pom 19 - inventory

8/9/2019 POM 19 - Inventory

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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Can become lost, stolen,damaged, outdated, or obsolete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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Upendra Kachru OPERATIONS MANAGEMENTProf. Upendra Kachru 19

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


PeriodPeriod

Fixed-Period Model:


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When to Order?

Time


PeriodPeriod

Fixed-Period Model:


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When to Order?

Time


Period PeriodPeriod

Fixed-Period Model:


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When to Order?

Time


Period PeriodPeriod

Fixed-Period Model:


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When to Order?

Time


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



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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



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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 .

pom 19 - inventory

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