3. Capacity
￮ an upper bound on the load that a facility or a
plant can serve or manufacture
￮ the maximum output that can be achieved in
a given time
￮ It is measured in terms of
￮ Output (number of units or number of pounds
manufactured )
￮ Input (number of machine hours or machines
needed to satisfy demand)
￮ in the form of:
￮ Plant
￮ Department
￮ Machine
￮ Store
￮ Worker
3
4. Importance of Capacity Decisions
￮ To take full advantage of the strong demand
￮ affect operating costs
￮ a major determinant of initial cost
￮ involve long-term commitment of resources
￮ affect competitiveness
￮ affects the ease of management
4
5. Measuring Capacity
5
￮ many ways to measure capacity
￮ Choose a measure that would be appropriate for a
particular production system
￮ Monetary value is a poor measure of capacity
￮ Single product
￮ number of items produced in any given day
￮ Multiple products
￮ state capacity in terms of each product
￮ preferred measure is the use of available
￮ inputs
6. Measuring Capacity
6
Business Inputs Outputs
Auto manufacturing Labor hours, machine
hours
Number of cars per shift
Steel mill Furnace size Tons of steel per day
Oil refinery Refinery size Gallons of fuel per day
Farming Number of acres
Number of cows
Bushels of grain per acre
per year
Gallons of milk per day
Restaurant Number of tables
Seating capacity
Number of meals served
per day
Theatre Number of seats Number of tickets sold per
performance
Retail sales Square feet of floor space Revenue generated per day
7. Design Capacity and Effective Capacity
￮ Design Capacity
￮ the maximum possible output in ideal conditions.
￮ no disruptions or problems of any kind.
￮ Effective Capacity
￮ is the maximum realistic output in normal conditions.
￮ normal conditions:
￮ set-up times
￮ Breakdowns
￮ Stoppages
￮ maintenance periods
7
8. Performance Measures
￮ Utilization
￮ is the ratio of actual output to design capacity
￮ = Actual Output / Design Capacity
￮ Efficiency
￮ is the ratio of actual output to effective capacity
￮ = Actual Output / Effective Capacity
8
10. Example 1
10
Given the information below, compute the efficiency and the
utilization of the vehicle repair department:
Design Capacity = 50 trucks per day
Effective Capacity = 40 trucks per day
Actual Output = 36 trucks per day
11. Example 2
11
A machine is designed to work for one 8-hour shift a day, 5 days a
week. The machine can produce 100 units an hour, but 10% of its
time is taken by maintenance and set-ups. In one week the machine
made 3,000 units. What measures can you use to describe its
performance?
Solution:
Design capacity = production per hour x # of hrs. available
= 100 x 8 x 5 = 4,000 units a week
Effective capacity = production per hour x # of hrs. that can be used
= 100 x 8 x 5 x 0.9 = 3,600 units a week
Actual output = 3,000 units a week
Utilization = 3,000 / 4,000 = 0.75 or 75%
Efficiency = 3,000 / 3,600 = 0.833 or 83.3%
12. Example 3
12
A ski lift at Mount Rainier has pairs of chairs pulled on
a continuous wire from the bottom of a ski run to the
top. Ordinarily, one pair of chairs arrives at the bottom
of the slope every five seconds. If the lift works 10
hours a day for 100 days a year, what is its designed
capacity? On a typical day, 10% of users need help
getting on the lift, and they cause average delays of 10
seconds. A further 25% of people using the lift are
alone, and only one chair of the pair is used. How can
you describe the performance of the lift?
13. Example 3
13
Solution:
Design capacity = # of hours available per day x 3,600 / arrival rate
= 10 hrs/day x 3,600 sec/hr / 5 sec = 7,200 pairs a day
= 14,400 customers a day
Delay = (7,200 customers a day) x 0.10 = 720
= 720 x 10 seconds = 7,200 seconds of delay
Effective capacity = (# of hours available per day x 3,600 – 7,200) / arrival rate
= 5,760 pairs a day
= 11,520 customers a day
Actual output = 11,520 customers a day – 25% = 8,640 customers a day
Utilization = 8,640 / 14,400 = 0.60 or 60%
Efficiency = 8,640 / 11,520 = 0.75 or 75%
14. Example 4
14
Trivistor Soft Drinks has a bottling hall with three distinct parts:
2 bottling machines each with a maximum throughput of 100 litres a
minute and average maintenance of one hour a day.
3 labelling machines each with a maximum throughput of 3,000
bottles an hour and planned stoppages averaging 30 minutes a day;
(1 bottle = 1 litre)
A packing area with a maximum throughput of 10,000 cases a day.
The hall works 12 hours a day filling litre bottles and putting them in
cases of 12 bottles. What can you say about the capacity? What is
the utilization of each part? If the line develops a fault that reduces
output to 70,000 bottles, what is the efficiency of each part?
Bottling Labelling Packing
15. Example 4
15
Solution:
Design Capacities
Bottling = 100 litres/minute x 2 machines x 60 min/hr x 12 hrs/day
= 144,000 litres/day or 144,000 bottles/day
Labelling = 3,000 bottles/hour x 3 machines x 12 hrs/day
= 108,000 bottles/day
Packing = 10,000 cases/day x 12 bottles/case
= 120,000 bottles/day
The maximum throughput of the bottling hall is 108,000 bottles a
day, and this is its design capacity.
16. Example 4
16
Solution:
Effective Capacities
Bottling: = 144,000 x 11/12 = 132,000 bottles/day
Labelling: = 108,000 x 11.5/12 = 103,500 bottles/day
Packing: = 120,000 bottles/day
The limiting capacity is still the labeling operation, and effective capacity is
103,500 bottles/day. If the output of the hall is 103,500 bottles a day.
