bmm4733_quality engineering industrial engineering chapter 1 introduction to ie (part 3) mohamad...
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BMM4733_Quality Engineering
Industrial Engineering
Chapter 1 Chapter 1 Introduction to IE (Part Introduction to IE (Part
3)3)Mohamad Zairi bin BaharomMohamad Zairi bin Baharom
Faculty of Mechanical EngineeringFaculty of Mechanical EngineeringUniversiti Malaysia PahangUniversiti Malaysia Pahang
Mohamad Zairi bin BaharomMohamad Zairi bin BaharomFaculty of Mechanical EngineeringFaculty of Mechanical Engineering
Universiti Malaysia PahangUniversiti Malaysia Pahang
Learning Objective:
Determine process selection with break-even analysis
Contents: Production section with break-even analysis
Break-even analysis
Production Selection with Break-even Analysis
A quantitative technique
Useful for comparing capacity alternativesAt what volume of sales and
production we can expect to earn a profit
The components are;VolumeCostRevenueProfit
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
Break-even Analysis (cont..)Volume: level of production
Cost: fixed cost and variable costFixed 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
Profit corri
dor
Loss
corridor
Total revenue line
Total cost line
Variable cost
Fixed cost
Break-even pointTotal cost = Total revenue
–
900 –
800 –
700 –
600 –
500 –
400 –
300 –
200 –
100 –
–| | | | | | | | | | | |
0 100 200 300 400 500 600 700 800 900 10001100
Co
st in
do
llars
Volume (units per period)
Break-even Analysis (cont..)
ccff = fixed cost= fixed cost
vv = volume (i.e., number of units produced and sold)= volume (i.e., number of units produced and sold)
ccvv = variable cost per unit= variable cost per unit
pp = price per unit= price per unit
Variables:
Break-even Analysis (cont..)
Total costTotal cost= fixed cost + total variable cost= fixed cost + total variable costTCTC = = ccff + + vcvcvv
Total revenueTotal revenue == volume x pricevolume x priceTRTR = = vpvp
ProfitProfit= total revenue - total cost= total revenue - total costZZ == TR - TCTR - TC
= = vpvp - ( - (ccff + + vcvcvv))
Break-even Analysis (cont..)
TRTR = TC= TCvpvp = = ccff + + vcvcvv
vpvp - - vcvcvv = = ccff
vv((p - cp - cvv)) = = cf
vv ==
ccff
p p -- c cvv
Break even volume:
Break-even Analysis (cont..)
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..)2,000
$5 per unit
$10 per unit
2,000400
10 5
f
v
f
v
c
c
price
cv
p c
2,000
$5 per unit
$10 per unit
2,000400
10 5
f
v
f
v
c
c
price
cv
p c
. 2,000 5
. 10
f vTC c v c v
TR v p v
. 2,000 5
. 10
f vTC c v c v
TR v p v
$
Units400
LOSS
PROFIT
Total cost
Totalrevenue
Break-Even Point
2,000
4,000
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 2The 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 BVolume where cost of A = cost of B
Rule for choosing process:Rule for choosing process:Demand above point of indifference Demand above point of indifference choose process with choose process with lowest variable costlowest variable costDemand below point of indifference Demand below point of indifference choose process with choose process with lowest fixed costlowest fixed cost
Example 2 (cont..)
Process Fixed cost
Variable cost
A $2,000 $5
B $10,000 $2
2,000 5.
10,000 2.
2,000 5. 10,000 2.
2667
A
B
A B
TC v
TC v
TC TC
v v
v
2,000 5.
10,000 2.
2,000 5. 10,000 2.
2667
A
B
A B
TC v
TC v
TC TC
v v
v
Point of indifference
Cost
units1000
5000
10,000
TC process A
TC process B
Point of indifference = 2667
15,000
2000 3000 4000
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
Total cost forEach alternative
Total cost forEach alternative
Point ofindifference
Point ofindifference
Choose alternative withThe lowest variable cost
Choose alternative withThe lowest variable cost
Choose alternative withThe lowest fixed cost
Choose alternative withThe lowest fixed cost
Above
Below
Example 2 (cont..)
Example 3Texloy 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 $50,000Variable cost$5/unit $4/unit $2/unit
Example 3 (cont..)
Total cost for process A = $10,000 + $5vTotal cost for process B = $20,000 + $4vTotal cost for process C = $50,000 + $2v
Point of indifferenceAlways begin with the process that has the lowest fixed cost and compare it to the process with the next lowest fixed cost.
Cost
units
TC process A
TC process B
10,000 15,000
TC process C
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 CIf demand is less than 15,000 but greater than 10,000, we should choose process BAt 15,000 units we can actually choose either B or C
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
units
TC process A
TC process B
10,000 15,000
TC process C
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.