© 2006 Prentice Hall, Inc. S7 – 1

Operations ManagementOperations ManagementSupplement 7 – Capacity PlanningSupplement 7 – Capacity Planning

© 2006 Prentice Hall, Inc.

PowerPoint presentation to accompany Heizer/Render Principles of Operations Management, 6eOperations Management, 8e

© 2006 Prentice Hall, Inc. S7 – 2

Capacity

The throughput, or the number of units a facility can hold, receive, store, or produce in a period of time

Determines fixed costs Determines if demand will be

satisfied Three time horizons

© 2006 Prentice Hall, Inc. S7 – 3

Modify capacity Use capacity

Planning Over a Time Horizon

Intermediate-range planning

Subcontract Add personnelAdd equipment Build or use inventory Add shifts

Short-range planning

Schedule jobsSchedule personnel Allocate machinery*

Long-range planning

Add facilitiesAdd long lead time equipment *

* Limited options exist

Figure S7.1

© 2006 Prentice Hall, Inc. S7 – 4

Design and Effective Capacity

Design capacity is the maximum theoretical output of a systemNormally expressed as a rate

Effective capacity is the capacity a firm expects to achieve given current operating constraintsOften lower than design capacity

© 2006 Prentice Hall, Inc. S7 – 5

Utilization and Efficiency

Utilization is the percent of design capacity achieved

Efficiency is the percent of effective capacity achieved

Utilization = Actual Output/Design Capacity

Efficiency = Actual Output/Effective Capacity

© 2006 Prentice Hall, Inc. S7 – 6

Bakery Example

Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, 3 – ‘8 hour shifts’

Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls

© 2006 Prentice Hall, Inc. S7 – 7

Bakery Example

Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, 3 – ‘8 hour shifts’

Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls

© 2006 Prentice Hall, Inc. S7 – 8

Bakery Example

Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, 3 – ‘8 hour shifts’

Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls

Utilization = 148,000/201,600 = 73.4%

© 2006 Prentice Hall, Inc. S7 – 9

Bakery Example

Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, 3 – ‘8 hour shifts’

Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls

Utilization = 148,000/201,600 = 73.4%

© 2006 Prentice Hall, Inc. S7 – 10

Bakery Example

Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, 3 – ‘8 hour shifts’

Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls

Utilization = 148,000/201,600 = 73.4%

Efficiency = 148,000/175,000 = 84.6%

© 2006 Prentice Hall, Inc. S7 – 11

Bakery Example

Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, 3 – ‘8 hour shifts’

Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls

Utilization = 148,000/201,600 = 73.4%

Efficiency = 148,000/175,000 = 84.6%

© 2006 Prentice Hall, Inc. S7 – 12

Bakery Example

Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, 3 – ‘8 hour shifts’Efficiency = 84.6%Efficiency of new line = 75%

Expected Output = (Effective Capacity)(Efficiency)

= (175,000)(.75) = 131,250 rolls

© 2006 Prentice Hall, Inc. S7 – 13

Bakery Example

Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, three- ‘8 hour shifts’Efficiency = 84.6%Efficiency of new line = 75%

Expected Output = (Effective Capacity)(Efficiency)

= (175,000)(.75) = 131,250 rolls

© 2006 Prentice Hall, Inc. S7 – 14

Managing Demand

Demand exceeds capacity Curtail demand by raising prices,

scheduling longer lead time Long term solution is to increase capacity

Capacity exceeds demand Stimulate market Product changes

Adjusting to seasonal demands Produce products with complimentary

demand patterns

© 2006 Prentice Hall, Inc. S7 – 15

Economies and Diseconomies of Scale

Economies of scale

Diseconomies of scale

25 - Room Roadside Motel 50 - Room

Roadside Motel

75 - Room Roadside Motel

Number of Rooms25 50 75

Av

era

ge

un

it c

os

t(d

olla

rs p

er

roo

m p

er n

igh

t)

