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PPrreeppaarreedd BByy

BBrriijj BBhhoooosshhaann

AAsssstt.. PPrrooffeessssoorr

BB.. SS.. AA.. CCoolllleeggee ooff EEnngggg.. AAnndd TTeecchhnnoollooggyy

MMaatthhuurraa,, UUttttaarr PPrraaddeesshh,, ((IInnddiiaa))

SSuuppppoorrtteedd BByy::

PPuurrvvii BBhhoooosshhaann

In This Chapter We Cover the Following Topics

Art. Content Page

4.1 Meaning of Inventory

Need/Purpose of Holding Inventory

Classification of Inventories

Inventory Functions (Need for Inventories)

3

3

3

5

4.2 Meaning of Inventory Control

Objectives of Inventory Control

Functions of Inventory Control

Essentials of a Good Inventory Control System

Scope of Inventory Control

Advantages of Inventory Control

5

6

6

6

7

8

4.3 Levels of Inventory 8

4.4 Determining Inventory Level 9

4.5 Inventory Models

Assumptions in Deterministic Models

10

11

4.6 Inventory Costs (Cost Associated With Inventories) 11

4.7 Economic Order Quantity (EOQ)

Method of calculation of EOQ

Optimum Lot Size

Inventory Model Considering Quantity Discount

13

13

14

15

4.8 Economic Order Quantity When Stock Replenishment is Not Instantaneous (Gradual

Replenishment)

18

4.9 Economic Lot Size When Shortages are Allowed 19

4.10 Economic Lot Size with Different Rate of Demand in Different Cycles (Replenishment

is Instantaneous)

21

4.11 Re-ordering Systems (Inventory Control Systems)

Two Bin System

Periodic Inventory Ordering System (Ordering Cycle System)

22

22

23

For more information log on www.brijrbedu.org

Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)

Copyright by Brij Bhooshan @ 2013

2 Chapter-3 Inventory Control

Periodic Review System

Difference between P and Q types of Inventory Control System

24

24

4.12 Inventory Control Techniques

ABC Analysis

SDE Analysis

VED Analysis

HML Analysis

FSN Analysis

FNSD Analysis

MNG-Analysis

SOS Analysis

XYZ Analysis

A Summary of Selective Control Techniques

24

25

28

28

28

29

29

29

30

30

30

Please welcome for any correction or misprint in the entire manuscript and your valuable sug-

gestions kindly mail us [email protected].




3 Industrial Management

4.1 MEANING OF INVENTORY

The meaning of inventory is “stock of goods” or “a list of goods”. In manufacturing concern, it

include raw materials, work-in-progress, finished goods, tools & equipments, etc. Inventory is

defined as the list of movable goods which helps directly or indirectly in the production of goods

for sale. Inventory is a service to production. It is just a sort of investment in the form of raw

materials, tools, gauges, supplies etc. Inventory may also be defined as a comprehensive list of

movable items which are required for manufacturing the products and to maintain the plant

facilities in working conditions. In other words, inventory can be defined as the stock of goods,

commodities or other resources that are stored at any given period for future production. The

following are the few examples of the type of inventory held by various organizations:

Type of Organization Type of inventories held

Manufacturer Raw materials, spare parts, semi-finished goods, finished goods

Hospital Number of beds, stock of drugs, specialized personnel

Airline Company Seating capacity, Spare parts, specialized maintenance crew

Need/Purpose of Holding Inventory

Transaction Motive→ Every firm has to maintain some level of inventory to meet the day-to-

day requirements of sales, production process, customer demand, etc. This motive makes the

firm to keep the inventory of finished goods as well as raw materials. The inventory level will

provide smoothness to the operations of the firm. A business firm exists for business transac-

tions which require stock of goods and raw materials.

Precautionary Motive→ A firm should keep some inventory for unforeseen circumstances

also. For example, the fresh supply of raw material may not reach the factory due to strike of

the transporters or due to natural calamities in a particular area. There may be labor problems

in the factory and the production process may halt (stops). So the firm must have inventories of

raw materials as well as finished goods for meeting such emergencies.

Speculative Motive→ The firm may be tempted to keep some inventory in order to capitalize

an opportunity to make profit, e.g., sufficient level of inventory may help the firm to earn extra

profit in case of expected shortage in the market. Such inventory allocations are made to meet

seasonal demand, sales promotion and to meet customer requirements during periods in which

the production facility is in-operable.

Classification of Inventories

The inventories which play a direct role in the manufacture of a product and become an integral

part of the finished product are called direct inventories.

Direct Material Inventories→ These materials undergo transformation in the manufacturing

operation and thereafter sent to distributors or final customers. The examples of such invento-

ries include:

1. Production Inventories→ These are the materials which are machined or processed be-

fore they are ready to be used in assembly of the finished products. Raw materials, parts

and components which are consumed in the production process of goods, come under the

category of production material inventories. The purpose of holding these materials is to

ensure uninterrupted production process. They include items like steel (angles, chan-

nels, flats, tubes, plates, shafts etc.), copper, tin, lead, cotton, rubber, forgings, castings,

leather, wood etc.

2. In-Process Inventories (Work in Progress)→ These goods are partially completed/finished

goods that are still in the production operation, i.e., semi-finished products found at

various stages in the production process are called in-process inventories. Raw materials





become work in progress at the end of first operation and remain in that classification

until they become piece parts or finished goods. Work in progress can be found on the

conveyors, pallets, in and around the machines and in temporary storage awaiting for

the next operation.

3. Purchased parts→ These are some purchased items (components, sub-assemblies, fin-

ished parts etc.) purchased from outside suppliers instead of manufacturing in the fac-

tory itself. (For example, ball bearings, screws, nuts, bolts, tyres required in automobile

industries.

4. Finished Goods Inventories→ These inventory items are final products, available for sale

and distribution, i.e., completed products ready for shipping. They help to reduce the

risk associated with stoppage of output on account of strikes, breakdowns, shortage of

materials, etc.

Indirect Materials Inventories→ These materials in the inventory are required for manufac-

turing process but do not undergo transformation in the process. Example of such inventories

includes:

1. MRO (Tool) Inventories→ Maintenance, repair and operating supplies which are used in

the production process but do not become a part of the products are called MRO items,

and their stocking is called MRO inventories. Items like lubricating oil, old cloths, ma-

chine spare parts, etc. are not a part of the product produced but they are required for

the smooth functioning of the production process and so their stock is maintained. Vari-

ous tools used for processing are classified as:

(i) Standard tools used on machines such as lathe tools, milling cutters, drills,

reamers, taps, hobs, broaches, chasers, form tools etc.

(ii) Hand tools, such as hand saws, chisels, drill guns, hammers, mallets, pliers,

spanners, wrenches, punches etc.

2. Consumables (or Supply)→ Consumables are products that are required repeatedly, i.e.,

items which “used-up” or discarded after use. For example, consumable office supplies

are such products as paper, pens, file folders, computer disks, toner/ink cartridges, etc.

Supplies include

(i) Miscellaneous consumable stores such as brooms, cotton waste, toilet paper, vim

powder, jute etc.

(ii) Welding, soldering and tinning materials such as electrodes, welding rods, solder,

spelter etc.

(iii) Abrasive materials such as emery cloth, emery belts, sand paper emery, graphite

etc.

(iv) Brushes, maps, bobs etc.

(v) Empties such as bags, glass bottles, cardboard boxes, drums, jars, tins etc.

(vi) Oils and greases such as kerosene, transformer oil, petrol, diesel, lubricating and

cutting oils.

(vii) General office supplies such as candles, sealing wax, ink and ink pads, nibs, pen-

cil and refills, files, pins, clips, carbon paper, stencil paper, tracing paper, erasers

etc.

(viii) Printed forms such as envelops, letterheads, enquiry forms, order acceptance

forms, quotation/ tender forms, requisition forms, goods receipt reports, discrep-

ancy notes, vouchers, invoices, debit note, credit note etc.

Ledgers and journals such as goods inward register, goods receipt register, cash book, loan

book, sales journal, general ledger etc. Electric supplies such as cables, clips, cut-outs, fuses,

lamps, lamp holders, plugs, hoses, switches, etc.





