Section Objectives

1

• Section Objectives
• After completing this section, you should be able
  to
• 1. Explain the importance of capacity planning.
• 2. Discuss ways of defining and measuring
  capacity.
• 3. Describe some of the factors that determine
  effective capacity.
• 4. Discuss the major considerations related to
  developing capacity alternatives.
• 5. Describe approaches that are useful for
  evaluating process selection and capacity
  alternatives.

2

• Capacity
• Definition
• The amount of output generated by a production
  system over some interval of time.
• Defined by
• 1. Resources available - e.g. 2,000 direct labour
  hours per year
• 2. Output capabilities - e.g. 5,000 widgets per
  month
• Capacity depends on
• 1. Resources - input availability
• 2. Product mix - a different mix redefines
  capacity
• 3. Technology - degree of capital investment
• 4. Time frame - capacity is influenced by the
  time frame used to measure it

• Significance of Capacity Decisions
• 1. Commitment to satisfy market demand for
  specific outputs
• 2. Commitment to provide employment for labour
  force.
• 3. Major capital investment for the organization.
• 4. Inaccuracy of long-term demand forecasts
  limits capacity decisions.
• 5. Incorrect capacity decisions can be costly to
  the organization.

3

• Difficulties in Measuring Actual Capacity
• 1. Diversity of output mix
• single output - use output measure of capacity.
• multiple outputs - use input measure of capacity
• 2. Specification of time interval representing
  real capacity
• maximum capacity
• normal capacity
• short-range, intermediate-range and long-range
  capacity
• 3. Day-to-day variation
• employee absenteeism
• equipment breakdown
• maintenance and repair
• work setups / changeovers
• employee vacations

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Measuring Capacity Illustration 1
A grocery store has five regular checkout lines
and one express line(12 items or less). Based on
a sampling study, it takes 11 minutes on average
for a customer to go through the regular line and
4 minutes to go through an express line. The
store is open from 9 a.m. to 9 p.m. daily, seven
days a week. A) What is the stores maximum
capacity? B) What is the capacity if the number
of regular checkout lines operating is according
to the following schedule?(The express
line is always open.) Hour / Day Mon. Tue. Wed.
Thur. Fri. Sat. Sun. 9 - 12 1 1
1 1 3 5 2 12 - 4 2 2
2 2 3 5 4 4 - 6 3 3
3 3 5 3 2 6 - 9 4
4 4 4 5 3 1
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Efficiency and Utilization
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Efficiency/Utilization Example

• Design capacity 50 trucks/day
• Effective capacity 40 trucks/day
• Actual output 36 units/day
• Actual output 36
  units/day
• Efficiency 90
• Effective capacity 40
  units/ day
• Utilization Actual output 36
  units/day 72
• Design capacity
  50 units/day

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Measuring Capacity - Illustration 2
A roller coaster at Treasure Island Amusement
Park consists of 15 cars, each of which can
carry up to 3 passengers. If each run takes 1.5
minutes and the time to unload and load riders is
3.5 minutes, what is the maximum capacity of the
system in number of passengers per hour? Would
the actual capacity observed actually equal this
value? Explain.
Measuring Capacity - Illustration 3
An automobile transmission-assembly plant
normally operates one shift per day, 5 days a
week. During each shift, 400 transmissions can
be completed. Over the next 4 weeks, the plant
has planned shipments according to the following
schedule Week 1 2 3
4 Shipments 1800 1700 2200 2100
a. What is the normal capacity? b. At what
percent of capacity is the plant actually
operating?
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Measuring Capacity - Illustration 4
A company manufactures 4 products on 3 machines.
Production for the next six months is given
below Product Jan Feb Mar Apr
May June 1 200 0 200 0 200 0 2 100 100
100 100 100 100 3 50 50 50 50
50 50 4 100 0 100 0 100 0
The number of hours each product requires on each
machine is given in the following table
Product
Machine 1 2 3 4 1 0.25 0.15 0.15 0.25
2 0.33 0.20 0.30 0.50
3 0.20 0.30 0.25 0.10
Setup times are 20 of operation times. The
number of machine hours available in next 6
months are
Machine Jan Feb Mar Apr May June
1 120 60 60 60 60 60 2 180 60 180 60 180 60
3 120 60 120 60 120 60
Determine if there is enough capacity to meet
product demand.
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• Definitions of Long-Range Capacity
• 1. Production Capacity - The maximum production
  of an organization.
• 2. Maximum Practical Capacity - that output
  attained within the normal operating schedule of
  shifts per day and days per week while bringing
  in high-cost, inefficient facilities.
• 3. Output Rate Capacity - a measure of production
  capacity based on an organizations outputs. e.g.
  automobiles per month.
• 4. Aggregate Unit of Capacity - a measure of
  production capacity that is used when an
  organizations outputs are diverse. e.g. sales
  dollars per month, tons per month, or other
  measures of capacity.
• 5. Input Rate Capacity - a measure of production
  capacity based on an organizations inputs. e.g.
  available seat-miles per month.
• 6. Percentage of Capacity Utilization - a measure
  of production capacity based on the relative
  outputs generated per inputs required in some
  time period. e.g. actual number of automobiles
  produced divided by the quarterly automobile
  production capacity, or the number of
  labour-hours used during the month divided by the
  number of labour-hours available in the work
  force.

