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S7S7 Capacity and Constraint Management
Capacity and Constraint Management
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PowerPoint presentation to accompany PowerPoint presentation to accompany Heizer and Render Heizer and Render Operations Management, 10e Operations Management, 10e Principles of Operations Management, 8ePrinciples of Operations Management, 8e
PowerPoint slides by Jeff Heyl
OutlineOutline
CapacityDesign and Effective CapacityCapacity and Strategy
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Capacity ConsiderationsManaging DemandDemand and Capacity Management in the Service Sector
Outline Outline –– ContinuedContinuedBottleneck Analysis and Theory of Constraints
Process Times for Stations, Systems, and Cycles
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Theory of ConstraintsBottleneck Management
Break-Even AnalysisSingle-Product CaseMultiproduct Case
Outline Outline –– ContinuedContinuedReducing Risk with Incremental ChangesApplying Expected Monetary Value to Capacity Decisions
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Applying Investment Analysis to Strategy-Driven Investments
Investment, Variable Cost, and Cash FlowNet Present Value
Learning ObjectivesLearning ObjectivesWhen you complete this supplement, When you complete this supplement, you should be able to:you should be able to:
1. Define capacity
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2. Determine design capacity, effective capacity, and utilization
3. Perform bottleneck analysis4. Compute break-even analysis
Learning ObjectivesLearning ObjectivesWhen you complete this supplement, When you complete this supplement, you should be able to:you should be able to:
5. Determine the expected monetary value of a capacity decision
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value of a capacity decision6. Compute net present value
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Process StrategiesProcess Strategies
The objective of a process strategy is The objective of a process strategy is to build a production process that to build a production process that meets customer requirements and meets customer requirements and product specifications within costproduct specifications within cost
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product specifications within cost product specifications within cost and other managerial constraintsand other managerial constraints
CapacityCapacityThe throughput, or the number of units a facility can hold, receive, store, or produce in a period of timeDetermines
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ete esfixed costsDetermines if demand will be satisfiedThree time horizons
Planning Over a Time Planning Over a Time HorizonHorizon
Intermediate- Subcontract Add personnel
Long-range planning
Add facilitiesAdd long lead time equipment *
Options for Adjusting Capacity
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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*
* Difficult to adjust capacity as limited options exist
Design and Effective Design and Effective CapacityCapacity
Design capacity is the maximum theoretical output of a system
N ll d t
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Normally expressed as a rateEffective capacity is the capacity a firm expects to achieve given current operating constraints
Often lower than design capacity
Utilization and EfficiencyUtilization and Efficiency
Utilization is the percent of design capacity Utilization is the percent of design capacity achievedachieved
Utilization = Actual output/Design capacity
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Efficiency is the percent of effective capacity Efficiency is the percent of effective capacity achievedachieved
p g p y
Efficiency = Actual output/Effective capacity
Bakery ExampleBakery 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
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Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
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Bakery ExampleBakery 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
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Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
Bakery ExampleBakery 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
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Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
Utilization = 148,000/201,600 = 73.4%
Bakery ExampleBakery 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
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Design capacity = (7 x 3 x 8) x (1,200) = 201,600 rolls
Utilization = 148,000/201,600 = 73.4%
Bakery ExampleBakery 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
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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 ExampleBakery 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
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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 ExampleBakery 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 shiftsEffi i 84 6%
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Efficiency = 84.6%Efficiency of new line = 75%
Expected Output = (Effective Capacity)(Efficiency)
