Industrial Engineering
Chapter 1
Introduction to IE (Part 3)
Mohamad Zairi bin Baharom
Faculty of Mechanical Engineering
Universiti Malaysia Pahang
BMM4733_Quality Engineering
Learning
Objective:
Determine process
selection with breakeven analysis
Contents:
 Production section
with break-even analysis
 Break-even analysis
Production Selection with Break-even Analysis
A quantitative technique
Useful for comparing capacity alternatives
At what volume of sales and production
we can expect to earn a profit
The components are;
Volume
Cost
Revenue
Profit
Break-even Analysis
Technique for evaluating process and
equipment alternatives
Objective is to find the point in dollars and
units at which cost equals revenue
Requires estimation of fixed costs, variable
costs, and revenue
Break-even Analysis (cont..)
Volume: level of production
Cost: fixed cost and variable cost
Fixed cost: remains constant regardless of the number of units produced
(cost of the machine used, cost of installing the machine, cost of designing
and fabricating the work holding devices, cost of the space for machine)
Variable cost: vary with the volume of the units produced (cost of machine
operator’s time, cost of running the machine, cost of cutting tools, cost of
material used).
Revenue: the price at which the item is sold
Total revenue: price times volume sold
Profit: difference between total revenue and total cost
Break-even Analysis (cont..)
–
Total revenue line
900 –
800 –
Cost in dollars
700 –
Break-even point
Total cost = Total revenue
Total cost line
600 –
500 –
Variable cost
400 –
300 –
200 –
100 –
Fixed cost
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–
0 100 200 300 400 500 600 700 800 900 1000 1100
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Volume (units per period)
Break-even Analysis (cont..)
Variables:
cf = fixed cost
v = volume (i.e., number of units produced and sold)
cv = variable cost per unit
p = price per unit
Break-even Analysis (cont..)
Total cost= fixed cost + total variable cost
TC = cf + vcv
Total revenue = volume x price
TR = vp
Profit= total revenue - total cost
Z = TR - TC
= vp - (cf + vcv)
Break-even Analysis (cont..)
Break even volume:
TR = TC
vp = cf + vcv
vp - vcv = cf
v(p - cv) = cf
cf
v= p-c
v
Example 1
Travis and Jeff own an adventure company called
Whitewater Rafting. Due to quality and
availability problems, the two entrepreneurs have
decided to produce their own rubber rafts. The
initial investment in plant and equipment is
estimated to be $2,000. labor and material cost is
approximately $5 per raft. If the rafts can be sold
at a price of $10 each, what volume of demand
would be necessary to break even?
Example 1 (cont..)
c f  2, 000
Total
PROFIT
revenue
Total cost
cv  $5 per unit
price  $10 per unit
4,000
$
cf
2, 000
v

 400
p  cv 10  5
2,000
LOSS
TC  c f  v.cv  2, 000  5v
TR  v. p  10v
400
Break-Even Point
Units
Example 1 (cont..)
The intersection of these two lines is the break even
point
If demand is less than the break even point, the
company will operate at a loss
If demand exceeds the break even point, the
company will be profitable
The company need to sell more than 400 rafts to
make a profit
Example 1 (cont..)
Break even analysis – useful when evaluating
different degrees of automation
More automated processes have higher fixed costs
but lower variable costs
The best process depends on the anticipated
volume of demand for the product and the trade
offs between fixed and variable costs
Example 2
The owner of Whitewater Rafting believe demand
for their product will far exceed the break even
point in example 1. they are now contemplating a
larger initial investment of $10,000 for more
automated equipment that would reduce the
variable cost of manufacture to $2 per raft.
Compare the old manufacturing process in
example 1 with the new process proposed here.
For what volume of demand should each process
be chosen?
Example 2 (cont..)
Point of Indifference
Volume where cost of A = cost of B
Rule for choosing process:
Demand above point of indifference
choose process with
lowest variable cost
Demand below point of indifference
choose process with
lowest fixed cost
Example 2 (cont..)
Process
Fixed
cost
Variable
cost
A
$2,000
$5
B
$10,000
$2
Cost
TC process A
TC process B
15,000
Point of indifference
TC A  2, 000  5.v
10,000
TCB  10, 000  2.v
TC A  TCB
2, 000  5.v  10, 000  2.v
v  2667
5000
1000 2000 3000
Point of indifference = 2667
4000
units
Example 2 (cont..)
If demand is less than or equal to 2667 rafts, the
alternative with the lowest fixed cost (process A)
should be chosen
If demand is greater than or equal to 2667 rafts,
the alternative with the lowest variable cost
(process B) is preferred
Example 2 (cont..)
Total cost for
Each alternative
Point of
indifference
Below
Above
Choose alternative with
The lowest variable cost
Choose alternative with
The lowest fixed cost
Example 3
Texloy Mfg Company must select a process for its
new product, TX2, from among three different
alternatives. The following cost data have been
gathered;
Process A
Fixed cost $10,000
Variable cost $5/unit
Process B
Process C
$20,000
$4/unit
$50,000
$2/unit
For what volume of demand would each process
be desirable?
Example 3 (cont..)
Total cost for process A = $10,000 + $5v
Total cost for process B = $20,000 + $4v
Total cost for process C = $50,000 + $2v
Point of indifference
Always begin with the process that has the
lowest fixed cost and compare it to the
process with the next lowest fixed cost.
Cost
TC process B
TC process A
10,000 15,000
TC process C
units
Example 3 (cont..)
Process A versus Process B;
$10,000 + $5v = $20,000 + $4v
v = 10,000 units
If demand is less than or equal to
10,000, we should choose the
alternative with the lowest fixed
cost (Process A).
If demand is greater than 10,000,
we should choose the alternative
with the lowest variable cost
(Process B)
At 10,000 units we can actually
choose either A or B
Process B versus Process C;
$20,000 + $4v = $50,000 + $2v
v = 15,000 units
If demand is greater than or equal
to 15,000, we should choose
process C
If demand is less than 15,000 but
greater than 10,000, we should
choose process B
At 15,000 units we can actually
choose either B or C
Example 3 (cont..)
Summary

Below 10,000 units, choose
process A
Cost
TC process B
TC process A


TC process C
Between 10,000 units and 15,000
units, choose process B
Above 15,000 units, choose
process C
10,000 15,000
units
Exercise
A firm plans to begin production of a new product.
The manager must decide whether to purchase
one part from a vendor at $7 each or to produce
them in house. Either of two processes could be use
for in house production; one would have an annual
fixed cost of $160,000 and a variable cost of $5
per unit, and the other would have an annual
fixed cost of $190,000 and a variable cost of $4
per unit. Determine the range of annual volume for
which each of the alternatives would be best.