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6 1Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Capacity Planning

6

For Operations Management, 9e byKrajewski/Ritzman/Malhotra 2010 Pearson Education

PowerPoint Slides

by Jeff Heyl

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Planning Capacity

Capacity is the maximum rate of output ofa process or system

Accounting, finance, marketing,operations, purchasing, and humanresources all need capacity information tomake decisions

Capacity planning is done in the long-term

and the short-termQuestions involve the amount of capacity

cushion and expansion strategies

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Planning Capacity

Capacity planning

(long-term) Economies and

diseconomies of scale

Capacity timing and sizingstrategies

Systematic approach to

capacity decisions

Constraint management

(short-term) Theory of constraints

Identification andmanagement ofbottlenecks

Product mix decisions

using bottlenecks Managing constraints in a

line process

Capacity management

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Measures of Capacity Utilization

Output measures of capacity

Input measures of capacity

Utilization

Utilization = 100%Average output rate

Maximum capacity

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Capacity and Scale

Economies of scaleSpreading fixed costs

Reducing construction costs

Cutting costs of purchased materials Finding process advantages

Diseconomies of scale

Complexity

Loss of focus

Inefficiencies

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Capacity and Scale

Figure 6.1 Economies and Diseconomies of Scale

250-bedhospital

500-bedhospital

750-bedhospital

Output rate (patients per week)

Averageunit

cost

(dollarsperpatient)

Economiesof scale Diseconomiesof scale

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Faisal Saeed

Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

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Capacity Timing and Sizing

Sizing capacity cushionsCapacity cushions are the amount of

reserve capacity a process uses to handlesudden changes

Capacity cushion = 100% Average Utilization rate (%)

Expansionist strategies

Wait-and-see strategies

Combination of strategies

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Planned unusedcapacity

Time

Capac

ity

Forecast of capacityrequired

Time betweenincrements

Capacityincrement

(a) Expansionist strategy

Figure 6.2 Two Capacity Strategies

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Time

Capac

ity

(b) Wait-and-see strategy

Planned use ofshort-term options

Time betweenincrements

Capacityincrement


Forecast of capacityrequired

Figure 6.2 Two Capacity Strategies

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Linking Capacity

Capacity decisions should be linked toprocesses and supply chains throughoutthe organization

Important issues are competitive priorities,quality, and process design

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Systematic Approach

1. Estimate future capacity requirements

2. Identify gaps by comparing requirementswith available capacity

3. Develop alternative plans for reducing thegaps

4. Evaluate each alternative, bothqualitatively and quantitatively, and makea final choice

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Systematic Approach

Step 1 is to determine the capacity requiredto meet future demand using anappropriate planning horizon

Output measures based on rates ofproduction

Input measures may be used when

Product variety and process divergence is high

The product or service mix is changing

Productivity rates are expected to change

Significant learning effects are expected

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Systematic Approach

For one service or product processed atone operation with a one year time period,the capacity requirement,M, is

Capacity

requirement =

Processing hours required for years demand

Hours available from a single capacity unit(such as an employee or machine) per year,

after deducting desired cushion

M=Dp

N[1 (C/100)]

where

D = demand forecast for the year (number of customers serviced orunits of product)

p = processing time (in hours per customer served or unit produced)

N= total number of hours per year during which the process operates

C= desired capacity cushion (expressed as a percent)

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Systematic Approach

Setup times may be required if multipleproducts are produced

Capacityrequirement =

Processing and setup hours required foryears demand, summed over all services

or productsHours available from a single capacity unitper year, after deducting desired cushion

M=

[Dp + (D/Q)s]product 1 + [Dp + (D/Q)s]product 1+

+ [Dp + (D/Q)s]productn

N[1 (C/100)]

whereQ = number of units in each lots = setup time (in hours) per lot

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Bashir Ahmad


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Estimating Capacity Requirements

EXAMPLE 6.1

A copy center in an office building prepares bound reports fortwo clients. The center makes multiple copies (the lot size) ofeach report. The processing time to run, collate, and bind eachcopy depends on, among other factors, the number of pages.The center operates 250 days per year, with one 8-hour shift.

Management believes that a capacity cushion of 15 percent(beyond the allowance built into time standards) is best. Itcurrently has three copy machines. Based on the followingtable of information, determine how many machines are neededat the copy center.

