sessions 1 & 2-inventory mgmt

8/8/2019 Sessions 1 & 2-Inventory Mgmt

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Chapter 7/Sessions 1&2

Inventory Management

(Chapter 16 of Khan & Jain)


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Learning Objectives

Meaning of Inventory

Objectives of Inventory Management

Costs & Benefits of Holding Inventory

Techniques of Inventory Management

Economic Order Quantity (EOQ) Model

A B C System

Order Point System & Safety Stock


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Meaning of Inventory Management

The term inventory is composed of assets that will be

sold in future in the normal course of business operations.

The assets in inventory comprise of Raw Materials,

Work-in-progress & Finished Goods.

Inventory Management is concerned with deciding the

optimal levelof inventory.


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Objective of Inventory Management

The objective of Inventory Management consists of two

counter-balancing parts:

i. To minimize investments in inventory, and

ii. To meet the demand for products by efficiently organizingthe production and sales operations.

An optimum levelof inventory is determined on the basis

of the trade-off between the costs and benefits associated

with inventory.


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Costs associated with Inventory

Excluding the purchase price, the costs associated with inventory

fall into two basic categories:

i. Ordering or Set-up Costs:

This category of costs is associated with the acquisition or ordering

of inventory.

Ordering costs include costs involved in:a) preparing a purchase order or requisition form;

b) receiving, inspecting, and recording the goods received to ensure

both quantity and quality;

c) follow-up of orders;

d) costs of stationery and other clerical costs. Ordering Costs are generallyfixed per order placed, irrespective of

the size of the order.

However, size of the order has an impact on the Total Ordering

Costs incurred in a year.


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Ordering Costs

Order Size No of orders in a year Total Ordering Costs

Order Size No of orders in a year Total Ordering Costs

Total ordering costs are inversely relatedto the Inventory

Order Size.


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Costs associated with Inventory

ii. Carrying Costs: This second category of costs is associated with the maintenance

or carryingof inventory.

Carrying Costs are divided into the following categories:

a. Cost of Storage

This means & includes the cost of storing one unit of inventory by

the firm for ex. Rent of space occupied by the inventory, the cost

of people employed for the security of the inventory, cost of air

conditioning, cost of insurance, cost of pilferage (loss),

warehousing costs, handling cost, etc.

b. Cost of Financing orOpportunity Cost of funds locked up in

inventory


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Carrying Costs

Inventory Order Size Inventory Carrying Costs

Inventory Order Size Inventory Carrying Costs

The carrying costs are directly relatedto the Inventory

Order Size.


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Total Cost of Holding Inventory

The sum of the Ordering and Carrying Costs represents the

Total Cost of inventory (excluding the cost price of inventory).

If the inventory order size is increased () , the ordering cost

shall decrease () and inventory carrying cost shall increase ()

If the inventory order size is reduced () , the ordering cost shall

increase () and inventory carrying cost shall decrease ()

The optimal inventory order size is the size at which the Total

Costof holding inventory is minimum.

This is computed by using one of the most popular techniques of

Inventory Management-Economic Order Quantity Model

(explained later)


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Benefits of Holding Inventory

Raw Materials inventory This is maintained to ensure

smooth supply to the Productions department;

Work-in-progress inventory This is maintained to

ensure conversion of the same into Finished Goods

without much consumption of time (as consumption ofRM into FG would relatively require much time);

Finished Goods inventory This is maintained to ensure

timely supply of goods when demand for the same arises

from customers.

The appropriate level of inventory is determined in terms

of a trade-off between the benefits and costs associated

with holding or maintaining inventory.


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Techniques of Inventory Management

1) Economic Order Quantity (EOQ) Model

EOQ refers to that level of inventory order at which the totalcost of holding inventory (i.e. ordering cost + inventorycarrying cost) is minimal.

When a firm orders inventory equal to the EOQ, it is able toorder & maintain its inventory at the lowest possible cost.

EOQ is also known asEconomic Lot Size.


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Economic Order Quantity

Mathematical / Short-cut Approach

The EOQ can be computed by using the following

formula:

EOQ = 2AB

CWhere, A= Annual usage of inventory (in units)

B= Ordering Cost per order

C= Inventory Carrying Cost per unit per year


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Example # 1

A firms inventory planning period is one year.Its inventory requirement for this period is 1600 units.

Assume that its acquisition costs are Rs 50 per order.

The carrying costs are expected to be Re 1 per unit per

year for an item of inventory.

Compute theEconomic Order Quantity (EOQ) on the

basis of the aforesaid information.

