Download (Ordering)Cost

CHAPTER FOURTEEN
Independent
Demand Inventory
Planning
McGraw-Hill/Irwin
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
*** Important note ***
• Since the text contains advanced
materials on inventory management,
which will confuse you, do not refer to the
text.
• Notations and method should be used
consistently as this slides do.
Types of Inventory
• Inventory: supply of items held to meet demand
Suppliers
Raw Material
Components
MRO
Maintenance, repair &
operating supplies
Work in
Process (WIP)
Finished
Goods (FGI)
Transportation
Distribution
Customers
7–3
Inventory Control Objectives
• We need to answer the following questions
in order to balance supply and demand,
and balance costs and service levels.
–When do I order?
–How much do I order?
–Where do I deploy the inventory?
How
much?
14–4
Functions of Inventory
• To meet anticipated demand
• To smooth production requirements
• To decouple operations
• To protect against stock-outs
Functions of Inventory (Cont’d)
• To help hedge against price increases
• To permit operations through WIP
• To take advantage of quantity discounts
Disadvantages of Inventories
Difficult to Control
Determining optimal amounts
Storage and maintenance
Handling inventory is a non-value added
activity
Inventory Management
• Independent Demand: demand is
beyond control of the organization
• Dependent Demand: demand is
driven by demand of another item
14–8
Inventory Counting Systems
• Periodic inventory System
Physical count of items made at periodic intervals
• Perpetual Inventory System
System that keeps track
of inventory continuously, thus
monitoring
current levels of
each item
Bullwhip Effect
Inventory oscillations become progressively
larger looking backward through the supply chain
Managing Inventory Across the Supply Chain
• Collaborative planning, forecasting and
replenishment (CPFR): supply chain partners
sharing information
• Vendor-managed Inventory (VMI): the vendor is
responsible for managing inventory for the customer
–Vendor monitors and replenishes inventory balances
–Customer saves holding costs
–Vendor has higher visibility of inventory usage
7–11
Inventory Management in the supply
chain : Example (Wal-Mart)
P&G:
Cross-docking:
Managing Inventory – ABC Analysis
• ABC analysis: ranking inventory by importance
• Pareto’s Law: small percentage of items have a
large impact profit
100
95
80
Cumulative
Percentage
of Revenue
50
A
Items
0
0
B
Items
C
Items
20
50
100
Cumulative Percentage of Items
7–13
Financial Impact of Inventory
• Set-up (Ordering)Cost
–Purchased items: placing and receiving orders
• Holding (Carrying ) Costs
–Opportunity cost (including cost of capital)
–Storage and warehouse management
–Taxes and insurance
–Obsolescence, spoilage, & shrinkage
–Material handling, tracking and management
7–14
Total Inventory Costs
• Total Inventory Costs: sum of all relevant
annual inventory costs. i.e. total set-up cost
+ total holding cost.
14–15
Total Inventory Costs
TIC = annual ordering cost + annual carrying cost
= (D/Q)(S) + (Q/2)(IC)
N = D/Q
A = Q/2
Where:
N = orders per year
D = annual demand
Q = order quantity
A = average inventory level
S = order cost per order
C = unit cost
I = % carrying cost per year
14–16
Total Inventory Costs
Note that frequently holding cost is given as a single
number meaning H = IC
Example: H =$2/item/year
14–17
Total Inventory Costs
If we need 3,000 units per year at a unit price of $20
and we order 500 each time, at a cost of $50 per
order with a carrying cost of 20%, what is the TIC?
N = D/Q = 3000 / 500 = 6 order per year
A = Q/2 = 500 / 2 = 250 average inventory
TIC = ordering cost + carrying cost
= S (D/Q) + (IC)(Q/2)
= $50 (3000/500) + ($20*0.20)*(500/2) = $1,300
Where:
N = D/Q
D = 3,000
Q = 500
S = $50
A = Q/2
I= 0.20
C = $20
14–18
Total Inventory Costs
If we need 3,000 units per year at a units price of $20
and we order 200 each time, at a cost of $50 per
order with a carrying cost of 20%, what is the TIC?
N = D/Q = 3000 / 200 = 15 order per year
A = Q/2 = 200 / 2 = 100 average inventory
TIC = ordering cost + carrying cost
= S (D/Q) + ( IC )(Q/2)
= 50 (3000/200) + ($20*0.20)*(200/2) = $1,150
Where:
N = D/Q
D = 3,000
Q = 500
S = $50
A = Q/2
I = 0.20
C = $20
Example 14-2
14–19
Economic Order Quantity (EOQ)
• Economic Order Quantity (EOQ): minimizes
total acquisition costs; point at which holding
and orders costs are equal
• How much to order
EOQ 
D = Annual Demand
S= Ordering cost
I= Percent of unit cost
C = Unit cost
H= IC= holding cost of item
per year
2 DS
2 DS
or
IC
H
14–20
EOQ Model
1 year
Q
Average
inventory
0
Many orders but low average inventory
Tim e
1 ye ar
Q
Ave rage
inve ntory
0
Fe w orde rs but high ave rage inve ntory
Time
Economic Order Quantity (EOQ)
Carrying + Order
Cost
Carrying Cost
Order Cost
EOQ
Order Quantity (Q)
14–22
Economic Order Quantity (EOQ)
• If we need 3,000 units per year at a unit price of
$20, at a cost of $50 per order with a carrying
cost of 20%, what is lowest TIC order quantity?
2 DS
EOQ 
IC
2 * 3000 * 50