Inventory Functions (Need for Inventories)

No business can operate without inventories. Every firm must maintain adequate stock of in-

ventories for the following reasons:

To ensure against delays in deliveries: When an order is placed for fresh stock, the materi-

als are not immediately available but some time elapses before it arrives. This period between

the time of placing the order and the time of stock arrival (lead time) is often subjected to varia-

tions. A firm must therefore hold some reserve stock to allow production operations to continue

if delay in procurement occurs.

To allow for possible increase in output: Changes in the manufacturing programme may

occur because of variation in the demand. To meet the increased demand of the finished goods

the company should have enough stock of inventories so as to allow the production without in-

terference,

Maintain smooth and efficient production flow: When a company has little inventory and

runs out of stock, stock-out of essential materials means interruptions in production which

raises cost of production.

To keep better customer relations: Stock outs means stoppage or interruptions in produc-

tion, therefore it may delay the delivery of finished goods to the customer. After a few such de-

lays even a most patient customer will start looking for a supplier who will give him better ser-

vice.

To take advantage of quantity discounts: Materials and components may be cheaper when

purchased in large quantities owing to larger discounts and lower transportation costs. Fur-

thermore, paper work and inspection of incoming materials are also simplified when larger

quantities are ordered.

To utilize to advantage price fluctuations: Price fluctuations of materials have a marked

effect on the procurement policy of a company. If these fluctuations are to be used to some ad-

vantage, the company should purchase in adequate quantities when prices are low.

To ensure against scarcity of materials in the market: Sometimes there are wide fluctua-

tions in the output of certain materials and in the demand for them so that materials may be-

come scarce and difficult to get. A reserve stock held by the firm will ensure that production op-

erations are not affected by scarcities in the market.

To have a better utilization of men and machinery: If there is a stock out of materials the

men and machinery will remain idle. Therefore, the company should keep enough stock of in-

ventories to have better utilization of men and machinery.

4.2 MEANING OF INVENTORY CONTROL

The function of directing the movement of goods through the entire manufacturing cycle from

the requesitioning of raw materials to the inventory of finished goods orderly mannered to meet

the objectives of maximum customer-service with minimum investment and efficient (low-cost)

plant orientation. Inventory control is the process by which materials of the correct quality and

correct quantity are made available as and when required with due regard to economy in stor-

age and ordering costs, purchasing prices and working capitals. In other words, it is the tech-

nique of maintaining the size of the inventory at some desired level keeping in mind the best

economic interests of the production system. The desired level can neither be too high nor too

low because high level of inventory will lead to increase in carrying cost while low level of in-

ventory will lead to increase in ordering cost. Thus, the inventory control includes the following

aspects:





1. Size of inventory: Determining maximum and minimum level, establishing time sched-

ules, procedures and lot of sizes for new orders, ascertaining minimum safety levels, co-

ordinating sales, production and inventory policies.

2. Providing proper storage facilities, arranging the receipts, disbursements and procure-

ment of materials, developing the forms of recording these transactions.

Objectives of Inventory Control

Availability of Materials→ The first and the foremost objective of the inventory control is to

make all types of materials available at all times whenever they are needed by the production

departments so that the production may not be held up for want of materials.

To Check Wastage→ Inventory control not only ensures uninterrupted material supply to

production department but also ensures the control from purchasing to supply of finished goods

to customers. So in this way, it checks wastage whether it is about time, money or material.

To check Embezzlement (fraud) and Theft→ Inventory control is necessary for protection

from theft and embezzlement by maintaining necessary records.

For the Success of Business→ Customer‟s satisfaction is very much important for the success

of business. Customer‟s satisfaction is directly related to the goods supplied to them. If the

goods supplied to customers are low in cost with good quality at right time, it ensures the suc-

cess of business. Inventory control helps in achieving this goal.

Optimum Investment and Efficient use of Capital→ The prime objective of inventory con-

trol from financial point of view is to have an optimum level of investment in inventories. There

should neither be any deficiency of stock of raw materials so as to hold up the production proc-

ess nor there any excessive investment in inventories so as to block the capital that could be

used in an efficient manner otherwise.

Reasonable Price→ Inventory control ensures the supply of raw materials at a relatively low

price but without sacrificing the quality of it. It helps in controlling the cost of production and

the quality of finished goods in order to maximize the profits of the concern.

Minimizing Costs→ Minimizing inventory costs such as handling, ordering and carrying costs,

etc., is one of the main objectives of inventory management.

Functions of Inventory Control

1. To ensure smooth production operation by ensuring timely availability of material.

2. To minimize capital investment in inventory by better use of financial resources.

3. To help in minimizing loss by obsolescence, deterioration, damage, thefts, wastages, etc.

4. To protect against the uncertainties of demand and supply.

5. To help managers in decision making regarding inventory.

6. Better utilization of storing capacity.

7. To maintain reasonable stocks of materials at all times.

8. To facilitate regular and timely supply to customers increasing customer satisfaction.

9. To prepare accurate material reports.

Essentials of a Good Inventory Control System

Proper Co-ordination→ There should be a proper co-ordination between all the departments

who use materials, such as purchase department, store department, inspection department, ac-

counts department, production department and sales department.

Proper Classification→ Classification and identification of inventories by allotting proper

code number to each item and group should be done. This facilitates prompt recordings, locating

and dealing of materials.





Use of Standard Forms→ Standard forms should be used so that any information can be sent

to all departments within no time.

Internal Check System→ Audit should be done by an independent party to check effective-

ness of the inventory control system.

Proper Storing System→ Adequate and well-organized warehouse facilities with well-equipped

proper handling facilities must be there. Such facilities will reduce the wastage due to leakage,

wear and tea, sustained dust and mishandling of materials. Store location should be in between

the purchase department and production department, so that cost of internal transportation

can be minimized.

Proper Store Accounting→ An efficient inventory control necessitates maintenance of proper

inventory records. Any typical information regarding any particular item of inventory may be

taken from such records.

Proper Issuing System→ There should be a well-organized issuing system of material so that

production process does not suffer.

Fixing of various Stock Levels→ Minimum stock level, maximum stock level, re-order point,

safety level, etc. should be pre-determined to ensure the continuity of smooth production.

Determination of Economic Order Quantity→ Economic order quantity should be deter-

mined to minimize the cost of inventory.

Scope of Inventory Control

Inventory control can be used for:

Determination of Inventory Policies→ Inventories are the result of many interrelated deci-

sions and policies within an organization. These policies depend on companys internal

strengths and weaknesses and external opportunities and threats. The behavior of inventories

is the direct result of diverse policies and decisions within company. These relate to the invest-

ments, procurement, storage and finance which are directly influenced by inventory control sys-

tem.

Determining various Stock Levels→ Another important decision is maintaining inventory

and determining the right inventory level. An inventory level is a quantitative limit, which

should neither be much high nor too low. In both the cases, the total costs shall be higher. The

critical inventory levels are re-order level, minimum levels, maximum level, danger level and

average stock level.

Determining Economic Order Size→ Economic order size is that size of the purchase order

which gives maximum economy in purchasing any item of material. The other terms used for

economic order size are economic lot quantity and economic order quantity. The most advan-

tageous economic quantity will be at a point where the ordering cost and carrying cost are

equal, i.e., where total costs to order and to carry material are minimum.

Determining Safety or Buffer Stock→ The demand and supply can never be assessed ex-

actly. There is always a discrepancy between actual and estimated demand and supply quanti-

ties with fair degree of uncertainty. A buffer stock can be defined as the average inventory stock

available when the fresh supply arrives. It is presumed that this stock will be able to cope

(manage or handle) with the emergency. Factors affecting choices of buffer stocks are uncer-

tainty in demand, uncertainty in lead times and size of the batch. The larger the uncertainty

associated with any factor, large should be the size.

Determining Lead Time→ This is the time gap between placement of an order and the time of

actual supply. In other words, this is the time required to obtain the delivery of fresh supplies.

If this time is more, then the minimum inventory level will be high.

Determining Re-order Level/Point→ The reorder point refers to that inventory level at

which the procurement process of material should be initiated. In other words, reorder point is





the determination of the most appropriate timing for placing an order for the procurement of

materials.

