Introduction

Determining the ordering or manufacturing quantities of different items.

Investments in inventories. It can be determined by having fixed price,

quantity discounts, manufactured items, when stock replenishment is instantaneous and when it is gradual,etc.

There are two types of costs involved in the procuring & storing of the Material.

Procurement cost . Inventory carrying cost. When both these costs are properly balanced

the total cost of procurement + Inventory carrying cost is minimum. This is called as EOQ.

Ordering large lots reduces administrative work but increases investments in stocks. Ordering small lots frequently keeps the investments low but it increases administrative work because ,

Small lots require high order frequency. More Purchase requisitions are required.

Lot wise comparative statements required to be generated by Q.A.Department.

Frequency of Material receipt increases.More No. Of Postings.More bills to be handled.

All such activities increase the work content.

Mathematically,

EOQ = 2 x S x CP

CU x i

Where, S Annual Requirement

CP Procurement Cost/Order

CU Price / Unit

i Inventory Carrying Cost.

EOQOrder Quantity

Cost

Effect of Order Quantity on Costs

Annual Procurement Cost

Annual Inventory Carrying Cost

Annual Procurement Cost

EOQ when price is fixed

Assumptions :- The demand of the item occurs uniformly

over a period at the known rate. The replenishment of the stock is

instantaneous. The time elapses between the placing a

replenishment order & receiving the item into stock, called Lead time, is zero.

The price per unit is fixed & is independent of the order size.

The cost to place an order & process the delivery is fixed & does not vary with the lot size.

The inventory carrying changes vary directly & linearly with the size of the inventory & is expressed as a percentage of average inventory investment.

The item can be procured in the quantities desired , there being no restrictions of any kind.

The procured item has fairly long shelf life.

Determination of EOQ with Constraints

With Quantity Discounts. For Manufactured items

a) Instantaneous Replenishment

b) Non-Instantaneous Replenishment

EOQ of Manufactured Items when Stock

Replenishment is Instantaneous The item is consumed at the known demand rate

which is constant. Cost to setup a machine and order writing is fixed

and does not vary with size. Inventory carrying charges vary directly and linearly

with the size of inventory and are generally expressed as a percentage of average inventory investment.

The production rate is infinite. The item can be manufactured free from restriction of

any kind.

Time

Lot Size (q)

Inventory Build-up under Instantaneous Replenishment Method

EOQ of Manufactured Items when Stock Replenishment is Gradual

The item is consumed at the known demand rate which is constant.

Cost to setup a machine and order writing is fixed and does not vary with size.

Inventory carrying charges vary directly and linearly with the size of inventory and are generally expressed as a percentage of average inventory investment.

The inventory does not increase by the quantity on the shop order but rather gradually at a rate (p-d), where ‘p’, the production rate is infinite & ‘d’ is the demand rate.

The item can be manufactured in the desired quantity free from restrictions of any kind.

Mathematically,

EOQ = 2 x S x CP

(1-d ) x CU x i

p

Time

(p-

d)t

Stock Consumed

Stoc

k G

radu

ally

repl

enis

hed

tT

Sto

ckInventory Build-up under

Non-Instantaneous Replenishment Method