Aminullah Assagaf_P10-Ch.13_Inventory Management-32.pptx

Inventory Management
Chapter 13







Elements of Inventory Management
Inventory Control Systems
Economic Order Quantity Models
Quantity Discounts
Reorder Point
Order Quantity
System
for a Periodic Inventory
Copyright 2006 John Wiley & Sons, Inc. 12-2
Lecture Outline

 Stock of items kept to meet future
demand
Purpose of inventory management

how many units to order

when to order

What Is Inventory?




Raw materials
Purchased parts and supplies
Work-in-process (partially
products (WIP)
Items being transported
Tools and equipment
completed)


Types of Inventory

Inventory and Supply Chain
 Bullwhip effect
demand information is distorted
from the end-use customer
as it moves away

higher safety stock inventories to are stored
compensate
Seasonal or cyclical demand
to





Inventory provides independence from vendors
Take advantage of price discounts
Inventory provides independence between
stages and avoids work stop-pages
Inventory and Supply
Management

 Customers usually perceive quality
service as availability of goods they want
when they want them
Inventory must be sufficient to provide

high-quality customer service in TQM
Inventory and Quality
Management

 Carrying cost
 cost of holding an item in inventory
 Ordering cost
 cost of replenishing inventory
 Shortage cost
 temporary or permanent loss of
when demand cannot be met
sales
Inventory Costs

Inventory Control Systems
 Continuous system (fixed-
order-quantity)
 constant amount ordered
when inventory declines to
predetermined level
 Periodic system (fixed-time-
period)
 order place
amount after fixed passage of
time
d for variable
Inventory Control Syst

Economic Order Quantity
 EOQ
optimal order quantity that will
minimize total inventory costs
Basic EOQ model


 Production quantity model
Economic Order Quant
(EOQ) Models

 Demand is known with certainty and
is constant over time
No shortages are allowed
Lead time for the receipt of orders is
constant
Order quantity is received all at once



Assumptions of Basic
EOQ Model

time time
placed receipt placed receipt
Inventory
Level
Demand
Inventory Order Cycle
Order quantity, Q
rate
Reorder point, R
0 Lead Lead Time
Order Order Order Order

Annual ordering cost =
Annual carrying cost =
Total cost = +
EOQ Cost Model
Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity
CoD
Q
CcQ
2
CoD CcQ
Q 2

costs at optimal point
TC = +
=
= +
o
Q2 =
c
Q2
2
Qopt =
Cc
Deriving Qopt
CoD CcQ
Q 2
TC CoD Cc
Q Q2
2
C0D Cc
0 = +
2CoD
Qopt =
Proving equality of
CoD CcQ
Q 2
2C D
C
2CoD
Cc
EOQ Cost Model

cost ($)
Minimum 2
Qopt
Total Cost
Carrying Cost =
Ordering Cost =
EOQ Cost Model (cont.)
Annual
Slope = 0
CcQ
total cost
CoD
Q
Optimal order Order Quantity, Q

Qopt = TCmin = +
Qopt = TCmin = +
(0.75) 2,000 2
EOQ Example
Cc = $0.75 per yard Co = $150 D = 10,000 yards
2CoD CoD CcQ
Cc Q 2
2(150)(10,000) (150)(10,000) (0.75)(2,000)
Qopt = 2,000 yards TCmin = $750 + $750 = $1,500
Orders per year = D/Qopt Order cycle time = 311 days/(D/Qopt)
= 10,000/2,000 = 311/5
= 5 orders/year = 62.2 store days

 An inventory system in which an order is
received gradually, as inventory is
simultaneously being depleted
AKA non-instantaneous receipt model

assumption that Q is received all at once is relaxed

 p - daily rate at which an order is received over
time, a.k.a. production rate
d - daily rate at which inventory is demanded

Production Quantity
Model

Q
inventory
(1-d/p)
receipt receipt
receipt period
invent
Production Quantity Model
(cont.)
Inventory
level
Maximum
Q(1-d/p)
inventory
level
Average
2 level
0
Begin End Time
Order order order

Production Quantity Model
p
p o
Q d C 1 -
Average inventory level = 1 -
TC = + 1 - p
Q 2
p = production rate d = demand rate
Maximum inventory level = Q -
Q
d
= Q 1 -
d
2C D
Qopt = d
2 p c p
CoD CcQ d
Production Quantity
(cont.)

