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7Suppl Capacity Planning

Heizer and Render Heizer and Render Principles of Operations Management, 8ePrinciples of Operations Management, 8e

PowerPoint slides by Jeff Heyl

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Capacity The throughput, or the number of

units a facility can hold, receive, store, or produce in a period of time

Determines capital requirements and, therefore, fixed costs

Determines if demand will be satisfied Three time horizons

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Planning Over a Time Horizon

Figure S7.1

Modify capacity Use capacity

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 *

* Difficult to adjust capacity as limited options exist

Options for Adjusting Capacity

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Design and Effective Capacity

Design capacity is the maximum theoretical output of a system in a given period Normally expressed as a rate

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

Measuring Capacity: maximum number of units produced in a specific time

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Utilization and Efficiency

Utilization is the percent of design capacity Utilization is the percent of design capacity achievedachieved

Efficiency is the percent of effective capacity Efficiency is the percent of effective capacity achievedachieved

Utilization = Actual output/Design capacity

Efficiency = Actual output/Effective capacity

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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

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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%

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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%

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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 shiftsEfficiency = 84.6%Efficiency of new line = 75%

Expected Output = (Effective Capacity)(Efficiency)

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

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Capacity and Strategy

Sustained profits come from building competitive advantage, not just from a good financial return on a specific process.

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

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Capacity Considerations

1. Forecast demand accurately: whatever the new product, its prospects and the life cycle of existing products must be determined.

2. Understand the technology and capacity increments: Aid technology decisions by analysis of cost, human resources, quality, and reliability.

3. Find the optimum operating level (volume): If smaller, fixed cost is too

burdensome, if larger, the facility becomes more than one manger task1. Build for change: Build flexibility into facility and

equipment

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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

Ave

rage

uni

t cos

t(d

olla

rs p

er ro

om p

er n

ight

)

Figure S7.2

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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 complementary demand patterns

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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)

Combining both demand patterns reduces the variation

Snowmobile motor sales

Jet ski engine sales

Figure S7.3

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Tactics for Matching Capacity to Demand

1. Making staffing changes2. Adjusting equipment

Purchasing additional machinery Selling or leasing out existing equipment

3. Improving processes to increase throughput4. Redesigning products to facilitate more throughput5. Adding process flexibility to meet changing product

preferences6. Closing facilities

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Demand and Capacity Management in the Service Sector

Demand management Appointment, reservations, FCFS rule

Capacity management Full time,

temporary, part-time staff

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Bottleneck Analysis and Theory of Constraints

Each work area can have its own unique capacity

Capacity analysis determines the throughput capacity of workstations in a system

A bottleneck is a limiting factor or constraint A bottleneck has the lowest effective

capacity in a system

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Process Times for Stations, Systems, and Cycles

The process time of a stationprocess time of a station is the time to produce a unit at that single workstation

The process time of a systemprocess time of a system is the time of the longest process in the system … the bottleneck

The process cycle timeprocess cycle time is the time it takes for a product to go through the production process with no waiting

These two might be quite different!

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A Three-Station Assembly Line

Figure S7.4

2 min/unit 4 min/unit 3 min/unit

A B C

QuickTime™ and a decompressor

are needed to see this picture.

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Process Times for Stations, Systems, and Cycles

The system process timesystem process time is the process time of the bottleneck after dividing by the number of parallel operations

The system capacitysystem capacity is the inverse of the system process time

The process cycle timeprocess cycle time is the total time through the longest path in the system

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Capacity Analysis Two identical sandwich lines Lines have two workers and three operations All completed sandwiches are wrapped

Wrap

37.5 sec/sandwich

Order

30 sec/sandwich

Bread Fill Toast

15 sec/sandwich 20 sec/sandwich 40 sec/sandwich

Bread Fill Toast

15 sec/sandwich 20 sec/sandwich 40 sec/sandwich

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Capacity Analysis Wrap

37.5 sec

Order

30 sec

Bread Fill Toast

15 sec 20 sec 40 sec

Bread Fill Toast

15 sec 20 sec 40 sec

Toast work station has the longest processing time – 40 seconds

The two lines each deliver a sandwich every 40 seconds so the process time of the combined lines is 40/2 = 20 seconds

At 37.5 seconds, wrapping and delivery has the longest processing time and is the bottleneck

Capacity per hour is 3,600 seconds/37.5 seconds/sandwich = 96 sandwiches per hour

Process cycle time is 30 + 15 + 20 + 40 + 37.5 = 142.5 seconds

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Capacity Analysis Standard process for cleaning teeth Cleaning and examining X-rays can happen

simultaneously

Checkout

6 min/unit

Check in

2 min/unit

DevelopsX-ray

4 min/unit 8 min/unit

DentistTakesX-ray

2 min/unit

5 min/unit

X-rayexam

Cleaning

24 min/unit

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Capacity Analysis

All possible paths must be compared Cleaning path is 2 + 2 + 4 + 24 + 8 + 6 = 46 minutes X-ray exam path is 2 + 2 + 4 + 5 + 8 + 6 = 27

minutes Longest path involves the hygienist cleaning the

teeth Bottleneck is the hygienist at 24 minutes Hourly capacity is 60/24 = 2.5 patients Patient should be complete in 46 minutes

