4ME-04:INDUSTRIAL

ENGINEERING
Dr Alok Khatri
Associate Professor,
Department of Mechanical Engineering
Contents of Section 3
• Materials Management and Inventory Control: Field and scope of
material management, Material Requirement Planning and
programme, Inventory Control: Classification of Costs, Direct and
Indirect Cost, Labour, Material and Over-Head, Prime Cost, Factory
Cost, Fixed Cost, Variable Cost, Increment Cost, Allocation of
Over-Head Costs, Break even Analysis, Types of Inventories,
Determining Economic Order Quantity (EOQ), Quantity Discounts,
Lead Time and Re-order Level, ABC, VED, FSN Models, Re-order
Cycle Systems, Procedure for Purchase and Storage.
 Material Management

Definition
It is concerned with planning, organizing and controlling the flow of
materials from their initial purchase through internal operations to
the service point through distribution.
OR

Material management is a scientific technique, concerned with

Planning, Organizing &Control of flow of materials, from their initial
purchase to destination.
AIM OF MATERIAL MANAGEMENT

To get
1. The Right quality
2. Right quantity of supplies
3. At the Right time
4. At the Right place
5. For the Right cost
PURPOSE OF MATERIAL MANAGEMENT

• To gain economy in purchasing

• To satisfy the demand during period of replenishment
• To carry reserve stock to avoid stock out
• To stabilize fluctuations in consumption
• To provide reasonable level of client services
Objectives of materials management
1. Minimization of materials costs
2. To reduce inventory for use in production process and to develop high
inventory turnover ratios.
3. To procure materials of desired quality when required, at lowest
possible overall cost of the country.
4. To reduce paper work procedure in order to minimize delays in
procuring materials.
5. To note changes in market conditions and other factors affecting the
concern.
6. The purchase, receive, transport, store materials efficiently
7. To reduce cost, through simplification, standardization, value analysis
etc.
8. To conduct studies in new areas e.g., equality consumption and cost of
materials so as to minimize cost of production
Objectives of materials management

Primary Secondary
• Right price • Forecasting
• High turnover • Inter-departmental harmony
• Low procurement & storage cost • Product improvement
• Continuity of supply • Standardization
• Consistency in quality • Make or buy decision
• Good supplier relations • New materials & products
• Development of personnel • Favorable reciprocal relationships
• Good information system
Four basic needs of Material management

1. To have adequate materials on hand when needed

2. To pay the lowest possible prices, consistent with quality and value
requirement for purchases materials
3. To minimize the inventory investment
4. To operate efficiently
Function of Materials Management
1. Materials planning and programming
2. Purchasing materials inspection of materials
3. Inspection of Materials
4. Classification, codification and standardization in stores
5. Storage of materials
6. Issuing of materials
7. Maintenance of proper inventory records
8. Materials receiving
Basic principles of material management
1. Effective management & supervision It depends on managerial
functions of
• Planning
• Organizing
• Staffing
• Directing
• Controlling
• Reporting
• Budgeting
2. Sound purchasing methods
3. Skillful & hard poised negotiations
4. Effective purchase system
5. Should be simple
6. Must not increase other costs
7. Simple inventory control programme
Scope of Material Management
Scope of Material Management
1. Materials planning and control: Based on the sales forecast and production
plans, the materials planning and control is done. This involves estimating the
individual requirements of parts, preparing materials budget, forecasting the
levels of inventories, scheduling the orders and monitoring the performance in
relation to production and sales.
2. Purchasing: This includes selection of sources of supply finalization in terms
of purchase, placement of purchase orders, follow-up, maintenance of smooth
relations with suppliers, approval of payments to suppliers, evaluating and
rating suppliers.
3. Stores management or management: This involves physical control of materials,
preservation of stores, minimization of obsolescence and damage through
timely disposal and efficient handling, maintenance of stores records, proper
location and stocking. A store is also responsible for the physical verification
of stocks and reconciling them with book figures. A store plays a vital role in
the operations of a company.
Scope of Material Management
4. Inventory control or management:
Inventory generally refers to the materials in stock. It is also called
the idle resource of an enterprise. Inventories represent those items,
which are either stocked for sale or they are in the process of
manufacturing or they are in the form of materials, which are yet to
be utilized. The interval between receiving the purchased parts and
transforming them into final products varies from industries to
industries depending upon the cycle time of manufacture. It is,
therefore, necessary to hold inventories of various kinds to act as a
buffer between supply and demand for efficient operation of the
system. Thus, an effective control on inventory is a must for smooth
and efficient running of the production cycle with least interruptions.
Material Planning- BOM
1. One of the techniques of material planning is bill of material
explosion. Material planning through bill of material explosion.
2. Bill of materials is a document which shows list of materials
required, unit consumption location code for a given product.
3. An explosive chart is a series of bill of material grouped in a
matrix form so that combined requirements for different
components can be done requirements of various materials are
arrives at from the demand forecast, using bill of materials,
through explosion charts.
Material Planning
Material Requirement Planning (MRP)
• Material requirements planning (MRP) is a very useful technique
and it is used by all kinds of production and manufacturing
industries for materials planning and budgeting. ... production and
manufacturing.

• Computer-based information system for ordering and scheduling of

dependent demand inventories.

• It is a production planning process that starts from the demand for

finished products (independent demand) and plans the production
step by step of subassemblies and parts (dependent demand).
Material Requirement Planning (MRP)
MRP Inputs: Master Production Schedule
Master Production Schedule (MPS)

• Time-phased plan specifying timing and quantity of production for

each end item.
• MPS comes from sales and marketing
• MPS covers about 1-3 months into the future
• Must cover cumulative lead time

Cumulative lead time: The sum of the lead times that sequential phases
of a process require, from ordering of parts or raw materials to
completion of final assembly.
MRP inputs: Bill of materials (BOM)
Bill of materials (BOM):
A listing of all of the raw materials, parts, subassemblies,
and assemblies needed to produce one unit of a product.

Product structure tree:

Visual depiction of the requirements in a bill of materials,
where all components are listed by levels.
MRP input: Inventory levels

• Beginning inventory on hand

• Scheduled receipts
• Pipeline inventory not received yet but it is in the process of coming to the
inventory. We know when this will be available for use.
Product Structure Tree
Level Chair
0

1 Leg Back
Assembly Assembly
Seat

Cross Side Cross Back

2 Legs (2)
bar Rails (2) bar Supports (3)

3
Explosion Example
• How many leg assemblies are needed for 1 chair?
• How many Cross bars are needed for 5 chairs?

• Computing how many parts are required per a final

product is called BOM explosion.

