decsion making powerpoint
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Supplement A
Decision Making
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Decision Making Tools
Break-even analysis Analysis to compare processes by finding the volume at which
two processes have equal total costs.
Preference matrix Table that allows managers to rate alternatives based on several
performance criteria.
Decision theory Approach when outcomes associated with alternatives are
in doubt. Decision Tree
Model to compare alternatives and their possibleconsequences.
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Break-even analysis notation
Variable cost (c)-
The portion of the total cost that varies directly withvolume of output.
Fixed cost (F)
The portion of the total cost that remains constantregardless of changes in levels of output.
Quantity (Q) The number of customers served or units produced per
year.
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Example A.1
A hospital is considering a new procedure to be offered at
$200 per patient. The fixed cost per year would be $100,000
with total variable costs of $100 per patient. What is the
break-even quantity for this service? Use both algebraic and
graphic approaches to get the answer.
The formula for the break-even quantity yields
Q=F
p- c= 1,000 patients=
100,000
200100
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Example A.1
The following table shows the results for Q = 0 and Q= 2,000
Quantity(patients)
(Q)Total Annual Cost ($)
(100,000 + 100Q)Total Annual Revenue ($)
(200Q)
0 100,000 0
2,000 300,000 400,000
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Example A.1
Total annual costs
Fixed costs
Break-even quantity
Profits
Loss
Patients (Q)
Dollars(inthou
sands)
400
300
200
100
0 | | | |
500 1000 1500 2000
(2000, 300)
Total annual revenues
The two linesintersect at1,000patients, the
break-evenquantity
(2000, 400)
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Application A.1
The Denver Zoo must decide whether to move twin polar bears to SeaWorld or build a special exhibit for them and the zoo. The expected
increase in attendance is 200,000 patrons. The data are:
Revenues per Patron for Exhibit
Gate receipts $4
Concessions $5
Licensed apparel $15
Estimated Fixed Costs
Exhibit construction $2,400,000
Salaries $220,000Food $30,000
Estimated Variable Costs per Person
Concessions $2
Licensed apparel $9
Is the predictedincrease inattendancesufficient tobreak even?
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Application A.1
Q TR=pQ TC= F+ cQ0 $0 $2,650,000
250,000 $6,000,000 $5,400,000
7
6
5
4
3
2
1
0| | | | | |
50 100 150 200 250
Costandrevenue
(millionsofdollars)
Q(thousands of patrons)
Wherep = 4 + 5 + 15 = $24F = 2,400,000 + 220,000 + 30,000
= $2,650,000c = 2 + 9 = $11
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Application A.1
Q TR=pQ TC= F+ cQ
0 $0 $2,650,000
250,000 $6,000,000 $5,400,000
Wherep = 4 + 5 + 15 = $24F = 2,400,000 + 220,000 + 30,000
= $2,650,000c = 2 + 9 = $11
Algebraic solution of Denver Zoo problem
pQ = F + cQ
24Q = 2,650,000 + 11Q
13Q = 2,650,000
Q = 203,846
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Example A.2
If the most pessimistic sales forecast for the proposedservice from Example 1 was 1,500 patients, what would bethe procedures total contribution to profit and overhead peryear?
200(1,500)[100,000 + 100(1,500)]pQ(F+ cQ) =
= $50,000
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Make-or-buy decision notation
Fb
The fixed cost (per year) of the buy option
Fm The fixed cost of the make option
cb The variable cost (per unit) of the buy option
cm The variable cost of the make option
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Example A.3
A fast-food restaurant featuring hamburgers is addingsalads to the menu
The price to the customer will be the same
Fixed costs are estimated at $12,000 and variable costs
totaling $1.50 per salad
Preassembled salads could be purchased from a local
supplier at $2.00 per salad
Preassembled salads would require additional
refrigeration with an annual fixed cost of $2,400
Expected demand is 25,000 salads per year
What is the break-even quantity?
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The formula for the break-even quantity yields thefollowing:
Q=FmFbcbcm
= 19,200 salads=12,0002,400
2.01.5
Example A.3
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Application A.2
At what volume should the Denver Zoo be
indifferent between buying special sweatshirts from
a supplier or have zoo employees make them?
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Buy
Make
Fixed costs $0 $300,000
Variable costs
$9
$7
Q =FmFbcbcm
Q =300,0000
97Q = 150,000
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Preference Matrix
A Preference Matrix is a table that allows you to
rate an alternative according to several
performance criteria.