Checkout

6 min/unit

Check in

2 min/unit

DevelopsX-ray

4 min/unit 8 min/unit

DentistTakesX-ray

2 min/unit

5 min/unit

X-rayexam

Cleaning

24 min/unit

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Theory of Constraints Five-step process for recognizing and

managing limitationsStep 1:Step 1: Identify the constraintStep 2:Step 2: Develop a plan for overcoming the constraintsStep 3:Step 3: Focus resources on accomplishing Step 2Step 4:Step 4: Reduce the effects of constraints by offloading work or

expanding capabilityStep 5:Step 5: Once overcome, go back to Step 1 and find new

constraints

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Bottleneck Management

1. Release work orders to the system at the pace of set by the bottleneck

2. Lost time at the bottleneck represents lost time for the whole system

3. Increasing the capacity of a non-bottleneck station is a mirage

4. Increasing the capacity of a bottleneck increases the capacity of the whole system

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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

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Break-Even Analysis

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

payments Variable costs are costs that vary with

the volume of units produced Labor, materials, portion of utilities Contribution is the difference between

selling price and variable cost

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Break-Even Analysis

Costs and revenue are linear functions Generally not the case in the

real world We actually know these costs

Very difficult to verify Time value of money is often

ignored

AssumptionsAssumptions

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Profit corrid

or

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

Cos

t in

dolla

rs

Volume (units per period)Figure S7.5

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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 cost per unitTC= total costs = F + Vx

TR = TCor

Px = F + Vx

Break-even point occurs whenBreak-even point occurs when

BEPx =F

P - V

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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 cost per unitTC= 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

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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)

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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

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Break-Even Example

BEP$ =F

∑ 1 - x (Wi)Vi

Pi

Multiproduct CaseMultiproduct Case

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

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

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Multiproduct Example

Annual ForecastedItem Price Cost Sales UnitsSandwich $5.00 $3.00 9,000Drink 1.50 .50 9,000Baked potato 2.00 1.00 7,000

Fixed costs = $3,000 per month

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Multiproduct Example

Annual ForecastedItem Price Cost Sales UnitsSandwich $5.00 $3.00 9,000Drink 1.50 .50 9,000Baked potato 2.00 1.00 7,000

Fixed costs = $3,000 per month

Sandwich $5.00 $3.00 .60 .40 $45,000 .621 .248Drinks 1.50 .50 .33 .67 13,500 .186 .125Baked 2.00 1.00 .50 .50 14,000 .193 .096 potato

$72,500 1.000 .469

Annual WeightedSelling Variable Forecasted % of Contribution

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

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Multiproduct

Annual ForecastedItem Price Cost Sales UnitsSandwich $5.00 $3.00 9,000Drink 1.50 .50 9,000Baked potato 2.00 1.00 7,000

Fixed costs = $3,000 per month

Sandwich $5.00 $3.00 .60 .40 $45,000 .621 .248Drinks 1.50 .50 .33 .67 13,500 .186 .125Baked 2.00 1.00 .50 .50 14,000 .193 .096 potato

$72,500 1.000 .469

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

= = $76,759$3,000 x 12.469

Daily sales = = $246.02$76,759

312 days

.621 x $246.02$5.00 = 30.6 31

sandwichesper day

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Reducing Risk with Incremental Changes(a) Leading demand with

incremental expansion

Dem

and

Expected demand

New capacity

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

Dem

and New

capacity Expected demand

(b) Capacity lags demand with incremental expansion

Dem

and

New capacity

Expected demand

Figure S7.6

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Expected Monetary Value (EMV) and Capacity Decisions

Determine states of nature Future demand Market favorability

Analyzed using decision trees Hospital supply company Four alternatives

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Expected Monetary Value (EMV) and Capacity Decisions

-$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

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Expected Monetary Value (EMV) and Capacity Decisions

-$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

EMV = (.4)($100,000) + (.6)(-$90,000)

Large Plant

EMV = -$14,000

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Expected Monetary Value (EMV) and Capacity Decisions

-$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

-$14,000

$13,000

$18,000

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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

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Net Present Value (NPV)

where F = future valueP = present valuei = interest rate

N = number of years

P = F(1 + i)N

F = P(1 + i)N

In general:

Solving for P:While this works fine, it is cumbersome for larger values of N

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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

Portion of Table S7.1

Year 6% 8% 10% 12% 14%1 .943 .926 .909 .893 .8772 .890 .857 .826 .797 .7693 .840 .794 .751 .712 .6754 .792 .735 .683 .636 .5925 .747 .681 .621 .567 .519

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Present Value of an Annuity

An annuity is an investment which generates uniform equal payments

S = RXwhere X = factor from Table S7.2

S = present value of a series of uniform annual receiptsR = receipts that are received every year of the life of the investment

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Present Value of an Annuity

Portion of Table S7.2

Year 6% 8% 10% 12% 14%1 .943 .926 .909 .893 .8772 1.833 1.783 1.736 1.690 1.6473 2.676 2.577 2.487 2.402 2.3224 3.465 3.312 3.170 3.037 2.9145 4.212 3.993 3.791 3.605 3.433

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Present Value of an Annuity

$7,000 in receipts per for 5 yearsInterest rate = 6%

From Table S7.2X = 4.212

S = RXS = $7,000(4.212) = $29,484

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Limitations

1. Investments with the same NPV may have different projected lives and salvage values

2. Investments with the same NPV may have different cash flows

3. Assumes we know future interest rates4. Payments are not always made at the end

of a period