• MRP answers these questions in view of production lead

times: Not only it tells how many, but also when.
MRP Processing
• Gross requirements: (Forecasted)Demand period by period
• Net requirements(t)
=Gross requirements(t)-Projected inventory(t-1)
-Scheduled receipt(t)
• If Net requirement(t) > 0

set Planned order receipts(t)>=Net requirement(t)

• Planned-order receipts is the production planned
• Projected inventory(t)
=Projected inventory(t-1)+Scheduled receipt(t)
+Planned order receipts(t)-Gross requirements(t)
• Planned order release(t-LT)=Planned-order receipts(t)
MRP Processing
1. Establish gross requirements.
2. Determine net requirements by subtracting scheduled receipts and
on hand inventory from the gross requirements
3. Time phase the net requirements.
4. Determined the planned order releases
5. The planned order releases aggregated over all the end items will
result in the gross requirements for level one items, the gross
requirements for this items are then netted and time phased to
determined their own order releases. The process is continued
until all the items have been exploded.
MRP Table
 MRP example with LT=2

Periods 0 1 2 3
Gross requirements 6 11 7 Inputs
Scheduled receipts 2 3 0
Projected on hand 10 6 0 0
Net requirements 0 2 7
Outputs
Planned order receipts 2 7
Planned order releases 2 7
Other Considerations

• Safety Stock
• Not much for items with dependent demand
• Lot sizing
• Lot-for-lot ordering
• Economic order quantity
• Fixed-period ordering
• Part-period model
 MRP example with Lot size=5 and LT=2

Periods 0 1 2 3
Gross requirements 6 11 9 Inputs
Scheduled receipts 2 3 0
Projected on hand 10 6 3 4
Net requirements 5 10
Outputs
Planned order receipts 5 10
Planned order releases 5 10
MRP Steps
Example According to bill of material, one unit of final
item ‘ A’ requires two units of item ‘ B’ and
four units of item ‘ C’ . Again, one unit of item
‘ B’ requires two units of item ‘ D’ and one
unit item ‘ E’ . Items ‘ C’ , ‘ D’ and ‘ E’
are purchased from different suppliers with
various lead time. The beginning inventory levels
of items ‘ A’ , ‘ B’ , ‘ C’ , ‘ D’ and
‘ E’ are 100, 0, 100, 50 and 0 respectively.
The assembly time with items ‘ B’ and ‘ C’
to produce final item ‘ A’ is 2 weeks. The
assembly time with items ‘ D’ and ‘ E’ to
produce item ‘ B’ is 1 week. The time intervals
between ordering and receiving for items ‘ C’ ,
‘ D’ and ‘ E’ are 3, 2 and 1 week
respectively. The items ‘ C’ and ‘ D’ are
purchased with lot-for-lot (LFL) ordering policy
but the item ‘ E’ is purchased with lot-size (LS)
orderingpolicy. There are total five orders in the
master production schedule (MPS).
Process of Manual Calculation
• The required quantity of final item ‘ A’ is 250 for the first order.
The firm already has 100 units of final item in inventory. So the firm
needs 150 units of ‘ A’ to meet the first order. For 150 units of
‘ A’ it requires 300 units of item ‘ B’ and 600 units of item
‘ C’ . Again, for 300 units of ‘ B’ the firm needs 600 units of
item ‘ D’ and 300 units of item ‘ E’ . The inventory level of item
‘ D’ is 50. So, the net requirement of item ‘ D’ is 550. If the firm
orders today for 550 units of ‘ D’ from supplier it can receive the
order after two weeks. In the meantime the required quantity of item
‘ E’ will be available for lower lead time. It will takes another one day
to produce the required quantity of item ‘ B’ with items ‘ D’ and
‘ E’ . In the meantime the required quantity of item ‘ C’ will be
available. Finally, it will take another two more days to produce the
required quantity of final item ‘ A’ with items ‘ B’ and ‘ C’ . It
will take total five weeks to meet the first order. The first order can be
delivered in the sixth week. So, the order no.1 can’ t be met in third week.
This order needs another 3 more weeks to meet.
Steps of Software Algorithm (C language)
Step 1 : Structure has been used to declare the variables of each item (item ID, item name, inventory
level, lead time, lot size, number of item needed for each upper item, upper item ID, Number of
lower item etc).
Step 2 : Input the total number of level and information of each item (Bill of Materials).
Step 3 : Input the total number of deliveries and timing & required quantity of final item for each
delivery (Master Production Schedule).
Step 4 : Temporary inventory level variable is used to hold the inventory level of each item
temporarily which will be destructed after calculation.
Step 5 : Finding out the order release date and temporary inventory level of independent item (final
item) for each delivery
Step 6 : Finding out the order release date and temporary inventory level of all dependent items
(sub items) for each delivery. If an item occurs more than once it will update the temporary
inventory level for all repeated items simultaneously.
Step 7 : If the order release date of an item is negative it means that the Order Release falls
before the planning period. So, the delivery can’ t be possible.
Step 8 : Then searching for the maximum negative value of order release date among all items for
the deliveries which are not possible. This maximum negative value yields the number of weeks/days
required to meet the missing deliveries.
Step 9 : For a missing delivery shift the inventory level of all items to the next delivery.
Step 10 : Again finding out the order release date and temporary inventory level of all items for
the remaining deliveries because of missing the delivery
Steps of Software Algorithm (C language)
Step 11 : Repeat steps 9 and 10 for the remaining missing
deliveries.
Step 12 : Holding the missing deliveries in an array.
Step 13 : Finally calculate the order release date and inventory level
of all items for which deliveries are possible. Step 14 : Show which
deliveries can’ t be met and the required weeks/days to meet those
deliveries.
Step 15 : Show the output of MRP that is the time-phased
requirements for assemblies, parts and raw materials.
Step 16 : Show the final inventory level of all items.
Step 17 : Finally save the MRP output to a text file
Software Inputs
• Enter the total number of levels: 2
• Enter the total number of items in level-1: 2
• Enter the items ID for levels-1: 127
• 181
• Enter the total number of items in level-2: 2
• Enter the items ID for levels-2:
• 148
• 201 Give the information for final item:
• ------------------------------------------
• ID: 101 Name: A Inventory level: 100
• Lead time: 2
• Give the information for item ID-127:
• ---------------------------------------------
• Name: B Upper item ID: 101
• Number of lower item in the next level: 2
• Number of item needed for each upper item: 2
• Inventory level: 0
• Lead time: 1
• Give the information for item ID-181:
• --------------------------------------------
Software Inputs
• Name: C Upper item ID: 101
• Number of lower item in the next level: 0
• Number of item needed for each upper item: 4
• Inventory level: 100
• Lead time: 3
• Lot size [Enter 32000 when ‘ lot for lot’ otherwise enter lot size]: 32000 Give the information for item
ID-148:
• --------------------------------------------
• Name: D Upper item ID: 127
• Number of lower item in the next level: 0
• Number of item needed for each upper item: 2
• Inventory level: 50
• Lead time: 2
• Lot size [Enter 32000 when ‘ lot for lot’ otherwise enter lot size]: 32000
• Give the information for item ID-201:
• --------------------------------------------
• Name: E Upper item ID: 127
• Number of lower item in the next level: 0
• Number of item needed for each upper item: 1
• Inventory level: 0
• Lead time: 1
• Lot size [Enter 32000 when ‘ lot for lot’ otherwise enter lot size]: 250 C
• --------------------------------------------
Software Inputs
• Enter the total number of orders: 5
• In which week/day order no.1 has to be released: 3
• Number of final item required for order no.1: 250
• In which week/day order no.2 has to be released: 7
• Number of final item required for order no.1: 200
• In which week/day order no.3 has to be released: 8
• Number of final item required for order no.1: 150
• In which week/day order no.4 has to be released: 10
• Number of final item required for order no.1: 300
• In which week/day order no.5 has to be released: 12 Number of
final item required for order no.1: 250
Software Inputs
Software Inputs
Software Outputs
Software Outputs

