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OM Inventory Management 1
Operations
Management
Inventory Management
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OM Inventory Management 2
AMAZON.com
Jeff Bezos, in 1995, started AMAZON.com
as a virtual retailer no inventory, no
warehouses, no overhead; just a bunch of
computers.
Growth forced AMAZON.com to excel in
inventory management!
AMAZON is now a worldwide leader in
warehouse management and automation.
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OM Inventory Management 3
Order Fulfillment at AMAZON
1. You order items;, computer assigns yourorder to distribution center [closest facility
that has the product(s)]
2. Lights indicate products ordered to workerswho retrieve product and reset light.
3. Items placed in crate with items from other
orders, and crate is placed on conveyor.Bar code on item is scanned 15 times
virtually eliminating error.
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Order Fulfillment at AMAZON
4. Crates arrive at central point where items
are boxed and labeled with new bar code.
5. Gift wrapping done by hand (30 packages
per hour)
6. Box is packed, taped, weighed and labeled
before leaving warehouse in a truck.
7. Order appears on your doorstep within a
week
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The Functions of Inventory
To decouple or separate various parts of
the production process
To have a stock of goods that will provide aselection for customers
To take advantage of quantity discounts
To hedge against inflation and upward price
changes
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Higher costs
Item cost (if purchased)
Ordering (or setup) cost
Costs of forms, clerks wages etc.
Holding (or carrying) cost
Building lease, insurance, taxes etc.
Difficult to control
Hides production problems
Disadvantages of Inventory
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Types of Inventory
Raw material
Work-in-process (WIP)
Maintenance/repair/operating
supplies (MRO)
Finished goods
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Inventory Management
Two ingredients of inventory mgmt
systems
Classification of inventory items
Basis for establishing inventory policies
Maintenance of accurate inventory
records
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ABC Analysis
Divides on-hand inventory into 3 classes
A class, B class, C class
Basis is usually annual $ volume
$ volume = Annual demand x Unit cost
A (70%-80% of total annual $ volume); B (15-25%), C (5%)
Other criteria could include Delivery problems
Quality problems
High unit cost
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OM Inventory Management 10
Classifying Items as ABC
% of Inventory Items
020
40
60
80
100
0 50 100
% Annual $ Usage
A
B
C
Class % $ Vol % Items
A 80 15B 15 30
C 5 55
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OM Inventory Management 11
ABC Analysis
Policies then established for each class
after analysis
Policies based on ABC analysis could
include
Focus more on development of class Asuppliers
Have tighter physical control of A items
Forecast A items more carefully
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OM Inventory Management 12
Record Accuracy
Good Inventory policies are meaningless
if mgmt does not know what inventory is
on hand
Incoming and outgoing record-keeping
must be good
Stock-room security must be good
Cycle count ingcan result in accurate
record keeping
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OM Inventory Management 13
Cycle Counting
Continuous audit for verifying accuracy ofinventory records
Physically counting inventory on a regular
basis Used often withABCclassification
Aitems counted most often (e.g., daily)
Cause of inaccuracies traced andappropriate remedial action taken
Does not require the facilities to be shutdown for this periodic audit
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OM Inventory Management 14
Advantages of Cycle Counting
Eliminates shutdown and interruption ofproduction necessary for annual physical
inventories
Eliminates annual inventory adjustments Provides trained personnel to audit the
accuracy of inventory
Allows the cause of errors to be identifiedand remedial action to be taken
Maintains accurate inventory records
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OM Inventory Management 15
Independent versusDependent Demand
Independent demand- demand for item isindependent of demand for any other item
Demand for cars is independent of demand for
white boards
Dependent demand- demand for item isdependent upon the demand for some
other item Demand for car wipers is dependent on
demand for cars
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OM Inventory Management 16
Inventory Costs
Holding costs- associated with holding or
carrying inventory over time
Ordering costs- associated with costs of
placing order and receiving goods
Setup costs- cost to prepare a machineor process for manufacturing an order
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OM Inventory Management 17
Inventory Models
When to order and how much to order
Fixed order-quantity models
Economic order quantity Production order quantity
Quantity discount
Probabilistic models
Fixed order-period models
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OM Inventory Management 18
EOQ Assumptions
Known, constant and independent
demand
Known and constant lead time Instantaneous and complete receipt of
material
No quantity discounts
Only order (setup) cost and holding cost
considered
No stock outs
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OM Inventory Management 19
Inventory Usage Over Time
Time
In
ventoryLeve
l
AverageInventory
(Q*/2)
0
Minimuminventory
Order quantity = Q(maximuminventory level)
Usage Rate
EOQ M d l
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OM Inventory Management 20
EOQ ModelHow Much to Order?
