1. Operations Management Capacity Planning Supplement 7

2. Outline Capacity. Managing Demand and Capacity.
Utilization.
Efficiency.
Managing Demand and Capacity.
Break-Even & Crossover Analysis.
Net Present Value.

3. Capacity Planning Capacity planning answers:
How much long-range capacity is needed?
Add or remove facilities or equipment.
How much intermediate-range capacity is needed?
Add or remove personnel, equipment or shifts; Use or build inventory; Subcontract.
This slide provides some reasons that capacity is an issue. The following slides guide a discussion of capacity.

4. Definition and Measures of Capacity
The maximum output of a system in a given period.
The maximum capacity that can be achieved under ideal conditions.
Example: 200/day
The expected capacity given the current operating environment and constraints;
may be viewed as a percentage of design capacity.
Example: 180/day or 90%
Design Capacity:
Effective capacity:
This slide can be used to frame a discussion of capacity.
Points to be made might include:
- capacity definition and measurement is necessary if we are to develop a production schedule
- while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis.
Students should be asked to suggest factors which might prevent one from achieving maximum capacity.

5. Utilization & Efficiency
Utilization = Percent of design capacity achieved.
Efficiency = Percent of effective capacity achieved.
Actual output
Utilization =
Design capacity
Actual output
It might be useful at this point to discuss typical equipment utilization rates for different process strategies if you have not done so before.
Efficiency =
Effective capacity

6. Utilization & Efficiency Example
Design capacity = 120/day.
Effective capacity = 100/day.
Actual output = 80/day.
Actual output
Utilization =
= 80/120 = 67%
Design capacity
It might be useful at this point to discuss typical equipment utilization rates for different process strategies if you have not done so before.
Actual output
Efficiency =
= 80/100 = 80%
Effective capacity

7. Anticipated Output Anticipated output
= Design Capacity x Effective Capacity % x Efficiency
Example:
Design capacity = 150 units per day
Effective capacity = 80%
Efficiency = 90%
Anticipated output = 150 x 0.80 x 0.90 = 108 per day.
Efficiency = 90%; Utilization = 108/150=72%
It might be useful at this point to discuss typical equipment utilization rates for different process strategies if you have not done so before.

8. Capacity Planning Process
Forecast demand accurately.
Compute needed capacity.
Develop alternative plans.
Understand technology and capacity increments.
Evaluate capacity plans.
Quantitative & Qualitative factors.
Build for change.
Select and implement best capacity plan.
This slide outlines the capacity planning process. It is probably useful to discuss, at least briefly, each step in the process. If time permits, the boxes representing Quantitative factors, Qualitative factors, Evaluation of Capacity Plans, and Selecting the Best Capacity Plan, merit the most attention.

9. Managing Existing Capacity
To make capacity match demand, either:
Adjust demand = Demand management.
Adjust capacity = Capacity management.
Use or build inventory.
Find complementary products for seasonal demands.
You might begin by reminding students that the real issue is matching capacity to demand, and that we can do that by varying either capacity or demand.
It might also be helpful to have students consider the magnitude of variation we can achieve for each of the alternatives listed above - and the consequences of using the alternative.

10. Managing Existing Capacity
Demand Management
Capacity Management
Vary prices.
Vary promotion.
Backorder.
Offer complementary products.
Vary staffing.
Change equipment & processes.
Change methods.
Redesign the product/service for faster processing.
You might begin by reminding students that the real issue is matching capacity to demand, and that we can do that by varying either capacity or demand.
It might also be helpful to have students consider the magnitude of variation we can achieve for each of the alternatives listed above - and the consequences of using the alternative.

11. Complementary Products
Sales (Units)
5,000
Total
4,000
Snow-mobiles
3,000
2,000
1,000
Jet Skis
Ask students to suggest difficulties one might encounter when attempting to balance capacity through the use of complementary products. J M M J S N J M M J S N J
Time (Months)

12. Capacity Expansion Options
1. Add capacity in advance of increasing demand.
Advantages:
Can capture market.
Discourage competition.
Disadvantages:
Expensive and risky.
Demand may not materialize.
Size of needed expansion relies on forecast.
Expected Demand
Time in Years
Demand
New Capacity
Small expansions
Large expansion
This slide probably requires some discussion or explanation. Perhaps the best place to start is the left hand column where capacity either leads or lags demand incrementally. As you continue to explain the options, ask students to suggest advantages or disadvantages of each.

13. Capacity Expansion Options (cont.)
Add new capacity after demand materializes.
Advantages:
Lower cost.
Less risk.
Size of expansion known.
Disadvantages:
May be too late to market.
Expected Demand
Time in Years
Demand
New Capacity
Small expansions
This slide probably requires some discussion or explanation. Perhaps the best place to start is the left hand column where capacity either leads or lags demand incrementally. As you continue to explain the options, ask students to suggest advantages or disadvantages of each.

14. Break-even Analysis To evaluate process & equipment alternatives.
Objective:
Find the point ($ or units) at which total cost equals total revenue, -or-
Find the range of output over which different alternatives are preferred.
Assumptions:
Revenue & costs are related linearly to volume.
All information is known with certainty.
No time value of money.
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?

15. Break-even Analysis - Costs
Fixed costs: Costs independent of the volume of units produced.
Depreciation, taxes, debt, mortgage payments, etc.
Variable costs: Costs that vary with the volume of units produced.
Labor, materials, portion of utilities, etc.

