pom 19 - inventory
TRANSCRIPT
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Upendra Kachru OPERATIONS MANAGEMENT
Managing
Inventory
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Inventory is the stock of any
item or resource used in an
organization.WHAT IS
INVENTORY?
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Water Tank Analogy for Inventory
Supply RateInventory Level
Demand Rate
Inventory Level
Buffers Demand Rate
from Supply Rate
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Reasons To NOT Hold Inventory
Carrying cost Financially calculable
Takes up valuable factory space Especially for in-process inventory
Inventory covers up problems That are best exposed and solved
Driver for increasing inventory turns (finished goods) and lean
production/Just in time for work in process
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Inventory Hides Problems
Poor
Quality
Unreliable
Supplier
MachineBreakdown
Inefficient
Layout
Bad
Design
Lengthy
Setups
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To Expose Problems:
Reduce Inventory Levels
Poor
Quality
Unreliable
Supplier
MachineBreakdown
Inefficient
Layout
Bad
Design
Lengthy
Setups
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Remove Sources of Problems
and Repeat the Process
Poor
Quality
UnreliableSupplier
Machine
BreakdownInefficientLayout
Bad
Design
Lengthy
Setups
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Consumes capital
Requires storage space
Incurs taxes
Requires insurance
Can become lost, stolen,damaged, outdated, or obsolete
Must be counted, sorted, verified,stored, retrieved, moved, issued,
and protected
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INVENTORY PROFILE
In-
Process
Inventory(WIP)Orders in Temporary Storage
Orders Waiting to be Worked
Orders Being Inspected
Orders Being Worked
Nonproductive
Productive
Outputs
Inputs
Finished
Goods
Raw
Materials
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Cost of Inventory at Different Stages
Inventory Costs are additive
RAW MATERIALS INVENTORY PROFILE
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RAW MATERIALS INVENTORY PROFILE
Excess StockSurplus / Idle
Working Stock
Safety Stock
Outputs
Inputs
Nonproductive
Productive
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Inventory Objectives
Maximize
Customer
Service
Operating
Efficiency
Minimize
InventoryInvestment
Balancing Objectives
1. Provide customer service
2. Support plant efficiency
3. Minimize inventory investment
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MULTI PERIODINVENTORY
MODELS
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Fixed-Order Quantity Models (Q): Event triggered
(Example: running out of stock) Fixed-Time Period Models (T): Time triggered (Example:
Monthly sales call by sales representative)
Multi-Period Inventory Models
Time T1 T2
InventoryLevel
Q
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Continuous Review System (Q)A system designed to track the remaining inventory
of an item each time a withdrawal is made, to determine
whether it is time to replenish
Periodic Review System (P)A system in which an items inventory position isreviewed periodically rather than continuously
Qand PSystems
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Continuous Review System (EOQ) Individual review frequencies
Possible quantity discounts
Lower, less-expensive safety stocks
Periodic Review System (P)
Convenient to administer
Orders may be combined
Inventory position only required at review
Comparison of Qand PSystems
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Fixed order Quantity and Fixed-Time
Period Differences
Feature Fixed-order quantity Model Fixed-Time Period Model
Order quantity The same amount ordered each time Quantity varies each time order is
placed
When to place order Reorder point when inventory position
dips to a predetermined level
Reorder when the review period
arrives
Record keeping Each time a withdrawal or addition ismade
Counted only at review period.
Size of inventory Less than fixed-time period model Larger than fixed-order quantity
model
Time to maintain Higher due to perpetual record
keeping
Type of items Higher-priced, critical, or importantitems.
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EOQ Model - The Inventory Cycle
Profile of Inventory Level Over Time
Quantity
on hand
Q
Receiveorder
Placeorder
Placeorder
Lead time
Reorder
point
Receiveorder
Receiveorder
Usagerate
Time
The inventory cycle determines when an order should be placed and how much
should be ordered so as to minimize average annual variable costs.
The EOQ Model Assumptions
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The basic assumptions in the EOQ Model are as
follows: The rate of demand for the item is deterministic and is a
constant D units per annum independent of time.
Lead time is zero or constant and it is independent of
both demand as well as the quantity ordered.
