Module – 3:
• Capacity & Location Planning:
• Importance of capacity decisions, defining and
measuring capacity, determinants of effective
capacity, determining capacity requirement,
developing capacity alternatives, evaluating
alternatives.
• Need for location decisions, nature of locations
decisions, general procedure for making
locations decisions, evaluating locations
decisions, facilities layout – need for layout
decisions, types of processing. (8 hours)
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Dept. of ME, JSSATE, Bengaluru

Module Outcome:
At the end of this module, you will be able to:
CO# Course Outcome
Bloom’s
Level
3
List various capacity and location plans to determine
the suitable capacity required for meeting the
forecast demand of an organization.
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Dept. of ME, JSSATE, Bengaluru
Learning Objectives:
After completing this module, you should be able to:

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Dept. of ME, JSSATE, Bengaluru
• The ability to achieve, store or produce.
• For an organization, capacity would be the ability of
a given system to produce output within the
specific time period (The max. capability to
produce).
• In operations management, capacity is referred as an
amount of the input resources available to produce
relative output over period of time.
• In general terms, capacity is referred as maximum
production capacity, which can be attained within a
normal working schedule.
• Examples….
Capacity

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Dept. of ME, JSSATE, Bengaluru
• Design Capacity:
• Planned (engineered) rate of output of goods or
services under normal, or full-scale, operating
conditions.
• Examples of ….sugar, cement, automobile, hospital,
etc.
• Based on long-range forecasts (5-10 years?)
• Affected (~ reduced) by market conditions, need for
product mix, tight quality specifications, imbalance
of equipment or labour, etc. (leads to system
capacity).
Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• System Capacity:
• The maximum output of a specific product or
product mix that the system of workers and
machines is capable of producing as an integrated
whole.
• Typically less than or equal to Design Capacity of the
individual components.
• Affected by actual demand, managerial performance
– scheduling, staffing, controlling, etc., worker
inefficiencies, machine inefficiencies, etc. (leads to
actual output).
Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
Capacity in Organizations
Design Capacity
(1500 TPD)
System Capacity (Effective
Capacity)
(1200 TPD)
Actual Output (Capacity )
(900 TPD)
Affected by long-range effects:
Product mix, Market conditions,
Tight quality specifications
Inherent imbalance of equipment
& labour
Affected by short-range effects:
Actual demand; Managerial
performance, Worker (skill, effort)
& Machine inefficiencies (wear,
breakdown, scrap loss)
Relationship among Design capacity, System capacity and Actual Output
System Efficiency (or System Utilization) = Actual output / System capacity

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Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• A chemical product is produced by a series of four
processing steps, mixing, heating, molding & cooling
at a rate of 50 litres/min. The individual capacities of
the processes and the actual output of the system is
given below:
• Mixing – 48 litres/min.; Heating – 50 litres/min;
Molding – 43 litres/min.; Cooling - 46 litres/min.;
The actual output = 40 litres/min.
• What is the system capacity? System efficiency?
Capacity in Organizations

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Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• System capacity = Capacity of most limited process
• = 43 litres/min
• System efficiency = actual output / system capacity
• = 40/43 = 0.93 or 93%
Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• A manufacturer of shoes has determined that the production
facility has a design capacity of 300 shoes per week. The
effective or system capacity, however, is 230 shoes per week.
What is the manufacturer's capacity utilization relative to both
design and effective capacity if output is 200 shoes per week?
• Solution:
• Utilization is computed as the ratio of actual output over
capacity.
Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• The design capacity of an engine repair station is 80 trucks/day.
The effective capacity is 40 engines/day and the actual output is
36 engines/day. Calculate the utilization and efficiency of the
operation. If the efficiency for next month is expected to be
82%, what is the expected output?
• Solution:
• Utilization = Actual output / Design capacity
• = 36/80 = 0.45 or 45%
• System efficiency = Actual output / System or effective capacity
• = 36/40 = 0.90 or 90%
• Expected output = Effective or System Capacity * System
Efficiency
• = 40*0.82 = 32.8 engines/day
Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• A firm is willing to install automatic molding
machines to produce 250,000 good castings per year.
The molding operation takes 1.5 min per casting, but
its output is typically about 3% defective. Determine
the number of automatic molding machines the
company should buy if each one of them will be used
2000 hours per year.
• Actual output required = 250,000 good castings/year
• Required system capacity = actual output / SE
• 250,000/0.97 = 257,732 castings/year OR
• 257,732/2000 = 129 castings / hour
Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• Individual machine capacity
• = Time available in min/Time required per casting in min
• = 60 min per her/1.5 min per casting
• = 40 castings per machine per hour
• Number of machines required
• = Total number of castings required per hour /
Individual machine capacity
• = 129/40 = 3.2 machines
Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• A product line manufacturing shoes has five stations in
series whose individual capacities per shift are given in
the following table. The actual output of the line is 500
pairs per shift. Find:
• The system capacity
• The system efficiency
Capacity in Organizations
Station No. 1 2 3 4 5
Individual capacity /shift 600 650 650 550 600