Also calculate theT

otal Costof holding inventory at theEOQ level.


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Solution

Given that,A= Annual usage of inventory = 1600 units

B= Ordering Cost per order = Rs 50 per order

C= Inventory Carrying Cost per unit per year = Re 1

EOQ = 2AB = 2 x 1600 x 50

C 1

EOQ = 160000

EOQ = 400 units


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Solution

Total Cost of holding inventory at EOQ level =Ordering Cost + Inventory Carrying Cost

Ordering Cost = No. of orders in a year x Ordering cost per

order

Ordering Cost = Annual usage x Ordering Cost per order

Qty. ordered per order

Ordering Cost = 1600 x 50

400

Ordering Cost = Rs 200


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Solution

Inventory Carrying Cost =Average Inventory carried in a year x Inventory carrying cost

per unit per year

Inventory Carrying Cost =

Qty. ordered per order x Inventory carrying cost per unit per year

2

Inventory Carrying Cost at EOQ level = 400 x 1 = Rs 200

2

Total Cost of holding inventory = Rs 200 + Rs 200

Total Cost of holding inventory = Rs 400


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Economic Order Quantity

Trial & Error/Analytical Approach

1 Size of order (units) 1,600 800 400 200 1002 Number of orders

(Annual Req. Order Size)

1 2 4 8 16

3 Cost per order (Rs) 50 50 50 50 50

4 Total Ordering Cost(rows 2 x 3)

50 100 200 400 800

5 Carrying Cost per unit per year 1 1 1 1 1

6 Average inventory (in units)

(row 1 2)

800 400 200 100 50

7 Total Carrying Cost(rows 5x6) 800 400 200 100 50

8 Total Cost of holding

inventory (rows 4 + 7)

850 500 400 500 850


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Example # 2

A firms inventory planning period is one year.Its inventory requirement for this period is 600 units.

Assume that its acquisition costs are Rs 10 per order.

The annual carrying costs are expected to be 20% of

the purchase price of inventory.

Cost of purchase of inventory is Rs 6 per unit.

A discount of 5 % has been offered on an order of 200

units.Evaluate the discount offer.


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Solution

Given that,A= Annual usage of inventory = 600 units

B= Ordering Cost per order = Rs 10 per order


= 20% of purchase price = 20% x Rs 6 = Rs 1.20

EOQ = 2AB = 2 x 600 x 10

C 1.20

EOQ = 10000

EOQ = 100 units


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Proposal Evaluation

S. No. Particulars EOQ Discount Offer

1 Size of order (units) 100 200

2 Number of orders 6 3

3 Cost per order (Rs) 10 10

4 Total Ordering Cost(rows 2 x 3) 60 30

5 Cost of purchase per unit (Rs) 6 5.70

6 Carrying Cost p.u. per year (@ 20% ofpurchase price)

1.20 1.14

7 Average inventory (in units) (row 1 2) 50 100

8 Total Carrying Cost(rows 6 x 7) 60 114

9 Total Cost of holding Inventory

(rows 4 + 8)

120 144

10 Total Cost of purchase (Rs)

(row 5 x 600 units)

3600 3420

11 Total Cost of Inventory (rows 8 + 10) 3,720 3,564


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Assumptions of EOQ Model

i. The annual usage (consumption) of inventory is known with

certainty.

ii. The rate of usage or consumption of inventory is steady over a

period of time.

iii. The lead time between placing an order for inventory and supply

of inventory by the suppliers is zero.

iv. Ordering and Carrying costs of inventory are constant.


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Limitations of EOQ Model

i. The assumption of a known annual usage or consumption of

inventory is not practical as there is likelihood of a discrepancybetween the actual and expected consumptions.

ii. The assumption of a constant usage or consumption of

inventory and zero lead time between the order and supply of

inventory are of doubtful validity due to the following reasons:

a) Deliveries from suppliers may be slower than expected for

reasons beyond control.

b) It is also possible that there may be an unusual and unexpected

demand for stocks.

To meet such contingencies, firms have to keep additionalinventory which is known asSafety Stock.

ii. A more difficult situation may occur when the no. of orders to

be placed or the EOQ may turn out to be a fraction.