Advantages of Inventory Control

1. There is no shortage of materials at any stage of production.

2. Materials are made available at most economical rates.

3. Delays or interruptions in production due to non-availability of material do not occur.

4. Exact and accurate delivery dates can be forecast.

5. Production schedules and delivery dates are maintained.

6. The materials are protected from spoilage, deterioration, pilferage etc.

7. There is an increase in overall efficiency/productivity of the company.

4.3 LEVELS OF INVENTORY

Minimum Inventory Level→ The minimum stock level represents the lowest quantitative

balance of materials in hand which must be maintained in hand at all times so that the assem-

bly line or production may not be stopped on account of non-availability of materials.

Minimum stock level = Re-order level – (Average/Normal usage

× Lead Time/Average Re-order period)

Maximum Inventory Level→ Maximum stock level represents the maximum quantity of in-

ventory which can be kept in store at any time. This quantity is fixed keeping in view of disad-

vantages of over-stocking.

Maximum Level = (Re-order level + EOQ) – (Minimum Usage

× Minimum Re-order period)

Re-order Inventory Level→ This is the fixed point between the maximum stock level and

minimum stock level at which the order for next supply of materials is to be placed to the ven-

dor/supplier.

Re-order Level = Maximum usage × Maximum Re-order period

Average Inventory Level→ It is average quantity which must be available for a given period

of time.

Average Inventory Level = [Minimum Level + Maximum Level] / 2

Application 4.1: From the following particulars, calculate: (a) Re-order level, (b) Minimum

level, (c) Maximum level, (d) Average level:

Normal usage 100 units per day Economic Order Quantity (EOQ) 5000 units

Maximum usage 130 units per day Minimum usage 60 units per day

Re-order period 25 to 30 days

Solution:

(a) Re-order level = Maximum usage × Maximum Re-order period

= 130 × 30 = 3900 units

(b) Minimum level = Re-order level – (Average/Normal usage × Average Re-order period)

= 3900 – (100 × 27.5) = 1150 units

Average Re-order period = (25+30)/2 = 27.5 days

(c) Maximum level = (Re-order level + EOQ) – (Minimum Usage × Minimum Re-order pe-

riod)

= (3900+5000) – (60 × 25) = 7400 units





(d) Average Level = [Minimum Level + Maximum Level] / 2

= (1150 + 7400)/2 = 4275 units

4.4 DETERMINING INVENTORY LEVEL

The object of inventory control is to establish level of inventory which will serve to minimize the

company's costs and maximize its revenues.

The amount of inventory a company should carry is determined by four basic variables:

(1) Order Quantity (2) Lead Time (3) Safety stock (4) Reorder point.

If the inventory is plotted against time, the result looks like a sawtooth pattern.

Starting from the instant when inventory OA is in stores, it consumes gradually in a quan-

tity from A along AD at a uniform rate, until point D is reached and again the inventory raises

to the original level when a fresh stock (order) is received.

Diagram 4.1 Inventory level

Re-order Point: It is pre-known that it takes days between initiating the order and receiving

the required quantity. Therefore, when the quantity reaches the point 'B' purchase requisition

is initiated. So that at the point 'D' when only reserve stock is left, the order material is sup-

posed to reach and again the total quantity shoots up to its maximum value i.e. the point 'A'.

Re-order point indicates that at this time the purchase order should be initiated and if not done

so, the inventory may exhaust and even the reserve stock utilized before the new material ar-

rives. It may result in stoppage of production.

Let us assume that, in our example, 1 month is required for delivery of the 500 units (order

quantity) and that the item is used at a rate of 200 units per month. As a result, 200 units will

be used during the procurement period. Suppose, the company does not want the inventory to

drop below 100 units, an order must be placed when the inventory level reaches 300 units. This

is equal to the minimum inventory of 100 units plus the 200 units which will be used while the

order is being processed.

In equation form we can say that:

Reorder point = Min. Inventory + Procurement time × Consumption rate.

In our example, the consumption rate was given as being 200 units per month and the pro-

curement time as 1 month. Substituting these values and the minimum inventory of 100 units

in the above equation we get.

Reorder point = 100 units + (1 month) × (200 units / month) = 300 units.

To continue with our example, we can say that the minimum inventory will be 100 units, the

reorder point will be 300 units, and the reorder quantity will be 500 units. Since, these 500

Consumption trend

Qu

an

tity

Time (Days) O

E

A

B

C

D

Q/2

Q

S = safety stock

R P

L





units are expected to be received when the inventory reaches to 100 units. The maximum inven-

tory on hand at any one time will be equal to order quantity + minimum inventory = 600 units.

Lead Time: There is always some interval between the time the need for the material is de-

termined and the time the material is actually received. This period is known as lead time. It

consists of requistition, time (R) + Procurement time (P).

Requisition time consists of time required to prepare purchase requisition and placing the

order to a selected vendor.

Procurement time consists of:

(a) Time taken to deliver purchase order to the seller,

(b) Time for the seller to get or prepare the inventory for dispatch.

(c) Time for inventory to be dispatched from the supplier and to reach the customer.

The lead time depends upon the following factors:

1. Shortest lead time items are those which a local supplier has in stock for immediate de-

livery, even in such a case, a company usually allows a week's lead time to permit both

the buyer and supplier to process the order efficiently and economically.

2. Much longer lead time items are those which are made to order or supplied by out of

town supplier and also more complex items.

3. Lead time also varies for identical items from supplier to supplier.

4. Lead time varies at various stages of business cycle. For example, a machine tool manu-

facturer may require one or two months time when the business is depressed but at the

peak period it may take a year or more.

Safety Stock: If the use rate and lead time could be predicted correctly, it would be possible to

limit maximum inventory of items to the order quantity. In this case the maximum inventory

would be equal to the order quantity Q. The average inventory would be equal to Q/2, and

minimum inventory would be zero.

In practice this cannot be done because:

(a) Supplier may fail to keep delivery promises.

(b) The forecast of use rate may be inaccurate.

Therefore, extra inventory is needed to protect against unreliable forecast and protection

against stock outs. This extra inventory is known as reserve stock, safety stock, base stock or

buffer stock. In this case the maximum inventory is equal to the order quantity + the safety

stock and minimum inventory is equal to the safety stock.

Safety stock can be calculated by the relation,

Safety stock = K × time leadduring nconsumptio Average ;

where, K is a factor based on acceptable frequency of stock-outs in a given number of years.

Excess safety stock will increase the inventory investment, inadequate safety stock fails to give

desired protection against stock-outs. The exact quantity of safety stock of an item depends

upon its lead time demand, carrying charges and importance of items which may be measured

in terms of its stock out costs.

4.5 INVENTORY MODELS

Economic lot size of an item depends on the following:

1. Possibility of placing repeat orders.

2. Nature of demand.

3. Availability of discount.

4. Single or multiple product manufacture.

Inventory models considering the above aspects can be classified as under.





Static Inventory Models: It is applicable in cases where only one order can be placed to meet

the demand. Repeat orders are either impossible or too expensive. Typical examples of items

under this group are: perishable goods like bread, vegetables etc., seasonal products like cool-

ers, umbrellas, crackers, sweaters, rain coats etc.

Dynamic Inventory Models: It is applicable for items where repeat orders can be placed to

replenish stock. Dynamic inventory models can be classified as:

1. Deterministic models.

2. Probabilistic models.

1. Deterministic Models: These models are based on the assumption that the demand as

well as lead time of an item are deterministic (i.e. known with certainty). Further these

models may be (i) purchase inventory models and (ii) Production inventory models.

Diagram 4.2 Deterministic inventory models

2. Probabilistic Models: These models take into account the variations in demand and lead

time of an item.

Assumptions in Deterministic Models

The following assumptions are made in deterministic models:

1. The demand of the item is known exactly for a given period.

2. The demand of the item occurs uniformly over a period of time.

3. The cost of placing an order is fixed and does not vary with the lot size. Similarly, set up

costs are also constant.

4. The inventory carrying charges are directly proportional to the order quantity. .

5. The price per unit is fixed and is independent of the order size (in case of fixed price in-

ventory models).

6. Orders are received instantaneously (Replenishment is instantaneous).

7. The item can be purchased free from restrictions of any kind.

8. The item has fairly long shelf life, there being no fear of deterioration or spoilage.

4.6 INVENTORY COSTS (COST ASSOCIATED WITH INVENTORIES)

The fixed order quantity system is based on selecting that order quantity which will minimize

the total variable cost of managing the inventory. In determining the 'Economic Order Quan-

tity' it is assumed that the cost of managing the inventory consists of two parts i.e.