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Dept. of ME, JSSATE, Bengaluru
• Solution:
• (a) The capacity of station 4 is the least. That is 550
pairs/shift. It is called station with bottleneck
operations.
• Hence system capacity = 550 pairs/shift
• (b) The actual output is 500 pairs/shift
• Hence, system efficiency
• = actual output / system capacity
• = 500/550 = 0.9091 = 90.91%
Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• Rated capacity is the theoretical output that could be
attained if a process were operating at full speed
without interruption, exceptions, or downtime.
• Effective capacity takes into account the efficiency with
which a particular product or customer can be
processed, and the utilization of the scheduled hours or
work.
• Effective daily capacity = no. of machines or workers x
hours per shift x no. of shifts x utilization x efficiency
• Utilization refers to the percentage of available working
time that a worker actually works or a machine actually
runs.
Capacity in Organizations – Some terms

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Dept. of ME, JSSATE, Bengaluru
• Scheduled maintenance, lunch breaks, and setup time are
examples of activities that reduce actual working time.
• Efficiency refers to how well a machine or worker performs
compared to a standard output level. Standards can be
based on past records of performance or can be developed
from the work-measurement techniques.
• An efficiency of 100% is considered normal or standard
performance, 125% is above normal, and 90% is below
normal. Efficiency is also dependent on product mix.
• Load is the standard hours of work (or equivalent units of
production) assigned to a production facility.
Capacity in Organizations – Some terms

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Dept. of ME, JSSATE, Bengaluru
• Facilities factors: Key factor is the design of facilities (size &
provision for future expansion). Location factors such as
costs of transportation, nearness to market, supply of
suitable labours, energy sources, etc. are also important.
• Plant layout and utilities affect labour efficiency and hence
effective capacity.
• Product/Service factors: Uniformity in products/services
(Product lines than product mix) provides opportunities for
standardisation of methods and materials. This leads to
greater effective capacity.
• Process factors: The quantity and quality capability of a
process or equipment increase the rate of output and hence
the effective capacity.
Determinants of Effective Capacity

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• Human resource factors: The actual output may be affected
by job design, activities involved, training, skill & experience
required to perform a job, employer motivation, employee
absenteeism, etc.
• Operational factors: Scheduling problems such as different
capability equipment and different job requirements may
hinder the effective capacity. In addition, factors such as
inventory decisions, late deliveries by suppliers, quality of
purchased material and parts, inspection and QC procedures
may also have an impact on effective capacity.
• External factors: Product standards, safety regulations,
labour activities, pollution control norms, etc. may hinder
effective capacity.
Determinants of Effective Capacity

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• Designing flexibility into the system
• Differentiating between new and mature
products or services
• Taking a big-picture approach to capacity
changes
• Preparing to deal with chunks of capacity
• Attempting to smooth out capacity requirements
• Identifying the optimal operating level
Developing Capacity Alternatives

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Dept. of ME, JSSATE, Bengaluru
• An auto component manufacturer has a plan of buying
hydraulic forging machines that can produce 170,000
good parts per year. These machines will be a part of a
product line. The system efficiency of the product line
is 85%.
• (a) What is the required system capacity?
• (b) Assume that it takes 100 seconds to forge each
part and the plant operates 2000 hours per year. If the
machines are used only 60% of the time and are 90%
efficient, what is the actual output of the machines
per hour?
• (c) How many forging machines would be required?
Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• (a) System capacity = actual output required per year /
system efficiency
• = 170,000/0.85 = 200,000 parts per year
• = 200,000 / 2000 hours = 100 parts per hour
• (b) Output per hour = Unit capacity x % utilization x
efficiency
• = (3600/100) x 0.60 x 0.90 = 19.44 ≅ 20 parts / hour
(..per machine)
• (c) No. of machines required = System capacity /
Output per hour
• = 100 / 20 = 5 forging machines
Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• A department works on 8 hours/shift, 250 days in a
year and has the data on the demand of a product and
standard processing time as given below:
• Determine the number of machines required.
Capacity in Organizations
Product Annual
demand, units
Processing (standard)
time/product in hours
X 300 4
Y 400 6
Z 500 3

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Dept. of ME, JSSATE, Bengaluru
• Solution:
• Total processing time (hours) required
• Annual production capacity of one machine
• = 8 x 250 = 2000 hours per year
• No. of machines required
• = Workload per year / Prodn. Capacity of each machine
• = 5100/2000 = 2.55 ≅ 3 machines
Capacity in Organizations
Product Annual
demand, units
Processing (standard)
time/product in hours
Total PT needed,
Hours
X 300 4 300 x 4 = 1200
Y 400 6 400 x 6 = 2400
Z 500 3 500 x 3 = 1500
Total 5100

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Dept. of ME, JSSATE, Bengaluru
• A firm operates 6 days a week on single shift of 8
hours/day basis. There are 10 machines of the same
capacity in the firm. If the machines are utilized 75% of
the time at a system efficiency of 80%, what is the
rated output in terms of standard hours per week?
• Soln.:
• Maximum no. of hours of work possible per week
= No. of machines x No. of days in a week x No. of hours in a day
= 10 x 6 x 8 = 480 hours
• When utilization is 75% only, then the above answer is
= 480 x 0.75 = 360 hours
• Rated output = Utilized hours x System efficiency
• = 360 x 0.80 = 288 standard hours
Capacity in Organizations