• The firm has to start purchase process from week no.

2 to meet the remaining orders. It should order 300
units of item ‘ C’ and 350 units of item ‘ D’
from suppliers in second week and so on. The firm
should start assembly process with items ‘ D’ and
‘ E’ to produce 200 units of item ‘ B’ .
Benefits of MRP

• Low levels of in-process inventories

• Ability to track material requirements

• Ability to evaluate capacity requirements

• Means of allocating production time

• Eventually it is a database with limited decision

making capability
Cost

“ The amount of expenditure incurred on or attributable to a

specified thing or activity”

“ Loss or penalty incurred especially in gaining something”

"Cost means the amount of expenditure (actual or notional) incurred

on, or attributable to, a given thing”
Classification of cost
Classification is the process of grouping costs according to their
common features.
1.By Nature or Element
2. Functions
3. Variability/ Behavior
4. controllability
5. Normality
6. Inventory
7. Time
• Classification of cost
• Classification of cost
Nature or Elements
• This is the analytical classification of costs. Let us divide as per their
natures. So basically there are three broad categories as per this
classification, namely Labor Cost, Materials Cost and Expenses. These
heads make it easier to classify the costs in a cost sheet. They help
ascertain the total cost and determine the cost of the work-in-progress.
• Material Costs: Material costs are the costs of any materials we use in
the production of goods. We divide these costs further. For example, let’
s divide material costs into raw material costs, spare parts, costs of
packaging material etc.
• Labor Costs: Labor costs consists of the salary and wages paid to
permanent and temporary employees in the pursuit of the manufacturing
of the goods
• Expenses: All other expenses associated with making and selling the goods
or services.
• Nature or Element Cost

1. Materials Cost (Direct + Indirect)

2. Labor costs (Direct + Indirect)
3. Expenses (Direct + Indirect)
• Observations:
• Direct material +Direct Labor + Direct Expenses= Prime Cost
• Indirect material +Indirect Labor + Indirect Expenses= Overhead
• Nature or Element Cost
Classification by Functions
• This is the functional classification of costs. So the classification
follows the pattern of basic managerial activities of the
organization.
• The grouping of costs is according to the broad divisions of
functions such as production, administration, selling etc.
• Production Costs: All costs concerned with actual manufacturing or
construction of the goods
• Commercial Costs: Total costs of the operation of an enterprise
other than the manufacturing costs. It includes the admin costs,
selling and distribution costs etc.
 Classification on Variability/ Behavior of cost
• FIXED COST: The cost which does not vary but remains constant within a given
period of time and range of activity in spite of the fluctuations in production, is
known as fixed cost. Example: rent, insurance of factory buildings etc. remain the
same for different levels of production. It do not change in total with changes in
activity levels .

• VARIABLE COST: These costs tend to vary with the volume of output. Any increase
in the volume of production results in an increase in the variable cost and vice
versa. change in total as the level of activity changes. There is a definitive
physical relationship to the activity measure
• Example: cost of material, cost of labour etc.

• Semi-variable Cost: The cost which does not vary proportionately but
simultaneously can not remain stationery at all times is known as semi variable
cost. It can also be called as semi-fixed cost.
• Example: Depreciation, repairs etc.
Classification on Variability/ Behavior of cost
Classification by Traceability
• This aspect one of the most important classification of costs, into direct
costs and indirect costs. This classification is based on the degree of
traceability to the final product of the firm.

• Direct Costs: So these are the costs which are easily identified with a
specific cost unit or cost centers. Some of the most basic examples are
the materials used in the manufacturing of a product or the labor
involved with the production process.

• Indirect Costs: These costs are incurred for many purposes, i.e. between
many cost centers or units. So we cannot easily identify them to one
particular cost center. Take for example the rent of the building or the
salary of the manager. We will not be able to accurately determine how
to ascertain such costs to a particular cost unit.
Classification by Normality
• This classification determines the costs as normal costs and
abnormal costs. The norms of normal costs are the costs that
usually occur at a given level of output, under the same set of
conditions in which this level of output happens.
• Normal Costs: This is a part of the cost of production and a part
of the costing profit and loss. These are the costs that the firm
incurs at the normal level of output in standard conditions.
• Abnormal Costs: These costs are not normally incurred at a given
level of output in conditions in which normal levels of output occur.
These costs are charged to the profit and loss account, they are not
a part of the cost of production.
By Controllability
• CONTROLLABLE COSTS: These are the costs which can be influenced by
the action of a specified member of an undertaking. A business
organization is usually divided into a number of responsibility centres
and each centre is headed by an executive. The executive can thus control
the costs incurred in that particular responsibility centre.

• UNCONTROLLABLE COSTS: Costs which can not be influenced by the action

of a specified member of an undertaking.

