Transcript Inventory Management MBA 8452 Systems and Operations Management Irwin/McGraw-Hill

MBA 8452 Systems and Operations Management
Inventory
Management
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Introduction to Operations Management/
Operations Strategy
Process Analysis
and Design
Project
Management
Process
Analysis
Planning for Production
Process Control
and Improvement
Capacity Management
Quality
Management
Aggregate Planning
Job Design
Just in Time
Manufacturing
Layout/
Assembly Line Balancing
Services
Statistical
Process Control
Scheduling
Inventory Control
Supply Chain
Management
Waiting Line Analysis
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Objective: Inventory Management
• Be able to explain the Purpose of
inventory
• Describe the different Inventory
Models
• Explain the Physical systems
• Explain the importance of Inventory
accuracy
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What is Inventory?

Definition--The stock of any item or
resource used in an organization

Raw materials

Finished products

Component parts

Supplies

Work in process
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Purposes of Inventory
1. To maintain independence of operations
2. To meet variation in product demand
3. To allow flexibility in production scheduling
4. To provide a safeguard for variation in raw
material delivery time
5. To take advantage of economic purchaseorder size
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Inventory Costs

Holding (or carrying) costs

Setup (or production change) costs
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Ordering costs

Shortage (or backlog) costs
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Independent vs. Dependent Demand
Independent Demand
(Demand not related to other items)
Dependent Demand
(Derived)
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Inventory Control Systems

Fixed-Order Quantity Models


Constant amount ordered when inventory
reaches a predetermined level
Fixed-Time Period Models

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Order placed for variable amount after
fixed passage of time
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Fixed-Order Quantity Models
Assumptions of EOQ






Demand for the product is constant and uniform
throughout the period
Lead time (time from ordering to receipt) is
constant
Price per unit of product is constant
Inventory holding cost is based on average
inventory
Ordering or setup costs are constant
All demands for the product will be satisfied (No
back orders are allowed)
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EOQ Model--Basic
Fixed-Order Quantity Model
Inventory
Level
Q
Q
Q
R
L
L
Time
R = Reorder point
Q = Economic order quantity
L = Lead time
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Basic Fixed-Order Quantity Model
Total Annual Cost =
Annual
Annual
Purchase + Ordering +
Cost
Cost
Annual
Holding
Cost
Derive the Total annual Cost Equation, where:
TC - Total annual cost
D - Demand
C - Cost per unit
Q - Order quantity
S - Cost of placing an order or setup cost
R - Reorder point
L - Lead time
H - Annual holding and storage cost per unit of inventory
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Basic Fixed-Order Quantity
(EOQ) Model Formula
Annual
Annual
Total Annual Cost = Purchase + Ordering +
Cost
Cost
Annual
Holding
Cost
Annual Purchase Cost = (#units)(cost/unit) = DC
D
Q
TC = DC +
S +
H
Q
2
Annual Ordering Cost = (#orders)(cost/order) =
(D/Q)S
Annual Holding Cost =
(avg. inventory)(unit holding cost) = (Q/2)H
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Cost Minimization Goal
C
O
S
T
Total Cost
Holding
Costs
Annual Cost of
Items (DC)
Ordering Costs
QOPT
Order Quantity (Q)
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Deriving the EOQ

Using calculus, we take the derivative of the total cost
function and set the derivative (slope) equal to zero
2DS
2(Annual Demand)(Or der or Setup Cost)
Q OPT =
=
H
Annual Holding Cost
Reorder Point, R = dL
_
d = average demand per time unit
L = Lead time (constant)
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EOQ Example
Annual Demand = 1,000 units
Days per year considered in average daily demand = 365
Cost to place an order = $10
Holding cost per unit per year = $2.40
Lead time = 7 days
Cost per unit = $15
Determine the economic order quantity and the reorder point.
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Solution
2DS
2(1,000 )(10)
QOPT =
=
= 91.287 units
H
2.40 Round up if greater than 0.5
91 units
1,000 units / year
d =
= 2.74 units / day
365 days / year
Always round up
_
R eorder point, R = d L = 2.74units / day (7days) = 19.18 or 20 units
When the inventory level reaches 20, order 91 units.
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Problem

Retailer of Satellite Dishes
D = 1000 units
S = $ 25
H = $ 100
How much should we order?
What are the Total Annual Stocking Costs?
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Satellite Problem
5000
4000
3000
Cost
Setup Cost
Holding Cost
2000
Total Cost
1000
0
0
5
10
15
20
25
30
35
40
45
50
Lot size
55
60
65
70
75
80
85
90
95
100
EOQ with quantity discounts


What if we get a price break for buying a
larger quantity?
To find the lowest cost order quantity:


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Since “C” changes for each price-break, H=iC
Where, i = percentage of unit cost attributed to
carrying inventory
and , C = cost per unit
Find the EOQ at each price break.
Identify relevant and feasible order quantities.
Compare total annual costs
The lowest cost win.
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Problem
Copper may be purchased for
$ .82 per pound for up to 2,499 pounds
$ .81 per pound for between 2,500 and 4,999 pounds
$ .80 per pound for orders greater than 5,000 pounds
Demand = 50,000 pounds per year
Holding costs are 20% of the purchase price per year
Ordering costs = $30
How much should the company order to
minimize total costs?
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Problem 29
44
(Costs in $,000)
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Feasible
<2500
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<2500 - 4999
>5000
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40
0
20
40
60
(Order Quantity 100's of units)
80
100
What if demand is not Certain?