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Dept. of ME, JSSATE, Bengaluru
• Capacity planning is: determining optimum
utilization of resource (human and
equipment/machines).
• Plays an important role decision-making process, for
example, extension of existing operations,
modification to product lines, starting new products,
etc.
• Capacity planning based on the timeline is classified
into three main categories long range, medium range
and short range.
Capacity Planning

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Dept. of ME, JSSATE, Bengaluru
• Long-term capacity planning is a strategic decision
that establishes a firm’s overall level of resources.
• Extends over a time horizon long enough to obtain
those resources—usually a year or more for building
or expanding facilities or acquiring new businesses.
• Capacity decisions affect product lead times,
customer responsiveness, operating costs, and a
firm’s ability to compete.
• Inadequate capacity can lose customers and limit
growth.
• Excess capacity can drain a company’s resources and
prevent investments in more lucrative ventures.
Capacity Planning, Long-term
Critical
Decision:
When
to
increase
&
how
much
to
increase

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Dept. of ME, JSSATE, Bengaluru
• Capacity lead strategy: Capacity is expanded in
anticipation of demand growth.
• Average capacity strategy: Capacity is expanded to
coincide with average expected demand.
• Capacity lag strategy: Capacity is increased after an
increase in demand has been documented.
• How much to increase capacity depends on
– the volume and certainty of anticipated demand;
– strategic objectives in terms of growth, customer
service, and competition; and
– The costs of expansion and operation.
Capacity Expansion Strategies
Source: OM by Russel & Taylor

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Capacity Expansion Strategies
Source: OM by Russel & Taylor
Lead
Average
Lag

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Dept. of ME, JSSATE, Bengaluru
• The strategic capacity planning undertaken by
organization for a medium time horizon (6-18
months) is referred to as medium term capacity
planning (aggregate planning).
• The strategic planning undertaken by
organization for a daily, weekly or quarterly
time frame is referred to as short term capacity
planning (CRP).
Capacity Planning, Medium & Short Range

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Dept. of ME, JSSATE, Bengaluru
• Capacity requirements planning is the process of
determining short-range capacity requirements.
• It is a technique for determining what personnel and
equipment capacities are required to meet the
production objectives embodied in the ‘master
schedule’ and ‘material requirement plan’ (MRP).
• MRP and CRP together accomplish, specifically, what
materials and capacities are needed and when they are
needed.
• MRP and CRP can be done, although, manually and in
isolation, they are integrated within a computerized
system.
Capacity Requirement Planning (CRP)

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• Inputs
• Planned orders and released orders from MRP system
• Loading information from the work centre status file
• Routing information from the shop routing file
• Changes which modify capacity
• Outputs
• Loading reports of planned & released orders on key work
centres
• Verification reports to the MRP system
• Capacity modification data
• Rescheduling data to the MPS
Inputs and Outputs of CRP

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PART – II
Facility Location Planning
Dept. of ME, JSSATE, Bengaluru 37
• Need for location decisions, nature of
locations decisions, general procedure for
making locations decisions, evaluating
locations decisions, facilities layout – need
for layout decisions, types of processing.

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• A place where specific activities occur.
• Example .., Sports and military activities occur in sports
and military facilities. Nuclear research scientists work in
a nuclear research facility.
• The term is also used for buildings, equipment, and
services that are used for a particular purpose.
• Example ..,
– shopping facilities are places where we can buy things.
– Medical facilities may refer to a hospital (medical equipment,
doctors, pharmaceutical shop, etc. housed in a building),
– Restaurant facilities refer to a building where rooms are
available for stay, food is served, etc.
– University facilities ….
Facility

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Dept. of ME, JSSATE, Bengaluru
• A manufacturing facility means a factory or a plant.
The term may refer to any place that makes things, or
plants that generate electricity.
• Examples…plants that manufacture automobiles,
pharmaceuticals, chemicals, petroleum products, food
products, sanitary products, etc.
• A service facility may refer to a place where a specific
service is offered.
• Examples…hospitals, hotels, petrol bunks, medical
shops, banks, educational institutes, etc.
Facility

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Dept. of ME, JSSATE, Bengaluru
• Facility Location is the right location for the
manufacturing facility which will have sufficient access
to the customers, workers, transportation, etc.
• One of the most critical factors determining the
success of a business firm is its location.
• Facility location planning is the process of determining
the right geographical site for a firm’s operations for
achieving maximum operating economy and
effectiveness.
• The objective of facility location decision is to minimise
the sum of all costs affected by location.
Facility (Plant) Location

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Dept. of ME, JSSATE, Bengaluru
• Location decisions are strategic, long-term and non-repetitive in
nature. The reasons for making location decisions are:
• When business is newly started
• When a business firm wants to expand its markets by adding
new locations to the existing one
• When an organization experiences growth in the demand for its
products or services and the existing facility is not capable of
meeting the demand
• When the costs of inputs (due to depletion) and distribution of
outputs increase, relocation may be thought of
• Shifts in markets may cause firms to relocate
• Social and economical reasons such as shortage of labours,
electricity, changes in customers’ lifestyle, government
regulations, etc.
The Need for Location Decisions