• Example: Expenditure incurred by the tool room is controllable by the

foreman in charge of that section but the share of the tool room
expenditure which is apportioned to a machine shop is not to be controlled
by the machine shop foreman.
Classification by time when completed
• SUNK COSTS: These are costs which have been created by a
decision that was made in the past that cannot be changed by any
decision that will be made in the future. Investment in plant &
machinery are prime examples of such costs. Since sunk costs can
not be altered by later decisions, they are irrelevant for decision
making.
• Costs incurred in the past that cannot be changed by present or
future decisions.
• Estimated Cost: An estimated cost is an approximate projection of
future expenses incurred in goods production or completion of a
project. It includes both fixed and variable costs like labor,
material, and capital.
 Factory Cost/ Manufacturing Cost & Total Cost
• Manufacturing cost, refers to the production cost or factory cost
which is basically the sum of three elements such as:

Factory Cost = Prime Cost (Direct material + Direct labor + Direct Expenses) +
Factory overhead

Total Cost = Factory Cost + Selling/ Distribution/ Administration overheads

Selling Cost = Total Cost + Profit/ loss

Direct cost
Direct cost are the cost which can be directly traced to a product or
service.

PRIME COST
Prime Cost
Direct material cost: A direct material is one which goes into a
salable product or its use is directly essential for the completion
of that product e.g. a HSS bit for making a turning tool for lathe,
alloys for making alloy steels, Cloth, collar, buttons, thread for
manufacturing an apparel etc.

Direct labor cost: cost of labor that is directly involved in

manufacturing of product e.g. the wages of a welder fabricating a
structure, operational staff wages cost etc.

Direct expenses: Expenses which can be identified with and allocated

to cost centres or cost units e.g. the cost of special design or lay
out, hiring of special machine, Hire of equipment for special job/
tools
Direct Cost
• A cost of a resource or activity that is acquired for or used by a
single cost object
• Cost object = A dining room table
• Cost of the wood that went into the dining room table
• Cost object = Line of dining room tables
• A manager’ s salary would be a direct cost if a manager were hired to
supervise the production of dining room tables and only dining room tables
Overheads
• The cost of indirect material, indirect labor and such other indirect expenses
including services.
• All expenses other than direct expenses.
• Manufacturing overheads
Indirect labor (Clerk, general worker etc.)
Indirect material ( consumable items- cotton, grease etc.)
Building overheads (Building Rent, insurance, repair,
water, fuel, power etc.)
• Administrative overheads
(Taxes, legal costs, office expenses etc.)
• Selling overheads
(Advertising, customer services, sales work force etc.)
• Distribution overhead
( Warehouse charges, transportation cost, loading/unloading
charges etc.)
• R & D overheads
Indirect Cost
• The cost of a resource that was acquired to be used by more than
one cost object
• The cost of a saw used in a furniture factory to make different
products
• It is used to make different products such as dining room tables, china
cabinets, and dining room chairs
Direct or Indirect?
• A cost classification can vary as the chosen cost object varies
• Consider a factory supervisor’ s salary
• If the cost object is a product the factory supervisor’ s salary is an indirect cost
• If the factory is the cost object, the factory supervisor’ s salary is a direct cost
• A cost object can be any unit of analysis including product, product
line, customer, department, division, geographical area, country, or
continent
Cost Allocation
• It is the process of assigning indirect costs to products, services,
business units, etc.

1. Define the cost pool: The collection of costs to be assigned to cost

objects
2. Determine the cost allocation rule: The method used to assign
costs in the cost pool to cost objects
3. Assign the costs in the cost pool to the cost object: Any end to
which a cost is assigned – product, product line, department,
customer, etc.
Assume net
Profit
Rs 10000.00
Break Even Analysis
• Reach a point in a business venture when the profits are equal to the costs.
• Cost-Volume-Profit Analysis
• Breakeven analysis is the business analysis performed to determine the probable
point when your business will be able to cover all its expenses and begin to make
a profit.
• Breakeven analysis can be done to determine either the breakeven point or the
breakeven volume.

• It is the point in your business transactions when profit is exactly equal to the
costs of doing business. It is the point that above it, the business starts making
profit (revenue exceeds costs).
• At the breakeven point: TOTAL REVENUE = TOTAL COST
Importance of BEP
• How many units the business must produce and sell in terms of
manufacturing business
• How many units to purchase and sell in the case of the merchandising
business
• In the services unit, the breakeven point indicates the number of billable hours
you must work in order to cover your costs.
• It helps in examining the effects of on-going business processes or activities
on the organization’s profitability.
• It helps in deciding about the substitution of new plants (and products).
• It is an essential component of a business or marketing plan, and is normally
incorporated in the feasibility studies.
Break Even Analysis
Income/ Profit

Operating profit = Total revenues – Total costs

Profit = TR – TC
Total revenue

Average selling price per unit × Units of output produced and sold

TR = PX
Total cost

[Variable cost per unit × Units of output ] + Fixed costs

TC = VX + F
 Profit Equation

Profit = Total revenue – Total costs

=

Profit = PX – (VX + F)

Profit = (Price – Variable costs) × Units of output – Fixed costs

= X(P – V) – F
Contribution Margin
This is the difference between price and variable cost.

It is what is leftover to cover fixed costs and then add to operating

profit.
Break Even Point
Break Even Analysis
• Break-even volume (units) = Fixed costs /Unit contribution
margin

BEP (Units) = F / ( P – V)

• Break-even volume (sales) = Fixed costs/ Contribution

margin ratio

BEP (Sales) = F / ( P – V) / P
BEP (Sales) = F / ( 1 – V/ P )
Break Even Analysis (Turn Over for profit)
• Target volume (units) = (Fixed costs + Target profit Unit)/
contribution margin

= (F + Target Profit) / ( P – V )

• Target volume (sales) = (Fixed costs + Target profit)/

Contribution margin ratio

= (F + Target Profit) / ( 1 – V/ P )
 EXAMPLE
Calculate break-even point in sales units and sales
dollars from following information:
Price per Unit = $15
Variable Cost per Unit = $7
Total Fixed Cost = $9,000
 SOLUTION
We have,
p = $15
v = $7, and
FC = $9,000

Substituting the known values into the formula for breakeven point in sales
units, we get:

Breakeven Point in Sales Units (x):

= 9,000 ÷ (15 − 7)
= 9,000 ÷ 8
= 1,125 units

Break-even Point in Sales Dollars = $15 × 1,125 = $16,875

INVENTORY
• The term inventory means the value or amount of materials or
resource on hand. It includes raw materials, work-in-process,
finished goods, etc.
Inventory control
• It means stocking adequate number and kind of stores, so that the materials are
available whenever required and wherever required. Scientific inventory control
results in optimal balance

• Inventory Control is the process by which inventory is measured and regulated

according to predetermined norms such as economic lot size for order or
production, safety stock, minimum level, maximum level, order level etc.