Price per unit of product is constant Inventory holding cost is based on average inventory
Ordering or setup costs are constant
The EOQ Model - Assumptions
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EOQ Model: Cost of Inventory
20
Ordering Costs (A
Holding
Costs (H)
Order Quantity (Q)
COST
Annual Cost of
Items (DC)
Total Cost
QOPT
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Average inventory level:
Holding cost per unit:
Ordering cost per unit:
2
Q
D
HQ
D
rvQ
2
2
Q
A
By adding the item, holding, and ordering costs together, we
determine the total cost curve, which in turn is used to find the
Qopt inventory order point that minimizes total costs
EOQ Model: Minimizing Cost
The EOQ Formula
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The EOQ Formula
R eorder poin t, R = d L_
d = average daily demand (constant)
L = Lead time (constant)
_
We also need a
reorder point to tell
us when to place an
order
CostHoldingAnnual
Cost)SetuporderDemand)(Or2(Annual
H
2DA
=rv
2DA
=QOPT
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EOQ Formula Total Annual Cost
TotalAnnual =
Cost
AnnualPurchase
Cost
AnnualOrdering
Cost
AnnualHolding
Cost+ +
TC=Total annual costD =Demand
P =Cost per unit
Q =Order quantity
A =Cost of placing an
order or setup costR =Reorder point
L =Lead time
H = v*r =Annual holding
and storage cost per
unit of inventory
TC = P*D + D*A / Q + Q*v*r / 2
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A company, for one of its class A items, placed 8 orders each for a lot of 150numbers, in a year. Given that the ordering cost is Rs. 5,400.00, theinventory holding cost is 40 percent, and the cost per unit is Rs. 40.00. Find
out if the company is making a loss in not using the EOQ Model for order
quantity policies.
What are your recommendations for ordering the item in the future? And
what should be the reorder level, if the lead time to deliver the item is 6months?
D = Annual demand = 8*150 = 1200 units
v = Unit purchase cost = Rs. 40.00
A = Ordering Cost = Rs. 5400.00
r = Holding Cost = 40%
OQ Model Problem
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Using the Economic Order Equation:
QEOQ = (2*A*D /r*v) = 900 units.
Minimum Total Annual Cost (TC) = 2*A*D*r*v = Rs. 14,400.00
The Total annual Cost under the present system = Rs. 45,000.00
The loss to the company = Rs. 45,000 Rs. 14,400 = Rs.30,600.00
Reorder Level = Ro = L*D = (6/12)* 1200 = 600 unitsThe company should place orders for economic lot sizes of 900 units in
each order.
It should have a reorder level at 600 units.
TC= = 2*5400*1200*0.40*40
QEOQ
= (2*5400*1200)/(0.40*40)
= Rs. (1200*5400/150 +0.40*40*150/2) = Rs.
(43,800 + 1200)
T l C i h P h i C
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Total Costs with Purchasing Cost
C
ost
EOQ
TC with
Purchasing
Cost
TC without
PurchasingCost
Purchasing Cost
0 Quantity
Adding Purchasing costdoesnt change EOQ
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Total Cost with Constant Carrying Costs
OC
EOQ Quantity
TotalCost TCa
TCc
TCbDecreasing
Price
CC a,b,c
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EOQ Model wi th Quant i ty Discounts
Quantity discounts, which are price incentives to purchaselarge quantities, create pressure to maintain a large
inventory.
For any per-unit price level, P, the total cost is:
Total annual cost = Annual holding cost + Annual ordering or
setup cost + Annual cost of materials
C= (H) + (A) + PD
Q
2
D
Q
Q tit Di t
Total cost curves with EOQs and price break
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Quantity DiscountsCfor P= Rs.4.00
Cfor P= Rs.3.50
Cfor P= Rs.3.00
PD for
P= Rs.4.00 PD for
P= Rs.3.50 PD forP= Rs.3.00
EOQ 4.00EOQ 3.50EOQ 3.00
First
price
break
Second
price
break
To
talcost(Rupees)
Totalcost(Rupees)
Purchase quantity (Q)
0 100 200 300
Purchase quantity (Q)
0 100 200 300
First
price
break
Second
price
break
Total cost curves with
purchased materials added
EOQs and price break
quantities
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Step 1. Beginning with the lowestprice, calculatethe EOQ for each price level until a feasible EOQis found. It is feasible if it lies in the range
corresponding to its price.
Step 2. If the first feasible EOQ found is for thelowest price level, this quantity is the best lot size.