(i) Ordering cost, (ii) Carrying cost.

Ordering cost (Inventory procurement cost): It is the cost of placing an order from a vendor.

This includes all costs incurred from calling for quotations to the point at which the item is

taken into stock. It consists of the expenditure connected with:

Production inventory models

Purchase inventory models

Deterministic models

Multiple product

inventory models

Single product

inventory models

Quantity discount

inventory models

Fixed price

inventory models





1. Receiving quotations.

2. Processing purchase requisition.

3. Receiving materials and then inspecting it.

4. Following up and expediting purchase order.

5. Processing sellers invoice.

If Co is the cost of placing an order and q the order quantity, then the unit cost of placing an

order =q

Co and this decreases at decreasing rate as the order quantity is increased. The bigger

the amount purchased in one lot lower the unit ordering cost.

If S = annual requirement then annual cost of ordering = Sq

Co .

Diagram 4.3 Inventory cost

Carrying cost: Carrying costs which are also known as holding costs are the costs incurred in

maintaining the stores in the firm. They are based on average inventory and consist of:

1. Storage cost: It includes: (a) Rent for storage facilities. (b) Salaries of personal and re-

lated storage expenses (Upkeep of material, record keeping) light, maintenance etc.

2. Cost of obsolescence: If two much inventory is there in the course of time the product

may cease its demand.

3. Cost of deterioration and spoilage etc.

4. Cost of insurance.

5. Cost of capital (interest lost on capital invested).

6. Sometimes special tax is to be paid for storing certain items.

7. Cost of pilferage (theft) and employing a person for safety.

Carrying costs are almost directly proportional to the order quantity. They are generally ex-

pressed as annual percentage of the unit purchase cost.

Assuming that the inventory decreases

through use or sale at a constant rate from

the order quantity to zero and then reple-

nished by another order quantity, the average

inventory is equal to q/2 carrying costs are

based on this average.

If Cu = Unit purchase cost

i = interest rate

Cui = annual carrying cost per unit.

So, annual carrying cost

2

qiCu

Diagram 4.4 Total Inventory Cost

In the Diagram 4.4 the ordering costs and the inventory carrying costs have plotted with re-

spect to quantity in Total cost is calculated by adding ordering cost and carrying cost. Total cost

is minimum at the point 'A', and hence A represents the Economic Order Quantity.

y

x

Ordering cost

Carrying cost

EOQ

A

Minimum

total cost

Total cost

An

nu

al

cost

Order quantity

q

Co

Order quantity

(a) Ordering cost

Ord

eri

ng c

ost

An

nu

al

cost

Carrying cost

Order quantity

(b) Carrying cost





Purchase Cost: This refers to the nominal cost of inventory. It is the purchase price for the

items that are bought from outside sources, and the production cost if the items are produced

within the organization. This may be constant per unit, or it may vary (differ) as the quantity

purchased/produced increases or decreases.

4.7 ECONOMIC ORDER QUANTITY (EOQ)

Economic Order Quantity is that order quantity which will minimize the total variable cost of

managing the inventory.

Method of Calculation of EOQ

Assuming that the inventory decreases at a constant rate from the order quantity 'q' to zero and

then replenished by another quantity.

Symbols used:

Let,

S = Annual consumption of the

product (units)

Co = Cost of placing an order

Cu = Unit cost of an item (unit price

Rs.)

q = Order quantity (units)

i = Interest rate charged per unit

per year.

Diagram 4.5 Economic order quantity

(Inventory carrying cost expressed as a percentage of average inventory investment).

Now, the total variable cost of managing the inventory per year

= Annual ordering cost + Annual cost of carrying the inventory = E say.

Therefore,

costcarrying

Inventory

Inventory

Average

order an

placing of Cost

yearper

orders of No.E

i.e. iCq

Cq

SE uo

2

to determine economic order quantity q that minimizes the total cost of managing the inven-

tory, we must differentiate E with respect to decision variable q and set the first derivative to

zero, i.e., for minimum total cost, dE/dq = 0.

Therefore, 02

12

iCq

SC

dq

dEu

o

i.e., iC

SCq

u

o2

Therefore, EOQ costcarrying Inventory price/unit

order an

placing of Cost

(units) nconsumptio

Annual2

q

An alternative formula for determining EOQ: The basic formula for EOQ, as derived

above, suggests the quantity (in terms of units) to be purchased to optimise the costs involved.

In this formula, consumption figure, S is considered in units (i.e. numbers, kgs, etc.). However,

sometimes, it is desirable to calculate order quantity in rupees instead of in units. This being

the case when the annual consumption of the items is specified in terms of monetary values.

The formula for EOQ in rupees can be derived as under:

Time

Qu

an

tity

EOQ

Q

Average

inventory

Reorder

Point

Q/2





Let A = Annual consumption in rupees (called annual usage)

Q = Economic order quantity (Rs.).

Now, we have iC

SCq

u

o2

Multiplying both sides of the equation by unit price, Cu, we get

u

u

ou C

iC

SCQCq

2

i.e., i

SCCQ uo2

i

ACQ o2

since,

uC

AS

When inventory carrying cost is specified in Rupees per unit.

Some firms prefer to specify the inventory carrying cost in "Rs. per unit" in place of "percentage

figure". The economic order quantity formula in such a situation can be stated as:

h

o

C

SCq

2

where Ch = Inventory holding cost (inventory carrying cost per unit per year)

(decimals)year per

costcarrying Inventory

unitper

costor Price

= Cu i.

Optimum Lot Size

If the item is being manufactured then it is necessary to determine the optimum lot size i.e. the

lot produced in one set up. Each lot that is manufactured requires a separate set up.

So, in this case if:

S = Annual production

N = Number of production runs per year

Co = Set up cost per production run

Cu = Unit cost of an item

i = Interest rate

Then, E = Annual carrying cost + Annual set up cost

NCN

SiC ou

2

where, S/N = Lot produced in one set up

For minimum cost, dE /dN = 0

Now, 02 2

ou CN

SiC

dN

dE

i.e., o

u

C

iSCN

2

2

or, o

u

C

iSCN

2

where N = optimum number of production runs.

Now, optimum production quantity per production run

runs production optimum ofNumber

productionannual Total Q





i.e., iC

SC

C

iSC

S

N

SQ

u

o

o

u

2

2

Inventory Model Considering Quantity Discount

The EOQ formula under the basic EOQ model is based on the assumption that the price per

unit is fixed irrespective of the order quantity. However, sometimes suppliers offer discount if

large quantities are purchased. Quantity discounts reduce material cost and procurement cost

but increase in inventory carrying cost. Therefore, a decision has to be made whether the pur-

chaser should stick to EOQ or raise the order quantity to take advantage of price discount. The

following procedure is adopted to take decision in such cases:

1. Calculate EOQ at different price levels.

2. Determine the quantity to be purchased at each price level.

3. Calculate annual total cost including annual material cost at the quantities determined

under step above.

4. Select an optimal purchase quantity which will involve the lowest total annual cost.

Application 4.2: ABC manufacturing company requires special involute gears at the rate of

300 numbers per year. Each gear costs Rs. 36. The procurement cost and inventory carrying

cost are estimated at Rs. 30 and 20% respectively.

If the supplier offers a discount of Rs. 2/- per gear on an order of 200 or above, will it be ad-

visable to purchase higher quantity?

Solution: Now.

S = Annual consumption = 300, Co = Procurement cost per order = Rs. 30,

1uC = Basic price per unit = Rs. 36,2uC = Discounted price per unit = Rs. 34,

i = inventory carrying cost (in decimals) = 0.20

The above prices are valid for the following quantities:

Price Range of quantity

Rs. 36 0 < q < 200

Rs. 34 200 q

The procedural steps are as follows:

1. Calculate EOQ at different price levels.

Table 4.1 Application 4.2

Price Range of purchase

quantity EOQ

iC

SC

u

o2

Quantity to be purchased

at the indicated price

1 2 3 1

Rs. 60 0 < q < 200 5020.036

300302

50

Rs. 56 250 q 5120.034

300302

200

2. Determine the quantity to be purchased at each price level as indicated in column 4 of

the Table 4.1.

