Capacity Planning Capacity Planning

Production Planning and Control

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 Used to plan overtime horizon

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 *

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

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

Bakery Example

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

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

Bakery Example

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

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

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

Bakery Example

Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, 8 hours, 3 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%

Bakery Example

Actual production last week = 148,000 rollsEffective capacity = 175,000 rollsDesign capacity = 1,200 rolls per hourBakery operates 7 days/week, 8 hours, 3 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%

Bakery Example

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

Expected Output = (Effective Capacity)(Efficiency)

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

Capacity and Strategy

Capacity decisions impact all 10 decisions of operations management as well as other functional areas of the organization

Capacity decisions must be integrated into the organization’s mission and strategy

Managing Demand

Demand exceeds capacity Limit 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

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

Aver

age

unit

cost

(dol

lars

per

room

per

nig

ht)

Capacity Considerations

Forecast demand accurately Understanding the technology and

capacity increments Find the optimal operating level

(volume) Build for change

Tactics for Matching Capacity to Demand

1. Making staffing changes

2. Adjusting equipment and processes Purchasing additional machinery Selling or leasing out existing equipment

3. Improving methods to increase throughput

4. Redesigning the product to facilitate more throughput

Complementary Demand Patterns

4,000 –

3,000 –

2,000 –

1,000 –

J F M A M J J A S O N D J F M A M J J A S O N D J

Sale

s in

uni

ts

Time (months)

By combining both, the

variation is reduced

Snowmobile sales

Jet ski sales

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

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

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

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

Profit corridor

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

Cost

in d

olla

rs

Volume (units per period)

Break-Even AnalysisBEPx =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

Break-Even AnalysisBEPx =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

Break-Even Example

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

BEP$ = =F1 - (V/P)

$10,0001 - [(1.50 + .75)/(4.00)]

Break-Even Example

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

BEP$ = =F1 - (V/P)

$10,0001 - [(1.50 + .75)/(4.00)]

= = $22,857.14$10,000.4375

BEPx = = = 5,714FP - V

$10,0004.00 - (1.50 + .75)

Break-Even Example

50,000 –

40,000 –

30,000 –

20,000 –

10,000 –

–| | | | | |

0 2,000 4,000 6,000 8,000 10,000

Dol

lars

Units

Fixed costs

Total costs

Revenue

Break-even point

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

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

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

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$67,200

312 days

.446 x $215.38$2.95

= 32.6 33sandwiches

per day

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

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

Net Present Value (NPV)

where F = future valueP = present valuei = interest rate

N = number of years

P =F

(1 + i)N

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

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

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

Questions?