• Inventory Control is also the supervision of supply, storage, and accessibility of

items in order to ensure an adequate supply without excessive oversupply.

• Inventory control pertains primarily to the administration of established

policies, systems & procedures in order to reduce the inventory cost. The
well-functioning inventory system is a process of overseeing the flow of items
into and out of your stock.
OBJECTIVES OF INVENTORY CONTROL
• To avoid both over-stocking and under-stocking of inventory.
• To minimize losses due to deterioration, pilferage, wastages and damages.
• To ensure perpetual inventory control so that materials shown in stock ledgers should be
actually lying in the stores.
• To ensure right quality goods at reasonable prices.
• To maintain investments in inventories at the optimum level as required by the
operational and sales activities.
• To eliminate duplication in ordering or replenishing stocks. This is possible with help of
centralizing purchases.
• To meet unforeseen future demand due to variation in forecast figures and actual figures.
This is possible with the knowledge of safety stock.
• To reduce loss due to changes in prices of inventory items.
• To balance various costs of inventory such as order cost or set up cost and inventory
carrying cost.
• To balance the stock out cost/opportunity cost due to loss of sales against the costs of
inventory.
INVENTORY CONTROL
Inventory Control Purposes
• When to order for replenishment?
• How much to order?
• Two major classes of policies
• Continuous review policies
• Periodic review policies
Type of Inventory
Inventory Related Costs
• Costs of ordering
• Costs of carrying inventory
• Inventory Storage Cost
• Cost of capital
• Out-of-stock costs
Ordering Cost
• Cost of procurement and inbound logistics costs form a part of Ordering
Cost. Ordering Cost is dependent and varies based on two factors - The
cost of ordering excess and the cost of ordering too less.
• Both these factors move in opposite directions to each other. Ordering
excess quantity will result in carrying cost of inventory. Where as
ordering less will result in increase of replenishment cost and ordering
costs.
• These two above costs together are called Total Stocking Cost. If you plot
the order quantity vs the TSC, you will see the graph declining gradually
until a certain point after which with every increase in quantity the TSC
will proportionately show an increase. This functional analysis and cost
implications form the basis of determining the Inventory Procurement
decision by answering the two basic fundamental questions - How Much to
order and When to Order.
Carrying/ Holding Cost
• Inventory storage and maintenance involves various types of costs
namely:
• Inventory Storage Cost
• Cost of Capital
• Inventory carrying involves Inventory storage and management
either using in house facilities or external warehouses owned and
managed by third party vendors. In both cases, inventory
management and process involves extensive use of Building,
Material Handling Equipment, IT Software applications and
Hardware Equipment coupled managed by Operations and
Management Staff resources.
Inventory Storage Cost

• Inventory storage costs typically include Cost of Building Rental

and facility maintenance and related costs. Cost of Material
Handling Equipment, IT Hardware and applications, including cost of
purchase, depreciation or rental or lease as the case may be.
• Further costs include operational costs, consumables,
communication costs and utilities, besides the cost of human
resources employed in operations as well as management.
Cost of Capital

• Includes the costs of investments, interest on working capital, taxes

on inventory paid, insurance costs and other costs associate with
legal liabilities.
• The inventory storage costs as well as cost of capital is dependent
upon and varies with the decision of the management to manage
inventory in house or through outsourced vendors and third party
service providers.
Cost of Out of stock/shortage

• Inventory is the stock of materials or finished goods a

manufacturer or seller keeps to cater to fluctuations in
unanticipated demand from the consumer end. Just as carrying
excess inventory results in high cost incurred by the seller, the
flipside is the inventory shortage cost.
• It involves, if a good is not available to purchase at the moment,
the customer will come back when the item arrives
• Under this, certain customers when possess stock outs, will change
their place of purchase but only temporary
Main Techniques of Inventory Control

The major Inventory Control techniques are as follows:

1. Economic Order Quantity
2. Inventory Models
3. ABC/VED/ FSN/SDE Analysis
4. Material Requirements Planning
 Economic Order Quantity (EOQ)
The Economic Order Quantity (EOQ) is the number of units that a company should
add to inventory with each order to minimize the total costs of inventory— such as
holding costs, order costs, and shortage costs.

EOQ = Average Monthly Consumption X Lead Time [in months] + Buffer

Stock – Stock on hand
The Inventory Cycle
Profile of Inventory Level Over Time
Quantity Usage
on hand rate

Reorder
point

Time
Receive Place Receive Place Receive
order order order order order
Lead time
Inventory Cycle
Main points of graph

Re-order level: stock level at which fresh order is placed.

Average consumption per day x lead time + buffer stock

Lead time: Duration time between placing an order & receipt

of material. Ideally – 2 to 6 weeks.

Buffer Stock :Buffer stock is an excess amount of raw

materials kept on hand to guard against any unplanned
inventory shortages leading into the production process.
Data/ Symbols for Inventory
• : A n n u a l D e m an d ( u n its p e r y e ar)
• : U n it P ric e ( p u rc h ase p ric e o f th e ite m )
• : O rd e rin g o r S e tu p C o st p e r O rd e r
• : I n v e n to ry H o ld in g ( C arry in g ) C o st/u n it p e r y e ar
• : H m ay b e g iv e n as i p e rc e n t o f
• : T o tal A n n u al C o s t
• : T o tal A n n u a l V aria b le C o s t
• : O rd e r Q u an tity
• : E c o n o m ic O rd e r Q u a n tity ( o p tim al v alu e o f )
Inventory Level Variations
O rd e r S iz e , = 600

S u p p o s e A n n u al D e m a n d
= 1200
S u p p o se u n its are p u rc h as e d
at a tim e , w h e re ,
= 600
= 400 e tc .

T h e fig u re s o n th e R H S s h o w
O rd e r S iz e , = 400
in v e n to ry v ariatio n s fo r
d iffe re n t v alu e s o f as su m in g
a c o n stan t a n d c o n tin u o u s
d e m an d o f 100 u n its p e r m o n th .
Average Inventory and Number of Orders
O rd e r S iz e , = 400

A v e rag e in v e n to ry = /2.
N u m b e r o f o rd e rs = .