3. Calculate annual total cost including annual material cost at quantities determined un-

der step 2.






Cost Order quantity

(a) Annual cost of materials (CuS) 300 × 36

= Rs. 10,800

300 × 34

= Rs. 10,200

(b) Annual procurement cost

Sq

Co

3050

300

= Rs. 180

30200

300

= Rs. 45

(c) Annual inventory carrying cost

iqCu 2

1

20.036502

1

= Rs. 180

20.0342002

1

= Rs. 680

Annual total cost [C = a + b + c] = Rs. 11,160 = Rs. 10,925

4. Select an optimal purchase quantity.

From the annual total cost figures calculated above, we find that the cost incurred is the least

when quantity purchased is 200 numbers.

Therefore, economic purchase quantity = 200 numbers.

Application 4.3: Calculate EOQ, if it is given that annual usage = 60 units, procurement cost =

15 per order, cost per piece = 100 and cost of carrying inventory is 10%.

Solution: Given that Co = 60, S = 15, Cu i = 10 (10% of ₹ 100)

1341.1310

156022EOQ

iC

S C

u

o units.

Application 4.4: A company requires 16000 units of raw material costing Rs. 2 per unit. The

cost of placing an order is Rs. 45 and the carrying costs are 10% per year per unit of the average

inventory. Determine: (i) the economic order quantity (ii) cycle time (iii) total variable cost of

managing the inventory.

Solution: Now, S = 16000, Co = Rs. 45, Cu = Rs. 2, i = 0.1.

(i) 26841.02

160004522

iC

SCq

u

o units.

(ii) No. of orders per year q

nconsumptioAnnual

62684

16000

Cycle time6

1

rorders/yea of No.

1 year = 2 months.

(iii) Total variable cost of managing the inventory.

26841.022

1645

2

1

qiC

q

SCE u

o

= 270 + 268.4 = Rs. 538.4

Application 4.5: ABC manufacturing company needs ball bearings of worth Rs. 28,800 per

year. The cost of placing an order is Rs. 48 and inventory carrying cost as a percentage of aver-

age inventory investment is 12%. Determine:

(i) Value of each assignment.

(ii) Number of orders per year.





Solution: In this example, value of each assignment i.e. value of EOQ is to be determined and

the annual consumption is specified in monetary values.

(i) Value of each assignment = S × Cu = Rs. 18800

where S = annual consumption in units 4

Cu = unit cost of an item.

Value of each assignment = EOQ × Cu = qCu

Now, iC

SCq

u

o2

Therefore, i

SCCC

iC

SCCq uo

u

u

ou

22

Substituting the values we get,

12.0

28800482uCq Rs. 4800

(ii) Number of orders/year 64800

28800

Therefore, the ball bearings should be procured six times in year and the value of

each assignment is Rs. 4800.

Application 4.6: A company needs 600 units per month, the procurement cost is Rs. 36 per or-

der, the cost of holding it in stock is Rs. 1.20 per unit per year, determine the quantity that

should be procured at a time to optimise the cost involved. If the consumption of the above item

increases to 40 numbers per day and its actual inventory cost is Rs. 0.50 per unit per month,

what will be the revised EOQ?

Solution: Given that: S = Annual consumption = 600 × 12 = 7200

Co = Rs. 36

Cu.i = inventory carrying (cost per unit per year) = Rs. 1.20

Now, EOQ 65820.1

72003622

iC

SCq

u

o units.

Revised EOQ: Assuming 300 working days in a year,

S = 40 × 300 = 12000

Co = Rs. 36

Cu.i = 0.50 × 12 = Rs.6.

3806

120003622

iC

SCq

u

o units.

Application 4.7: A company needs 2000 units per month. Cost of placing an order is Rs. 40. In

addition to Re. 0.50 the carrying costs are 10% per unit of average inventory per year, the pur-

chase price of Rs. 10.00 per unit Find the economic lot size to be ordered and the total minimum

cost.

Solution: Now, S = 2000 × 12 = 24000 unit/year

Co = Rs. 40, Cu = Rs. 10

Now, inventory carrying cost is 10% per unit of average inventory in addition to Re. 0.50.

Hence, Cui = 0.50 + 10% of Rs. 10.00

= Rs. 1.50 per unit of average inventory.





Then, 113250.1

240004022

iC

SCq

u

o units

Total minimum cost = Cost of material + Procurement cost + Inventory carrying cost.

50.12

113240

1132

240001024000

= Rs. 2411697.06

Application 4.8: A manufacturer purchases items in lots of 800 units which is a four months

requirement. The cost per unit is Rs. 100 and the ordering cost is Rs. 120 per patch order. The

inventory carrying cost is estimated as 20% of the average inventory investment.

(i) Determine the annual variable cost managing the inventory.

(ii) How much saving can be obtained from the EOQ purchases?

Solution: Now, S = 800 × 3 = 2400 units

Co = Rs. 120, Cu = Rs. 100, i = 0.20

(i) So, iCq

q

SCE u

o

2

2.01002

800

800

2400120Rs. 8360

(ii) Now, 1702.0100

2400012022

iC

SCq

u

o units

Then, iCq

q

SCE u

o

2

2.01002

170

170

2400120Rs. 3394.12

Therefore, annual saving if EOQ purchases are made in place of purchasing after every four

months. = Rs. 8360 Rs. 3394.12 = Rs. 4965.88.

4.8 ECONOMIC ORDER QUANTITY WHEN STOCK REPLENISHMENT IS NOT IN-

STANTANEOUS (GRADUAL REPLENISHMENT)

It is a more general and realistic situation. Suppose it takes time 1t for replenishment and time

2t is required for inventory to be exhausted. In this case each order cycle is of )( 21 tt time

units. Again the demand rate in each cycle is assumed to be uniform. The inventory pattern

under this model appears as shown in Diagram 4.6.

Let, S = Annual consumption,

Cu = cost per unit,

Co = cost of placing an order,

P = rate of replenishment per unit of time (in

units),

d = daily consumption rate,

1t = time for replenishment,

i = inventory carrying cost (decimal).

Then inventory under this system builds up at the

rate (P d) and is maximum at the end of production

run.

Diagram 4.6 Inventory built-up under non-

instantaneous replenishment

Maximum inventory at the end of production run = (P d) 1t ,

Inven

tory

Level

Time

T

2t

1t





Therefore, average inventory 2

)( 1tdP

P

qdP

2

)((where q = quantity replenished during time 1t = P × 1t )

P

dq1

2

Thus, annual inventory carrying cost iCP

dqu

1

2

And annual cost of ordering oCS

q

Therefore, annual variable cost of managing the inventory

= Annual cost of ordering + Annual inventory carrying cost

iCP

dq

q

SCE u

o

1

2

For minimum total annual cost dE/dq = 0.

012

12

iC

P

d

q

SC

dq

dEu

o

or,

iCP

d

SCq

u

1

2 0

Application 4.9: The XYZ manufacturing company requires 1000 units of particular item per

month; the average demand occurs at the rate of 30 units per day. The production process is ca-

pable of producing 50 unita per day. Each item produced in the plant costs rupees ten. The set

up cost per order is Rs. 100. The inventory carrying cost is 15% of the average inventory cost.

Calculate:

(i) The quantity to be produced in each production run.

(ii) Number of production runs per year.

Solution: Now, S = 1000 × 12 = 12000 units,

Co = Set up cost = Rs. 100,

Cu = unit cost of item = Rs. 10,

p = rate of replenishment (daily production rate) = 50,

d = daily consumption rate = 30,

i = 0.15 %,

(i) Now, 2000

15.01050

301

120001002

1

2 0

iCP

d

SCq

u

units

(ii) No. of production runs 62000

12000

q

S.

4.9 ECONOMIC LOT SIZE WHEN SHORTAGES ARE ALLOWED

There are situation in business enterprises wherein due to some other considerations shortages

are permitted.

Assumptions

1. Replenishment is instantaneous.





2. Back orders are carried out as the fresh stock arrives.

3. Time period of one cycle is fixed.

The situation is illustrated graphically in Diagram 4.7. The period of one cycle is t units.