Figure S7.2

© 2006 Prentice Hall, Inc. S7 – 16

Capacity Considerations

Forecast demand accurately Understanding the technology

and capacity increments Find the optimal operating level

(volume) Build for change

© 2006 Prentice Hall, Inc. S7 – 17

Approaches to Capacity Expansion

(a) Leading demand with incremental expansion

Dem

and

Expected demand

New capacity

(b) Leading demand with one-step expansion

Dem

and

New capacity

Expected demand

(d) Attempts to have an average capacity with incremental expansion

Dem

and

New capacity Expected

demand

(c) Capacity lags demand with incremental expansion

Dem

and

New capacity

Expected demand

Figure S7.4

© 2006 Prentice Hall, Inc. S7 – 18

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

© 2006 Prentice Hall, Inc. S7 – 19

Break-Even Analysis

Fixed costs are costs that continue even if no units are producedDepreciation, taxes, debt, mortgage

payments

Variable costs are costs that vary with the volume of units producedLabor, materials, portion of utilitiesContribution is the difference between

selling price and variable cost

© 2006 Prentice Hall, Inc. S7 – 20

Break-Even Analysis

Costs and revenue are linear functionsGenerally not the case in the real

world

We actually know these costsVery difficult to accomplish

There is no time value of money

Assumptions

© 2006 Prentice Hall, Inc. S7 – 21

Profit corri

dor

Loss

corridor

Break-Even AnalysisTotal 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)Figure S7.5

© 2006 Prentice Hall, Inc. S7 – 22

Break-Even Analysis

BEPx =Break-even point in unitsBEP$ =Break-even point in dollarsP = Price per unit (after all discounts)

x = Number of units producedTR = Total revenue = PxF = Fixed costsV = Variable costsTC = Total costs = F + Vx

TR = TCor

Px = F + Vx

Break-even point occurs when

BEPx =F

P - V

© 2006 Prentice Hall, Inc. S7 – 23

Break-Even Analysis

BEPx =Break-even point in unitsBEP$ =Break-even point in dollarsP = Price per unit (after all discounts)

x = Number of units producedTR = Total revenue = PxF = Fixed costsV = Variable costsTC = Total costs = F + Vx

BEP$ = BEPx P

= P

=

=

F(P - V)/P

FP - V

F1 - V/P

Profit = TR - TC= Px - (F + Vx)= Px - F - Vx= (P - V)x - F

© 2006 Prentice Hall, Inc. S7 – 24

Break-Even Example

Fixed costs = $10,000 Material = $.75/unitDirect labor = $1.50/unit Selling price = $4.00 per unit

BEP$ = =F

1 - (V/P)$10,000

1 - [(1.50 + .75)/(4.00)]

© 2006 Prentice Hall, Inc. S7 – 25

Break-Even Example

Fixed costs = $10,000 Material = $.75/unitDirect labor = $1.50/unit Selling price = $4.00 per unit

BEP$ = =F

1 - (V/P)$10,000

1 - [(1.50 + .75)/(4.00)]

= = $22,857.14$10,000

.4375

BEPx = = = 5,714F

P - V$10,000

4.00 - (1.50 + .75)

© 2006 Prentice Hall, Inc. S7 – 26

Break-Even Example

BEP$ =F

∑ 1 - x (Wi)Vi

Pi

Multiproduct Case

where V = variable cost per unitP = price per unitF = fixed costs

W = percent each product is of total dollar salesi = each product

© 2006 Prentice Hall, Inc. S7 – 27

Multiproduct Case Derivation

© 2006 Prentice Hall, Inc. S7 – 28

Multiproduct Example

Annual ForecastedItem Price Cost Sales UnitsSandwich $2.95 $1.25 7,000Soft drink .80 .30 7,000Baked potato 1.55 .47 5,000Tea .75 .25 5,000Salad bar 2.85 1.00 3,000

Fixed costs = $3,500 per month

© 2006 Prentice Hall, Inc. S7 – 29

Multiproduct Example

Annual ForecastedItem Price Cost Sales UnitsSandwich $2.95 $1.25 7,000Soft drink .80 .30 7,000Baked potato 1.55 .47 5,000Tea .75 .25 5,000Salad bar 2.85 1.00 3,000

Sandwich $2.95 $1.25 .42 .58 $20,650 .446 .259Soft drink .80 .30 .38 .62 5,600 .121 .075Baked 1.55 .47 .30 .70 7,750 .167 .117 potatoTea .75 .25 .33 .67 3,750 .081 .054Salad bar 2.85 1.00 .35 .65 8,550 .185 .120