17. Example 4
17
Solution:
Utilization
Bottling: =103,500/144,000 = 0.72 or 72%
Labelling =103,500/108,000 = 0.96 or 96%
Packing =103,500/120,000 = 0.86 or 86%
Efficiency
With an actual output of 70,000 bottles, the efficiency of each operation is:
Bottling =70,000/132,000 = 0.53 or 53%
Labelling =70,000/103,500 = 0.68 or 68%
Packing =70,000/120,000 = 0.58 or 58%
18. Determinants of Effective
Capacity
18
Facilities Factors
• Transportation costs
• Distance to market
• Labor supply
• Energy sources
• Layout
Product/Service Factors
• Product/service mix
• The more uniform the output, the more opportunities there
are for standardization
Process Factors
• Quantity Capabilities
• Quality Capabilities
21. 21
• Design Flexibility into systems
• Differentiate between new and mature
products and services
• Take a “big picture” approach to capacity
changes
• Prepare to deal with capacity “chunks”
• Attempt to smooth out capacity requirements
• Identify the optimal operating level
Design Capacity Alternatives
23. 23
A department works one 8-hour shift, 250 days a
year, and has the following figures for usage of a
machine that is currently being considered:
How many machines are needed to meet annual
demand?
Example 5
Product
Annual
Demand
Std Processing
Time Per Unit (hr)
Processing Time
Needed (hr)
1 400 5 2000
2 300 8 2400
3 700 2 1400
Total 5800
24. 24
Solution:
Annual capacity of a machine
= Working hours/day x working days per year
= 8 x 250
= 2,000 hours/machine
Number of machines
= Total Processing Time Needed / Annual Capacity of a machine
= 5,800 hours / 2,000 hours/machine
= 2.90 machines 3 machines
Example 5
27. Cost-Volume Analysis Symbols
27
P = TR – TC or P = Q(R – v) – FC
TR = R x Q
TC = FC + VC
VC = v x Q
QBEP = FC/(R-v)
Where:
FC = fixed cost
VC = total variable cost
v = variable cost per unit
TC = total cost
TR = total revenue
R = revenue per unit
Q = quantity or volume of output
QBEP = breakeven quantity
P = profit
28. Cost-Volume Analysis Assumptions
28
• One product is involved
• Everything that is produce can be sold
• The variable cost per unit is the same
regardless of the volume
• Fixed cost do not change with volume
changes.
• The revenue per unit is the same regardless
of volume.
• Revenue per unit exceeds variable cost per
unit.
29. 29
The owner of Old-Fashioned Berry Pies, S. Simon, 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 retail
for $7.00 each.
a) How many pies must be sold in order to break-even?
b) What would the profit (loss) be if 1,000 pies are made
and sold in a month?
c) How many pies must be sold to realize a profit of
$4,000?
Solution:
a) QBEP = FC/(R-v) = $6,000/($7 - $2) = 1,200 pies/month
b) P = Q(R – v) – FC = 1,000($7 - $2) - $6,000 = ($1,000)
[loss]
c) P = Q(R – v) – FC
$4,000 = Q($7 - $2) - $6,000
Q = 2,000 pies
Example 6
30. 30
a) How many pies must be sold in order to break-even?
b) What would the profit (loss) be if 1,000 pies are made
and sold in a month?
c) How many pies must be sold to realize a profit of
$4,000?
Solution:
a) QBEP = FC/(R-v) = $6,000/($7 - $2) = 1,200 pies/month
b) P = Q(R – v) – FC = 1,000($7 - $2) - $6,000 = ($1,000)
[loss]
c) P = Q(R – v) – FC
$4,000 = Q($7 - $2) - $6,000
Q = 2,000 pies
Example 6
31. 31
A manager has the option of purchasing one, two, or three
machines. Fixed costs and potential volumes are as
follows:
Variable cost is $10 per unit, and revenue is $40 per unit.
a) Determine the break-even point for each range.
b) If projected annual demand is between 580 and 660
units, how many machines should the manager purchase?
Example 7
Number of
Machines
Total Annual
Fixed Cost
Corresponding
Range of Output
1 $ 9,600 0 to 300
2 15,000 301 to 600
3 20,000 601 to 900
32. 32
Solution:
a) QBEP = FC/(R-v)
For 1 machine:
QBEP = FC/(R-v)
= $9,600/($40 - $10)
= 320 units [not in range, so there is no BEP]
For 2 machines:
QBEP = FC/(R-v)
= $15,000/($40 - $10)
= 500 units
For 3 machines:
QBEP = FC/(R-v)
= $20,000/($40 - $10)
= 666.67 units
Example 7
33. 33
Solution:
b) Comparing the projected range of demand to the two ranges for
which a break-even point occurs, you can see that the break even
point is 500, which is in the range 301 to 600. This means that
even if demand is at the low end of the range, it would be above
the break-even point and thus yield a profit. That is not true of
range 601 to 900. At the top end of projected demand, the volume
would still be less than the break-even point for that range, so there
would be no profit. Hence, the manager should choose 2
machines.
Example 7
34. 34
Solution:
b) Comparing the projected range of demand to the two ranges for
which a break-even point occurs, you can see that the break even
point is 500, which is in the range 301 to 600. This means that
even if demand is at the low end of the range, it would be above
the break-even point and thus yield a profit. That is not true of
range 601 to 900. At the top end of projected demand, the volume
would still be less than the break-even point for that range, so there
would be no profit. Hence, the manager should choose 2
machines.
Example 7