Step 3. Otherwise, calculate the total cost for the
price break quantity at each lower price level. The
quantity with the lowest total cost is optimal.
Finding Q with Quantity Discounts
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Annual demand (D) = 936 units
Ordering cost (A) = Rs. 45Holding cost (H) = rv = 25% of unit price
Order Quantity Price per Unit
0 75 Rs. 60.0076 499 Rs. 58.80500 or more Rs. 57.00
A supplier forApollo Hospital has introduced
quantity discounts to encourage larger orderquantities of a special catheter. The price
schedule is:
Problem
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EOQ 57.00 = 2DSH2(936)(45)0.25(57.00)
= = 77 units
EOQ 58.80 =2DS
H
2(936)(45)
0.25(58.80)= = 76 units
These quantities are feasible because they lie in therange corresponding to its price.
Not feasible
Feasible
Step 1: Start with lowest price level:
EOQ 60.00 =2DS
H
2(936)(45)
0.25(60.00)= = 75 units Feasible
Step 2: The first feasible EOQ of 75 does not correspond to the lowest price level
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= Rs. 56,999
C= (rv) + (A) + PD
Q
2
D
Q
C75 = [(0.25)(Rs. 60.00)] + (Rs. 45) + Rs. 60.00(936)75
2
936
75
= Rs. 57,284
C300 = [(0.25)(Rs. 58.80)] + (Rs. 45) + Rs. 58.80(936)
300
2
936
300
= Rs. 57,382
C500 = [(0.25)(Rs.57.00)] + (Rs.45) + Rs. 57.00(936)500
2
936
500
The best purchase quantity is 500 units,
which qualifies for the deepest discount.
Step 2: The first feasible EOQ of 75 does not correspond to the lowest price level.Therefore compare its total cost with the price break quantities (300 and 500 units) at
the lower price levels (Rs.58.80 and Rs.57.00)
QUANTITY DISCOUNTS
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Lower unit cost Higher holding costs
Lower ordering costs Larger inventory investment
Fewer stockouts Older stock
Price increase hedge Slow inventory turnover
QUANTITY DISCOUNTS
Advantages Disadvantages
Fi ed Time Period Models
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In many retail merchandising systems, a fixed-timeperiod system is used. Sales people make routinevisits to customers and take orders. Inventory,
therefore, is counted only at particular times.
Fixed-time period models generate order quantities
that vary from period to period, depending on theusage rates.
Fixed-Time Period Models
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Fixed-Period Model
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 stock-out between intervals
Useful when vendors visit routinely Example: P&G rep. calls every 2 weeks
Fixed-Period Model:
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When to Order?
Time
Inventory Level Target maximum
Period
Fixed-Period Model:
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When to Order?
Time
Inventory Level Target maximum
PeriodPeriod
Fixed-Period Model:
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When to Order?
Time
Inventory Level Target maximum
PeriodPeriod
Fixed-Period Model:
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When to Order?
Time
Inventory Level Target maximum
Period PeriodPeriod
Fixed-Period Model:
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When to Order?
Time
Inventory Level Target maximum
Period PeriodPeriod
Fixed-Period Model:
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When to Order?
Time
Inventory Level Target maximum
Period PeriodPeriod
T = Time between orders
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I
L)(dQ
L = Lead Time
usageperiodAveraged
T Time between orders
I = Existing Inventory
Q = Order Size
I
LddQ
dQuantityOrderAverage
Total Annual Cost = Purchase Cost + Ordering
Cost + Holding Cost
Q/2)H/Q) (
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Order Quantity = Average demand over the
vulnerable period + safety stock - Inventory
currently on hand
LT )(d
Where
z = Number of standard deviations for a specified service probability
T + L= Standard deviation of demand over the review and lead time
Accounting for Safety Stock:
SSI
L)(dQ
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Fixed Order Period
Standard deviation of demand over T+L =
T = Review period length (in days) = std dev per day
Order quantity =
LTLT
IzLTdq LT )(
Two-Bin System
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Two Bin System
When the first bin is empty,
stock is taken from the secondbin and an order is placed.
There should be enough stock
in the second bin to last until
more stock is delivered.
Single Period Inventory Model
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Single-Period Inventory Models are a
special case of periodic inventory systems.