20 * 0.20
 273.86
D = 3,000
S= $50
C = $20
I = 20%
Example 14-3
14–23
EOQ Example
What is the optimal order quantity?
Example : D=48,000 units/year
S= $20/order
I= 18%, c=$100
EOQ theorem
Example : D=12,000 units/year
S= $60/order, H= $10/unit/year
Q= order quantity,
Q*=optimal order quantity
What is the optimal order quantity?
Production Order Quantity Model
Production Order Quantity Model
= POQ Model
It is also called Economic Production Quantity
Model
= EPQ Model
POQ Model
■
Suited for Production Environment
■
Provides Production lot size
POQ M o d el:
In v en t o r y Lev els
Inventory Level
Inventory level with no demand
Production
Portion of
Cycle
Q*
Supply Supply
Begins
Ends
Max. Inventory
Q·(1- d/p)
Time
Demand portion of
cycle with no supply
POQ Model Equations
Let,
D= Demand per year
S= Setup cost
H=Holding cost
d=demand per day
p=production per day
POQ Model Equations
■
■
Optimal order quantity or production lot size
Max. Inventory level
■
Setup cost
■
Holding cost
Production Order Quantity
D = 500,000
S= $2,000
I= 25%
C = $10
d = 2,000
p = 5,000
POQ 
2 DS