16. Break-even Chart Volume (units/period) Total revenue line Dollars
Profit
Loss
Total revenue line
Dollars
Fixed cost
Variable cost
Total cost line
Breakeven point
Total cost = Total revenue
Volume (units/period)

17. Break-even Equations F = Fixed cost per unit time.
V = Variable cost per unit produced.
x = Number of units produced per unit time.
P = Revenue (price) per unit
TC = Total costs per unit time = F + Vx
TR = Total revenue per unit time = Px
Profit = TR - TC
At break-even point: Total Cost = Total Revenue

18. Break-even Example 1
A firm produces radios with a fixed cost of $7,000 per month and a variable cost of $5 per radio. If radios sell for $8 each:
1a) What is the break-even point?
TR = TC so 8x = x
x = 7000/3 = 2, radios per month
1b) What output is needed to produce a profit of $2,000/month?
Profit = 2000/month so
TR - TC = 8x - ( x) = 2000
x = 9000/3 = 3,000 radios per month

19. Break-even Example 1 - continued
1c) What is the profit or loss if 500 radios are produced each week?
First, get monthly production:
50052/12 = 2, radios per month
Then calculate profit or loss
TR - TC = 8 (  )
= $-500 per month
($500 loss per month)

20. Break-even Example 2
A firm produces radios with a fixed cost of $7,000 per month and a variable cost of $5 per radio for the first 3,000 radios produced per month. For all radios produced each month after the first 3,000 the variable cost is $10 per radio (for added overtime and maintenance costs). If radios sell for $8 each:
2a) What are the break-even point(s)?
Now TC has two parts depending on the level of production:
For x  3000/month: TC = x
For x > 3000/month: TC = (3000) + 10(x-3000)
= x
For any x: TR = 8x

21. Break-even Example 2 - continued
For x  3000/month: TC = x
For x > 3000/month: TC = x
For any x: TR = 8x
For x  3000/month: x = 8x so x = 2,333.33/month
This is < 3000/month, so it is a valid break-even point.
For x > 3000/month: x = 8x so x = 4000/month
This is > 3000/month, so it is also a valid break-even point.

22. Break-even Example 2 Volume (units/month) 40 Dollars (Thousands)
Total revenue line 32 24
Total cost line 16
Break-even
points 8
1000
2000
3000
4000
Volume (units/month)

23. Break-even Example 3
A firm produces radios with a fixed cost of $7,000 per month and a variable cost of $5 per radio for the first 2,000 radios produced per month. For all radios produced each month after the first 2,000 the variable cost is $10 per radio (for added overtime and maintenance costs). If radios sell for $8 each:
3a) What are the break-even point(s)?
Again TC has two parts depending on the level of production:
For x  2000/month: TC = x
For x > 2000/month: TC = (2000) + 10(x-2000)
= x
For any x: TR = 8x

24. Break-even Example 3 - continued
For x  2000/month: TC = x
For x > 2000/month: TC = x
For any x: TR = 8x
For x  2000/month: x = 8x so x = 2,333.33/month
This is not < 2000/month, so it is not a break-even point!!
For x > 2000/month: x = 8x so x = 1500/month
This is not > 2000/month, so it is not a break-even point!!
THERE ARE NO BREAK-EVEN POINTS!

25. Break-even Example 3 Volume (units/month) 40 Dollars (Thousands) 32 24
Total cost line
Total revenue line 16 8
1000
2000
3000
4000
Volume (units/month)

26. Other Break-even Possibilities40
Dollars (Thousands) 32 24
Total cost line
Total revenue line 16 8
1000
2000
3000
4000
Volume (units/month)

27. Crossover Chart Process A: Low volume, high variety
Process B: Repetitive
Process C: High volume, low variety
Total cost - Process A
Total cost - Process B
Total cost - Process C
This slide can be used to introduce the role of breakeven analysis in the process selection decision.
Process A
Process B
Process C
Lowest cost process

28. Crossover Example
Consider three production processes with different fixed and variable costs:
Process A: FA = $5000/week VA = $10/unit
Process B: FB = $8000/week VB = $4/unit
Process C: FC = $10000/week VC = $3/unit
Over which range of output is each process best?
First write total cost expressions:
A: 5, x
B: 8, x
C: 10, x

29. Crossover Example A: 5,000 + 10x B: 8,000 + 4x C: 10,000 + 3x
1. At x = 0, A is best (since 5000 < 8000 < 10000).
2. As x gets larger, either B or C may become better than A:
B < A when x < x or x > 500/week
C < A when x < x or x > /week
So A is best only for x < 500/week and
B is best starting at x > 500/week

30. Crossover Example A: 5,000 + 10x B: 8,000 + 4x C: 10,000 + 3x
3. Eventually, C will become better than B (note that C has a lower variable cost than B).
C < B when x < x or x > 2000/week
so B is best for 500/week < x < 2000/week and
C is best starting at x > 2000/week

31. Crossover Example Summary:
A is best for output of units per week.
B is best for output of units per week.
C is best for output greater than 2000 units per week.
500
714
2000
A<B
A<C
B<C
A<B<C
B<A
C<A
B<C<A
B<A<C
C<B
C<B<A

32. Time Value of Money - Net Present Value
Future cash receipt of amount F is worth less than F today.
F = Future value N years in the future.
P = Present value today.
i = Interest rate.
This slide suggests that the process selection decision should be considered in light of the larger strategic initiative

33. Annuities An annuity is a annual series of equal payments.
R = Amount received every year for N years.
S = Present value today.
S = RX
where X is from Table S7.2.
Example: What is present value of $1,000,000 paid in 20 equal annual installments?
For i = 6%/year, S =  = $573,500
For i = 14%/year, S =  = $331,150
This slide suggests that the process selection decision should be considered in light of the larger strategic initiative

34. Limitations of Net Present Value
Investments with the same NPV will differ:
Different lengths.
Different salvage values.
Different cash flows.
Assumes we know future interest rates!
Assumes payments are always made at the end of the period.
A commentary on Net Present Value, and the larger issues of models in general.