The criteria can be scored on any scale as long as the samescale is applied to all the alternatives being compared.
Each score is weighted according to its perceived
importance, with the total weights typically
equaling 100. The total score is the sum of the weighted scores (weight
score) for all the criteria and compared against scores for
alternatives.
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The following table shows the performance criteria, weights,
and scores (1 = worst, 10 = best) for a new thermal storage air
conditioner. If management wants to introduce just one new
product and the highest total score of any of the other product
ideas is 800, should the firm pursue making the air conditioner?
Example A.4
Performance Criterion Weight (A) Score (B) Weighted Score (A B)
Market potential 30 8 240
Unit profit margin 20 10 200
Operations compatibility 20 6 120
Competitive advantage 15 10 150
Investment requirements 10 2 20
Project risk 5 4 20
Weighted score = 750
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Because the sum of the weighted scores is 750, it falls shortof the score of 800 for another product. This result is
confirmed by the output from OM Explorers Preference
Matrix Solver below
Example A.4
Total 750
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Application A.3
The following table shows the performance criteria, weights, andscores (1 = worst, 10 = best) for a new thermal storage airconditioner. If management wants to introduce just one newproduct and the highest total score of any of the other productideas is 800, should the firm pursue making the air conditioner?
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Performance Criterion Weight (A) Score (B) Weighted Score (A B)Market potential 10 5 50
Unit profit margin 30 8 240
Operations compatibility 20 10 200
Competitive advantage 25 7 175Investment
requirements
10 3 30
Project risk 5 4 20
Weighted score = 715
No.
Because
715 >800
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Decision Theory Steps
List a reasonable number of feasible alternatives
List the events (states of nature)
Calculate the payoff table showing the payoff foreach alternative in each event
Estimate the probability of occurrence for eachevent
Select the decision rule to evaluate the alternatives
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Example A.5
A manager is deciding whether to build a small or a largefacility
Much depends on the future demand
Demand may be small or large
Payoffs for each alternative are known with certainty
What is the best choice if future demand will be low?
Possible Future Demand
Alternative Low HighSmall facility 200 270
Large facility 160 800
Do nothing 0 0
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Example A.5
The best choice is the one with the highest payoff
For low future demand, the company should build a smallfacility and enjoy a payoff of $200,000
Under these conditions, the larger facility has a payoff ofonly $160,000
Possible Future Demand
Alternative Low High
Small facility 200 270
Large facility 160 800
Do nothing 0 0
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Decision Making under Uncertainty
Maximin
Maximax
Laplace
Minimax Regret
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Example A.6
Reconsider the payoff matrix in Example 5. What is the bestalternative for each decision rule?
a. Maximin. An alternatives worst payoff is the lowest
number in its row of the payoff matrix, because thepayoffs are profits. The worst payoffs ($000) are
Alternative Worst Payoff
Small facility 200
Large facility 160
The best of these worst numbers is $200,000, so thepessimist would build a small facility.
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Example A.6
b. Maximax. An alternatives best payoff ($000) is thehighest number in its row of the payoff matrix, or
Alternative Best Payoff
Small facility 270
Large facility 800
The best of these best numbers is $800,000, so theoptimist would build a large facility.
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Example A.6
c. Laplace. With two events, we assign each a probabilityof 0.5. Thus, the weighted payoffs ($000) are
The best of these weighted payoffs is $480,000, sothe realist would build a large facility.
0.5(200) + 0.5(270) = 2350.5(160) + 0.5(800) = 480
Alternative Weighted Payoff
Small facilityLarge facility
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Example A.6
d. Minimax Regret. If demand turns out to be low, the bestalternative is a small facility and its regret is 0 (or 200200). If a large facility is built when demand turns out tobe low, the regret is 40 (or 200160).
RegretAlternative Low Demand High Demand
MaximumRegret
Small facility 200200 = 0 800270 =530 530
Large facility 200160 = 40 800800 = 0 40
The column on the right shows the worst regret for eachalternative. To minimize the maximum regret, pick alarge facility. The biggest regret is associated with havingonly a small facility and high demand.
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Application A.4
Fletcher (a realist), Cooper (a pessimist), and Wainwright (anoptimist) are joint owners in a company. They must decidewhether to make Arrows, Barrels, or Wagons. The governmentis about to issue a policy and recommendation on pioneertravel that depends on whether certain treaties are obtained.The policy is expected to affect demand for the products;
however it is impossible at this time to assess the probabilityof these policy events. The following data are available:
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Payoffs (Profits)
AlternativeLand Routes
No treaty
Land Routes
Treaty
Sea Routes
OnlyArrows $840,000 $440,000 $190,000
Barrels $370,000 $220,000 $670,000
Wagons $25,000 $1,150,000 ($25,000)
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Application A.4
Which product would be favored by Fletcher (realist)? Fletcher (realistLaplace) would choose arrows
Which product would be favored by Cooper (pessimist)?