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• Facility Planning
• Principle 1 Production units(plants) have an
  optimal rate of output for minimum cost. This
  is frequently known as the best operating level.

Short-Run Average Cost
Volume
Principle 2 Minimum cost and optimal operating
rate are functions of the size of a production
unit. This is known as economies of scale.
Long-Run Average Cost
Volume
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SHORT-TERM CAPACITY ADJUSTMENT
Increase Capacity
Decrease Capacity
Type of System
Hire Employees Add Shifts Overtime Subcontract Dep
lete Inventory Defer Maintenance Standardize
Output
Layoff Employees Reduce Shifts Reduce
Workweek Shutdown Facilities Lease
Facilities Employee Attrition
Manufacturing Systems
Hire Employees Overlap Shifts Change Workforce
Mix Overtime Offload Activities Defer Maintenance
Standardize Output
Fire / Layoff Employees Reduce Work
Schedules Shutdown Facilities Lease
Facilities Employee Attrition
Service Delivery Systems
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• Ways of Changing Long-Range Capacity
• Expand Capacity
• 1. Subcontract with other companies to become
  suppliers of the expanding firms components or
  entire products.
• 2. Acquire other companies, facilities or
  resources.
• 3. Develop sites and / or buildings or buy
  equipment.
• 4. Expand, update or modify existing facilities.
• 5. Reactivate facilities that are on a standby
  basis.
• Reduce Capacity
• 1. Sell existing facilities, sell inventories and
  layoff or transfer employees.
• 2. Mothball facilities and place on standby
  status, sell inventories and layoff or transfer
  employees.
• 3. Develop and phase in new products as other
  products decline.

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Changing Capacity - Illustration 1
A small firm intends to increase capacity of a
bottleneck operation by adding a new machine.
Two alternatives, A and B, have been identified,
and the associated costs and revenues have been
estimated. Annual fixed costs would be 40,000
for A and 30,000 for B variable costs per unit
would be 10 for A and 12 for B. Revenue per
unit would be 15 for A and 16 for B. a.
Determine each alternatives breakeven point in
units. b. At what volume of output would the two
alternatives yield the same profit? c. If
expected annual demand is 12,000 units, which
alternative would yield the higher profit?
Changing Capacity - Illustration 2
A producer of pottery is considering the addition
of a new plant to absorb the backlog of demand
that exists. The primary location being
considered will have fixed costs of 9,200 per
month and variable costs of 70 cents per unit
produced. Each item is sold to retailers at a
price that averages 90 cents.
a. What volume per month is necessary in order to
break even? b. What profit would be realized on a
monthly volume of(1)61,000 units? (2) 87,000
units?
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LONG-TERM CAPACITY EXPANSION
Advantages
Disadvantages
Capacity Expansion
- Minimizes Immediate Capital Investment - Less
Risk / Cost of Over-forecasting Demand
- Higher Cost per Sq. Ft. for Construction -
Inflationary Pressures on Future Construction -
Unable to Handle Unexpected Demand - Higher Cost
per Unit of Output(?)
Small Increments
- Lower Cost per Sq. Ft. for Construction -
Absorb Demand Increases Beyond Estimates - Lower
Cost per Unit of Output(?)
- Requires Large Capital Investment - Opportunity
Cost of Investing in Excess Capacity - Higher
Risk / Cost of Over-Forecasting Demand
Large Increments
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• Algebraic C-V-P Analysis
• The calculation of the breakeven point is not
  easily done using a graph. It is more easily
  done by using a formula. The following formulas
  are available
• Breakeven point (units) FC / (P V)
• Where FC fixed costs
• P selling price per unit
• V variable cost per unit

The owner of Old-Fashioned Berry Pies is
contemplating adding a new line of pies, which
will require leasing new equipment for a monthly
payment of 6,000. Variable costs would be 2.00
per pie, and pies would sell for 7.00 each. How
many pies must be sold to breakeven? Solution
FC 6,000 VC 2 per pie
SP 7 per pie Breakeven point
(units) 6,000 / (7 2) 1,200 pies/month
Example 1 Breakeven Point in Units
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• Algebraic C-V-P Analysis - continued
• The breakeven point can also be calculated in
  dollars. This calculation is particularly useful
  where the ratio of variable cost to selling price
  is given.
• Breakeven point (dollars) FC / 1 (V/P)
• Where FC fixed costs
• V/P ratio of variable costs to selling price

