1. Capacity Planning

2. Capacity
Capacity (I): is the upper limit on the load that an operating unit can handle.
Capacity (II): the upper limit of the quantity of a product (or product group) that an operating unit can produce (= the maximum level of output)
Capacity (III): the amount of resource inputs available relative to output requirements at a particular time

3. Examples of Capacity Measures

4. Capacity Design capacity Effective capacity
maximum output rate or service capacity an operation, process, or facility is designed for
= maximum obtainable output
= best operating level
Effective capacity
Design capacity minus allowances such as personal time, maintenance, and scrap (leftover)
Actual output = Capacity used
rate of output actually achieved. It cannot exceed effective capacity.

5. Capacity Efficiency and Capacity Utilization
Actual output
Efficiency =
Effective capacity
Utilization =
Design capacity

6. Determinants of Effective Capacity
Facilities, layout
Product and service factors
Process factors
Human factors
Policy (shifts, overtime)
Operational factors
Supply chain factors
External factors

7. Capacity Cushion
level of capacity in excess of the average utilization rate or level of capacity in excess of the expected demand.
Capacity cushion = (designed capacity / capacity used) – 1
Sources of Uncertainty
Manufacturing
Customer delivery
Supplier performance
Changes in demand

8. The „Make or Buy” problem
Available capacity
Expertise
Quality considerations
Nature of demand
Cost
Risk

9. Developing Capacity Alternatives
Design flexibility into systems
Take stage of life cycle into account (complementary product)
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

10. Adapting capacity to demand through changes in workforce
PRODUCTION RATE (CAPACITY)

11. Adaptation with inventory
DEMAND
Inventory reduction
Inventory accumulation
CAPACITY

12. Adaptation with subcontracting
DEMAND
SUBCONTRACTING
PRODUCTION (CAPACITY)

13. Adaptation with complementary product
PRODUCTION (CAPACITY)
DEMAND
DEMAND
PRODUCTION (CAPACITY)

14. Production units have an optimal rate of output for minimal cost.
Economies of Scale
Economies of scale
If the output rate is less than the optimal level, increasing output rate results in decreasing average unit costs
Diseconomies of scale
If the output rate is more than the optimal level, increasing the output rate results in increasing average unit costs
Production units have an optimal rate of output for minimal cost.
Minimum cost
Average cost per unit
Rate of output
Minimum average cost per unit

15. Evaluating Alternatives II.
Minimum cost & optimal operating rate are
functions of size of production unit.
Small
plant
Medium
plant
Average cost per unit
Large
plant
Output rate

16. Seminar exercises

17. Designed capacity in calendar time
CD= N ∙ sn ∙ sh ∙ mn ∙ 60 (mins / planning period)
CD= designed capacity (mins / planning period)
N = number of calendar days in the planning period (365)
sn= maximum number of shifts in a day (= 3 if dayshift + swing shift + nightshift)
sh= number of hours in a shift (in a 3 shifts system, it is 8 per shift)
mn= number of homogenous machine groups

18. Designed capacity, with given work schedule
C’D= N ∙ sn ∙ sh ∙ mn ∙ 60 (mins / planning period)
C’D= designed capacity (mins / planning period)
N = number of working days in the planning period (≈ 250 wdays/yr)
sn= number of shifts in a day (= 3 if dayshift + swing shift + nightshift)
sh= number of hours in a shift (in a 3 shifts system, it is 8)
mn= number of homogenous machine groups

19. Effective capacity in working minutes
CE = CD - tallowances (mins / planning period)
CD= designed capacity
tallowances = allowances such as personal time, maintenance, and scrap (mins / planning period)
b =  ∙ CE
b = expected capacity (that we use in product mix decisions)
CE = effective capacity
 = performance percentage

20. Exercise 1.
A company produces a product in 2 shifts pattern and 250 days in a given year. Two machines are available in the workstation. The maintenance needs 8 hours in a month. The performance rate in the first shift is 90%, in the second shift 80%. Each product needs 25 minutes to be finished.
a) Determine the designed capacity for one year.
b) Determine the effective capacity for one year.
c) Determine the expected capacity for one year.
d) Determine the number of products we can produce.
e) Determine the utilization and efficiency if the actual output is pieces.
d) Determine capacity cushion.

21. Exercise 2.
Set up the product-resource matrix using the following data!
RP coefficients: a11: 10, a22: 20, a23: 30, a34: 10
The planning period is 4 weeks (there are no holidays in it, and no work on weekends)
Work schedule:
R1 and R2: 2 shifts, each is 8 hour long
R3: 3 shifts
Homogenous machines:
1 for R1
2 for R2
1 for R3
Maintenance time: only for R3: 5 hrs/week
Performance rate:
90% for R1 and R3
80% for R2

22. Solution (bi) Ri = N ∙ sn ∙ sh ∙ mn ∙ 60 ∙ 
N=(number of weeks) ∙ (working days per week)
R1 = 4 weeks ∙ 5 working days ∙ 2 shifts ∙ 8 hours per shift ∙ 60 minutes per hour ∙ 1 homogenous machine ∙ 0,9 performance = = 4 ∙ 5 ∙ 2 ∙ 8 ∙ 60 ∙ 1 ∙ 0,9 = minutes per planning period
R2 = 4 ∙ 5 ∙ 2 ∙ 8 ∙ 60 ∙ 2 ∙ 0,8 = mins
R3 = (4 ∙ 5 ∙ 3 ∙ 8 ∙ 60 ∙ 1 – 5 hrs per week ∙ 60 minutes ∙ 4 weeks) ∙ 0,9= ( – 1200 ) ∙ 0,9= mins

23. Solution (RP matrix) P1 P2 P3 P4 10 20 30 b (mins/y) R1 17 280 R2P1 P2 P3 P4
b (mins/y) R1 10
17 280 R2 20 30
30 720 R3
24 840

24. Exercise 1.2
Complete the corporate system matrix with the following marketing data:
There are long term contract to produce at least:
50 P1
100 P2
120 P3
50 P4
Forecasts says the upper limit of the market is:
units for P1
1 200 for P2
1 000 for P3
2 000 for P4
Unit prices: P1=100, P2=200, P3=330, P4=100
Variable costs: R1=5/min, R2=8/min, R3=11/min

25. Solution (CS matrix) 10 20 30 P1 P2 P3 P4 b (mins/y) R1 17 280 R2P1 P2 P3 P4
b (mins/y) R1 10
17 280 R2 20 30
30 720 R3
24 840
MIN (pcs/y) 50
100
120
MAX (pcs/y)
10 000
1 200
1 000
2 000
price
200
330
Contr. Marg. 40 90
-10

26. What is the optimal product mix to maximize revenues?
P3= ( ∙20-)/30= 957<MAX
P4=24 840/10=2484>2000

27. What if we want to maximize profit?
The only difference is in P4 because of its negative contribution margin.
P4=50

28. Exercise 2 P1 P2 P3 P4 P5 P6 6 3 2 4 1 b (hrs/y) R1 2 000 R2 R3 1 000P1 P2 P3 P4 P5 P6
b (hrs/y) R1 6
2 000 R2 3 2 R3 4
1 000 R4
6 000 R5 1
5 000
MIN (pcs/y)
200
100
400
MAX (pcs/y)
20000
500
2000
p (HUF/pcs) 50
cm (HUF/pcs) 80 40
-30 20
-10

29. Solution Revenue max. P1=333 P2=400 P3=400 P4=200 P5=1000
Contribution max.
P1=333
P2=500
P3=250
P4=100
P5=1000