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Dept. of ME, JSSATE, Bengaluru
• Strategic Importance
– Long term commitment/costs
– Impact on investments, revenues, and operations
– Supply chains
• Objectives
– Profit potential
– No single location may be better than others
– Identify several locations from which to choose
• Options
– Expand existing facilities
– Add new facilities
– Move
The Nature of Location Decisions
Source: OM by W J Stevenson

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Dept. of ME, JSSATE, Bengaluru
• Decide on the criteria to use for evaluating location
alternatives, such as increased revenues, decreased
cost, or community service.
• Identify important factors, such as location of markets
or raw materials.
• (The factors will differ depending on the type of facility.
For example, retail, manufacturing, distribution,
healthcare, and transportation all have differing factors
that guide their location decisions).
• Develop location alternatives:
– Identify a country or countries for location.
– Identify the general region for a location.
General procedure for making location decisions
Source: OM by W J Stevenson

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Dept. of ME, JSSATE, Bengaluru
• Develop location alternatives:
– Identify a small number of community alternatives.
– Identify site alternatives among the community
alternatives.
• Evaluate the alternatives and make a selection.
General procedure for making location decisions
Source: OM by W J Stevenson

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Source: OM by W J Stevenson
Factors Affecting Location Decisions
Level
Regional
Factors
Location of raw
materials or
supplies
Location of
markets
Labour
Considerations
Proximity, modes and costs of
transportation, quantity
available
Proximity, distribution costs,
target market, trade practices /
restrictions
Availability (general and for
specific skills), age distribution
of workforce, work attitudes,
union or nonunion,
productivity, wage scales,
unemployment
compensation laws

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Source: OM by W J Stevenson
Factors Affecting Location Decisions
Level
Community
Factors
Quality of life
Services
Attitudes
Taxes
Environmental
regulations
Utilities
Development
support
Considerations
Schools, churches, shopping,
housing, transportation,
entertainment, recreation, cost
of living
Medical, fire, and police
Pro / Con
State/local, direct and indirect
State / local
Cost and availability
Bond issues, tax abatement,
low-cost loans, grants

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Source: OM by W J Stevenson
Factors Affecting Location Decisions
Level
Site
Factors
Land
Transportation
Environmental /
legal
Considerations
Cost, degree of development
required, soil characteristics
and drainage, room for
expansion, parking
Type (access roads, rail spurs,
air freight)
Zoning restrictions

• Locational cost-profit-volume analysis
• Factor rating, and
• The center of gravity method.
• Cost-profit-volume analysis is also called break-even
analysis.
• Cost-profit-volume analysis is a technique for evaluating
location choices in economic terms.
• The different locations are compared economically,
either numerically or graphically.
Dept. of ME, JSSATE, Bengaluru 49
Source: OM by W J Stevenson
Evaluating Location Alternatives

• Procedure
• Determine the fixed and variable costs associated with each location
alternative.
• Plot the total-cost lines for all location alternatives on the same graph.
• Determine which location will have the lowest total cost for the
expected level of output. Alternatively, determine which location will
have the highest profit.
• Assumptions
1. One product is involved
2. Everything produced can be sold
3. Variable cost per unit is the same regardless of volume
4. Fixed costs do not change with volume
5. Revenue per unit is constant with volume
6. Revenue per unit exceeds variable cost per unit
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Source: OM by W J Stevenson
Cost-Profit-Volume Analysis

• The total cost (TC) is given by
• Total cost = FC + v *Q, where,
• FC - fixed cost; v – variable cost/unit; Q – quantity or
volume of output
• The volume of output is shown along abscissa and the cost
or sales revenue along ordinate
• Fixed cost line is a horizontal line from x = 0, and y =
fixed cost
• Total cost line is an inclined line from the beginning of
fixed cost line
• Total revenue line is an inclined line from the origin.
• The intersection of TC and TR line is called break-even
point Dept. of ME, JSSATE, Bengaluru 51
Source: OM by W J Stevenson
Cost-Profit-Volume Analysis

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Source: OM by W J Stevenson
Cost-Profit-Volume Analysis

• Total Revenue = Unit Selling Price (SP) x Sales quantity,
(Q)
• Total Cost = Total Fixed Cost (FC) + Total Variable Cost
(VC)
• Total profit, P = Total revenue – Total cost
• P = (Q x SP) – (FC + v x Q)
• P = Q (SP -v) – FC
Dept. of ME, JSSATE, Bengaluru 53
Source: OM by W J Stevenson
Cost-Profit-Volume Analysis
Where, SP – Selling Price / unit; VC – Variable Cost/unit

1. Jayna Steel India is planning to start a new factory for
manufacturing steel utensils. It is considering three location
options, viz. Bokaro, Jamshedpur and Bhilai. The fixed costs at the
three locations have been estimated as Rs. 8.15 million, 7.377
million, and 7.093 million respectively. The variable costs/unit at
the three locations are estimated at Rs. 500, Rs. 580, and Rs. 490
respectively. The factory will have an annual production capacity
of 10,000 utensils and in the initial years it will operate at 75%
efficiency. Find the best location option.
Dept. of ME, JSSATE, Bengaluru 54
Source: POM by Kanishka Bedi
Cost-Profit-Volume Analysis - Examples
Location Fixed cost,
Rs. Million
Variable
cost/unit, Rs
Annual utensils
required
Bokaro 8.15 500
10,000
Jemshedpur 7.377 580
Bhilai 7.093 490