Jimmy Stevens, Inc has fixed costs of 10,000
this period. Variable costs, consisting of
direct labor and materials, are 60 percent of
selling price. What is the breakeven point in
dollars? Solution FC 10,000
V/P 60 Breakeven point (dollars)
10,000 / (1 - .60) 25,000
Example 2 Breakeven Point In Dollars
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• Indifference Point Total Costs
• The procedure
• 1. Select the alternatives to be compared 2 or
  more.
• 2. Identify the fixed and variable costs for
  each alternative.
• 3. Let X the output level that is, the volume
  that produces equal costs between two
  alternatives.
• 4. Calculate the indifference point between pairs
  of alternatives as follows
• FC(A) VC(A) X FC(B) VC(B) X
• Where
• FC(A) the fixed costs for Alternative A
• VC(A) the variable cost per unit for
  Alternative A
• FC(B) the fixed costs for Alternative B
• VC(B) the variable cost per unit for
  Alternative B
• X the output level that produces
  equal total costs for both alternatives

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• Indifference Point Profit
• The procedure
• Select the alternatives to be compared 2 or
  more.
• Identify the selling price and fixed and variable
  costs for each alternative.
• Let X the output level that is, the volume
  that produces equal costs between two
  alternatives.
• Calculate the indifference point between pairs of
  alternatives as follows
• SP(A) VC(A X - FC(A) SP(B) VC(B X -
  FC(B) Where
• SP(A) the selling price per unit for
  Alternative A VC(A) the variable cost per unit
  for Alternative A
• FC(A) the fixed costs for Alternative A
• SP(B) the selling price per unit for
  Alternative A FC(B) the fixed costs for
  Alternative A
• VC(B) the variable cost per unit for
  Alternative A
• X the output level that produces
  equal total costs for both alternatives

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Long-Term Capacity Planning - Illustration 1
The ABC Company has a cost of capital of 10 and
projected sales increases of Year Sales
Growth 1 1,000 2 2,000 3 4,000 4 7,000 5 10,000
The company can either add a single expansion of
24,000 units today or an expansion of 8,000 units
today and another expansion of 16,000 units at
the end of Year 3. The respective costs are
outlined below
Average Operating Cost per Unit per Year
Unit Expansion Investment Cost
A B A B
Year
A B
1 2 3 4 5
24,000 8,000 600,000 240,000 16,000 (end of
Year 3) 430,000
18 17 15 15 12 17 10 12 18 19
Which alternative is preferred?
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Long-Term Capacity Planning - Illustration 2
The DEF Company has a cost of capital of 14 and
projected annual sales of Year Sales
1 1,000 2 2,000 3 4,000 4 6,500
5 9,500 6 13,000 36,000
The company can add capacity in either two or
three increments with the following costs
Average Operating Cost per Unit per Year
Unit Expansion Investment Cost
A B A B
Year
A B
0 1 2 3 4 5 6
11 12 10 12 11 10 8 10 7 8 8 8
5,250 3,000 200,000 135,000 5,000 275,000
9,750 475,000 7,000 425,000
Which alternative is preferred?
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Waiting Lines

• Queuing theory Mathematical approach to the
  analysis of waiting lines.
• Goal of queuing analysis is to minimize the sum
  of two costs
• Customer waiting costs
• Service capacity costs

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Implications of Waiting Lines

• Cost to provide waiting space
• Loss of business
• Customers leaving
• Customers refusing to wait
• Loss of goodwill
• Reduction in customer satisfaction
• Congestion may disrupt other business operations

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Queuing Analysis
Figure 19-1
Total cost
Customer waiting cost
Capacity cost


Total cost
Cost
Cost of service capacity
Cost of customers waiting
Optimum
Service capacity
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System Characteristics

• Population Source
• Infinite source customer arrivals are
  unrestricted
• Finite source number of potential customers is
  limited
• Number of observers (channels)
• Arrival and service patterns
• Queue discipline (order of service)

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Elements of Queuing System
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Queuing Systems
Multiple channel
Multiple phase
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Poisson Distribution
Figure 19-4
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System Performance
Measured by

• Average number of customers waiting
• Average time customers wait
• System utilization
• Implied cost
• Probability that an arrival will have to wait

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Waiting Time vs. Utilization
Figure 19-6
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Queuing Models Infinite-Source

• Single channel, exponential service time
• Single channel, constant service time
• Multiple channel, exponential service time
• Multiple priority service, exponential service
  time

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Queuing Models

• Single channel, exponential service time
• Single channel, constant service time
• Multiple channel, exponential service time
• Multiple priority service

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Priority Model
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Finite-Source Queuing