One time purchasing decision
Seeks to balance the costs of inventory
overstock and under stock
It is used for a wide variety of service and
manufacturing applications
Single-Period Inventory Model
Single-Period Inventory Model
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The model identifies two penalty costs which are incurred
regardless of a decision:
Cost of Overage
CO = Purchase Price - Salvage Value = c - s
For each item overstocked the vendor incurs a penalty cost
Cost of Underage
CU = Selling Price - Purchase Price = p - c
For each item understocked the vendor incurs a penalty
(opportunity) cost
Single-Period Inventory Model
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If we know the probability that the unit will be sold is P; theexpected marginal cost equation can be represented as:
P (Co) < (1- P) Cu
Here (1-P) is the probability of the unit not being sold. Solving for P, we
obtain
P < [Cu/ (Co + Cu)]
This equation states that we should continue to increase the
size of the order as long as the probability of selling what we
order is equal to or less than the Ratio Cu/ (Co + Cu).
The Classical Newsvendors Problem
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A newspaper vendor is faced with the problem of decidinghow many newspapers to order daily so as to maximize the
daily profit.
Daily demand (d) for newspapers is a random variable.
No reordering is possible during a day,
If the newsvendor orders fewer papers than customers demandhe or she will lose the opportunity to sell some papers.
If supply exceeds demand, the vendor will be stuck with paperswhich cannot be sold.
The Classical Newsvendor s Problem
Demand Data
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Based on observations over several weeks, the vendor has establishedthe following probability distribution of daily demand:
The vendor purchases daily papers at Rs.2 and sells them at Rs. 5apiece. Leftover papers are valueless and are discarded (i.e. nosalvage value).
Demand
d
Probability
P(d)
Cumulative Prob.
F(d) = P(D d)
35 or less
36
37
38
39
40
4142
43
44
45
46 or more
0.00
0.05
0.07
0.08
0.15
0.15
0.200.15
0.10
0.03
0.02
0.00
0.00
0.05
0.12
0.20
0.35
0.50
0.700.85
0.95
0.98
1.00
1.00
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Assume that there is already a policy in place to order a certain number of papersdaily, say 38.
Consider the decisions:
D1 : Continue the present policy: Stock 38 papers.
D2 : Order one more paper: Stock 39 papers.
The possible events are:
E1 : The 39th paper sells (i.e. demand 39 = demand > 38).E2 : The 39th paper does not sell (i.e. demand 39 = demand 38).
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Item 39 will notsell on a given day only if demand on that
day is for 38 or fewer items:
P(D 38) = F(38) = 0.20.
The probability that an item will notsell is the cumulative
probability associated with theprevious item. Item 39 will
sell on a given day only if demand on that day is for 39 ormore items:
P(D 39) = 1 - P(D 38) = 1 - F(38) = 1 -
0.2 = 0.80.
The expected payoff is:
Rs. 3(0.8) + (- Rs. 2)(0.2) = Rs. 2.
This implies an increase in profit ofRs. 2.00 as compared to the
alternative decision which has apayoff of Rs. 0.00. He should stock
the 39th paper.
Worked
E l
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After prayers at the Siababa temple
on Thursdays, people go to a vendor
to eat food. The vendor has
collected data over a few months
that show, on an average, 100 mealswere sold with a standard deviation
of 10 meals.
If our vendor wants to be 90
percent sure of not running out of
food each Thursday, how manymeals should he prepare?
Example
Problem and Solution
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If we assume that the distribution is normal and the vendor prepared food for
exactly 100 persons, the risk of food running out would be 50 percent. The demand
would be expected to be less than 100 meals 50 percent of the time, and greaterthan 100 the other 50 percent.
To be 90 percent sure of not falling short, he needs to prepare more food.
From the standard normal distribution, we can find out that he needs to haveadditional food to cover 1.282 standard deviations.
In order to ensure that he is 90 percent sure having sufficient food:The number extra food required would be 1.282 x 10 = 12.82, or 113 meals.
z
f(z)F(0.9)= +1.282
z*
Inventory Control by Classification
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The inventory of a medium sized business organization wouldcomprise thousands of items, each item with different usage,
price, lead time and specifications. There could be different
procurement and technical problems associated with different
items. In order to escape this quagmire many selective inventory
management techniques are used.
Systems
Inventory Classification Systems
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Vilfredo Paretos 80-20 rule.