= (175,000)(.75) = 131,250 rolls
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Bakery ExampleBakery 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 shiftsEffi i 84 6%
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Efficiency = 84.6%Efficiency of new line = 75%
Expected Output = (Effective Capacity)(Efficiency)
= (175,000)(.75) = 131,250 rolls
Capacity and StrategyCapacity and Strategy
Capacity decisions impact all 10 decisions of operations management as well as other f ti l f th i ti
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functional areas of the organizationCapacity decisions must be integrated into the organization’s mission and strategy
Capacity ConsiderationsCapacity Considerations
1. Forecast demand accurately2. Understand the technology and
capacity increments
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p y3. Find the optimum
operating level (volume)
4. Build for change
Economies and Economies and Diseconomies of ScaleDiseconomies of Scale
25 - room roadside motel
75 - room roadside motelit
cost
m p
er n
ight
)
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Economies of scale
Diseconomies of scale
roadside motel 50 - room roadside motel
roadside motel
Number of Rooms25 50 75
Aver
age
uni
(dol
lars
per
room
Figure S7.2
Managing DemandManaging DemandDemand exceeds capacity
Curtail demand by raising prices, scheduling longer lead timeLong term solution is to increase capacity
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Capacity exceeds demandStimulate marketProduct changes
Adjusting to seasonal demandsProduce products with complementary demand patterns
Complementary Demand Complementary Demand PatternsPatterns
4,000 –
ts
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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
Time (months)
Jet ski engine sales
Figure S7.3
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Complementary Demand Complementary Demand PatternsPatterns
4,000 –
ts S bil
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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
Time (months)
Snowmobile motor sales
Jet ski engine sales
Figure S7.3
Complementary Demand Complementary Demand PatternsPatterns
4,000 –
ts
Combining both demand patterns reduces the variation
S bil
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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
Time (months)
Snowmobile motor sales
Jet ski engine sales
Figure S7.3
Tactics for Matching Tactics for Matching Capacity to DemandCapacity to Demand
1. Making staffing changes2. Adjusting equipment
Purchasing additional machinerySelling or leasing out existing equipment
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Selling or leasing out existing equipment3. Improving processes to increase throughput4. Redesigning products to facilitate more
throughput5. Adding process flexibility to meet changing
product preferences6. Closing facilities
Demand and Capacity Demand and Capacity Management in the Management in the
Service SectorService SectorDemand management
Appointment, reservations, FCFS rule
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Capacity management
Full time, temporary, part-time staff
Bottleneck Analysis and Bottleneck Analysis and Theory of ConstraintsTheory of Constraints
Each work area can have its own unique capacityCapacity analysis determines the
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throughput capacity of workstations in a systemA bottleneck is a limiting factor or constraintA bottleneck has the lowest effective capacity in a system
Process Times for Stations, Process Times for Stations, Systems, and CyclesSystems, and CyclesThe process time of a stationprocess time of a station is the time to produce a unit at that single workstation
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The process time of a systemprocess time of a system is the time of the longest process in the system … the bottleneckThe process cycle timeprocess cycle time is the time it takes for a product to go through the production process with no waiting
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A ThreeA Three--Station Station Assembly LineAssembly Line
QuickTime™ and a decompressor
are needed to see this picture.
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Figure S7.4
2 min/unit 4 min/unit 3 min/unit
A B C
Process Times for Stations, Process Times for Stations, Systems, and CyclesSystems, and CyclesThe system process timesystem process time is the process time of the bottleneck after dividing by the number of parallel operations
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operationsThe system capacitysystem capacity is the inverse of the system process timeThe process cycle timeprocess cycle time is the total time through the longest path in the system
Capacity AnalysisCapacity AnalysisTwo identical sandwich linesLines have two workers and three operations All completed sandwiches are wrapped
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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
Capacity Capacity AnalysisAnalysis 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 secondsThe two lines each deliver a sandwich every 40 seconds so the process time of the combined