If = 400
A v e rag e I n v e n to ry
= 400/2 = 200
A v e ra g e I n v e n to ry d u rin g th e first fo u r m o n th s
is ( 400+ 0) /2 = 200.
# O rd e rs = 1200/400 = 3 F o r th e n e x t fo u r m o n th s it is ag ain ( 400+ 0) /2
= 200
S im ilarly fo r th e last fo u r m o n th s , th e av e rag e
in v e n to ry is ( 400+ 0) /2 = 200
T h is m e a n s th a t th e a v e r a g e in v e n t o r y
th r o u g h o u t th e y e a r is 200.
Graphs of Various Costs

E O Q is th e p o in t
at w h ic h A n nu al
O rd e rin g C o st
an d A n nu al
I n v e n to ry C o st
in te rse c t.
TC and TVC Formulae
T o ta l A n n u al C o s t = A n n u al O rd e rin g C o st +
A n n u al H o ld in g C o s t + A n n u a l P u rc h as e C o s t

T o ta l A n n u al V ariab le C o s t = A n n u al O rd e rin g C o st +
A n n u al H o ld in g C o s t
EOQ Formula
I n th e e q u a tio n s fo r an d , th e v alu e s o f an d a re k n o w n .
T h e o n ly u n k n o w n v a riab le is . O u r o b je c tiv e is to m in im iz e .

is m in im iz e d a t th a t v a lu e o f , w h e re ,
A n n u a l O r d e r in g C o s t = A n n u a l H o ld in g C o s t

S o lv in g th e a b o v e e q u a tio n fo r , g iv e s th e v a lu e o f ( ) a s s h o w n b e lo w .
EOQ Example
S u p p o se = 1,200 u n its, = $5.00, = $ 1.20 an d = $ 12.00.
fo r th is p ro b le m is g iv e n b e lo w .
Costs for Various Order Quantities
N o te th a t m in im u m c o s t is O rd e r S iz e ( )
A n n u al O rd e rin g
A n nual
I n v e n to ry
T o tal A n n u al
V a riab le C o s t
C o st
fo r = 100 ( ).
C o s ts ( )

50 $120 $ 30 $150

O rd e rin g C o st = I n v e n to ry 75 $ 80 $ 45 $125

C o st = 60 fo r = 100. 100 $ 60 $ 60 $120

c an b e c a lc u late d a s
125 $ 48 $ 75 $123

150 $ 40 $ 90 $130

. 175 $ 34 $105 $139

is a c o n s ta n t te rm an d 200 $ 30 $120 $150

is in d e p e n d e n t o f . 225 $ 27 $135 $162

250 $ 24 $150 $174

275 $ 22 $165 $187

300 $ 20 $180 $200

Types of Inventory Situations
• Order repetition— static versus dynamic situations.
• Demand distribution— certainty, risk, and uncertainty.
• Stability of demand distribution— fixed or varying.
• Demand continuity— smoothly continuous or sporadic and occurring
as lumpy demand; independent.
• Lead-time distributions— fixed or varying.
• Dependent or independent demand.
General Framework for Inventory Models-I
• Demand
- certainty
- risk, probability distribution of demand
- uncertainty, nothing known
• Lead time: The period between the order time and the delivery time
- certainty
- risk, probability distribution of demand
- uncertainty
• Inside or Outside Procurement
- purchased from outside; pure inventory problem
- integrated with production smoothing if inside
General Framework for Inventory Models-II
• Static and Dynamic Problems
- Static: one period problem, classic examples are
Christmas tree and newsboy problem
- Dynamic: decisions over time
• Behavior of Demand through Time and for Various Items
- Stationary Demand: EOQ models
- Time-dependent Demand: WW model, Silver/Meal Heuristic
- Dependent Demand: MRP
General Framework for Inventory Models-III
• Costs
- Price or Variable Production Costs: quantity discounts
- Ordering or Setup Costs
- Holding or Inventory Carrying Costs
- Stock out / Shortage costs
QUANTITY (PRICE) DISCOUNT
MODEL
Quantity (Price) Discount Model
Q u an tity d isc o u n t m o d e l is u se d w h e n th e v e n d o r ( s u p p lie r)
o ffe rs a d isc o u n t fo r b u y in g in la rg e q u a n titie s .

F o r e x am p le , th e su p p lie r m ay q u o te a p ric e o f $ 10.00 p e r u n it

fo r o rd e r siz e 1 to 999 a n d $ 9.50 fo r o rd e r siz e o f 1,000 o r m o re .

T h is sc e n ario is also c alle d a “p ric e b re ak ” at q u an tity 1,000.

T h e re c o u ld b e se v e ra l p ric e b re a k s.
Example: Quantity (Price) Discounts
T h e an n u a l d e m a n d ( ) fo r a n ite m is 240,000 u n its. T h e o rd e rin g c o st p e r o rd e r ( ) is
$ 30.00. T h e in v e n to ry c arry in g c o st p e r u n it p e r y e a r ( ) is 30% o f th e c o s t ( p ric e ) o f
th e ite m , th a t is , = 30% o f .

T h e v e n d o r h a s q u o te d th e fo llo w in g c o sts ( p ric e s ) .

P ric e 1: $ 2.80 fo r o rd e r q u a n tity le ss th a n o r e q u al to 29,999.

P ric e 2: $ 2.77 fo r o rd e r q u a n tity 30,000 an d a b o v e .

F in d th e E c o n o m ic O rd e r q u a n tity .
Example: Quantity (Price) Discounts
T o so lv e th is p ro b le m w e w ill c o m p are th e to tal c o s ts fo r b o th
p ric e s . A s in th e E O Q m o d e l, th e e c o n o m ic o rd e r q u an tity is
g iv e n b y th e fo llo w in g e q u a tio n ,

an d , th e to tal c o st ( ) is g iv e n b y th e fo llo w in g e q u atio n :

Example: Quantity (Price) Discounts
S ta rt c a lc u la tio n s b y fin d in g a t th e lo w e r p ric e ( $ 2. 77) .

T h e in v e n to ry c a rry in g c o st fo r th is p ric e is $0. 83 ( = 30% o f $ 2. 77) p e r u n it

p e r y e a r a n d th e e c o n o m ic o rd e r q u a n tity fo r th is p ric e is 4, 163.