d
IC 1  
p

2 * 500,000 * $2,000

 2,000 
25% * $101 

 5,000 
 36,514.84  36,515
Example 14-6
14–30
POQ Example
The Watkins Chemical Company produces a
chemical compound that is used as a lawn fertilizer.
The compound can be produced at a rate of 10,000
pounds per day. Demand for the compound is 0.6
million pounds per year. The fixed cost of setting up
for a production run of the chemical is $1,500, and the
variable cost of production is $3.50 per pound. The
company uses an annual interest rate of 22% to
account for the cost of capital, and the annual costs of
storage and handling of the chemical amount to 12%
of the value. Assume that there are 250 working days
in a year. What is the optimal lot size, maximum
inventory level, and total cost?
■
Quantity discounts
All-Units Discount Order Cost Function
C(Q)
C2=.28
C1=.29
C0=.30
500
1,000
Q
Incremental Discount Cost Function
C(Q)
C2=.28
295
C1=.29
150
C0=.30
500
1,000
Q
Quantity Discount Models
Material cost:
•Total material cost is affected by the Discount (%)
•Unit cost if first $5.00, then $4.80,
and finally $4.75
6-33
Quantity Discount Models
Total Cost Curves for each of the 3 discount plans
6-34
All-Units quantity discounts
1.
Consider the all-units quantity discount schedule below.
Units Ordered
1-400
401-800
801-1000
1001-1250
1251-1500
≥ 1501
Price Per Unit
$100
$90
$80
$70
$60
$50
EOQ at that Price
200
506
700
800
900
1400
What are the possible optimal order quantities?
Steps for Solving Quantity Discount
1. Compute EOQ for each discount price:
Q*
 2DS
IC
2. If EOQ < discount minimum level, let Q =
minimum.
3. For each EOQ or minimum Q, compute total
cost:
TC = DC + (D/Q)(S) + (Q/2)(H)
4. Choose the lowest cost quantity from all
levels.
6-36
All-Units quantity discounts
A supplier for Lower Florida Keys Health System
has introduced all-units quantity discounts
to encourage larger order quantities
of a special catheter. The price schedule is:
Order Quantity
Price per Unit
0-299
$60.00
300-499
$58.80
500 or more
$57.00
All-Units quantity discounts
The firm estimates that its annual demand
for this item is 936 units, its setup cost is $45
per order, and its annual holding cost is 25%
of the catheter’s unit price.
What’s the best order size?
All-Units quantity discounts
Calculate EOQ
All-Units quantity discounts
Total cost for the quantity discount case:
Homework problems for ch 14
• Problem 1. The I-75 Carpet Discount store
in Washington stocks carpet in its warehouse
and sells it through an adjoining showroom.
The store keeps several brands and styles of
carpet in stock; however, its biggest selling
item is Super Shag carpet. The store wants
to determine the optimal order size and total
inventory cost for this brand of carpet given
an estimated annual demand of 10,000 yards
of carpet, annual carrying cost of $0.765 per
yard, and an ordering cost of $150.
a) Decide the optimal order quantity
b) Calculate the minimum total annual
inventory cost
Homework problems for ch 14
• Problem 2. Ashlee’s Beach Chairs company
produces upscale beach chairs. Annual
demand for the chairs is estimated at 18,000
units. The frames are made in batches
before the final assembly process. Ashlee’s
frame department can produce 2,500 frames
per month. The setup cost is $800 per order,
and the annual holding cost is $18 per unit.
The company operates 20 days per month.
a) Determine the optimal lot size
b) Calculate the total holding cost
c) Calculate maximum inventory level
Homework problems for ch 14
Problem 3. Sharp inc, a company that
markets painless hypodermic needles to
hospitals, would like to reduce its inventory
cost by determining the optimal number of
hypodermic needles to obtain per order. The
annual demand is 1,000 units; the holding
cost per unit per year is $0.5. The inventory
manager of Sharp inc, calculated the optimal
order quantity of 200 units.
a) What is the ordering cost per order in the
company
b) What is the total ordering cost?
Homework problems for ch 14
Problem 4 . A produce distributor uses 800
packing crates a month, which it purchases at
a cost of $10 each. The manager has
assigned an annual carrying cost of 35
percent of the purchase price per crate.
Ordering costs are $28 each time. Currently
the manager orders once a month. How
much could the firm save annually in ordering
and carrying costs by using the EOQ?
Homework problems for ch 14
Problem 5. Ross White’s machine shop uses 2,500
brackets during the course of a year, and this usage
is relatively constant throughout the year. These
brackets are purchased for $15 each. The holding
cost per bracket per year is 10% of the unit cost and
the ordering cost per order is $18.75. There are 250
working days per year.
a) What is EOQ?
b) In minimizing cost, how many orders would be
made each year?
c) What would be the total annual inventory
cost?(i.e. addition of total ordering and holding cost)
Homework problems for ch 14
Problem 6. A hospital buys disposable
surgical packages from Pfishier, Inc.
Pfisher’s price schedule is $50.25 per
package on order of 1 to 199 packages, and
$49.00 per packages on orders of 200 or
more packages. Ordering cost is $64 per
order, and annual holding cost is 20 percent
of the per-unit purchase price. Annual
demand is 490 packages. What is the best
purchase quantity?