Planned Shortages with Back-Orders
`
Shortage: when customer demand cannot be met
`
Planned shortages could be beneficial
`
`
Cost of keeping item is more expensive than the profit from selling
it
Ex: car
1
Customer Demands an item
Alternatives for customers
when their demand cannot be
met from stock
Customer
demands an item
The item is out of
stock
Back Order
Lost Sales
Customer waits for the
next replenishment
Customer moves to
another suppliers
Customer keeps
all future
businesses
2
Customer
transfers some
future business
to another
supplier
Customer
transfers some
future business
to another
supplier
Customer
transfers all
future business
to another
supplier
Planned Shortages with Back-Orders
Optimal order
size
Optimal amount
to be backordered
Qo =
2 × RC × D × (HC + SC )
HC × SC
So =
2 × RC × HC × D
SC × ( HC + SC )
Time during which demand is
met
T1 = (Qo − S o ) / D
Time during which demand is
back-ordered
T2 = S o / D
Cycle time
T = T1 + T2
3
Ex 4: Back order
Demand for an item is constant at 100 units a
month.
` Unit cost is $50
` Reorder cost is $50
` Holding cost is 25% of value a year
` Shortage cost for back order is 40% of value a
year
Find an optimal inventory policy for the item
4
IM 322
Inventory Management
Chapter 5 Models for Uncertain Demand
-5-
Textbook:
Donald Waters, Inventory Control and Management, 2nd
ed
Chapter Outline
`
`
`
`
`
`
Uncertainty in inventory
management
Variables that take
uncertain value
Probabilistic models for
inventory model
Uncertain demand
Uncertain lead time
Service level / safety
stock
6
Areas of Uncertainty
For example
` Changes in customer demand during leadtime
` Price uncertainty
` Operations change
` New products
` Disrupted supply chain
` Trading conditions
` etc
7
Uncertain Demand
Inventory level
Q
Reorder
point, R
0
LT
LT
Time
8
Lead time
demand
`
`
`
`
Inventory level
Uncertain Demand –
Safety Stock
Buffer added to on hand
inventory during lead time
Extra reserved stock
To prevent stockout under
Q
Reorder
uncertain demand
point, R
Safety stock will not normally
be used, but it is available
under uncertain demand
0
How much safety stock
should we hold?
Judgment on service level
9
Safety Stock
LT
Time
LT
Service Level
10
Service Level
Several ways of measuring the service level
`
Percentage of order completely satisfied from stock
`
Percentage of units demanded that are delivered from
stock
`
Percentage of units demanded that are delivered on
time
`
Percentage of time there is stock available
`
Percentage of stock cycles without shortages
`
Percentages of item-months there is stock available
11
Reorder Level
Inventory level
Reorder
Reorder Level
Level (ROL)
(ROL)
Reorder
Reorder Level
Level (ROL)
(ROL)
==
==
LT
LT xx D
D
(LT
(LT xx D)
D) ++ Safety
Safety Stock
Stock
Q
Reorder
point, R
Safety Stock
0
12
LT
Time
LT
Reorder Point for a Service Level
Probability of
meeting demand during
lead time = service level
Average demand
during lead time
Probability of
a stockout
Safety stock
zσ LT
Demand
13
R
Reorder Point with Uncertain Demand
`
Reorder point with safety stock
`
Service level = probability of
NO stockout
σL
ROL = (LT × D ) + zσ LT
d = average demand
L = lead time
σ t = standard deviation of demand
Standard deviation
during leadtime
Safety Stock
z = number of standard deviations correspond ing to
the service level probabilit y
zσ t
14
L = safety stock
Ex 1: Uncertain Demand
PM Computers assembles microcomputers from generic
components. It purchases its color monitors from a
manufacturer in Taiwan. There is a long lead time of 25
days. Daily demand is normally distributed with a mean
of 2.5 monitors and a standard deviation of 1.2 monitors.
Determine the safety stock and reorder point
corresponding to a 90% service level
15
Ex 2 Uncertain Demand
`
`
`
`
ABC company finds that demand for an item is
normally distributed with a mean of 2,000 units a
year and standard deviation of 400 units.
Unit cost is $100, reorder cost is $200, holding
cost is 20% of value a year and lead time is fixed
at 3 weeks.
Describe an ordering policy that gives a 95%
service level.
What is the cost of safety stock?
16