$46,300 1.000 .625

Annual WeightedSelling Variable Forecasted % of Contribution

Item (i) Price (P) Cost (V) (V/P) 1 - (V/P) Sales $ Sales (col 5 x col 7)

Fixed costs = $3,500 per month

© 2006 Prentice Hall, Inc. S7 – 30

Multiproduct Example

Annual ForecastedItem Price Cost Sales UnitsSandwich $2.95 $1.25 7,000Soft drink .80 .30 7,000Baked potato 1.55 .47 5,000Tea .75 .25 5,000Salad bar 2.85 1.00 3,000

Fixed costs = $3,500 per month

Sandwich $2.95 $1.25 .42 .58 $20,650 .446 .259Soft drink .80 .30 .38 .62 5,600 .121 .075Baked 1.55 .47 .30 .70 7,750 .167 .117 potatoTea .75 .25 .33 .67 3,750 .081 .054Salad bar 2.85 1.00 .35 .65 8,550 .185 .120

$46,300 1.000 .625

Annual WeightedSelling Variable Forecasted % of Contribution

Item (i) Price (P) Cost (V) (V/P) 1 - (V/P) Sales $ Sales (col 5 x col 7)

BEP$ =F

∑ 1 - x (Wi)Vi

Pi

= = $67,200$3,500 x 12

.625

Daily sales = = $215.38

$67,200312 days

.446 x $215.38$2.95 = 32.6 33

sandwichesper day

© 2006 Prentice Hall, Inc. S7 – 31

Decision Trees and Capacity Decision

-$14,000

$13,000

$18,000

-$90,000Market unfavorable (.6)

Market favorable (.4)$100,000

Large plant

Market favorable (.4)

Market unfavorable (.6)

$60,000

-$10,000

Medium plant

Market favorable (.4)

Market unfavorable (.6)

$40,000

-$5,000

Small plant

$0

Do nothing

© 2006 Prentice Hall, Inc. S7 – 32

Strategy-Driven Investment

Operations may be responsible for return-on-investment (ROI)

Analyzing capacity alternatives should include capital investment, variable cost, cash flows, and net present value

© 2006 Prentice Hall, Inc. S7 – 33

Net Present Value (NPV)

where F = future valueP = present valuei = interest rate

N = number of years

P =F

(1 + i)N

© 2006 Prentice Hall, Inc. S7 – 34

NPV Using Factors

P = = FXF

(1 + i)N

where X = a factor from Table S7.1 defined as = 1/(1 + i)N and F = future value

Year 5% 6% 7% … 10%

1 .952 .943 .935 .9092 .907 .890 .873 .8263 .864 .840 .816 .7514 .823 .792 .763 .6835 .784 .747 .713 .621

Portion of Table S7.1

© 2006 Prentice Hall, Inc. S7 – 35

Present Value of an Annuity

An annuity is an investment which generates uniform equal payments

S = RX

where X = factor from Table S7.2S = present value of a series of uniform annual receiptsR = receipts that are received every year of the life of the investment

© 2006 Prentice Hall, Inc. S7 – 36

Present Value of an Annuity

© 2006 Prentice Hall, Inc. S7 – 37

Present Value of an Annuity

Portion of Table S7.2

Year 5% 6% 7% … 10%

1 .952 .943 .935 .9092 1.859 1.833 1.808 1.7363 2.723 2.676 2.624 2.4874 4.329 3.465 3.387 3.1705 5.076 4.212 4.100 3.791

© 2006 Prentice Hall, Inc. S7 – 38

Process, Volume, and Variety

Process Focusprojects, job shops

(machine, print, carpentry)

Standard Register

Repetitive(autos, motorcycles)

Harley Davidson

Product Focus(commercial

baked goods, steel, glass)Nucor Steel

High Varietyone or few units per run, high variety(allows customization)

Changes in Modulesmodest runs, standardized modules

Changes in Attributes (such as grade, quality, size, thickness, etc.) long runs only

Mass Customization(difficult to achieve, but huge rewards)Dell Computer Co.

Poor Strategy (Both fixed and variable costs

are high)

Low Volume

Repetitive Process

High Volume

VolumeFigure 7.1