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Use safety stock to cover uncertainty in demand.
Given: service probability which is the probability
demand will not exceed some amount.
The safety stock level is set by increasing the reorder
point by the amount of safety stock.
The safety stock equals z•L
where,
L = the standard deviation of demand during the
lead time.
For example for a 5% chance of running out z 1.65
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Problem
Annual Demand = 25,750 or 515/wk @ 50 wks/year
Annual Holding costs = 33% of item cost ($10/unit)
Ordering costs are $250.00
d = 25 per week
Leadtime = 1 week
Service Probability = 95%
Find:
a.) the EOQ and R
b.) annual holding costs and annual setup costs
c.) Would you accept a price break of $50 per order
for lot sizes that are larger than 2000?
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Fixed-Time Period Models


Check the inventory every review period and then
order a quantity that is large enough to cover
demand until the next order will come in.
The model assumes uncertainty in demand with
safety stock added to the order quantity.
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Fixed-Time Period Model with
Safety Stock Formula
q = Average demand + Safety stock – Inventory currently on hand
q = d(T + L) + Z  T + L - I
Where :
q = quantity t o be ordered
T = the number of days between reviews
L = lead time in days
d = forecast average daily demand
z = the number of standard deviations for a specified service probabilit y
 T + L = standard deviation of demand over the review and lead time
I = current inventory level (includes items on order)
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Determining the Value of T+L
 T +L =
  
T+L
i 1
2
di
Since each day is independen t and  d is constant,
 T + L = (T + L) d

2
The standard deviation of a sequence of
random events equals the square root of the
sum of the variances.
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Example of the Fixed-Time
Period Model
Given the information below, how many units should be ordered?
Average daily demand for a product is 20 units.
The review period is 30 days, and lead time is 10 days.
Management has set a policy of satisfying 96 percent
of demand from items in stock. At the beginning of the
review period there are 200 units in inventory. The daily
demand standard deviation is 4 units.
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Example of the Fixed-Time
Period Model: Solution
 T+ L =
(T + L) d =
2
 30 + 10  4  2 = 25.298
q = d(T + L) + Z  T + L - I
q = 20(30 + 10) + (1.75)(25. 298) - 200
q = 800  44.272 - 200 = 644.272, or 645 units
So, to satisfy 96 percent of the demand, you should
place an order of 645 units at this review period.
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Example Problem
A pharmacy orders antibiotics every two
weeks (14 days).
 the daily demand equals 2000
 the daily standard deviation of demand = 800
 lead time is 5 days
 service level is 99 %
 present inventory level is 25,000 units

What is the correct quantity to order to minimize
costs?
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Single – Period Model for items
w/obsolescence (newsboy problem)
For a single purchase
Amount to order is when marginal profit (MP)
for the nth unit is equal to marginal loss (ML) for
the nth unit.
 Adding probabilities
(p = probability of that unit being sold)
for the last unit ordered we want
P(MP)(1-P)ML or P  ML /(MP+ML)

Increase order quantity as long as this holds.
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Single–Period Model Example
Sam’s Bookstore
Demand Probability of
Demand
100
0.30
150
0.20
200
0.30
250
0.15
300
0.05
Sam’s Bookstore purchases
calendars from a publisher. Each
Calendar costs the bookstore $5 and is
Sold for $10. Unsold calendars can be
Returned to the publisher for a refund
Of $2 per calendar. The demand
Distribution shown in the table.
How many calendars should be
ordered?
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Single–Period Model Example

Solution: Pick the highest demand where the cumulative probability is
equal to or greater than (ML/(MP-ML)
Demand
Probability of
Demand
Demand
Cumulative
Probability of
Demand
100
0.30
100
1.00=1.00-0
150
0.20
150
0.70=1.00-.30
200
0.30
200
0.50=.70-.20
250
0.15
250
0.20=.50-.30
300
0.05
300
0.05=.20-.15
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Miscellaneous Systems
Optional Replenishment System
Maximum Inventory Level, M
q=M-I
Actual Inventory Level, I
M
I
Q = minimum acceptable order quantity
If q > Q, order q, otherwise do not order any.
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Miscellaneous Systems
Bin Systems
Two-Bin System
Order One Bin of
Inventory
Full
Empty
One-Bin System
Order Enough to
Refill Bin
Periodic Check
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Inventory Accuracy and
Cycle Counting

Inventory accuracy
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Do inventory records agree with physical
count?
Cycle Counting
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Frequent counts
 Which items?
 When?
 By whom?
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ABC Classification System

Items kept in inventory are not of equal importance in
terms of:

dollars invested

profit potential


sales or usage volume
60
% of
$ Value 30
0
% of
Use
30
A
B
C
60
stock-out penalties
So, identify inventory items based on percentage of total dollar
value, where “A” items are roughly top 15 %, “B” items as next
35 %, and the lower 65% are the “C” items.
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