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Example # 3

The Purchase Manager of an organization has collected the following

data pertaining to inventory:

Order Processing Cost for each order Rs 100

Inspection cost per lot Rs 50

Follow up cost for each order Rs 80

Other procurement cost for each order Rs 170Interest on the locked up capital 20 %

Pilferage while holding inventory 5 %

Other holding cost 15 %

Annual requirement 1000 units

Cost per item Rs 10

Calculate the EOQ


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Solution

S. No. Particulars Values

1 Order Processing Cost for each order 1002 Inspection cost per lot 50

3 Follow up cost for each order 80

4 Other procurement cost for each order 170

5 Ordering Cost per order (rows 1 + 2 + 3 + 4) 400

6 Interest on the locked up capital (@ 20 % of Rs 10) 2.00

7 Pilferage while holding inventory (@ 5 % of Rs 10) 0.50

8 Other holding cost (@ 15 % of Rs 10) 1.50

9 Carrying Cost per unit per annum (rows 6 + 7 + 8) 4.00

10 Annual Requirement (in units) 1000

11 EOQ (2 x 1000 units x Rs 400 Rs 4) 447.21

12 Economic Order Quantity (rounded off) (units) 447


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A B C System

A B C system is an inventory management technique thatdivides inventory into three categories of descendingimportance based on the rupee investment in each.

It is a widely-used classification technique to identifyvarious items of inventory for purposes of inventory

control.

This technique is based on the assumption that a firmshould not exercise the same degree of control on all itemsof inventory.

It should rather keep a more rigorous control on items thatare most costly, while items that are less expensive shouldbe given less control effort.


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A B C System Classification

On the basis of the cost involved, the various inventory items

are categorized into three classes:

Group A items

The items included in this group are the most costly itemsinvolving the largest investment.

The quantity of such items is usually less.

Being expensive items, inventory control should be the mostrigorous for this group and the most sophisticated inventorycontrol techniques should be applied to these items.

Group B items

These items stand midway between Group A & C items and areless costly.

Therefore, these items deserve less attention than group A itemsbut more attention than group C items.

Group C items

The items included in this group are the least costly & involverelatively small investments although the number of such items isfairly large.

Therefore, these items deserve minimum attention.


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Method of A B C System Classification

No definite procedure can be laid down for classifying the inventories

into A, B, C categories as this will depend upon a large number of

factors such as nature and varieties of items, specific requirements of

the business, etc.

However, the following method is generally adopted:

i. The quantity of each item of inventory expected to be used in a period

is estimated along with the cost of purchase per unit;

ii. The value of each of the above items of inventory is found out bymultiplying the quantity of each item with the price;

iii. The items are then rearranged in the descending order of their value

irrespective of their quantities;

iv. % investment of each item in the total investment shall be computed;

v. It will be observed that a small no. of a first few items may amount toa large % of the total value of the items whereas a large no. of the last

items amount to a very small % of the total value of the items.

vi. The management then will have to take a decision as to what

percentage of total value of items have to be covered by A, B and C

categories.


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% of A B C System Classification

Industry surveys, in general, have shown the following trends regarding the

components of inventories of manufacturing organizations:

Another example of typical breakdown of inventory items is as follows:

Group % ofTotal Value % ofTotal Quantity

A 70 15

B 20 30

C 10 55

Total 100 100

Group % ofTotal Value % ofTotal Quantity

A 70 10

B 25 35

C 05 55

Total 100 100


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Example (A B C System)

A firm has 7 different items in its inventory. The average number of each

of these items held, along with their unit costs, is listed below. The firm

wishes to introduce an A B C inventory system. Suggest a breakdown of

the items into A, B and C categories.

Item No. Average no. of units in inventory Average Cost per unit

1 32,000 Rs 11.002 10,000 Rs 102.40

3 30,000 Rs 3.00

4 20,000 Rs 60.80

5 28,000 Rs 10.286 20,000 Rs 1.30

7 60,000 Rs 3.40


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Solution (A B C System)

Item

No.

Average no. of units

in inventory

Avg. Cost per unit

(in Rs)

Total Cost

(in Rs)

1 32,000 Rs 11.00 3,52,000

2 10,000 Rs 102.40 10,24,000

3 30,000 Rs 3.00 90,000

4 20,000 Rs 60.80 12,16,000

5 28,000 Rs 10.28 2,88,000

6 20,000 Rs 1.30 26,000

7 60,000 Rs 3.40 2,04,000


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Solution (A B C System)

Item

No.

Avg. no.

of units ininventory

% ofTotal Units Total Cost

(in Rs)

% ofTotal Value

4 20,000 10

15

12,16,000 38

702 10,000 5 10,24,000 32

1 32,000 1630

3,52,000 1120

5 28,000 14 2,88,000 9

7 60,000 30

55

2,04,000 6.38

10

3 30,000 15 90,000 2.80

6 20,000 10 26,000 0.82

Total 2,00,000 100 ----------- 32,00,000 100.00 ------------


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Order Point System & Safety Stock

As studied earlier, the EOQ technique of inventory

management determines the size of an orderto acquireinventory so as to minimize the ordering as well as carrying

costs.