Cooper (pessimistMaximin) would choose barrels
Which product would be favored by Wainwright (optimist)?
Wainwright (optimistMaximax) would choose wagons
What is the minimax regret solution?
The Minimax Regret solution is arrows
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Decision Making Under Risk
Use the expected value rule
Weigh each payoff with associated probabilityand add the weighted payoff scores.
Choose the alternative with the best expectedvalue.
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For Fletcher, Cooper, and Wainwright, find the best decisionusing the expected value rule. The probabilities for the eventsare given below.
What alternative has the best expected results?
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Alternative
Land routes,
No Treaty
(0.50)
Land Routes,
Treaty Only
(0.30)
Sea routes,
Only (0.20)
Arrows 840,000 440,000 190,000
Barrels 370,000 220,000 670,000
Wagons 25,000 1,150,000 -25,000
Application A.5
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Application A.5
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Alternative
Land routes, No
Treaty
(0.50)
Land Routes,
Treaty Only
(0.30)
Sea routes
Only (0.20)Expected Value
Arrows (.50) * 840,000` + (.30)* 440,000 + (.20) * 190,000 590,000
Barrels (.50) * 370,000` + (.30)* 220,000 + (.20) * 670,000 385,000
Wagons (.50) * 25,000` + (.30)* 1,150,000 + (.20) * -25,000 352,500
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Arrows is the
best alternative.
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Payoff 1
Payoff 2
Payoff 3
Alternative 3
Alternative 4
Alternative 5
Payoff 1
Payoff 2
Payoff 3
E1& Probability
E2& Probability
E3& Probability
E2& Probability
E3& Probability
Payoff 1
Payoff 2
1stdecision
1
Possible2nd decision
2
Decision Trees
= Event node
= Decision node
Ei = Eventi
P(Ei) = Probability of eventi
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Example A.8
A retailer will build a small or a large facility at a new location
Demand can be either small or large, with probabilitiesestimated to be 0.4 and 0.6, respectively
For a small facility and high demand, not expanding will have apayoff of $223,000 and a payoff of $270,000with expansion
For a small facility and low demand the payoff is $200,000
For a large facility and low demand, doing nothing has a payoffof $40,000
The response to advertising may be either modest or sizable,with their probabilities estimated to be 0.3 and 0.7, respectively
For a modest response the payoff is $20,000 and $220,000 if theresponse is sizable
For a large facility and high demand the payoff is $800,000
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Example A.8
$200
$223
$270
$40
$800
$20
$220
Dont expand
Expand
Low demand [0.4]
2
High demand [0.6]
3
Do nothing
Advertise
Modest response [0.3]
Sizable response [0.7]
1
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Example A.8
$200
$223
$270
$40
$800
$20
$220
Dont expand
Expand
Low demand [0.4]
2
High demand [0.6]
3
Do nothing
Advertise
Modest response [0.3]
Sizable response [0.7]
1 0.3 x $20 = $6
0.7 x $220 = $154
$6 + $154 = $160
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Example A.8
$200
$223
$270
$40
$800
$20
$220
Dont expand
Expand
Low demand [0.4]
2
High demand [0.6]
3
Do nothing
Advertise
Modest response [0.3]
Sizable response [0.7]
1
$160$160
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Example A.8
$200
$223
$270
$40
$800
$20
$220
Dont expand
Expand
Low demand [0.4]
2
High demand [0.6]
3
Do nothing
Advertise
Modest response [0.3]
Sizable response [0.7]
1
$160$160
$270
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Example A.8
$200
$223
$270
$40
$800
$20
$220
Dont expand
Expand
Low demand [0.4]
2
High demand [0.6]
3
Do nothing
Advertise
Modest response [0.3]
Sizable response [0.7]
1
$160$160
$270
$242
x 0.6 = $480
0.4 x $160 = $64
$544
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Application A.6
a. Draw the decision tree for the Fletcher, Cooper, andWainwright Application 5
b. What is the expected payoff for the best alternativein the decision tree below?