T h e re fo re , w e h a v e to b u y a t le a st 30, 000 u n its to o b ta in th is p ric e d isc o u n t.

W e c a lc u la te th e to ta l c o st ( a t 30, 000) . U s in g th e e q u atio n ,

( a t 30,000) = ( 240, 000/30,000) * 30 + ( 30,000/2) * 0.83 + 240, 000* 2.77 = $ 677, 505.00
Example: Quantity (Price) Discounts
N o w c a lc u la te th e fo r th e h ig h e r p ric e $ 2. 80.

T h e v a lu e o f fo r th is p ric e is $ 0.84 ( 30% o f $ 2. 80).

T h e e c o n o m ic o rd e r q u an tity is 4,140.

T h is q u a n tity is fe a sib le b e c au se w e c a n b y u p to 29, 999 u n its a t $ 2. 80 p e r

u n it.

T h e to ta l c o st, ( at 4,140) w ill b e :

T C ( a t 4,1 40) = = ( 240, 000/4,1 40) * 30 + ( 4,1 40/2) * 0. 84 + 240,000* 2. 80 = $ 675,477.93.

T h e o rd e r q u a n tity fo r th is e x a m p le is 4, 140

sin c e ( a t 4, 140) < ( a t 30, 000) .

Lead-Times
• Lead time ( ) is the interval that elapses between the recognition that an order
should be placed and the delivery of that order.
• The diminishing stock level reaches a threshold (or limen) called
- the stock level of the reorder point.
• The threshold triggers the order for replenishment. The stock level at the reorder
point, , is enough to meet orders until the replenishment supply arrives and is
ready to be used.
Lead-Times
Eight lead-time (LT) considerations that apply to EOQ or EPQ
▶The amount of time required to recognize the need to reorder.
▶The interval for doing whatever clerical work is needed to prepare the
order.
▶Mail, e-mail, EDI, or telephone intervals to communicate with the supplier
(or suppliers) and to place the order(s).
▶Time that takes the supplier’ s organization to react to the placement of
an order?
▶Delivery time including loading, transit, and unloading.
▶Processing of delivered items by the receiving department.
▶Inspection to be sure items match specifications.
▶Time delays in updating records The effect of such delays on the
production schedule must be considered.

• The eight lead-time components are added to get the lead time.
Order Point Policies (OPP)
• Order point policies (OPP) define the stock level at which an order will
be placed. The reorder point ( ), triggers an order for more stock.

• OPP systems specify the number of units to order and when to order.

The two systems are:

▶Periodic, also known as fixed time, inventory systems.

▶Perpetual, also known as fixed quantity, inventory systems.

Periodic (Fixed Time) Inventory Systems
• The interval between orders is fixed while the ordered amount varies.
• The order size is determined by the amount of stock on-hand when the record is
read.
• It is the date that triggers the review and the order being placed.
A Fixed Interval Inventory Reorder System
 Perpetual (Fixed Quantity) Inventory Systems
• Perpetual, also known as fixed
quantity, inventory systems
continuously record inventory received
from suppliers and withdrawn by
employees.
• An order is placed when reorder point
is reached.
• The amount ordered is same (generally
or ) in each cycle.
• The interval between placing orders is
different in each cycle because of
demand variability.
Reorder Point and Safety (Buffer) Stock
• Shortages occur whenever actual demand in the lead-time period exceeds . The
likelihood of a shortage will be decreased by increasing the value of safety(
buffer) stock.
• Determining safety (buffer) stock level requires an economic balancing situation
between the cost of going out of stock versus the cost of carrying more inventory.
• The large buffer stock means that the carrying cost of stock is high to make
sure that the actual cost of stock-outages is small.
• The stock level of the reorder point ( ) is equal to the expected (average)
demand during the lead time period plus the safety stock ( ) quantity. Thus,
Expected Demand During Lead Time

T h e e x p e c te d d e m a n d d u rin g le a d tim e is a fu n c tio n o f a v e ra g e d e m a n d p e r

d a y ( ) a n d th e m ag n itu d e o f le a d tim e ( ) a n d is d e te rm in e d as

I t m a y b e n o te d th at c a lc u la tio n o f d e m an d d u rin g le a d tim e b e c o m e s c o m p le x

if le a d tim e also v arie s.
Safety Stock Calculations
T h e v a lu e o f d e p e n d s o n th e v a ria b ility o f d e m a n d a n d th e se rv ic e le v e l.

T h e se rv ic e le v e l is a m e a su re o f th e sto c k -o u t situ a tio n s a llo w e d . F o r e x a m p le ,

a 95% se rv ic e le v e l m e a n s th a t th e re w ill b e n o o u t-o f-sto c k situ a tio n 95% o f
th e tim e d u rin g le a d tim e .

A ss u m in g th a t th e d e m a n d fo llo w s a n o rm a l d istrib u tio n th e v a lu e o f c an b e

d e te rm in e d a s

w h e re , is th e s ta n d ard d e v ia tio n o f d e m a n d d u rin g le a d tim e a n d is a

m e a su re o f th e se rv ic e le v e l th a t w e w a n t to p ro v id e . is c a lle d sta n d a rd
n o rm a l ra n d o m v a ria b le a n d c a n b e fo u n d fro m its s ta tistic a l ta b le . F o r th e
95% se rv ic e le v e l th e v a lu e o f 1. 65
 Variations of the EOQ Model
• Deterministic non-zero lead time: L (yrs) =>
Reorder Point (ROP) = L(yrs)* D(units/yrs)

• Production Order Quantity Model:

• Finite Production Rate, P (units/yr)

IP

Q-D(Q/P)
P-D D time
TAC(Q) = Item-AC(Q) + Ordering-AC(Q)+Holding-AC(Q)
= C($/unit)*D(units/yr) +
S($/order) *D(units/yr) / Q(units/order) +
H($/unit x yr)*[Q*(1-D/P)*T / 2](units x yr order)*[1/T](orders/yr) =>
Q* = [ 2*S*D / (H*(1-D/P))]1/2
Application of the EOQ theory under total quantity discounts
• Suppose that the unit purchasing cost C depends on the ordered quantity, Q. In
particular, C obtains a certain value, C1, if Q lies in the interval (0,Q1], C2, if Q lies
in the interval (Q1,Q2], … , Cn, if Q lies in the interval (Qn-1,Qn], and Cn+1, if Q lies in
the interval (Qn,). Furthermore, C1 > C2 > … > Cn > Cn+1.
• Then, letting
ATC(i)(Q) = Ci*Q+S*D/Q + H(Ci)*Q/2
where
H(Ci) = I*Ci and I is the applying interest rate,
We obtain the following graphical representation for the curves ATC(i)(Q) and ATC(Q):