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plines is 40/2 = 20 secondsAt 37.5 seconds, wrapping and delivery has the longest processing time and is the bottleneckCapacity per hour is 3,600 seconds/37.5 seconds/sandwich = 96 sandwiches per hourProcess cycle time is 30 + 15 + 20 + 40 + 37.5 = 142.5 seconds
Capacity AnalysisCapacity AnalysisStandard process for cleaning teethCleaning and examining X-rays can happen simultaneously
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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
Capacity Capacity AnalysisAnalysis
All possible paths must be comparedCleaning path is 2 + 2 + 4 + 24 + 8 + 6 = 46 minutesX-ray exam path is 2 + 2 + 4 + 5 + 8 + 6 = 27
Checkout
6 min/unit
Checkin
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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X-ray exam path is 2 + 2 + 4 + 5 + 8 + 6 = 27 minutesLongest path involves the hygienist cleaning the teethBottleneck is the hygienist at 24 minutesHourly capacity is 60/24 = 2.5 patientsPatient should be complete in 46 minutes
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Theory of ConstraintsTheory of ConstraintsFive-step process for recognizing and managing limitationsStep 1:Step 1: Identify the constraintStep 2:Step 2: Develop a plan for overcoming the
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pp p p gconstraints
Step 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
Bottleneck ManagementBottleneck 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
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y3. Increasing the capacity of a non-
bottleneck station is a mirage4. Increasing the capacity of a bottleneck
increases the capacity of the whole system
BreakBreak--Even AnalysisEven Analysis
Technique for evaluating process and equipment alternativesObjective is to find the point in
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dollars and units at which cost equals revenueRequires estimation of fixed costs, variable costs, and revenue
BreakBreak--Even AnalysisEven AnalysisFixed costs are costs that continue even if no units are produced
Depreciation, taxes, debt, mortgage payments
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Variable costs are costs that vary with the volume of units produced
Labor, materials, portion of utilitiesContribution is the difference between selling price and variable cost
BreakBreak--Even AnalysisEven Analysis
Costs and revenue are linear functions
Generally not the case in the
AssumptionsAssumptions
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yreal world
We actually know these costsVery difficult to verify
Time value of money is often ignored
BreakBreak--Even AnalysisEven AnalysisTotal revenue line
Total cost lineBreak-even pointTotal cost = Total revenue
–
900 –
800 –
700 –
600 –
500dolla
rs
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Variable cost
Fixed cost
500 –
400 –
300 –
200 –
100 –
–| | | | | | | | | | | |
0 100 200 300 400 500 600 700 800 900 10001100
Cos
t in
d
Volume (units per period)Figure S7.5
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BreakBreak--Even AnalysisEven AnalysisBEPx = break-even point in
unitsBEP$ = break-even point in
dollarsP = price per unit (after
all discounts)
x = number of units produced
TR = total revenue = PxF = fixed costsV = variable cost per unit
TC = total costs = F + Vx
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TR = TCor
Px = F + Vx
BreakBreak--even point occurs wheneven point occurs when
BEPx = FP - V
BreakBreak--Even AnalysisEven AnalysisBEPx = break-even point in
unitsBEP$ = break-even point in
dollarsP = price per unit (after
all discounts)
x = number of units produced
TR = total revenue = PxF = fixed costsV = variable cost per unit
TC = total costs = F + Vx
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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
BreakBreak--Even ExampleEven Example
Fixed costs = $10,000 Material = $.75/unitDirect labor = $1.50/unit Selling price = $4.00 per unit
BEP = =F $10,000
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BEP$ = =1 - (V/P) 1 - [(1.50 + .75)/(4.00)]
BreakBreak--Even ExampleEven Example
Fixed costs = $10,000 Material = $.75/unitDirect labor = $1.50/unit Selling price = $4.00 per unit
BEP = =F $10,000
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BEP$ = =1 - (V/P) 1 - [(1.50 + .75)/(4.00)]
= = $22,857.14$10,000.4375
BEPx = = = 5,714FP - V
$10,0004.00 - (1.50 + .75)
BreakBreak--Even ExampleEven Example50,000 –
40,000 –
30,000 –s Total t
Revenue
Break-even point
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20,000 –
10,000 –
–| | | | | |0 2,000 4,000 6,000 8,000 10,000
Dol
lars
Units
Fixed costs
costs
BreakBreak--Even ExampleEven Example
BEP$ = F
∑ 1 (W )Vi
Multiproduct CaseMultiproduct Case
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∑ 1 - x (Wi)i
Pi
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 ExampleMultiproduct 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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Baked potato 2.00 1.00 7,000
Multiproduct ExampleMultiproduct 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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Baked potato 2.00 1.00 7,000
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)