The Pareto Rule is based on focusing efforts where the payoffis highest; i.e. high-value, high-usage items must be tracked
carefully and continuously.
Typically only 20 percent of all the items account for 80
percent of the total rupee usage, while the remaining 80percent of the items typically account for remaining 20
percent of the rupee value.
The large value items constitute only 20 percent, the ParetoRule makes analysis the task of inventory analysis relatively
easier.
y y
TYPICAL ABC INVENTORY ANALYSIS
ABC Analysis is based on the Pareto Rule
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40
20
0
20
40
60
80
60
A
BCP
ERCENT
OF
RUPEEVA
LUE
P
ERCENTOF
ITEMS
ABC Analysis is based on the Pareto Rule
A = HIGH VALUE ITEMSB = MEDIUM VALUE ITEMS
C = LOW VALUE ITEMS
ABC Analysis
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ABC Analysis
Divides on-hand inventory into 3 classes A class, B class, C class
Basis is usually annual Re. volume
Re. volume = Annual demand x Unit cost
Policies based on ABC analysis Develop class A suppliers more
Give tighter physical control of A items
Forecast A items more carefully
RELATIVE ANALYSIS OF ABC
CLASSIFICATIONS
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CLASSIFICATIONS
Item Degree of
Control
Type of Records Lot Sizes Frequency of
Review
Size of Safety
Stocks
A Tight Accurate / Complete Low Continuous SmallB Moderate Good Medium Occasional Moderate
C Loose Simple Large Infrequent Large
ABC EXCEPTIONS
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1. Difficult Procurement Items
2. Short Shelf Life
3. Large Storage Space Requirements
4. Items Operational Criticality
5. Likelihood of Theft
6. Difficult Forecast Items
Other Classification SystemsTitle Basis Main Uses
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ABC (Level of Usage) Value of consumptionraw material components and work-
in progress inventories
HML (High, medium, lowusage)
Unit price of the material Mainly to control purchase.
FSND (Fast, Slow moving,
Non moving, Dead )
Consumption pattern of the
componentControl obsolescence.
SDE (Scarce, difficult, easy
to obtain items)
Problems faced in
procurement
Lead time analysis and purchasing
strategies
GOLF (Government,
Ordinary, Local, Foreign)Source of the material Procurement strategies
VED (Vital, Essential,
(Desirable)Criticality of the component
To determine the stocking levels of
spare parts.
SOS (Seasonal, Off-
seasonal)Nature of suppliers
Seasonal items like agriculture
products
XYZ ( Value of Stock) Value of items in storageTo review the inventories and their
use scheduled intervals.
Inventory Metrics
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Average Inventory Investment: The rupee value of a
companys average level of inventory is one of the mostcommon measures of inventory.
Inventory Turnover Ratio: It is a ratio that measures howmany times during a year the inventory turns around.
Inventory turno ver = annu al cos t of
goods sold/average inventory
investment
Inventory Metrics
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Days of Inventory: This measure is an indication ofapproximately how many days of sales can be supplied solelyfrom inventory.
Days of inventory = avg. inventory
investment / (annual cost o f god sso ld/days per year)
Days of inv entory = days per year/
inventory turn over rate
Inventory Tracking
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Track additions and removals
Bar-coding
Point of use or point of sale (POS)
RFID
Physical count of items Periodic intervals
Cycle count
Find and correct errors
Classical Inventory Problems
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Ever - increasing storage space needs Slow-moving materials
Disposition of scrap, obsolete, & surplus
materials
Transaction recording errors Misplaced materials
Inventory System Improvement
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1. Standardize Stock Items
2. Reduce Lead Times
3. Reduce Cycle Times
4. Use Fewer Suppliers
5. Inform Suppliers of Expected Demand
6. Contract for Minimum Annual Purchases
7. Buy on Consignment
8. Consider Transportation Costs
9. Order Economical Quantities
10. Control Access to Storage Areas
11. Obtain Better Forecasts
Inventory System Improvement
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12. Dispose of Excess Stock
13. Improve Record Accuracy (cycle count)
14. Improve Capacity Planning
15. Minimize Setup Times
16. Simplify Product Structures
17. Multishift operations18. Continuous Improvement
Prof. Upendra Kachru
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C l i c k t o e d i t c o m p a n y s l o g a n .