Another aspect of inventory management is to answer the

question: when should the order to purchase inventory be

placed?

This aspect of inventory management is known as the Order

Point System.

The Order Point System helps to ascertain the following:

Maximum level of inventory Reorder level of inventory (also known as the Reorder Point)

Average level of inventory

Minimum level of inventory (known asSafety orBuffer stock)


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Reorder Level of Inventory/Reorder Point

The Reorder Pointmay be defined as the level of

inventory when fresh order should be placed with the

suppliers for procuring additional inventory equal to the

EOQ.

In order to calculate the Reorder point/level of inventory,

the following information is required:

i. Usage or Consumption of inventory per day or per week

ii. Lead or Delivery Time i.e. the time normally taken in

receiving the delivery after placing orders with the

suppliers (it is also known as the procurement time ofinventory)


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Maximum, Minimum & Average Levels

Maximum levelof inventory refers to the maximum units ofinventory maintained by the firm at all times. The firm does not

intend to invest in inventory beyond the maximum level.

Minimum levelof inventory refers to the minimum units of

inventory maintained by the firm at all times to guard itself against

a possible shortage of inventory caused either by increased usage

or delayed delivery of inventory. This acts as a bufferorcushion

against stock-out situations. For this reason, the minimum level

of inventory is also known asSafety orBuffer Stock.

Average levelof inventory refers to the average units of inventorymaintained by the firm at all times.


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Example (calculation of levels of inventory)

The following information is available with respect to an itemof inventory maintained by a firm:

Normal usage : 50 units per week

Minimum usage : 25 units per week

Maximum usage : 75 units per week

Re-order quantity : 300 units

Re-order or Delivery period : 4 to 6 weeks

Calculate the following:

i. Reorder level

ii. Minimum level

iii. Maximum level, and

iv. Average level of inventory


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Solution (calculation of levels of inventory)

i. Reorder level of inventory= Maximum Usage x Maximum Delivery Time

= 75 units per week x 6 weeks

= 450 units

ii. Minimum level of inventory

= Reorder level (Normal Usage x Average Delivery Time*)

= 450 (50 units per week x 5 weeks)

= 450 250

= 200 units

*Average Delivery Time = (Minimum DT + Maximum DT)2

= (4 + 6) 2

= 5 weeks


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iii. Maximum level of inventory= Reorder level + Re-order quantity (Minimum Usage x

Minimum Delivery Time)

= 450 + 300 (25 units per week x 4 weeks)

= 450 + 300 100

= 650 unitsiv. Average level of inventory

= Minimum level + Re-order quantity

2

= 200 units + 300/2

= 200 + 150

= 350 units


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Maximum Level 650 units

Reorder Level 450 units

Average Level 400 units

Minimum Level 200 units


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Alternate formula to calculate Reorder level

If a firm maintains a minimum level of inventory, the

Reorder point for such a firm can alternatively be calculated by

using the following formula:

Reorder Point = Minimum level + (Normal usage x Average

delivery time)

Using the above formula in the previous example:

Reorder Point = 200 units + (50 units per week x 5 weeks)

Reorder Point = 200 + 250

Reorder Point = 450 units


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Example

XYZ Ltd. are the manufacturers of picture tubes for T.V.

The following are the details of the operation during the current year.Annual requirement of tubes 5200 tubes

Ordering cost (per order) Rs 100

Inventory carrying cost per annum 20%

Cost of tubes (per tube) Rs 500

Normal usage per week 100 tubes

Minimum usage per week 50 tubesMaximum usage per week 200 tubes

Lead time to supply 6 to 8 weeks

Compute the following from the above information:

a) EOQ. If the supplier is willing to offer a discount of 5% on purchase of1500 units, is the discount offer worth accepting?

b) Reorder level

c) Maximum level

d) Minimum level, and

e) Average level of stock


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Solution

Given that,A= Annual usage of inventory = 5200 tubes

B= Ordering Cost per order = Rs 100


= 20% of purchase price = 20% x Rs 500 = Rs 100

EOQ = 2AB = 2 x 5200 x 100

C 100

EOQ = 10400

EOQ = 101.98 units = 102 units (rounded off)