Demand is more than supply. At the initial stage, there are q units in inventory which are ex-

hausted by time 1t . Then shortages are allowed for time 2t , after which inventory is replenished

instantaneously.

Evidently, ttt 21 .

The shortages are equal to S q (where, S = annual

demand)

Shortages cost for time 11 tiCqt u ,

The cost due to shortages for time 22 )(2

1tCqSt s

where, Cs = per unit shortage cost

Let the number of units ordered at time 1t = Q units

Then, q = Q Sh where Sh = Shortage in time 2t .

Diagram 4.7

The average inventory level in time

t

ttqtt

21

21

02

1

t

tSQ h 1 )(2

1

Now, if S represents the demand, then t = Q/S.

and, S

SQt h1 i.e.,

Q

SQ

t

t h1 .

Therefore average inventory level in time 121

)(

2

1t

t

SQtt h

Q

SQ h )(

2

1 2

Similarly, average back orderQ

Sh

2

2

Total variable cost of managing inventory osh

uh C

Q

SC

Q

SiC

Q

SQ

2

)(

2

122

Differentiating with respect to Q and equality to zero, we get

iC

iCCSSC

iC

SCiCCSQ

u

usho

u

oush )(2]2)([ 22

If E is also to be minimized with respect to Sh, then we get,

iCC

iCCSCq

us

uso )(2

Application 4.10: The ABC manufacturing company requires 1250 components per month

throughout the year for manufacturing electronic equipments. If ordering cost is Rs. 50 per or-

der, unit cost is Rs. 5.00 per component and annual inventory carrying costs are 10%, find EOQ.

If the company decides to operate with a back order inventory policy then taking back order cost

to be Rs. 7.50 per unit per year, find revised EOQ.

t

Time

Inven

tory

Level

2t 2t

1t 1t





Solution: Now, Co = Rs. 50, i = 0.20, Cu = Rs. 5, S = 1250 × 12

Then, EOQ 17321.05

1212505022

iC

SCq

u

o units

When back orders are permitted, then for shortages to be minimum.

EOQ su

suo

iCC

CiCSC )(2

178950.71.05

)50.71.05(121250502

units

4.10 ECONOMIC LOT SIZE WITH DIFFERENT RATE OF DEMAND IN DIFFERENT

CYCLES (REPLENISHMENT IS INSTANTANEOUS)

With varying demand rate the stock will be exhausted at different lime periods. With the policy

of ordering same quantity for replenishment of inventory, the situation can be represented

graphically as shown in Diagram 4.8.

Let S1, S2, ...... Sn = demand in different time pe-

riods,

S1 + S2 + S3 + ......... Sn = total demand in time T,

T = t1 + t2 + t3 + ......... tn.

Cost of ordering in time oo C

q

ST

Cost of purchasing S units = S × Cu.

Now inventory carrying cost for time T

Diagram 4.8

= (Average inventory in time t1) Cu.i + (Average inventory in time t2) Cu.i + ..

+ (Average inventory time tn) Cu.i.

iCtqiCtqiCtq unuu )(2

1 )(

2

1 )(

2

121

iTCqiCtttq uun

2

1 )(

2

121

Hence the total cost incurred in time T

iTCqSCq

SCuu

o

2

1

Minimizing with respect to q, we get, EOQ

iTC

SCq

u

o2

Here, n

n

ttt

SSS

T

S

21

21 = Average demand in different periods.

Application 4.11: A company requires 5000 units per year which costs Rs. 10 per unit. Order-

ing cost is estimated to be Rs. 100 per order, carrying costs are 15% per annum of average In-

ventory, The supplier is prepared to give 2% discount in price if the company purchases 10,000

units or more but less than 20,000 lot size. A further discount of 1% in price of original value is

available on the orders of 20,000 or more units. Find economical lot size and the minimum total

cost.

Solution: Step 1: Calculate EOQ at different price levels, and Determine the quantity to be

purchased at each price level which equals either EOQ or price-break quantity.

Time

Inven

tory

Level

2t 3t 1t






Price level EOQ Quantity to be purchased

at the indicated price

1. Basic price

(without discount) (Rs. 10) 15.010

000,501002

= 2582

2582

2. Rs.9.80

(2% discount) 15.080.9

000,501002

= 2609

10000

3. Rs. 9.70

(3% discount) 15.070.9

000,501002

= 2622

20000

Step 2: Calculate total cost including annual material cost at the quantities decided above.


Cost element Quantity to be purchased (q)

2582 10,000 20,000

1. Annual cost of ma-

terial (S × Cu)

50,000 × 10

= Rs 5,00,000

50,000 × 9.80

= Rs. 4,90,000

50,000 × 9.70

= Rs. 4,85,000

2. Annual procurement

costq

SCo 2582

000,50100

= Rs 1936.50

000,10

000,50100

= Rs. 500

000,20

000,50100

= Rs.250

3. Annual inventory

carrying cost iqCu2

1

2

258215.010

= Rs. 1936.50

2

000,1015.010

= Rs.7500

2

000,2015.010

= Rs. 15000

Annual Total cost = Rs. 503873 = Rs. 4,98000 = Rs. 500250

The EOQ = 1000 units and minimum total cost = Rs. 498000.

4.11 RE-ORDERING SYSTEMS (INVENTORY CONTROL SYSTEMS)

Though EOQ formula gives the optimum quantity for re-ordering it does not give any informa-

tion about the time, when re-ordering should be done. In actual practice the problem becomes

serious due to uncertainty produced by the variation in the rate of consumption and variation in

delivery period. In order to overcome this problem, systematic inventory ordering system should

be designed. The ordering system should answer die following questions. How much to-order?

When to order?

The common systems used for controlling the ordering level are:

1. Two bin system.

2. Periodic inventory ordering system.

3. Combination of two bin and periodic inventory ordering systems.

Two Bin System

Two bin system is also called as fixed order quantity system or mini-max system. This is the

oldest and most commonly used inventory control system. In this system the stock location of

each item is divided in two sections (bins). The first bin holds the normal issue stock and it is

intended for satisfying current demand. The second bin holds the reserve supply of materials

equal to the amount that will be consumed during the lead time plus safety stock if any.





The second bin comes into use only after the first bin

is emptied. Therefore, when the first piece is with-

drawn from the second bin, the purchasing order is to

be initiated. When a fresh stock is received, the level

of the second bin is restored to its original high value

and the balance is put in the first bin from which cur-

rent demand is now supplied again.

In most of the cases actual second bin is not always

required. The reorder point quantity can be separated

from the normal issue stock by wrapping it or by plac-

ing a separator.

Diagram 4.9

Advantages of Two Bin System:

1. The main advantage of the two bin system is simplicity and reliability.

2. It is comparatively cheap to operate and easy to explain to new stock control personnel,

3. Reorder point is indicated easily.

Disadvantages of Two Bin System:

1. When different items have to be ordered from the same supplier in order to reduce

transportation cost or to take advantage of credit or discount, it is necessary to order

several items simultaneously, even when only one reaches the reorder point, while the

basic idea of the two bin systems is that items are independent of each other in the re-

plenishment procedure.

2. Because of absence of adequate data on stock levels and consumption rates in the sim-

pler form, it is difficult to re-evaluate order quantity.

The bin system is more suitable for „C class items.

Periodic Inventory Ordering System (Ordering Cycle System)

The periodic inventory ordering system is based on periodic reordering of all items. There-

fore in this system orders for replenishment are placed at fixed intervals of time. The order

quantity is not fixed but the ordering interval is fixed. The order quantity is determined such

that the total inventory is always brought up to certain level. In this system the fixed ordering

interval may be fortnightly, monthly, quarterly etc. And order quantity is decided by consider-

ing the balance stock. Diagram 4.10 shows the periodic inventory cycle system.

Advantages of Ordering Cycle System:

1. The main advantage of this system over the

two bin system is that all orders for reple-

nishment are issued at the same time.

2. The ordering mechanism is regular and not

subjected to warning signals from the stores.

Disadvantages of Ordering Cycle System:

Usually, more stock is held when this system is

adopted than with two bin system. The ordering cycle

system may be classified as:

Diagram 4.10

(a) All items in one cycle (b) Multicycles.