ATC ATC(1)
ATC(i)

ATC(n+1)

Q1 Qi-1 Qi Qn Q
Application of the EOQ theory under total quantity discounts
• The previous plot suggests the following algorithm for computing the EOQ under total
quantity discounts:
• For each curve TAC(i) (Q) compute the quantity Q(i) that minimizes TAC over that curve; this can be
done as follows:
• Compute Q*(i) according to the standard EOQ formula while using Ci in the evaluation of H(Ci).
• If Q*(i) belongs in the application interval for TAC(i)(Q), then set
Q(i) = Q*(i) (since Q*(i) is a feasible point).
• If Q*(i) lies to the left of the application interval for TAC(i)(Q), then set Q(i) = minimum of the
application interval for TAC(i)(Q).
• If Q*(i) lies to the right of the application interval for TAC(i)(Q), then set Q(i) = maximum of the
application interval for TAC(i)(Q).
• For each selected Q(i), compute the corresponding TAC(i)(Q(i)), and pick a Q(i), that provides the
smallest TAC(i)(Q(i)) value.
• Remark: A more efficient implementation of the above algorithm is as follows:
• Start the above computations from TAC(n+1)(Q(n+1)), and carry them on in decreasing order of i, until
you exhaust all i’ s, or you find an interval for which Q(i) = Q*(i). In the latter case, you can ignore
all the remaining i’ s.
 A continuous review model with
probabilistic demand and constant lead time
Model Assumptions:
• Stochastic demand rate; in particular, daily demand is a random variable (r.v.)
dd  N(Dd, d2).
• Infinite Operational Horizon, Continuous Review
• Lead time is deterministic; in particular L days.
Then,
• The TAC is minimized by Q* = [2*S*Da/H]1/2, where
Da = Dd * (business days in a year).
• However, setting ROP = L*Dd, will result in 50% probability of experiencing a stock-out
during every cycle!
• To see this, notice that the demand experienced over L days is
another r.v. dL= dd(1)+dd(2)+… +dd(L), and therefore, dL N(L*Dd, L* d2).
 A continuous review model with
probabilistic demand and constant lead time
• Typically, we want to reduce the probability of stockout during a single replenishment
cycle to a value equal to 1-a, where a(0.5,1.0) is known as the desired .
• This effect can be achieved by setting ROP = L*Dd+ss, where ss is known as the required
safety stock. ss can be computed by solving the following inequality:
Prob {dL L*Dd+ss}  a 
Prob {(dL-L*Dd) / (d*L)  ss / (d*L)}  a 
ss / (d*L)  za
where za is the a-th percentile of the standardized normal distribution.
• Hence,
ROP = L*Dd + za* d*L
Periodic Review Policies
• In the case of periodic review policies, we fix the reorder interval T, and every time
we place a replenishment order, we check the current inventory position (IP), and
order enough to bring this position up to a pre-specified level S.
• T is frequently determined by external factors like the supplier delivery schedules. In
case of choice, an optimized selection of T is
T* = round(Q* / Dd)
where Dd is the expected daily demand, Q* = [2*S*Da/H]1/2, and
Da = Dd * (business days in a year).
• Furthermore, an analysis similar to that provided in the previous two slides,
establishes that the minimal re-order level S* that guarantees a service level a, is:
S* = T**Dd+za* d*T*,
where za and d have the meanings defined in the previous slides.
• Remark: Notice that periodic review policies will tend to carry more safety stock
than continuous review policies, when applied on the same system, since, in general,
T*>L. This is the price of “ convenience” provided by these policies, compared to
their continuous review counterparts.
ABC Inventory System
ABC ANALYSIS (ABC = Always Better Control)
• This is based on cost criteria.
• It helps to exercise selective control when confronted with large
number of items it rationalizes the number of orders, number of
items & reduce the inventory.

About 10 % of materials consume 70 % of resources

About 20 % of materials consume 20 % of resources
About 70 % of materials consume 10 % of resources
ABC Inventory System
‘ A’ ITEMS

• Small in number, but consume large amount of resources

Must have:
• Tight control
• Rigid estimate of requirements
• Strict & closer watch
• Low safety stocks
• Managed by top management
‘ B’ Items
Intermediate

Must have:
• Moderate control
• Purchase based on rigid requirements
• Reasonably strict watch & control
• Moderate safety stocks
• Managed by middle level management
‘ C’ Items

• Larger in number, but consume lesser amount of resources

Must have:
• Ordinary control measures
• Purchase based on usage estimates
• High safety stocks
ABC analysis does not stress on items those are less costly but
may be vital
 VED ANALYSIS
• Based on critical value & shortage cost of an item
–It is a subjective analysis.
•Items are classified into:
Vital:
•Shortage cannot be tolerated.
Essential:
•Shortage can be tolerated for a short period.
Desirable:
■ Shortage will not adversely affect, but may be using more resources. These must
be strictly Scrutinized

V E D ITEM COST

A AV AE AD CATEGORY 1 10 70%

B BV BE BD CATEGORY 2 20 20%

C CV CE CD CATEGORY 3 70 10%

CATEGORY 1 - NEEDS CLOSE MONITORING & CONTROL

CATEGORY 2 - MODERATE CONTROL.
CATEGORY 3 - NO NEED FOR CONTROL
SDE ANALYIS
Based on availability
Scarce
Managed by top level management
Maintain big safety stocks
Difficult
Maintain sufficient safety stocks
Easily available
Minimum safety stocks
FSN ANALYSIS
Based on utilization.
Fast moving.
Slow moving.
Non-moving. (Non-moving items must be periodically reviewed to prevent
expiry & obsolescence)
HML ANALYSIS
Based on cost per unit
Highest
Medium
Low
This is used to keep control over consumption at departmental level for deciding the frequency
of physical verification.
 PROCURMENT OF EQUIPMENT
Points to be noted before purchase of an equipment:
• Latest technology
• Availability of maintenance & repair facility, with
minimum down time
• Post warranty repair at reasonable cost
• Upgradeability
• Reputed manufacturer
• Availability of consumables
• Low operating costs
• Installation
• Proper installation as per guidelines
THANKS