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Adeyl Khan, Faculty, BBA, NSU
C 11Inventory ManagementPencils, papers, clips, advertisements-flyer, visiting cards, nuts, bolts, trucks,
needles, airplanesRaw materials, semi-finished goods,
finished goods
What is the worth?Let top management see the money
withheld
Adeyl Khan, Faculty, BBA, NSU
Inventory- a stock or store of goods
12-3
Independent Demand
B(4)
E(1)D(2)
C(2)
F(2)D(3)
A Dependent Demand
Independent demand is uncertain. Dependent demand is certain.
Adeyl Khan, Faculty, BBA, NSU
Inventory Models
Independent demand – finished goods, items that are ready to be sold
• E.g. a computer
Dependent demand – components of finished products
• E.g. parts that make up the computer
12-4
Adeyl Khan, Faculty, BBA, NSU
Types of Inventories
Raw materials & purchased partsPartially completed goods called
work in progressFinished-goods inventories
manufacturing firms retail stores (merchandise )
Replacement parts, tools, & suppliesGoods-in-transit to warehouses or customers
12-5
Adeyl Khan, Faculty, BBA, NSU
Functions of Inventory
To meet anticipated demand Anticipation stock
To smooth production requirements Seasonal demand (e.g. Potato case!)
To decouple operations Buffer for continuous operation
To protect against stock-outs Delayed delivery, abrupt demand Safety stocks
12-6
Adeyl Khan, Faculty, BBA, NSU
Functions of Inventory …
To take advantage of order cycles Purchasing, Producing in Batches (Lots) Cycle stock for periodic
To help hedge against price increases Oil price
To permit operations Intermediate Stocks (WIP)
Pipeline inventory
To take advantage of quantity discounts
12-7
Adeyl Khan, Faculty, BBA, NSU
Objective of Inventory Control
To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds Level of customer service Costs of ordering and carrying inventory
Inventory turnover Ratio of average cost of goods sold to average inventory investment.
Days of inventory on hand
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Adeyl Khan, Faculty, BBA, NSU
Effective Inventory Management
A system to keep track of inventory (and S.O.)A reliable forecast of demandKnowledge of lead times (and variability)Reasonable estimates of
Holding costs Ordering costs Shortage costs
A classification system
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Adeyl Khan, Faculty, BBA, NSU
Inventory Counting Systems
Periodic System Physical count of items made at periodic intervals Small Retailers- checks and orders replenishment
Perpetual Inventory System Keeps track of removals from inventory continuously, thus monitoring current levels of each item Reorder point Q Also requires periodic counting
Errors, pilferage, spoliage
12-10
Cost?
Adeyl Khan, Faculty, BBA, NSU
Inventory Counting Systems …
Two-Bin System - Two containers of inventory; reorder when the first is empty 2nd cart has enough inventory for the lead
time Order card
Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached
12-11
Adeyl Khan, Faculty, BBA, NSU
Key Inventory Terms
Lead time: time interval between ordering and receiving the orderHolding (carrying) costs: cost to carry an item in inventory for a length of time, usually a yearOrdering costs: costs of ordering and receiving inventoryShortage costs: costs when demand exceeds supply
12-12
Adeyl Khan, Faculty, BBA, NSU
The Inventory Cycle- Figure 12.2Profile of Inventory Level Over Time
Quantityon hand
Q
Receive order
Placeorder
Receive order
Placeorder
Receive order
Lead time
Reorderpoint
Usage rate
Time
Adeyl Khan, Faculty, BBA, NSU
ABC Classification System
Classifying inventory according to some measure of importance and allocating control efforts accordingly. A - very important B - mod. important C - least important
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Annual $ value of items
A
B
C
High
Low
Low HighPercentage of Items
Example 1- P 549
Adeyl Khan, Faculty, BBA, NSU
Cycle Counting
A physical count of items in inventoryCycle counting management
How much accuracy is needed? When should cycle counting be performed? Who should do it?
12-15
Adeyl Khan, Faculty, BBA, NSU
Economic Order Quantity Models
Economic order quantity (EOQ) model The order size that minimizes total annual cost
Economic production modelQuantity discount model
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Adeyl Khan, Faculty, BBA, NSU12-17
Total Cost*
Annualcarryingcost
Annualorderingcost
Total cost* = +
TC = Q2H D
QS+
Adeyl Khan, Faculty, BBA, NSU12-18
Cost Minimization Goal- Figure 12.4C
Order Quantity (Q)
The Total-Cost Curve is U-Shaped
Ordering Costs
QO
An
nu
al C
os
t
(optimal order quantity)
TCQ
HD
QS
2
Minimum Total Cost
Adeyl Khan, Faculty, BBA, NSU
• Only one product is involved• Annual demand requirements
known• Demand is even throughout the
year• Lead time does not vary• Each order is received in a
single delivery• There are no quantity discounts
Assumptions of EOQ Model
12-19
Adeyl Khan, Faculty, BBA, NSU
Deriving the EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal.