All items in one cycle: In this type all the items are replenished every cycle. This method is

particularly useful when the number of items are not too large and when the differences in the

use rate are not much.

Multicycle: In this type the items are divided into groups and each group has its own ordering

cycle, independent of the other groups. The groups are formed either by selecting items that

Time t t t t

3q 2q 1q

Inven

tory

Level

B

q

Reorder

point R

Time

Inven

tory

Level

2nd

Bin

1st

Bin

t S





have to be ordered from the same vendor or by taking items whose use rates are fairly equal.

This system is adopted when stores have to deal with a large variety of items.

Combination of the Two Bin And Ordering Cycle Systems: There are several stock control

systems in industry that try to combine certain advantages of the two bin and of the ordering

cycle system. Two bin system is more suitable for 'C' class items whereas fixed interval system

with varying order quantity is more economical for 'A' and 'B' class of items.

Periodic Review System

There are two most important review systems of inventory control. These are the following:

P system (or the Cycle System): This system has a fixed order period and so lets the size of the

order vary with fluctuations in demand. The amount that is ordered will vary in accordance

with whether the amount in inventory at the time of review is lower or higher than the average

demand.

Q System (or Two-Bin System or Perpetual Inventory System): The Q system has a fixed

order size and a varying order period.

Difference between P and Q types of Inventory Control System

No. Basis P Type Q type

1 Triggering Time triggered Event triggered

2 When to place or-

der

The time period is fixed for this

and hence also called the cycle

system.

The time is not fixed to place an

order.

3 Order quantity The order quantity is not fixed.

It depends on lead time and the

quantity on hand at the time of

ordering. Also called fixed-order

quantity system.

In this system EOQ is ordered

each time, as soon as the reorder

level is reached and hence the

system is called 0 (quantity) type

system.

4 Size of inventory The inventory size is large as

compared to fixed quantity sys-

tem

The inventory is small as com-

pared to fixed review period.

5 Supervision It does not need constant super-

vision as the quantity on hand

is the only requirement at the

time of ordering.

It needs constant supervision as

the quantity received each time

has to be recorded and EOQ

reached has to be found.

6 System time It has fixed time period system,

also called 1-Bin system.

It has fixed quantity system, also

called 2-Bin system.

4.12 INVENTORY CONTROL TECHNIQUES

Inventory in a company consists of thousands of different items in stock. The control of all these

items creates a serious problem to the management, if the same amount of control is exercised

on each of these items.

Therefore, in order to execute proper control, it is necessary to take selective approach and

find the attention required for each item according to its importance. This is essential for

achieving maximum benefits with minimum efforts and cost.

Depending upon the advantages and purposes, different analyses have been developed to

help in bringing practical solution to the problems of inventory control. Several techniques of

inventory control are in used and it depends on the convenience of the firm to adopt any of the

techniques.





The commonly used systems can be classified as:

1. ABC Analysis (Always Better Control or Alphabatical Approach),

2. SDE Analysis (Scarce, Difficult, Easily Available Analysis),

3. VED Analysis (Vital Essential and Desirable Analysis),

4. HML Analysis (High, Medium and Low Cost Inventory Analysis),

5. FSN Analysis (Fast moving. Slow moving and Non-moving items analysis),

6. SOS Analysis (Seasonal , Off-Seasonal), and

7. MNG Analysis (Moving items, Non-moving items, Ghost items analysis).

ABC Analysis

This is based on a very universal Pareto's Principle that a few high usage value items constitute

a major part of the capital invested in inventories, whereas bulk of items in inventory, having

low usage value constitute insignificant part of the capita. In any large number we have signifi-

cant few and insignificant many.

In ABC analysis (Always Better Control OR Always Be Careful System) it contemplates to

classify all the inventory items into three categories based on their usage values. Items of high

usage value but small in number are classified as 'A' items and would be under strict control. 'C'

items are large in number but require little capital and would be under simple control. Items of

moderate value and size are classified as 'B' items and would attract reasonable attention of the

management.

Under this analysis, the materials are divided into three categories viz., A, B and C. Past ex-

perience has shown that almost 10% of the items contributes to 70% of value consumption and

this category is called A category. About 20% of the items contribute to about 20% of value of

consumption and this is known as category B materials. Category C covers about 70% of

items of materials, which contribute only 10% of value of consumption. There may be some

variation in different organizations and an adjustment can be made in these percentages.

Class Number of items (%) Value of items (%)

A 10 70

B 20 20

C 70 10

A-B-C analysis helps to concentrate more efforts on category A since greatest monetary ad-

vantage will come by controlling these items. An attention should be paid in estimating re-

quirements, purchasing, maintaining safety stocks and properly storing of A category materials.

These items are kept under a constant review so that a substantial material cost may be con-

trolled. The control of C items may be relaxed and these stocks may be purchased for the year.

A little more attention should be given towards B category items and their purchase should be

undertaken at quarterly or half-yearly intervals.

A very simple empirical way to classify items may be adopted as follows:

Average annual usage value items ofnumber Total

yearper costmaterial Total X

A class items 6 X ,

C class items 0.5 X ,

In between we have B class items.

A Items: In the total inventory items, A items are few in number and thus represents a small

percentage of the total items. However, due to high cost and huge consumption, they represent

a large percentage of company's total expenditure. It is common that approx. 10% of the total

quantity of items represents 70% of the amount spent on these items. These items need accu-





rate, careful records, careful handling and storage under tight control. Minimum and maximum

limit and re-order point is set for A items. Such items should be thought of in advance and pur-

chased well in time. A detailed record of receipt and issue should be kept and proper handling of

facilities should be provided for them.

Such items being costly are purchased in small quantity oftenly and just before their use.

This, of course, increases the procurement cost and involve little risk of non-availability. How-

ever, inventory holding cost decreases and problems of storage and care taking are minimised.

B items: These are middle level items which do not require as detailed and close control as A

items, but they need move attention and control than C items. These items usually represent

20% of the total quantity of the items (approx.) and represent 15% to 20% of the total expendi-

ture on items.

C items: These are numerous in expensive items. They generally represent 70% to 75% of the

total quantity and 5 to 10% of the total expenditure on materials.

Control policies for A items:

1. A items are high valued items hence they should be ordered more, but in small quanti-

ties in order to reduce capital locked up at any time.

2. The future requirement must be planned in advance so that the required quantities ar-

rive a little before they are required for consumption.

3. Purchases and stock control of A items should be looked into by the top executives in

purchasing department.

4. Maximum efforts should be made to expedite the delivery.

The safety stock should be as less as possible (of 15 days or less).

A items are subjected to tight control regarding their issue, balance, storing method etc.

5. Ordering quantities, reorder point and minimum stock level should be revised more fre-

quently.

Policies for B items:

1. The policies for B items in general are in between those for A and C.

2. Order for these items must be placed less frequently.

3. The safety stock should be medium (3 months or less).

4. B items are subjected to moderate control.

Policies for C items:

1. C items are the low valued items therefore the safety stock of such items should be lib-

eral (requirement of 3 months or more).

2. Annual or six-monthly orders should be placed to reduce paper work and ordering cost

and to get advantage of quantity discount for large orders.

3. In case of these items only routine check is required.

Applications of ABC Analysis: The control policies for A, B and C items are based on the

principles:

1. To keep capital tied up in inventories as low as practicable.

2. To ensure that all the materials would be available when required.

ABC analysis can be effectively used in material management. The various stages where it can

be applied are:

(i) Information of items which require higher degree of control,

(ii) To evolve useful reordering strategy,

(iii) Stock records.

(iv) Priority treatment to different items.

(v) Determination of safety stock limits.

(vi) Stores layout.

(vii) Value analysis.





Steps in ABC Analysis:

1. Calculate the annual usage in units for each item.

2. Calculate annual usage of each item in terms of rupees (annual usage × unit cost).

3. Rank the items from highest annual usage in rupees to lowest annual usage in rupees.

4. Compute total value.

5. Find the % of high, medium and low valued items in terms of total value of items.

6. A graph can be plotted between % of items on x-axis and % of total value of item on y-

axis.