Order quantity
Annual Cost
Order (Setup) Cost Curve
OptimalOrder Quantity (Q*)
Minimumtotal cost
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OM Inventory Management 21
Deriving an EOQ
1. Develop an expression for setup or
ordering costs
2. Develop an expression for holding cost
3. Set setup cost equal to holding cost
4. Solve the resulting equation for the bestorder quantity
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Objective is to minimize total costs
Annualcost
Order quantity
Curve for totalcost of holding
and setup
Holding cost
curve
Setup (or order)cost curve
Minimumtotal cost
Optimal orderquantity (Q*)
Minimizing cost
OM Inventory Management 22
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Q = Number of pieces per orderQ* = Optimal number of pieces per order (EOQ)D = Annual demand in units for the inventory itemS = Setup or ordering cost for each orderH = Holding or carrying cost per unit per year
Annual holding cost = (Average inventory level)x (Holding cost per unit per year)
Order quantity2
= (Holding cost per unit per year)
= (H)Q2
Annual setup cost = SDQ
Annual holding cost = H
Q
2
The EOQ model
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Q = Number of pieces per orderQ* = Optimal number of pieces per order (EOQ)D = Annual demand in units for the inventory itemS = Setup or ordering cost for each orderH = Holding or carrying cost per unit per year
Optimal order quantity is found when annual setup costequals annual holding cost
Annual setup cost = SDQ
Annual holding cost = H
Q
2
Solving for Q*
2DS = Q2
HQ2= 2DS/H
Q* = 2DS/H
The EOQ model
OM Inventory Management 25
Production Order Quantity
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Production Order QuantityModel
Answers how much to order and when to
order
Allows partial receipt of materialnoinstantaneous receipt of materials
Other EOQ assumptions apply
Suited for production environment Material produced, used immediately
Provides production lot size
Lower holding cost than EOQ model
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Inventoryleve
l
Time
Demand part of cyclewith no production
Part of inventory cycle duringwhich production (and usage) istaking place
t
Maximuminventory
Production order quantity model
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Q = Number of pieces per order p = Daily production rateH = Holding cost per unit per year d = Daily demand/usage ratet = Length of the production run in days
= Maximuminventory levelTotal produced during the
production runTotal used during the
production run
= ptdt
However, Q = total produced = pt ; thus t = Q/p
Maximuminventory level = p d = Q 1
Qp
Qp
dp
Holding cost = (H) = 1 Hdp
Q2
Maximum inventory level
2
POQ model
OM Inventory Management 29
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Q = Number of pieces per order p = Daily production rateH = Holding cost per unit per year d = Daily demand/usage rateD = Annual demand
Q2=2DS
H[1 - (d/p)]
Q* =2DS
H[1 - (d/p)]p
Setup cost = (D/Q)SHolding cost = HQ[1 - (d/p)]1
2
(D/Q)S = HQ[1 - (d/p)]12
POQ model
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Q tit Di t M d l
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Quantity Discount Model
Answers how much to order & when to
order
Allows quantity discounts Reduced price when item is purchased in
larger quantities
Other EOQ assumptions apply
Trade-off is between lower price &
increased holding costOM Inventory Management 31
Q tit Di t M d l
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Reduced prices are often available whenlarger quantities are purchased
Trade-off is between reduced product costand increased holding cost
Total cost = Setup cost + Holding cost + Product cost
TC = S + H + PDDQ
Q2
Quantity Discount Model
OM Inventory Management 32
Q tit di t d l
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DiscountNumber Discou nt Quant i ty Discou nt (%)
DiscountPric e (P)
1 0to 999 no d iscount $5.00
2 1,000to 1,999 4 $4.80
3 2,000and over 5 $4.75
A typical quantity discount schedule
Quantity discount model
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Q tit di t d l
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1. For each discount, calculate Q*
2. If Q* for a discount doesnt qualify, choosethe smallest possible order size to get thediscount
3. Compute the total cost for each Q* oradjusted value from Step 2
4. Select the Q* that gives the lowest totalcost
Steps in analyzing a quantity discount
Quantity discount model
OM Inventory Management 34
Fi d P i d M d l
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Answers how much to order
Orders placed at fixed intervals
Inventory brought up to target amount
Amount ordered varies
No continuous inventory count
Possibility of stockout between intervals
Useful when vendors visit routinely
Example: P&G representative calls every 2
weeks
Fixed Period Model
OM Inventory Management 35
Inventory Level in a Fixed
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OM Inventory Management 36
yPeriod System
Various amounts (Qi) are ordered at regular time intervals(p) based on the quantity necessary to bring inventory up
to target maximum
p p p
Q1 Q2
Q3
Q4Target maximum
Time
On-HandInventory