Item Client X Client Y

Annual demand forecast (copies) 2,000 6,000

Standard processing time (hour/copy) 0.5 0.7

Average lot size (copies per report) 20 30

Standard setup time (hours) 0.25 0.40

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Estimating Capacity Requirements

SOLUTION

M=[Dp + (D/Q)s]product 1 + [Dp + (D/Q)s]product 1+ + [Dp + (D/Q)s]productn

N[1 (C/100)]

=[2,000(0.5) + (2,000/20)(0.25)]client X + [6,000(0.7) + (6,000/30)(0.40)]client Y

[(250 day/year)(1 shift/day)(8 hours/shift)][1.0 - (15/100)]

= = 3.125,305

1,700

Rounding up to the next integer gives a requirement offour machines.

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Systematic Approach

Step 2 is to identify gaps betweenprojected capacity requirements (M) andcurrent capacity

Complicated by multiple operations andresource inputs

Step 3 is to develop alternatives

Base case is to do nothing and suffer the

consequencesMany different alternatives are possible

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Systematic Approach

Step 4 is to evaluate the alternatives

Qualitative concerns include strategic fit anduncertainties

Quantitative concerns may include cash flowsand other quantitative measures

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Evaluating the Alternatives

EXAMPLE 6.2

Grandmothers Chicken Restaurant is experiencing a boom inbusiness. The owner expects to serve 80,000 meals this year.Although the kitchen is operating at 100 percent capacity, thedining room can handle 105,000 diners per year. Forecasteddemand for the next five years is 90,000 meals for next year,

followed by a 10,000-meal increase in each of the succeedingyears. One alternative is to expand both the kitchen and thedining room now, bringing their capacities up to 130,000 mealsper year. The initial investment would be $200,000, made at theend of this year (year 0). The average meal is priced at $10, andthe before-tax profit margin is 20 percent. The 20 percent figure

was arrived at by determining that, for each $10 meal, $8 coversvariable costs and the remaining $2 goes to pretax profit.

What are the pretax cash flows from this project for the nextfive years compared to those of the base case of doingnothing?

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SOLUTION

Recall that the base case of doing nothing results in losing allpotential sales beyond 80,000 meals. With the new capacity, thecash flow would equal the extra meals served by having a130,000-meal capacity, multiplied by a profit of $2 per meal. Inyear 0, the only cash flow is$200,000 for the initial investment.

In year 1, the 90,000-meal demand will be completely satisfiedby the expanded capacity, so the incremental cash flow is(90,000 80,000)($2) = $20,000. For subsequent years, thefigures are as follows:

Year 2: Demand = 100,000; Cash flow = (100,000 80,000)$2 = $40,000




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If the new capacity were smaller than the expected demand inany year, we would subtract the base case capacity from thenew capacity (rather than the demand). The owner shouldaccount for the time value of money, applying such techniquesas the net present value or internal rate of return methods (seeSupplement F, Financial Analysis, in myomlab). For instance,

the net present value (NPV) of this project at a discount rate of10 percent is calculated here, and equals $13,051.76.

NPV = 200,000 + [(20,000/1.1)] + [40,000/(1.1)2] +[60,000/(1.1)3] + [80,000/(1.1)4] + [100,000/(1.1)5]

= $200,000 + $18,181.82 + $33,057.85 + $45,078.89 +$54,641.07 + $62,092.13

= $13,051.76

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6 24

Mumtaz


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Tools for Capacity Planning

Waiting-line modelsUseful in high customer-contact processes

Supplement C, Waiting Lines is a fullertreatment of the models

Simulation

Can be used when models are too complex forwaiting-line analysis

Decision treesUseful when demand is uncertain and

sequential decisions are involved

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Waiting Line Models

Figure 6.3 POMS for Windows Output for Waiting Lines during Office Hours

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Decision Trees

1

Low demand [0.40]

High demand [0.60]

Low demand [0.40]

High demand [0.60]

$70,000

$220,000

$40,000

$135,000

$90,000Dont expand

Expand

2

Figure 6.4 A Decision Tree for Capacity Expansion

$135,000

$109,000

$148,000

$148,000

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Solved Problem 1

You have been asked to put together a capacity plan for a

critical operation at the Surefoot Sandal Company. Yourcapacity measure is number of machines. Three products(mens, womens, and childrens sandals) are manufactured.The time standards (processing and setup), lot sizes, anddemand forecasts are given in the following table. The firmoperates two 8-hour shifts, 5 days per week, 50 weeks per year.

Experience shows that a capacity cushion of 5 percent issufficient.

a. How many machines are needed?

b. If the operation currently has two machines, what is the

capacity gap?