Diagram 4.11

Application 4.12: The following example will give the clear and wide information about ABC

analysis


Item Annual usage units Unit cost ₹ Annual usage ₹ Ranking

a 30,000 0.01 300 6

b 2800 1.5 4200 1

c 300 0.10 30 9

d 1100 0.05 550 4

e 400 0.05 20 10

f 2200 1.00 2200 2

g 1500 0.05 75 8

h 8000 0.05 400 5

i 3000 0.30 900 3

j 800 0.10 80 7

Table showing ABC analysis (ABC Ranking)


Item

₹

Annual usage

Annual usage ₹

Cumulative

percent

Cumulative Ranking Annual

usage units

Cumulative

Percentage

a 4200 4200 41.91 A 2800 5.88

b 2200 6400 73.10 A 2200 9.98

c 900 7300 83.38 B 3000 15.97

d 550 7850 89.66 B 1100 18.16

e 400 8250 94.23 B 8000 34.13

f 300 8550 97.66 C 30,000 94.01

g 80 8630 98.57 C 800 95.68

% o

f to

tal

valu

e

100

90

80

70

60

50

40

30

20

10

10 20 30 40 50 60 70 80 90 100

% of items





h 75 8705 99.43 C 1500 98.60

i 30 8735 99.77 C 300 99.20

j 20 8755 100 C 400 100

SDE Analysis

S-D-E analysis takes into account various purchasing problems. The various purchasing prob-

lems may be non-availability, scarcity, long lead time, unreliable supply sources, etc. This

analysis uses the criteria of the availability of items. In this analysis,

S refers to scarce items, which are short in supply and their availability is scarce. This includes

imported items e.g. imported items which are generally in short supply.

D refers to difficult items, which cannot be procured easily. These items may not be available in

local market and have to be procured from far off cities or these are items for which there are a

limited number of suppliers, or items for which quality suppliers are difficult to get.

E refers to easily available items from the local markets.

The SDE analysis proves to be very useful in industrial situations where certain materials

are scarce in supply and gives proper guidelines for deciding inventory policies. This analysis

helps in inventory control by the formulation of purchasing policies. For scarce materials, for-

ward purchasing policies; for difficult materials, schedule purchasing policies, and; for easy ma-

terials, contract purchasing policies are commonly adopted.

VED Analysis

In VED analysis, the items are classified on the basis of their criticality to the production proc-

ess or other services. VED analysis specially pertains to the classification of maintenance spare

parts. The spares are split into three categories of importance from the viewpoint of functional

utility. In the VED classification of materials,

V stands for vital items, are the most critical having extremely high opportunity cost of short-

age and must be available in stock when demanded. If these items go out of stock or are not

readily available there will be loss of production.

E is for essential items, are quite critical with substantial cost associated with shortage and

should be available in stock by and large. Without which the performance or efficiency of the

equipment will be reduced. Non-availability of these items may result in temporary loss of pro-

ductivity.

D stands for desirable items. The remaining items which do not cause any immediate loss in

production fall under this category. Desirable group of items do not have very serious conse-

quences if not available when demanded but can be stocked for the sake of efficiency and less

fatigue.

The VED analysis is done mainly in respect of spare parts. Obviously the % risk of shortage

with the vital group of items has to be quite small but calling for a high degree of service. With

essential category we can take a relatively higher risk of shortage and for desirable category

even higher. Since even a C- class item maybe vital or an A- class item may be desirable we

should carry out a two-way classification of items grouping them in 9 distinct groups as

(1) A-V (2) A-E (3) A-D (4) B-V (5) B-E (6) B-D (7) C-V (8) C-E (9) C-D

Now for each of the above nine categories, attention can be at various levels and we can plan

for inventories accordingly.

HML Analysis

This is similar to the ABC analysis except that, in the analysis, the items are classified on the

basis of unit cost rather than their usage value. In ABC analysis total annual usage is consid-





ered. We may come across quite a few items which fall in B category, although their unit cost is

high. In HML analysis unit cost is also considered in order to find out the importance cf the

items. Limits of unit cost are fixed for high costs items (H), Medium costs items (M) and low

cost items (L) and all the items are segregated into H, M, and L categories depending upon their

unit cost This analysis is quite useful in deciding the safety stock in relation to the availability

of the material (SDE analysis).

This type of analysis is useful for keeping control over materials consumption at the depart-

mental level. For example, the management may determine that all items of the unit value

above ₹ 2000 will be H items, between ₹ 500 and ₹ 2000 will be M items and those below ₹ 500

will be L items. On this basis, the management may delegate authorities to various subordinate

officers to buy small cash items. The management may also decide that items of unit value

above ₹ 2000 will only be sanctioned by the General Manager.

FSN Analysis

Based on the consumption pattern of the items, the FSN classification of items is

F Fast moving S Slow-moving N Non-moving This speed classification helps in the ar-

rangement of stocks in the stores and in determining the distribution and handling patterns.

When analysis is carried out on the basis of the rate of movement of materials in stores or on

the basis of consumption pattern of components, it is known as the FSN analysis. The classifi-

cation comes in very handy when it is necessary to control obsolescence. The demand for fast

moving items is generally high. Thus, special care should be taken in respect of these items;

otherwise, the production may be interrupted due to the shortage of such materials. Inventories

which have only a low turnover are brought under the category of slow-moving items. These

items are not issued at frequent intervals.

The items with almost nil consumption are brought under the category of non-moving items.

All obsolete inventories constitute this category. There may be several reasons for bringing an

item into the Non-moving category, e.g., there might have been a change in technology or

change in the specification of a particular spare part or the item might no longer be in use.

FNSD Analysis

This analysis divides items into 4 categories in the descending order of their consumption rate.

F stands for fast moving items, stocks for which are consumed over a short span of time. Their

stocks must be observed constantly and all steps should be taken to replenish the stocks in time

to avoid stock- out situation.

N denotes normal moving items, stocks, for which are exhausted over a year so.

S represents slow moving items. Such items take 2 years or more to be consumed at the existing

consumption rate but they will be consumed any way. Their stock level must be carefully re-

viewed before placement of their replacement orders to minimise the risk of surplus stock being

left when such items become obsolete or dead.

D means dead stock and for such items no further demand can be foreseen. Dead stock repre-

sents money spent that cannot be realised but it occupies the useful space. Efforts should be

made to find alternative uses for such items, failing which they must be disposed off.

MNG-Analysis

In this analysis,

M refers to moving items. The rate of consumption of these items is quite high.

N refers to Non-moving items. These items are those which are not consumed in last one year.





G refers to Ghost items. These are those items which have nil-balance, both at the beginning

and at the end of last financial year and there were no transactions (receipts or issues) during

the year. These are non-existing items (for a fairly long period) for which the storekeeper keeps

bin-cards showing nil balance.

SOS Analysis

SOS analysis is based on the nature of supplies, where in,

S represents the Seasonal items and

OS represents the Off-Seasonal items.

This classification of items is done with the aim of determining proper procurement strate-

gies. The SOS analysis is made on the basis of the nature of supplies.

The seasonal items which are available only for a limited period should be produced and

stocked for meeting the need of the full year. The agriculture produce like raw mangoes, raw

materials for cigarette and paper industries, etc. are examples of such items. The prices of the

seasonal items which are available throughout the year are generally less during the harvest

season. The quantity required of such items should, therefore, be determined after comparing

the cost savings on account of lower prices, if purchased during season, with the higher cost of

carrying inventories to that if purchased throughout the year. The quantities needed of off-

seasonal items are required to be decided on different considerations.

XYZ Analysis

It is based on the closing inventory value of different items. Items whose inventory values are

high are classified as X items while those with low investment in them are termed as Z items.

Other items are the Y items whose inventory value is neither too high nor too low.

It can be easily visualised that the various types of analysis discussed above are not mutu-

ally exclusive. They can be and often are used jointly to ensure better control over materials.

For example you have seen above that ABC and VED analyses are combined together to classify

and control inventory depending on whether the items are A-V, B-- E, C--D etc. Similarly FSND

- XYZ combine classification exercise will help in timely prevention of obsolescence.

A Summary of Selective Control Techniques

Selective Control Techniques Basis of Classification Chief Uses

ABC Consumption value Controlling raw material

components and work in-

progress inventories.

VED Criticality of the item Determining the inventory

level of spare parts.

FNSD Consumption rate of the

items

Controlling obsolescence.

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