Production Quantity Model:
2CoD 2(150)(10,000)
Qopt = = = 2,256.8 yards
32.2
d
Cc 1 - 0.75 1 -
150
p
CoD
Q
CcQ
2
d
TC = + 1 - = $1,329
p
2,256.8
150
Q
p
Production run = = = 15.05 days per order
Cc = $0.75 per yard Co = $150 D = 10,000 yards
d = 10,000/311 = 32.2 yards per day p = 150 yards per day
Production Quantity M
Example

Production Quantity Model:
2,256.8
Q
p 150
Number of production runs =
D
=
10,000
= 4.43 runs/year
Maximum inventory level = Q 1 -
d
= 2,256.8 1 - 32.2
= 1,772 yards
Production Quantity
Example (cont.)

Price per unit decreases
quantity increases
as order
CoD
Q
CcQ
2
TC = + + PD
where
P = per unit price of the item
D = annual demand
Quantity Discounts

TC (d1 =$8 )
Inventory
cost
($)
ORDERSIZE PRICE
200+ 6 (d )
Quantity Discount Model (cont.)
0 - 99 $10 TC = ($10 )
100 – 199 8 (d1)
2
TC (d2 = $6 )
Carrying cost
Ordering cost
Q(d1 ) = 100 Qopt Q(d2 ) = 200

Co = $2,500
$190 per computer
200
Cc
D
=
=
90+ 900
Qopt = = = 72.5 PCs
CcQopt
CoD
2
Qopt
CcQ
CoD
2
Q
Quantity Discount: Example
QUANTITY PRICE
1 - 49 $1,400
50 - 89 1,100
2CoD 2(2500)(200)
Cc
190
For Q = 72.5
TC = + + PD = $233,784
For Q = 90
TC = + + PD = $194,105

Level of inventory at which a new order
is placed
R = dL
where
d =
L =
demand rate
lead time
per period
Reorder Point

Reorder Point: Example
Demand = 10,000 yards/year
Store open 311 days/year
Daily demand = 10,000 / 311
yards/day
Lead time = L = 10 days
= 32.154
R = dL = (32.154)(10) = 321.54 yards
Reorder Point: Ex

 Safety stock
 buffer added to on hand inventory during lead
time
 Stockout
 an inventory shortage
 Service level
 probability that the inventory
lead time will meet demand
available during
Safety Stocks

t, R
R
0
Inventory
level
Variable Demand with
a Reorder Point
Reo
poin
n
Q
rder
LT LT
Time

Safety Stock
0
Inventory
level Reorder Point with
a Safety Stock
Reorder
point, R
Q
LT LT
Time

R = dL + z L
d
where
d
L
d
z
=
=
=
=
average daily demand
lead time
the standard deviation of daily demand
number of standard deviations
corresponding to the service level
probability
safety stock
z L =
d
Reorder Point With
Variable Demand

The carpet store wants a reorder point with a 95%
service level and a 5% stockout probability
d = 30 yards per day
L = 10 days
d = 5 yards per day
For a 95% service level, z = 1.65
R = dL + z d L Safety stock = z d L
= 30(10) + (1.65)(5)( 10) = (1.65)(5)( 10)
= 326.1 yards = 26.1 yards
Reorder Point for
Variable Demand

Periodic Inventory System
Q = d(tb + L) + z d tb + L - I
where
d = average demand rate
tb = the fixed time between orders
L = lead time
d = standard deviation of demand
z d tb + L = safety stock
I = inventory level
Order Quantity for a
Periodic Inventory Sy

Fixed-Period Model with
d = 6 bottles per day
d = 1.2 bottles
tb = 60 days
L = 5 days
I = 8 bottles
z = 1.65 (for a 95% service level)
Q = d(tb + L) + z d tb + L - I
= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8
= 397.96 bottles
Fixed-Period Model w
Variable Demand

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