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Irwin/McGraw-Hill1
MBA 8452 Systems and Operations ManagementMBA 8452 Systems and Operations Management
Inventory Inventory ManagementManagement
Irwin/McGraw-Hill2
QualityManagement
StatisticalProcess Control
Inventory Control
Just in Time
Introduction to Operations Management/ Operations Strategy
ProjectManagement
Planning for ProductionProcess Analysisand Design
Process Controland Improvement
Waiting Line Analysis
Services
Manufacturing
Process Analysis
Job DesignAggregate Planning
Capacity Management
Supply ChainManagement
Layout/ Assembly Line Balancing
Scheduling
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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 purchase-order size
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Inventory Costs Holding (or carrying) costs
Setup (or production change) costs
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 Order placed for variable amount after
fixed passage of time
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Fixed-Order Quantity ModelsAssumptions 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--BasicFixed-Order Quantity Model
R = Reorder pointQ = Economic order quantityL = Lead time
L L
Q QQ
R
Time
InventoryLevel
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Basic Fixed-Order Quantity Model
Total Annual Cost =
AnnualPurchase
Cost
AnnualOrdering
Cost
AnnualHolding
Cost+ +
Derive the Total annual Cost Equation, where:TC - Total annual costD - DemandC - Cost per unitQ - Order quantityS - Cost of placing an order or setup costR - Reorder pointL - Lead timeH - Annual holding and storage cost per unit of inventory
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Basic Fixed-Order Quantity (EOQ) Model Formula
TC = DC + D
Q S +
Q
2 H
Total Annual Cost =Annual
PurchaseCost
AnnualOrdering
Cost
AnnualHolding
Cost+ +
Annual Purchase Cost = (#units)(cost/unit) = DC
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
Ordering Costs
HoldingCosts
QOPT
Order Quantity (Q)
COST
Annual Cost ofItems (DC)
Total Cost
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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
L = Lead time (constant)
d = average demand per time unit _
Cost Holding Annual
Cost) Setupor der Demand)(Or 2(Annual =
H
2DS = QOPT
Reorder Point, R = dL
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EOQ Example
Annual Demand = 1,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = $2.40Lead time = 7 daysCost per unit = $15
Determine the economic order quantity and the reorder point.
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Solution
units 91.287 = 2.40
)(10) 2(1,000 =
H
2DS = QOPT
d = 1,000 units / year
365 days / year = 2.74 units / day
Reorder point, R = d L = 2.74units / day (7days) = 19.18 or _
20 units
When the inventory level reaches 20, order 91 units.
91 units
Always round up
Round up if greater than 0.5
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Problem
Retailer of Satellite DishesD = 1000 unitsS = $ 25H = $ 100
How much should we order?
What are the Total Annual Stocking Costs?
Satellite Problem
0
1000
2000
3000
4000
5000
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Lot size
Co
st
Setup Cost
Holding Cost
Total Cost
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EOQ with quantity discounts
What if we get a price break for buying a larger quantity?
To find the lowest cost order quantity: 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 yearHolding costs are 20% of the purchase price per year
Ordering costs = $30
How much should the company order to minimize total costs?
Problem 29
40
41
42
43
44
0 20 40 60 80 100
(Order Quantity 100's of units)
(Co
sts
in $
,000
)
<2500
<2500 - 4999
>5000
Feasible
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What if demand is not Certain?
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/yearAnnual Holding costs = 33% of item cost
($10/unit)Ordering costs are $250.00d = 25 per week Leadtime = 1 weekService Probability = 95%
Find:a.) the EOQ and Rb.) annual holding costs and annual setup costsc.) 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
order)on items (includes levelinventory current = I
timelead and review over the demand ofdeviation standard =
yprobabilit service specified afor deviations standard ofnumber the= z
demanddaily averageforecast = d
daysin timelead = L
reviewsbetween days ofnumber the= T
ordered be oquantity t = q
:Where
I - Z+ L)+(Td = q
L+T
L+T
q = Average demand + Safety stock – Inventory currently on hand
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Determining the Value of T+L
The standard deviation of a sequence of random events equals the square root of the sum of the variances.
2
dL+T
d
L+T
1i
2dL+T
L)+(T =
constant, is andt independen isday each Since
= i
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Example of the Fixed-Time Period Model
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 percentof 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.
Given the information below, how many units should be ordered?
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Example of the Fixed-Time Period Model: Solution
or 644.272, = 200 - 44.272 800 = q
200- 298)(1.75)(25. + 10)+20(30 = q
I - Z+ L)+(Td = q L+T
units 645
So, to satisfy 96 percent of the demand, you should place an order of 645 units at this review period.
T+ L d2 2 = (T + L) = 30 + 10 4 = 25.298
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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 refundOf $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)
0.05300
0.15250
0.30200
0.20150
0.30100
Probability of Demand
Demand
0.05=.20-.15300
0.20=.50-.30250
0.50=.70-.20200
0.70=1.00-.30150
1.00=1.00-0100
Cumulative Probability of
Demand
Demand
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Miscellaneous SystemsOptional Replenishment SystemMaximum Inventory Level, M
MActual Inventory Level, I
q = M - I
I
Q = minimum acceptable order quantity
If q > Q, order q, otherwise do not order any.
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Miscellaneous SystemsBin Systems
Two-Bin System
Full Empty
Order One Bin ofInventory
One-Bin System
Periodic Check
Order Enough toRefill Bin
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Inventory Accuracy and Cycle Counting
Inventory accuracy Do inventory records agree with
physical count?
Cycle Counting 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
stock-out penalties
0
30
60
30
60
AB
C
% of $ Value
% of Use
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.