Time Standards

ProductProcessing

(hr/pair)Setup

(hr/pair)Lot size

(pairs/lot)Demand Forecast

(pairs/yr)

Mens sandals 0.05 0.5 240 80,000

Womens sandals 0.10 2.2 180 60,000

Childrens sandals 0.02 3.8 360 120,000

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Solved Problem 1

SOLUTION

a. The number of hours of operation per year,N, isN= (2shifts/day)(8 hours/shifts) (250 days/machine-year) = 4,000hours/machine-year

The number of machines required,M, is the sum of machine-hour requirements for all three products divided by thenumber of productive hours available for one machine:

M=[Dp+ (D/Q)s]men + [Dp+ (D/Q)s]women + [Dp+ (D/Q)s]children

N[1 - (C/100)]

=

[80,000(0.05) + (80,000/240)0.5] + [60,000(0.10) + (60,000/180)2.2]+ [120,000(0.02) + (120,000/360)3.8]

4,000[1 - (5/100)]

= = 3.83 or 4 machines14,567 hours/year

3,800 hours/machine-year

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Solved Problem 1

b. The capacity gap is 1.83 machines (3.832). Two more

machines should be purchased, unless managementdecides to use short-term options to fill the gap.

The Capacity RequirementsSolver in OM Explorer confirmsthese calculations, as Figure 6.5 shows, using only theExpected scenario for the demand forecasts.

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Solved Problem 1

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Solved Problem 2

The base case for Grandmothers Chicken Restaurant (seeExample 6.2) is to do nothing. The capacity of the kitchen in thebase case is 80,000 meals per year. A capacity alternative forGrandmothers Chicken Restaurant is a two-stage expansion.This alternative expands the kitchen at the end of year 0, raisingits capacity from 80,000 meals per year to that of the dining

area (105,000 meals per year). If sales in year 1 and 2 live up toexpectations, the capacities of both the kitchen and the diningroom will be expanded at the end of year 3 to 130,000 meals peryear. This upgraded capacity level should suffice up throughyear 5. The initial investment would be $80,000 at the end ofyear 0 and an additional investment of $170,000 at the end of

year 3. The pretax profit is $2 per meal. What are the pretaxcash flows for this alternative through year 5, compared withthe base case?

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Solved Problem 2

SOLUTIONTable 6.1 shows the cash inflows and outflows. The year 3 cashflow is unusual in two respects. First, the cash inflow fromsales is $50,000 rather than $60,000. The increase in sales overthe base is 25,000 meals (105,000 10,000) instead of 30,000meals (110,000 80,000) because the restaurants capacity falls

somewhat short of demand. Second, a cash outflow of $170,000occurs at the end of year 3, when the second-stage expansionoccurs.

The net cash flow for year 3 is $50,000 $170,000 =$120,000.

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Solved Problem 2

TABLE 6.1 | CASH FLOWS FOR TWO-STAGE EXPANSION AT GRANDMOTHERS CHICKEN RESTAURANT

Year

ProjectedDemand

(meals/yr)

ProjectedCapacity

(meals/yr)

Calculation of Incremental Cash FlowCompared to Base Case

(80,000 meals/yr)

CashInflow

(outflow)

0 80,000 80,000 Increase kitchen capacity to 105,000 meals = ($80,000)

1 90,000 105,000 90,000 80,000 = (10,000 meals)($2/meal) = $20,000

2 100,000 105,000 100,000 80,000 = (20,000 meals)($2/meal) = $40,000

3 110,000 105,000 105,000 80,000 = (25,000 meals)($2/meal) = $50,000

Increase total capacity to 130,000 meals = ($170,000)

($120,000)

4 120,000 130,000 120,000 80,000 = (40,000 meals)($2/meal) = $80,000

5 130,000 130,000 130,000 80,000 = (50,000 meals)($2/meal) =$100,000

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Solved Problem 2

NPV = 80,000 + (20,000/1.1) + [40,000/(1.1)2] [120,000/(1.1)3] +[80,000/(1.1)4] + [100,000/(1.1)5]

= $80,000 + $18,181.82 + $33,057.85 $90,157.77 +$54,641.07 + $62,092.13

= $2,184.90

For comparison purposes, the NPV of this project at a discountrate of 10 percent is calculated as follows, and equals negative$2,184.90.

On a purely monetary basis, a single-stage expansion seemsto be a better alternative than this two-stage expansion.However, other qualitative factors as mentioned earlier must beconsidered as well.

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