Multiproduct ExampleMultiproduct 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 = $3,000 per month
BEP$ =F
∑ 1 - x (Wi)ViPi
= = $76,759$3,000 x 12.469
Daily = = $246 02$76,759
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Baked potato 2.00 1.00 7,000
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)
sales = = $246.02312 days
.621 x $246.02$5.00 = 30.6 ≈ 31
sandwichesper day
Reducing Risk with Reducing Risk with Incremental ChangesIncremental Changes
(a) Leading demand with incremental expansion
Dem
and
Expected demand
New capacity
(b) Capacity lags demand with incremental expansion
Dem
and
New capacity
Expected demand
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(c) Attempts to have an average capacity with incremental expansion
Dem
and New
capacity Expected demand
Figure S7.6
Reducing Risk with Reducing Risk with Incremental ChangesIncremental Changes
(a) Leading demand with incremental expansion
New capacity
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Expected demand
Figure S7.6
Dem
and
Time (years)1 2 3
Reducing Risk with Reducing Risk with Incremental ChangesIncremental Changes
(b) Capacity lags demand with incremental expansion
New capacity
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Expected demand
Figure S7.6
Dem
and
Time (years)1 2 3
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Reducing Risk with Reducing Risk with Incremental ChangesIncremental Changes(c) Attempts to have an average capacity
with incremental expansion
New capacity
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Expected demand
Figure S7.6
Dem
and
Time (years)1 2 3
Expected Monetary Value Expected Monetary Value (EMV) and Capacity Decisions(EMV) and Capacity Decisions
Determine states of natureFuture demand
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Market favorabilityAnalyzed using decision trees
Hospital supply companyFour alternatives
Expected Monetary Value Expected Monetary Value (EMV) and Capacity Decisions(EMV) and Capacity Decisions
-$90,000Market unfavorable (.6)
Market favorable (.4) $100,000
Market favorable ( 4)
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Market favorable (.4)
Market unfavorable (.6)
$60,000
-$10,000
Medium plant
Market favorable (.4)
Market unfavorable (.6)
$40,000
-$5,000
$0
Expected Monetary Value Expected Monetary Value (EMV) and Capacity Decisions(EMV) and Capacity Decisions
-$90,000Market unfavorable (.6)
Market favorable (.4) $100,000
Market favorable ( 4)
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Market favorable (.4)
Market unfavorable (.6)
$60,000
-$10,000
Medium plant
Market favorable (.4)
Market unfavorable (.6)
$40,000
-$5,000
$0
EMV = (.4)($100,000) + (.6)(-$90,000)
Large Plant
EMV = -$14,000
Expected Monetary Value Expected Monetary Value (EMV) and Capacity Decisions(EMV) and Capacity Decisions
-$90,000Market unfavorable (.6)
Market favorable (.4) $100,000
Market favorable ( 4)
-$14,000
$18,000
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Market favorable (.4)
Market unfavorable (.6)
$60,000
-$10,000
Medium plant
Market favorable (.4)
Market unfavorable (.6)
$40,000
-$5,000
$0
$13,000
StrategyStrategy--Driven InvestmentDriven Investment
Operations may be responsible for return-on-investment (ROI)
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Analyzing capacity alternatives should include capital investment, variable cost, cash flows, and net present value
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Net Present Value (NPV)Net Present Value (NPV)
where F = future valueP t l
F = P(1 + i)N
In general:
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P = present valuei = interest rate
N = number of years
P = F(1 + i)N
Solving for P:
Net Present Value (NPV)Net Present Value (NPV)
where F = future valueP t l
F = P(1 + i)N
In general:
While this works
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P = present valuei = interest rate
N = number of years
P = F(1 + i)N
Solving for P:
While this works fine, it is
cumbersome for larger values of N
NPV Using FactorsNPV Using Factors
P = = FXF(1 + i)N
where X = a factor from Table S7.1 defined as = 1/(1 + i)N and
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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
Present Value of an AnnuityPresent Value of an AnnuityAn annuity is an investment which generates uniform equal payments
S = RX
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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 AnnuityPresent Value of an AnnuityPortion of Table S7.2
Year 6% 8% 10% 12% 14%1 .943 .926 .909 .893 .8772 1 833 1 783 1 736 1 690 1 647
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2 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
Present Value of an AnnuityPresent Value of an Annuity
$7,000 in receipts per for 5 yearsInterest rate = 6%
From Table S7.2
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X = 4.212
S = RXS = $7,000(4.212) = $29,484
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LimitationsLimitations1. Investments with the same NPV may
have different projected lives and salvage values
2. Investments with the same NPV may
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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
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