Solution:
• Find the total cost (TC) at each location.
• Choose the one that yields the least cost
• Q = 10,000 units/year; Efficiency = 75% or 0.75
• Hence, the production output/year = 10,000*0.75 = 7,500 units
Dept. of ME, JSSATE, Bengaluru 55
Source: POM by Kanishka Bedi
Cost-Profit-Volume Analysis - Examples
Location Fixed cost,
Rs. Million
Variable
cost/unit, Rs
Total Cost = FC + v*Q
Rs./year
Bokaro 8.15 500 81,50,000 + 500*7,500
= 1,19,00,000
Jemshedpur 7.377 580 73,77,000 + 580*7,500
= 1,17,27,000
Bhilai 7.093 490 70,93,000 + 490*7,500
= 1,07,68,000

Solution:
• Find the total cost (TC) at each location.
• Choose the one that yields the least cost
• Q = 10,000 units/year; Efficiency = 75% or 0.75
• Hence, the production output/year = 10,000*0.75 = 7,500 units
Dept. of ME, JSSATE, Bengaluru 56
Source: POM by Kanishka Bedi
Cost-Profit-Volume Analysis - Examples
Location Fixed cost,
Rs. Million
Variable
cost/unit,
Rs
Total Cost = FC + v*Q
Rs./year
Bokaro 8.15 500 81,50,000 + 500*7,500
= 1,19,00,000
Jemshedpur 7.377 580 73,77,000 + 500*7,500
= 1,17,27,000
Bhilai
(Best location)
7.093 490 70,93,000 + 490*7,500
= 1,07,68,000

2. A manufacturer of farm equipment is considering three locations
or sites (A, B, and C) for a new plant. Cost studies show that fixed
costs per year at the sites are $240,000, $270,000, and $252,000
respectively. The variable cost per unit are estimated to be $100,
$90, and $95 respectively. If the plant is designed to have an
effective system capacity of 2,500 units per year and is expected
to operate at 80% efficiency, what is the most economic location
on the basis of actual output?
Dept. of ME, JSSATE, Bengaluru 57
Source: OM by Joseph Monks
Cost-Profit-Volume Analysis - Examples
Location Fixed cost, $ Variable
cost/unit, $
Annual output
required
A 240,000 100
2500
B 270,000 90
C 252,000 95

Solution:
• Find the total cost (TC) at each location.
• Choose the one that yields the least cost
• Q = 2,500 units/year; Efficiency = 80% or 0.80
• Hence, the production output/year = 2500*0.80 = 2000 units
Dept. of ME, JSSATE, Bengaluru 58
Cost-Profit-Volume Analysis - Examples
Location Fixed cost, $ Variable
cost/unit, $
Total Cost = FC + v*Q
$/year
A 240,000 100
240000 + 100*2000
= 440,000
B 270,000 90
270000 + 90*2000
= 450,000
C 252,000 95
252000 + 95*2000
= 442,000
Source: OM by Joseph Monks

Solution:
• Find the total cost (TC) at each location.
• Choose the one that yields the least cost
• Q = 2,500 units/year; Efficiency = 80% or 0.80
• Hence, the production output/year = 2500*0.80 = 2000 units
Dept. of ME, JSSATE, Bengaluru 59
Cost-Profit-Volume Analysis - Examples
Location Fixed cost, $ Variable
cost/unit, $
Total Cost = FC + v*Q
$/year
A
(Best)
240,000 100
240000 + 100*2000
= 440,000
B 270,000 90
270000 + 90*2000
= 450,000
C 252,000 95
252000 + 95*2000
= 442,000
Source: OM by Joseph Monks

• Fixed and variable costs for four potential plant locations are
shown as follows.
• Expected output level = 10,000 units/year
• (a) Plot the total-cost lines for these locations on a single graph.
• (b) Identify the range of output for which each location
(alternative) is superior (i.e., has the lowest total cost).
• (c) If expected output at the selected location is to be 8,000 units
per year, which location would provide the lowest total cost?
Dept. of ME, JSSATE, Bengaluru 60
Source: OM by W J Stevenson
Cost-Profit-Volume Analysis - Examples
3

• a. Plot the graph
• Compute the total cost for each location at the given
output level:
• Plot each location’s fixed cost (at Output = 0) and the
total cost at 10,000 units; and connect the two points
with a straight line.
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Source: OM by W J Stevenson
Cost-Profit-Volume Analysis - Examples

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Source: OM by W J Stevenson
Cost-Profit-Volume Analysis - Examples
Total cost lines for two locations are shown
TC for both the locations is equal
TC of location B is less than
that of A till this point

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Source: OM by W J Stevenson
Cost-Profit-Volume Analysis - Examples

