1. BMM4733_Quality Engineering
Industrial Engineering
Chapter 1
Introduction to IE (Part 3)
Mohamad Zairi bin Baharom
Faculty of Mechanical Engineering
Universiti Malaysia Pahang
BMM4733_Quality Engineering

2. Contents: Learning Objective:
Determine process selection with break- even analysis
Contents:
Production section with break-even analysis
Break-even analysis

3. 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

4. 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
This chart introduces breakeven analysis and the breakeven or crossover chart. As you discuss the assumptions upon which this techniques is based, it might be a good time to introduce the more general topic of the limitations of and use of models. Certainly one does not know all information with certainty, money does have a time value, and the hypothesized linear relationships hold only within a range of production volumes. What impact does this have on our use of the models?

5. 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

6. Break-even Analysis (cont..)–
900 –
800 –
700 –
600 –
500 –
400 –
300 –
200 –
100 –
| | | | | | | | | | | |
Cost in dollars
Volume (units per period)
Total revenue line
Profit corridor
Loss corridor
Total cost line
Break-even point
Total cost = Total revenue
Variable cost
This chart introduces breakeven analysis and the breakeven or crossover chart. As you discuss the assumptions upon which this techniques is based, it might be a good time to introduce the more general topic of the limitations of and use of models. Certainly one does not know all information with certainty, money does have a time value, and the hypothesized linear relationships hold only within a range of production volumes. What impact does this have on our use of the models?
Fixed cost

7. 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

8. 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)

9. Break-even Analysis (cont..)
Break even volume:
TR = TC
vp = cf + vcv
vp - vcv = cf
v(p - cv) = cf
v = cf
p - cv

10. 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?

11. Example 1 (cont..) $ Units Total revenue PROFIT Total cost 4,000 2,000
LOSS
400
Units
Break-Even Point

12. 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

13. 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

14. 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?

15. 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
nnnnooo

16. Example 2 (cont..) Point of indifference Process Fixed cost Variable A
$2,000 $5 B
$10,000 $2
Cost
TC process A
TC process B
15,000
Point of indifference
10,000
5000
1000
2000
3000
4000
units
Point of indifference = 2667

17. 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

18. Example 2 (cont..) Above Below Total cost for Each alternative
Point of
indifference
Above
Choose alternative with
The lowest variable cost
Below
Choose alternative with
The lowest fixed cost

19. 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;
For what volume of demand would each process be desirable?
Process A Process B Process C
Fixed cost $10,000 $20,000 $50,000
Variable cost $5/unit $4/unit $2/unit

20. Example 3 (cont..) Cost 10,000 15,000 units TC process B TC process A
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
TC process C
10,000
15,000
units

21. 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

22. Example 3 (cont..) Summary Below 10,000 units, choose process A
Between 10,000 units and 15,000 units, choose process B
Above 15,000 units, choose process C
Cost
TC process B
TC process A
TC process C
10,000
15,000
units

23. 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.