Basic terminologies and EOQ models of Inventory Theory

BASIC
TERMINOLOGIES AND
EOQ MODELS OF
INVENTORY THEORY

3
• OPERATIONS RESEARCH is a branch of
mathematics – specially applied mathematics,
used to provide a scientific base for management
to take timely and effective decisions to their
problems. It tries to avoid the dangers from taking
decisions merely by guessing or by using thumb
rules.
• OR make use of techniques from other
mathematical sciences, such as
mathematical modeling, statistical analysis,
and mathematical optimization and then
operations research arrives at optimal or near-
optimal solutions to complex decision-
making problems.

APPLICATION
S of OR
4
FINANCE
BUDGETING
INVENTORY
CONTROL PRODUCTION
MANAGEMENT
FORECASTING
RESEARCH
AND
DEVELOPMENT
PERSONNEL
MANAGEMENT
and so on

WHAT IS ??
5
Inventory often called STOCK refers to
goods and materials that a business
holds for sale to customers in the
near future.

1-RAW MATERIAL
2-WORK IN
PROCESS
3- FINISHED
PRODUCT
PHASES
6

Definition of
Inventory
7
• Inventory theory is the sub specialty within
operations research and operations management
that is concerned with the design of production
system to minimize costs. It studies the decision
faced by firms and the military in connections
with manufacturing , warehousing , supply chains
, spare parts allocation and so on and provides
the mathematical foundation for logistics.
• The purpose of inventory theory is to to
determine rules that management can use to
minimize the costs associated with maintaining
inventory and meeting customer demand.

INVENTORY
DECISIONS
8
• Most businesses other than service
businesses are required to carry
inventory. In these businesses, good
management of inventory is essential.
The management of inventory
requires a number of decisions.
• Decisions regarding inventory can be
placed in two general categories:
1 - How much to order?
2 - When should the order be placed?

CARRYING COST :- Also known as holding costs,
these are costs involved with storing inventory
before it is sold.
SHORTAGE COST :- These costs, also called stock-
out costs, occur when businesses become out of
stock for whatever reason.
ORDERING COST :- Ordering costs are the
expenses incurred to create and process an order to
a supplier.
INVENTORY
RELATED
COSTS
9

BASIC TERMINOLOGIES
10
1.DEMAND
The amount of each supply that inventory management needs to order
per period is called DEMAND.
Independent
Dependent

11
2. LEAD TIME
The time gap between placing of an order and its true arrival is known as lead time in
inventory.
3. ORDER CYCLE
Order cycle time refers to the time period between placing of one order and the next
order. It is the time period between two orders that are placed.
4. TRADE CREDIT
Trade credit means an arrangement to buy goods and/or services on account without
making immediate cash or cheque payments.

12
5. REORDER POINT
A reorder point (ROP) is the minimum unit quantity that a business should have in
available inventory before they need to reorder more product.
6. REORDER QUANTITY
Reorder quantity is the total number of product units requested from a manufacturer or
supplier on an inventory replenishment purchase order.
7. DETERIORATION
Deterioration is defined as change, damage, decay, spoilage obsolescence and loss of
utility or loss of original value in a commodity that results in the decreasing usefulness
from the original one product.

13
8. PERISHABLE ITEMS
Perishable refers to items that have an expiration date, such food that will go bad if not
eaten in a certain amount of time. Perishable inventory can also be inventory that will
never be available again, such as hotel rooms, seats on an airplane flight, sports events
or restaurant reservations.
9. INFLATION
Inflation is the rate at which the general level of prices for goods and services is rising
and, consequently, the purchasing power of currency is falling.
10. WAREHOUSE
Warehousing is the house of storing goods that will be sold or distributed later.

EOQ
(ECONOMIC
ORDER
QUANTITY)
14
Economic order quantity (EOQ) is one of
the techniques of inventory control which
minimizes total carrying and ordering cost.
EOQ as a model has been introduced in
1913 by Ford W. Harris; and R. H. Wilson
was given credit for their in-depth analysis .

EOQ MODEL
-
ASSUMPTIONS
15
1. The demand rate is known and constant .
2. There is no time gap between placing an
order and receiving its supply, i.e. lead time
is zero.
3. Carrying cost is known and constant.
4. Ordering cost is known and constant.
5. Shortages are not allowed.

EOQ -
NOTATIONS
17
Q= Number of units ordered(supplied) per order
D = Demand in units of inventory per year
N = Number of orders placed per year
TC = Total inventory cost
Co = Ordering cost per order
C = Purchase price per inventory
Ch = Carrying cost per unit per period of time the
inventory is kept
Cs = Shortages cost per unit of inventory

Model 1:-EOQ Model with Uniform Demand
18

Ordering cost = no. of order per year × ordering cost per order
Carrying cost = Average units in inventory × carrying cost per unit
Total inventory cost ,
TC =
𝐷
𝑄
𝐶0 +
𝑄
2
𝐶h
and TC is minimum at the value of Q where the derivative of TC with respect
to Q is zero. Differentiating TC with respect to Q and then equating it to zero ,
we get

20
Q
This value of Q minimize the total inventory cost (TC) and hence it is the economic
order quantity.
Let this denote by Q*.
So, Q*
And optimum no. of orders placed per year, N*
Minimum total yearly inventory cost, TC*

Model 2:- EOQ Model with Different Rates
of Demand in Different Cycle
21

22
Let the demand in different periods of time t1, t2, …, tn be D1, D2, …, Dn respectively,
so that the total demand in time T is given by
D = D1+ D2+ …+ Dn where T = t1+ t2+ …+ tn
The cost of ordering in time T,
The carrying cost for time T,
=
1
2
𝑄𝐶hT
The total inventory cost ( TC )

23
This cost is minimum when its derivative with respect to Q is zero,
i.e. if,
Q* =
Total inventory cost,

REFERENCES
24
• Taha, H. A., ‘Operations Research : An
Introduction‘ . (2017). Pearson Education.
• Hillier, F. S., & Lieberman, G. J., Introduction to
operations research. (2015). San Francisco:
Holden Day.
• Inventory definitions and EOQ concept:
https://nptel.ac.in/courses/111102012

Basic terminologies and EOQ models of Inventory Theory

More Related Content

What's hot (20)

Similar to Basic terminologies and EOQ models of Inventory Theory (20)

Recently uploaded (20)

Basic terminologies and EOQ models of Inventory Theory