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Proposal Evaluation

S. No. Particulars EOQ Discount

1 Annual Requirement of tubes 5200 5200

2 Order Size 102 1500


4 Total Ordering Cost (5200 x Cost per order)

(in Rs) Order Size

5098 347

5 Cost of purchase per tube (Rs) 500 475

6 Carrying Cost of a tube per year

(20% x row 5)

100 95

7 Average inventory (Order size 2) 51 750

8 Total Carrying Cost (in Rs) (rows 6 x 7) 5100 71250

9 Total Cost of purchase (in Rs) (rows 1 x 5) 2600000 2470000

10 Total Cost of Inventory (rows 4 + 8 + 9) 2610198 2541597


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i. Reorder level of inventory= Maximum Usage x Maximum Delivery Time

= 200 tubes per week x 8 weeks

= 1600 tubes

ii. Minimum level of inventory

= Reorder level (Normal Usage x Average Delivery Time*)

= 1600 (100 tubes per week x 7 weeks)

= 1600 700

= 900 tubes

*Average Delivery Time = (Minimum DT + Maximum DT)2

= (6 + 8) 2

= 7 weeks


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iii. Maximum level of inventory= Reorder level + Re-order quantity (Minimum Usage x

Minimum Delivery Time)

= 1600 + 1500 (50 tubes per week x 6 weeks)

= 1600 + 1500 300

= 2800 tubesiv. Average level of inventory

= Minimum level + Re-order quantity

2

= 900 tubes + 1500/2

= 900 + 750

= 1650 tubes


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Maximum Level 2800 tubes

Average Level 1650 tubes

Reorder Level 1600 tubes

Minimum Level 900 tubes


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Example

A company manufactures a product from a raw material, which is

purchased at Rs 60 per kg. The company incurs a handling cost of

Rs 360 plus freight of Rs 390 per order. The carrying cost of inventory

of raw material is Re 0.50 per kg per month. In addition, the cost of

working capital finance on the investment in inventory of raw material is

Rs 9 per kg per annum. The annual production of the product is 1,00,000units and 2.5 units are obtained from one kg of raw material.

Required:

i. Calculate the EOQ

ii. If the company proposes to rationalize placement of orders on

quarterly basis, what percentage of discount in the price of rawmaterials should be negotiated?


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Solution

i. Calculation of EOQ

Given that,A= Annual usage of raw material (in kgs)

= 1,00,000 2.5 units = 40,000 kgs

B= Ordering Cost per order

= Rs 360 + Rs 390= Rs 750 per order

C= Inventory Carrying Cost per kg per year

= (Re 0.50 x 12 months) + Rs 9 per kg per annum

= Rs 6 + Rs 9 = Rs 15 per kg per annum

EOQ = 2AB = 2 x 40000 x 750 = 2000 kgs

C 15


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Solution

S. No. Particulars EOQ

basis

Quarterly

basis

1 Size of order (kgs) 2000 10000

(40000/4)

2 Number of orders 20 4


4T

otal Ordering Cost(rows 2 x 3) 15

,000 3

,000

5 Carrying Cost per kg per year 15 15

6 Average inventory (in kgs) (row 1 2) 1000 5000

7 Total Carrying Cost(rows 5 x 6) 15,000 75,000

8 Total Cost of holding Inventory

(rows 4 + 8)

30,000 78,000

9 Incremental Costs --------- 48,000

10 Discount to be negotiated (in Rs) --------- 48,000


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Solution

ii. Calculation of% of discount

The firm should negotiate for a discount of Rs 48,000 on its

total annual purchases of 40,000 kgs of raw material so as to

arrive at the most optimal cost of inventory of raw material.

Discount per kg of raw material = Rs 48000 40,000 kgs= Rs 1.20 per kg.

% discount on purchase price = Discount (in Rs) x 100

Purchase Price per kg

= Rs 1.20 x 100Rs 60

= 2 %


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Solution

S.

No.

Particulars EOQ Discount

(quarterly

basis)

1 Total Cost of holding Inventory 30,000 78,000

2 Purchase price of raw material (per

kg)

60 58.80*

3 Total cost of purchase

(row 2 x 40,000 kgs)

24,00,000 23,52,000

4 Total cost of raw material inventory

(rows 1 + 3)

24,30,000 24,30,000

* Discounted purchase price of raw material (per kg) = Rs 60 2%

= Rs 58.80


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Solved Problems & Review Questions

Khan & Jain- Fifth Edition

Chapter 16 - Inventory Management

Solved Problems: P.16.1 to 16.5, 16.7 to 16.11

Review Questions: 16.1, 16.5 to 16.8


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sessions 1 & 2-inventory mgmt

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