04/07/23Maroof Hussain Sabri1

Economic order quantity

‘EOQ’

Inventory

Definition

“The term inventory include materials- raw, in progress, finished packaging, spares, and other stock in order to meet an un expected demand or distribution in the future.”

Inventory cost

Ordering costs; Carrying cost; Capital cost; Store space cost; Inventory service cost; & Inventory risk cost;

Inventory management & control

Inventory management involves the: “Development and administration of

policies systems and procedures, which will minimize total cost related to inventory decisions and related functions such as production scheduling, purchasing and traffic”.

Inventory control Techniques

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ABC Technique; HML Technique; VED Technique; SED Technique; FSN Technique; &

EOQ Technique.

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What is EOQ ?

Economic order quantity is one of the techniques of inventory control which minimizes total holding and ordering costs for the year.

The economic order quantity is the technique

which solves the problem of the materials manager.

Definition of EOQ

“ EOQ is essentially an accounting formula that determines at which the combination of order, costs and inventory carrying cost are the least. The result is the most cost effective quality to order. In purchasing this is known as order quantity, in manufacturing it is known as the production lot size.”

- Dave Piasecki

EOQ Models

‘Q’ Models; &

‘P’ Models.

Assumption of the EOQ Models

Demand is known and is deterministic, i.e. constant;

The lead time, i.e. the time between placement of the order and the receipt of the order is known and constant;

The receipt of inventory is instantaneous. In other words the inventory from an order arrives in one batch at one point in time;

Quantity discount are not possible, in other words it dose not make any difference how much we order, the price of the product will still be the same; and

That only costs pertinent to inventory model are the cost of placing an order and cost of holding or storing inventory over time.

‘Q’ Model of EOQ

In ‘Q’ model, a fixed quantity of material is ordered when ever the stock on hand reaches the recorder point the fixed quantity of material ordered each time is nothing but the economic order quantity (EOQ). when the new consignment arrives the total stock shall be within the maximum and the minimum limits.

Graphic presentation of ‘Q’ Model

EOQ

RE-ORDERLEVEL

BUFFER STOCK

MAXIMUM LEVEL

MINIMUM LEVEL

E GINVENTORY

TIME PERIOD

K

A B C D

Mathematical method of EOQ

The objective is to determine the quantity to order which minimize the total annual inventory management cost;Minimize Total cost per period = inventory holding cost per period + order cost per period;Where order cost = the number of order placed in the period ‘x’ order cost; andCarrying cost = average inventory level ‘x’ the carrying costs of 1 unit of stock for one period.

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Mathematical formula of ‘Q’ Model

Where as ,

Q denotes order quantity; A denotes demand per time period (e.g.-annual

demand); S denotes carrying / holding cost of 1 unit of stock

for one period; and P denotes order cost.

EOQ = Square Root of 2AP/S

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Example: Q. Calculate the economic order quantity if annual demand for the product is 5,000 unit. The ordering cost is Rs 30 per order and holding cost is Rs 6/- per unit per annual.

Sol:- Given R=5000 unit Cp= Rs. 30 Ch=Rs. 6Now, _____ EOQ = J ( 2RCp/ CH) _____ = J(2*5000*30/6) ______ = J 5000

= 224 or 22.5 units.

Merits of ‘Q’ system

Each material can be in the most economical quantity;Purchasing an inventory control personnel automatically devote attention to the items that are needed only when required; andPositive control can be easily exerted to maintain total inventory investment at the desired level, simply by manipulating the plant maximum and minimum values.

Demerits of ‘Q’ system

The orders are raised at irregular intervals which may not be convenient to the suppliers;In case the lead time is very high supply of inventory may interpret;EOQ may give you an order quantity which is much below the supplier minimum, and there is always a chance that the ordering level for an item has been reached but not noticed in which case a stock out may occur; andThe items cannot be group and ordered at a time since the recorder points occur irregularly.

‘P’ model of EOQ

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In this model the stock position of each item of material is regularly is reviewed;

Under this model inventory is ordered based on fixed period.

QUALITY

UNITS OFSTOCK

Replenishment level

R1 15 days

Y1

Y2 Y3

R3R1

G

S3R2S2

S1

S2R2 R3 S3

Graphical Presentation of ‘P’ Model

Merits of P model

The ordering and inventory cost are low; The supplier will also offer attractive discount on sales are granted; and The system works well for material which exhibit an irregular or seasonal use and whose purchase must be planned in advance on the basis of sales estimates.

Demerits of ‘P’ model

It compels a periodic review of all item; this in itself make the system somewhat inefficient. because of difference in uses rate supply may not have to be order until succeeding review;Equally important the system demand the establishment of rather inflexibility order quantities. in The interest of the administrative efficiency; andThe periodic review system tends to peak the purchasing work around the review dates.