12-20
Q2H D
QS=
Cost Holding Annual
Cost) Setupor der Demand)(Or 2(Annual =
H
2DS = QOPT
Adeyl Khan, Faculty, BBA, NSU
Economic Production Quantity (EPQ)
Production done in batches or lotsCapacity to produce a part exceeds the
part’s usage or demand rate
Similar to EOQ Orders are received
incrementally during production
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Assumptions
• Only one item is involved
• Annual demand is known
• Usage rate is constant• Usage occurs
continually• Production rate is
constant• Lead time does not
vary• No quantity discounts
Adeyl Khan, Faculty, BBA, NSU12-22
Economic Run Size
QDS
H
p
p u0
2
We do not buy the product. We produce it. Total demand / year is DDemand / day or consumption rate is uProduction rate is p / day
Adeyl Khan, Faculty, BBA, NSU
u
p
p-u
u × ( number of working days ) = D = Total demand per year
EPQ: Incremental Replenishment(Production and Consumption)
Demand / day or consumption rate is uProduction rate is p / day
Adeyl Khan, Faculty, BBA, NSU
State Imax in terms of Q!
SQ
DH
I
2maxTC
EPQ: Ordering Cost and Carrying Cost
Adeyl Khan, Faculty, BBA, NSU
How much do we produce each time? QHow long does it take to produce Q? d1
What is our production rate per day? p1pdQ
)( 21 dduQ
EPQ : Production & Consumption; rate & time
1max )( dupI
2max udI
p-u u
I max
d1d2
How long does it take to consume Q? d1 +d2 What is our consumption rate per day ? u
Adeyl Khan, Faculty, BBA, NSU
Example- What is the optimal production size?A toy manufacturer
Uses 48000 parts for one of its products. Consumption rate is uniform throughout the
year. Working days are 240 / year. The firm can produce at a rate of 800 parts /
day Carrying cost is $1 / part / year Setup cost for production run is $45 / setup
Adeyl Khan, Faculty, BBA, NSU
What is Run Time, What is Cycle Time
1pdQ )(2002400 21 dd
18002400 d31 d
)( 21 dduQ
12)( 21 dd
Q0 using formula = 2400u = 48000 /240 = 200 units/day
QDS
H
p
p u0
2
p-u u
I max
d1d2
Adeyl Khan, Faculty, BBA, NSU
What is the Optimal Total Cost
1max )( dupI
2MaxI
HQ
DSTC
1800900900 TC
1800max I
3)200800(max I
2
18001
2400
4800045 TC
Adeyl Khan, Faculty, BBA, NSU
Reorder Point- ROP Reorder Point
When the quantity on hand of an item drops to this amount, the item is reordered
If setup time takes 2 days, at which level of inventory we should start setup? 2(200) = 400 200 ?
Adeyl Khan, Faculty, BBA, NSU
Yet Another ExampleA company has a yearly demand of 120,000
boxes of its product. The product can be produced at a rate of 2000 boxes per day. The shop operates 240 days per year. Assume that demand is uniform throughout the year. Setup cost is $8000 for a run, and holding cost is $10 per box per year.
a) What is the demand rate per dayb) What is the Economic Production Quantity
(EPQ)c) What is the run time d) What is the maximum inventorye) What is the total cost of the system
Adeyl Khan, Faculty, BBA, NSU
up
p
H
SDEPQ
2
5002000
2000
10
)120000)(8000(2
EPQ =16000
Yet Another Example …a) What is the demand rate per day
Demand per year is 120,000 there are 240 days per year Demand per day = 120000/240 = 500 u = D/240 = 500
b) What is the Economic Production Quantity (EPQ)
Adeyl Khan, Faculty, BBA, NSU
Yet Another Example … c) What is the run time
We produce 16000 units Our production rate is 2000 per day It takes 16000/2000 = 8 days d1 = EPQ/p = 8 days
d) What is the maximum inventory We produce for 8 days. Each day we produce 2000 units
and we consume 500 units of it. Therefore we add to our inventory at rate of 1500 per day for 8 days. That is
Imax = 8(1500) = 12000 Imax = pd1 = 8(1500) = 12000
Adeyl Khan, Faculty, BBA, NSU
Yet Another Example …e) What is the total cost of the system
2MaxI
HQ
DSTC
2
1200010
16000
1200008000 TC
1200006000060000 TC
Adeyl Khan, Faculty, BBA, NSU
Including the Purchasing Cost12-36
Annualcarryingcost
PurchasingcostTC = +
Q2H D
QSTC = +
+Annualorderingcost
PD +
Adeyl Khan, Faculty, BBA, NSU
Total Costs with Vs. Quantity Ordered
12-37
Co
st
EOQ
TC with PD
TC without PD
PD
0 Quantity
Adding Purchasing costdoesn’t change EOQ
Adeyl Khan, Faculty, BBA, NSU
Total Cost with Constant Carrying Costs
12-38
OC
EOQ Quantity
Tota
l Co
st
TCa
TCc
TCbDecreasing Price
CC a,b,c
Adeyl Khan, Faculty, BBA, NSU
ROP with EOQ Ordering Safety Stock
Stock that is held in excess of expected demand due to variable demand rate and/or lead time.