• (b) The approximate ranges for which the various
alternatives will yield the lowest costs are shown in the
graph:
• Location A: More than (beyond) 11,200 units/year ---
approx.
• Location B: From 0 to 5000 units/year
• Location C: Between 5000 to 11,200 units/year
• Location D: Not at all suitable.
• (c) From the graph, for 8,000 units per year, location C
provides the lowest total cost.
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Source: OM by W J Stevenson
Cost-Profit-Volume Analysis - Examples

4. Sigma Instruments Pvt. Ltd. is considering three locations for its
new factory – Bengaluru, Hyderabad, and Chennai. The estimates
of different costs at the three location options are given below.
The company is financed by SBI for its construction at an interest
rate of 15% p.a. Find an economic location for the production of
5000 – 10,000 units per annum.
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Cost-Profit-Volume Analysis - Examples
Cost details Bengaluru Hyderabad Chennai
Transportation cost, Rs./unit 10 20 9
Cost of materials, Rs./unit 120 110 100
Taxes, Rs./year 40,000 35,000 45,000
Cost of construction of the
factory, Rs.
5 million 4 million
4.7
million
Electricity, Rs./year 22,000 15,000 25,000
Labour, Rs./unit 26 21 23
Source: POM by Kanishka Bedi

• Find the total FC and VC for each location
• Find the TC for each location for outputs of 5000 units and 10,000
units/year.
• Plot the Break-even chart
• Decide the economic location for the given output range.
• For 5000 units/year (Q), the Total Cost at:
• Location B: TC = FC + v*Q = 812,000+156*5000 = Rs. 15,92,000
• Location H: TC = FC + v*Q = 650,000+151*5000 = Rs. 14,05,000
• Location C: TC = FC + v*Q = 775,000+132*5000 = Rs. 14,35,000
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Cost-Profit-Volume Analysis - Examples
Location FC, Rs./year VC, (v) Rs./unit
B 812,000 156
H 650,000 151
C 775,000 132
Source: POM by Kanishka Bedi

• For 10,000 units/year (Q), the Total Cost at:
• Location B: TC = FC + v*Q = 812,000+156*10000
• = Rs. 23,72,000
• Location H: TC = FC + v*Q = 650,000+151*5000
• = Rs. 21,60,000
• Location C: TC = FC + v*Q = 775,000+132*5000
• = Rs. 20,95,000
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Cost-Profit-Volume Analysis - Examples
Source: POM by Kanishka Bedi
Units Bengaluru Hyderabad Chennai
0 812,000 650,000 775,000
5,000 15,92,000 14,05,000 14,35,000
10,000 23,72,000 21,60,000 20,95,000

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TC at Hyderabad = TC at Chennai
650,000+151*Q = 775,000+132*Q
Hence, Q = 6580 units

5. Potential locations, A, B and C have the cost structures shown in
the table for a product expected to sell at $130.
• (a) Find the most economic location for an expected volume of
6000 units/year.
• (b) What is the expected profit, if the selected site is used?
• (c) For what output range each location is suitable?
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Cost-Profit-Volume Analysis - Examples
Source: POM by Kanishka Bedi
Potential Location FC, $/year VC, (v) $/unit
A 150,000 75
B 200,000 50
C 400,000 25

• (a)
• For 6,000 units/year (Q), the Total Cost at:
• Location A: TC = FC + v*Q = 150,000 + 75*6000 = $ 600,000
• Location B: TC = FC + v*Q = 200,000 + 50*6000 = $ 500,000
• Location C: TC = FC + v*Q = 400,000 + 25*6000 = $ 550,000
• Conclusion: The most economical location is B.
• (b) Expected profit = $(130 *6000) – 500,000 = $280,000
• (c) Preference of locations
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Cost-Profit-Volume Analysis - Examples
Source: POM by Kanishka Bedi

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Cost-Profit-Volume Analysis - Examples
Source: POM by Kanishka Bedi

• (c) Preference of locations:
• From the graph,
• Up to 2000 units/year, Location A is suitable
• Between 2000 to 7400 units, Location B is suitable
• Beyond 7400 units, Location C is suitable.
• Analytically:
• Compare A & B:
• TC at A = TC at B to find a quantity, Q
• 150,000 + 75*Q = 200,000 + 50*Q
• Hence, Q = 50000/25 = 2000 units
• Compare B & C:
• TC at B = TC at C to find a quantity, Q
• 200,000 + 50*Q = 400,000 + 25*Q; Hence Q = 8000 units
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Cost-Profit-Volume Analysis - Examples
Source: POM by Kanishka Bedi

• 6. A dry cleaning firm is considering four possible sites for its new
operation. They expect to clean 10,000 garments/month. The
table below shows the various cost elements:
• Find the most economic location and range of output where each
location is suitable.
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Cost-Profit-Volume Analysis - Examples
Source: POM by Sanders

