Review the items inventory position IP every
  T time periods. Place an order equal to (OUL-IP)
  where OUL is the target inventory, that is, the
  desired IP just after placing a new order.
• The periodic review system has two parameters T
  and OUL.
• Here Q varies, and time between orders (TBO) is
  fixed.

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Periodic Review System
OUL
OUL
IP
IP
Order received
On-hand inventory
Order placed
Order placed
Q1
Q3
Q2
OH
OH
Order placed
L
L
L
Time
T
T
Protection interval
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Finding OUL

• The new order must be large enough to make the
  inventory position, IP, last not only beyond the
  next review, which is T periods from now, but
  also for one lead time (L) after the next review.
  IP must be enough to cover demand over a
  protection interval of T L.
• OUL

Safety stock for protection interval
Average demand during protection interval

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Selecting the Reorder Interval (T )

• Administratively convenient (such as each Friday)

• Approximation of EOQ

• Example Suppose D 1200 /year and EOQ 100

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Example
Given the following data

• D2,500/week
• sD500
• L 2 weeks
• T 4weeks
• CSL0.9

(42)x2,50015,000

• DTL(TL)D

• ssFs-1(CSL)xsTLFs-1(0.9)xsTL

1,570

• OULDTLss

1,50001,57016,570
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Periodic System versus Continuous System
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Evaluating Fill Rate Given a Replenishment Policy

• For a continuous review policy

Expected shortage per replenishment cycle (ESC)
is the average units of demand that are not
satisfied from inventory in stock per cycle
f (x) is density function of demand distribution
during the lead time
ESC
fr1-
Q

• In the case of normal distribution, we have

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Evaluating Fill Rate Given a Replenishment Policy

• For a continuous review policy

Expected shortage per replenishment cycle (ESC)
is the average units of demand that are not
satisfied from inventory in stock per cycle
f (x) is the density function of demand
distribution during the lead time
ESC
fr1-
Q

• In the case of normal distribution, we have

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Evaluating Fill Rate Given a Replenishment Policy

• For a continuous review policy

Expected shortage per replenishment cycle (ESC)
is the average units of demand that are not
satisfied from inventory in stock per cycle
f (x) is density function of demand distribution
during the lead time
ESC
fr1-
Q

• In the case of normal distribution, we have

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Evaluating Fill Rate Given a Replenishment Policy

• For a continuous review policy

Expected shortage per replenishment cycle (ESC)
is the average units of demand that are not
satisfied from inventory in stock per cycle
f (x) is density function of demand distribution
during the lead time
ESC
fr1-
Q

• In the case of normal distribution, we have

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Proof
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Proof
sLdz
Substituting Z(X-DL)/sL and dxsLdz , we have
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Proof
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Proof
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Proof
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Proof
dw2zdz/2
dwzdz
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Proof
ESC derivation
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Proof
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Evaluating Fill Rate Given a Replenishment Policy

• For a continuous review policy

Expected shortage per replenishment cycle (ESC)
is the average units of demand that are not
satisfied from inventory in stock per cycle
f (x) is density function of demand distribution
during the lead time
ESC
fr1-
Q

• In the case of normal distribution, we have

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Example
For a continuous review system with the following
data

• Lot size ,Q10,000
• DL5,000
• sL 707

• ssROP-DL6,000-5,0001,000

• ESC

-1,0001-NORMDIST(1000/707,0,1,1)

• 707xNORMDIST(1000/707,0,1,1)
• 25

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Excel-Demo
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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 with the increase of the
  lot size even though cycle service level does
  not change.

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Factors Affecting Fill Rate -- Page 42

• Safety inventory
• Fill rate increases if safety inventory is
  increased. This also increases the cycle service
  level.

fr 1- ESC/Q

• Lot size
• Fill rate increases on increasing the lot
  size even though cycle service
• level does not change.

fr 1- ESC/Q
CSL F(ROP, DL, sL) is independent of Q
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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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Excel-Demo
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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
The required safety inventory grows rapidly with
an increase in the desired product availability
(fill rate).
Fill Rate Safety Inventory
97.5 67
98.0 183
98.5 321
99.0 499
99.5 767
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Two Managerial Levers to Reduce Safety Inventory
Safety inventory increases with an increase in
the lead time and the standard deviation of
periodic demand.

• Reduce the supplier lead time (L)

• If lead time decreases by a factor of k, safety
  inventory in the retailer decreases by a factor
  of .

• It is important for the retailer to share some of
  the resulting benefits to the supplier.

• Reduce the underlying uncertainty of demand ( sD )

• If sD is reduced by a factor of k, safety
  inventory decreases by a factor of k.
• The reduction in sD can be achieved by reducing
  forecast uncertainty, such as by sharing demand
  information through the supply chain.

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Impact of Supply (Lead time) Uncertainty on
Safety Inventory

• Assume demand per period and replenishment lead
  time are normally distributed
• DAverage demand per period
• sDStandard deviation of demand per
  period (demand uncertainty)
• L Average lead time for
  replenishment
• SLStandard deviation of lead time
  (supply uncertainty)

• Consider continuous review policy, we have
• Demand during the lead time is N(DL,sL2)

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Example

• Suppose we have

Required safety inventory,

• A reduction in lead time uncertainty can help
  reduce safety inventory

SL sL ss(units) ss(days)
6 15,058 7.72
5 12,570 6.44
4 10,087 5.17
3 7,616 3.90
2 5,172 2.65
1 2,828 1.45
0 1,323 0.68
19,298 16,109 12,927 9,760 6,628 3,625 1,695
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