Service Level Probability that demand will not exceed
supply during lead time.
12-40
When to Reorder
Adeyl Khan, Faculty, BBA, NSU
Determinants of the Reorder Point
The rate of demandThe lead timeDemand and/or lead time variabilityStockout risk (safety stock)
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Adeyl Khan, Faculty, BBA, NSU
Safety Stock- Figure 12.12
12-42
LT Time
Expected demandduring lead time
Maximum probable demandduring lead time
ROP
Qu
an
tity
Safety stock
Safety stock reduces risk ofstockout during lead time
Adeyl Khan, Faculty, BBA, NSU
Reorder Point- Figure 12.13
12-43
ROP
Risk ofa stockout
Service level
Probability ofno stockout
Expecteddemand Safety
stock0 z
Quantity
z-scale
The ROP based on a normalDistribution of lead time demand
ROPs = Exp. Demand + z. σdLT
See also: Fig 11.14
Adeyl Khan, Faculty, BBA, NSU
Shortage and Service LevelService level determines ROP
E(n) = E(z) z σdLT
E(n) = Expected number of short/cycle E(z) = Standardized number of units-short
from table 11.3 σdLT = Standard deviation of lead time
Example 10 @ Page 56844
Adeyl Khan, Faculty, BBA, NSU
Fixed-Order-Interval Model
Orders are placed at fixed time intervalsOrder quantity for next interval?Suppliers might encourage fixed intervalsMay require only periodic checks of inventory levelsRisk of stockout
Fill rate – the percentage of demand filled by the stock on hand
12-45
Adeyl Khan, Faculty, BBA, NSU
Fixed-Interval tradeoffsBenefits
• Tight control of inventory items
• Items from same supplier may yield savings in:• Ordering• Packing• Shipping costs
• May be practical when inventories cannot be closely monitored
Disadvantages
• Requires a larger safety stock
• Increases carrying cost
• Costs of periodic reviews
12-47
Adeyl Khan, Faculty, BBA, NSU
Single Period Model
Model for ordering items with limited useful livesPerishables
Shortage cost is generally the unrealized profits per unit
Excess cost is the difference between purchase cost and salvage value of items left over at the end of a period
Continuous stocking levels• Identifies optimal stocking
levels• Optimal stocking level
balances unit shortage and excess cost
Discrete stocking levels• Service levels are discrete
rather than continuous• Desired service level is
equaled or exceeded
12-48
Adeyl Khan, Faculty, BBA, NSU
Optimal Stocking Level
12-49
Service Level
So
Quantity
Ce Cs
Balance point
Service level =Cs
Cs + CeCs = Shortage cost per unitCe = Excess cost per unit
Adeyl Khan, Faculty, BBA, NSU
Example 15
Ce = $0.20 per unitCs = $0.60 per unitService level = Cs/(Cs+Ce) = .6/(.6+.2)Service level = .75
12-50
Service Level = 75%
Quantity
Ce Cs
Stockout risk = 1.00 – 0.75 = 0.25
Adeyl Khan, Faculty, BBA, NSU
Operations Strategy
Too much inventory Tends to hide problems Easier to live with problems than to eliminate them Costly to maintain
Wise strategy Reduce lot sizes Reduce safety stock
12-51
Adeyl Khan, Faculty, BBA, NSU
Learning Objectives
Define the term inventory and list the major reasons for holding inventories; and list the main requirements for effective inventory management. Discuss the nature and importance of service inventoriesDiscuss periodic and perpetual review systems. Discuss the objectives of inventory management. Describe the A-B-C approach and explain how it is useful.
12-53
Adeyl Khan, Faculty, BBA, NSU
Learning Objectives
Describe the basic EOQ model and its assumptions and solve typical problems. Describe the economic production quantity model and solve typical problems. Describe the quantity discount model and solve typical problems. Describe reorder point models and solve typical problems. Describe situations in which the single-period model would be appropriate, and solve typical problems.
12-54
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