Dept. of ME, JSSATE, Bengaluru 74

• 7. Titan Ltd., is considering two location options for its new clock
manufacturing facility, Pune and Noida. The company estimates
that the FC and VC at Pune are Rs. 2 million and Rs. 30/clock. At
Noida, the estimates are Rs. 1.8 million and Rs. 40 respectively.
The selling prices are different at Pune and Noida, Rs. 120/clock
and Rs. 100/clock respectively.
• The company would like to choose a location where the break-
even volume is less. Choose the best location.
• Solution:
• BE Volume at Pune = FC/(SP-VC) = 2000000/(120-30) = 22,222
• BE Volume at Noida = FC/(SP-VC) = 1800000/(100-40) = 30,000
• Pune is the best location
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Cost-Profit-Volume Analysis - Examples
Source: POM by Kanishka Bedi

8. A firm is considering four locations for its new factory – A, B, C,
and D. The estimates of different costs at the four location
options are given below. The firm will finance the new plant from
bonds bearing an interest of 10% p.a. Find an economic location
for the production of 50,000 – 100,000 units per annum.
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Cost-Profit-Volume Analysis - Examples
Cost ($) details A B C D
Transportation cost, per unit 0.02 0.10 0.10 0.05
Materials & equipment, per unit 0.43 0.60 0.40 0.55
Taxes, per year 33k 28k 63k 35k
Plant construction cost, $ million 4.60 3.90 1.0 4.80
Electricity, per year 30k 26k 30k 28k
Labour, per unit 0.75 1.10 0.80 0.90
Water, per year 7k 6k 7k 7k
Source: POM by J. Monks

• Find the total FC and VC for each location
• Find the TC for each location for outputs of -- units and --
units/year.
• Plot the Break-even chart
• Decide the economic location for the given output range.
• For 100,000 units/year (Q), the Total Cost at:
• Location A: TC = FC + v*Q = 530,000+1.2*100k = $650,000
• Location B: TC = FC + v*Q = 450,000+1.8*100k = $630,000
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Cost-Profit-Volume Analysis - Examples
Location FC, $./year VC, (v) $./unit
A 530,000 1.2
B 450,000 1.8
C 500,000 1.3
D 550,000 1.5
Source: POM by Kanishka Bedi

• Location C: TC = FC + v*Q = 500,000+1.3*100k = $630,000
• Location D: TC = FC + v*Q = 550,000+1.5*100k = $700,000
• From the BE Chart:
• Location B is suitable for a volume of 50,000 to 100,000 units.
• Location C is suitable for a quantity 100,000 to130,000 units
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Cost-Profit-Volume Analysis - Examples
Source: POM by Kanishka Bedi

• A means of assigning weights (quantitative value) to all the
factors related to each location alternative and deriving a
composite score that can be used for comparison.
• Both qualitative and quantitative factors are considered.
• Steps:
• Develop a list of factors
• Assign a weight to each factor (from 0 to 1 or 1 to 100)
• Determine the composite score for each location using:
Composite score = Σwi*si where,
• wi is the weight for factor , i; si is the score for factor, i
• Choose the location with maximum composite score
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Factor Rating Analysis

• A company is evaluating four locations for a new plant and has
weighed the relevant factors as shown below. Develop a
quantitative factor comparison for the location and identify the
best one.
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Factor Rating Analysis - Examples
Factor Assigned
weight
Score of Location
1 2 3 4
Production cost 0.33 50 40 35 30
Raw material supply 0.25 70 80 75 80
Labour availability 0.20 55 70 60 45
Cost of living 0.05 80 70 40 50
Environment 0.02 60 60 60 90
Market 0.15 80 90 85 50

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Factor Rating Analysis - Examples
Factor Assigned
weight
Weighted Score of Location
1 2 3 4
Production cost 0.33 50*0.33 =
16.50
40*0.33 =
13.20
35 30
Raw material
supply
0.25 70*0.25 =
17.50
80*0.25 =
20.00
75 80
Labour
availability
0.20 55*0.20 =
11.00
70*0.20 =
14.00
60 45
Cost of living 0.05 80*0.05 = 4.00 70*0.05 =
3.50
40 50
Environment 0.02 60*0.02 = 1.2 60*0.02 =
1.20
60 90
Market 0.15 80*0.15 = 12 90*0.15 =
13.50
85 50
Total score 62.00 65.40 58.20 50.70

• A company is evaluating two locations for a new plant and has
weighed the relevant factors as shown below. Develop a
quantitative factor comparison for the location and identify the
best one.
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Factor Rating Analysis - Examples

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Factor Rating Analysis - Examples
Decision: Location 2 is the best

• Location of a production centre or warehouse which will
minimize the costs of distributing (transporting)
specified volumes of a product to surrounding markets
or locations.
• It is an approach that seeks to compute geographic
coordinates for a potential single new facility that will
minimize costs.
• The main inputs considered are:
• Distances of markets
• Volume of goods shipped
• Shipping costs
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Centre of Gravity Method

• Steps:
• Determine the relative distances between existing
facilities.
• The distances are established by placing existing
facilities on a co-ordinate grid system.
• Find the best location of the new facility using the
formula,
• Cx = X coordinate of center of gravity; Cy = Y coordinate of
center of gravity; dix = X coordinate of the ith location;
diy = Y coordinate of the ith location; Vi = volume of goods
moved to or from ith location
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Centre of Gravity Method
V
V
d
=
C
i
i
ix
x
∑
∑ C =
d V
V
y
iy i
i
∑
∑

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Centre of Gravity Method

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Centre of Gravity Method

• A food delivery firm would like to establish a new food production
& distribution centre in a suitable location. It has estimated the
possible number of food containers to be distributed every day to
eight market locations whose distances are given below:
• Identify the economic food production/distribution centre.
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Centre of Gravity Method - Example
Market # Volume X, km Y, km
1 8 2.5 10
2 20 3 5
3 12 6.5 8
4 10 11 10
5 30 11 8
6 20 10 4
7 40 13 3.5
8 30 12 2

• X-coordinate of proposed location = 1678/170 = 9.9 km
• Y-coordinate of proposed location = 896/170 = 5.3 km
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Centre of Gravity Method - Example
Market # Volume, Vi Xi, km Yi, km Vi*Xi Vi*Yi
1 8 2.5 10 20 80
2 20 3 5 60 100
3 12 6.5 8 78 96
4 10 11 10 110 100
5 30 11 8 330 240
6 20 10 4 200 80
7 40 13 3.5 520 140
8 30 12 2 360 60
Total ΣV = 170 Σ=1678 Σ=896

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Centre of Gravity Method - Example

• X-coordinate of proposed warehouse = 1360/200 = 6.8 miles
• Y-coordinate of proposed warehouse = 1520/200 = 7.6 miles
• TC of market A = {(8-6.8)+(12-7.6)}*40*0.12 = $26.88
• TC of market B = {(6-6.8)  + (4-7.6) } *20*0.10 = $8.80
• TC of market C = {(2-6.8)  + (8-7.6) } *60*0.10 = $31.20
• TC of market D = {(10-6.8)+(6-7.6) } *80*0.10 = $38.40
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Centre of Gravity Method - Example
Market # Demand in
tons, Vi
Xi, miles Yi, miles Vi*Xi Vi*Yi
A 40 8 12 320 480
B 20 6 4 120 80
C 60 2 8 120 480
D 80 10 6 800 480
Total ΣV = 200 Σ=1360 Σ=1520

Facility Layout Planning
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• After the site location decision has been made, the next
focus in production planning is the facility’s layout.
• The goal is to determine the most efficient and effective
design for the particular production process.
• A manufacturer might opt for a U-shaped production
line, for example, rather than a long, straight one, to
allow products and workers to move more quickly from
one area to another.
• Facility layout is the physical arrangement of various
departments/units, machines/equipment within the
departments, stores, walking spaces, etc. within the
plant premises.
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Facility Layout

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• The basic objective of layout is to ensure a smooth flow
of work, material, and information through a system.
• The layout and design of the space within the facility
(plant premises) impact greatly on how the work is done
• The key to good facility layout and design is the
integration of the needs of people (personnel and
customers), materials (raw, finished, and in process),
and machinery in such a way that they create a single,
well-functioning system.
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Facility Layout

• Space utilization
• Shipping and receiving
• Ease of communication and support
• Impact on employee morale and job satisfaction
• Promotional value (small businesses where visitors in
the form of customers, vendors, investors, etc., - the
facility layout must be an attractive one that further
burnishes the company's reputation)
• Safety—The facility layout should enable the firm to
effectively operate in accordance with Occupational
Safety and Health Administration guidelines and other
legal restrictions.
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Facility Layout –Factors Affecting

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Facility Layout –Types
Source: OM by Gaither, et al
Process Layout
The process layout arranges workflow around the production process. All
workers (machines/equipment) performing similar tasks are grouped
together.
Products pass from one workstation to another (but not necessarily to
every workstation).
This layout is best for firms that produce small numbers of a wide variety
of products.

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Facility Layout –Types
Source: OM by Gaither, et al
Product or Assembly line Layout
• Products that require a continuous or repetitive production process use
the product (or assembly-line) layout.
• When large quantities of a product must be processed on an ongoing
basis, the workstations or departments are arranged in a line with
products moving along the line.
Ex., Automobiles, food-processing plants, pharmaceuticals, consumer
goods, etc.

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Facility Layout –Types
Source: OM by Gaither, et al
Fixed Position Layout

• Some products cannot be put on an assembly line or
moved about in a plant.
• A fixed-position layout lets the product stay in one
place while workers and machinery move to it as
needed.
• Products that are impossible to move—ships, airplanes,
and construction projects—are typically produced using
a fixed-position layout.
• The fixed-position layout is also common for on-site
services such as housecleaning services, pest control,
and landscaping.
• https://www.youtube.com/watch?v=-ovNi1cB7a4&feature=emb_logo
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Facility Layout –Types

• Cellular layouts combine some aspects of both product
and fixed-position layouts.
• Work cells are small, self-contained production units
that include several machines and workers arranged in a
compact, sequential order.
• Each work cell performs all or most of the tasks
necessary to complete a manufacturing order.
• There are usually five to 10 workers in a cell, and they
are trained to be able to do any of the steps in the
production process.
• The goal is to create a team environment wherein team
members are involved in production from beginning to
end. Dept. of ME, JSSATE, Bengaluru 103
Facility Layout –Types Cellular Layout

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Cellular Layout
Facility Layout –Types