Alternative
Land routes,
No Treaty
(0.50)
Land Routes,
Treaty Only
(0.30)
Sea routes, Only
(0.20)
Arrows 840,000 440,000 190,000
Barrels 370,000 220,000 670,000
Wagons 25,000 1,150,000 -25,000
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Application A.6
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Solved Problem 1
A small manufacturing business has patented a newdevice for washing dishes and cleaning dirty kitchen sinks
The owner wants reasonable assurance of success
Variable costs are estimated at $7 per unit produced and
sold Fixed costs are about $56,000 per year
a. If the selling price is set at $25, how many units must beproduced and sold to break even? Use both algebraic andgraphic approaches.
b. Forecasted sales for the first year are 10,000 units if theprice is reduced to $15. With this pricing strategy, whatwould be the products total contribution to profits in thefirst year?
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Solved Problem 1
a. Beginning with the algebraic approach, we get
Q=F
pc
= 3,111 units
=56,000
257
Using the graphic approach, shown in Figure A.6, we first drawtwo lines:
The two lines intersect at Q= 3,111 units, the break-even
quantity
Total revenue =Total cost =
25Q56,000 + 7Q
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Total costs
Break-even
quantity
250
200
150
100
50
0
Units (in thousands)
Dollars(inthousands)
| | | | | | | |
1 2 3 4 5 6 7 8
Total revenues
3.1
$77.7
Solved Problem 1
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Solved Problem 1
b. Total profit contribution = Total revenueTotal cost
= pQ(F+ cQ)
= 15(10,000)[56,000 + 7(10,000)]
= $24,000
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Solved Problem 2
Herron Company is screening three new product idea: A, B, and C.Resource constraints allow only one of them to be commercialized. The
performance criteria and ratings, on a scale of 1 (worst) to 10 (best),
are shown in the following table. The Herron managers give equal
weights to the performance criteria. Which is the best alternative, as
indicated by the preference matrix method?
Rating
Performance Criteria Product A Product B Product C
1. Demand uncertainty and project risk 3 9 2
2. Similarity to present products 7 8 63. Expected return on investment (ROI) 10 4 8
4. Compatibility with currentmanufacturing process
4 7 6
5. Competitive Strategy 4 6 5
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Solved Problem 2
Each of the five criteria receives a weight of1/5 or 0.20
The best choice is product B as Products A and C are well behind interms of total weighted score
(0.20 3) + (0.20 7) + (0.20 10) +(0.20 4) + (0.20 4)
= 5.6
(0.20 9) + (0.20 8) + (0.20 4) +(0.20 7) + (0.20 6)
= 6.8
(0.20 2) + (0.20 6) + (0.20 8) +(0.20 6) + (0.20 5)
= 5.4
Product Calculation Total Score
A
B
C
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Solved Problem 3
Adele Weiss manages the campus flower shop. Flowers mustbe ordered three days in advance from her supplier in Mexico.Although Valentines Day is fast approaching, sales are almostentirely last-minute, impulse purchases. Advance sales are sosmall that Weiss has no way to estimate the probability of low
(25 dozen), medium (60 dozen), or high (130 dozen) demand forred roses on the big day. She buys roses for $15 per dozen andsells them for $40 per dozen. Construct a payoff table. Whichdecision is indicated by each of the following decision criteria?
a. Maximinb. Maximax
c. Laplace
d. Minimax regret
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Solved Problem 3
The payoff table for this problem is
Demand for Red Roses
AlternativeLow
(25 dozen)Medium
(60 dozen)High
(130 dozen)
Order 25 dozen $625 $625 $625
Order 60 dozen $100 $1,500 $1,500
Order 130 dozen ($950) $450 $3,250
Do nothing $0 $0 $0
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Solved Problem 3
a. Under the Maximin criteria, Weiss should order 25 dozen, because
if demand is low, Weisss profits are $625, the best of the worst
payoffs.
b. Under the Maximax criteria, Weiss should order 130 dozen. The
greatest possible payoff, $3,250, is associated with the largest
order.c. Under the Laplace criteria, Weiss should order 60 dozen. Equally
weighted payoffs for ordering 25, 60, and 130 dozen are about
$625, $1,033, and $917, respectively.
d. Under the Minimax regret criteria, Weiss should order 130 dozen.
The maximum regret of ordering 25 dozen occurs if demand is
high: $3,250$625 = $2,625. The maximum regret of ordering 60
dozen occurs if demand is high: $3,250$1,500 = $1,750. The
maximum regret of ordering 130 dozen occurs if demand is low:
$625($950) = $1,575.Copyright 2013 Pearson Education, Inc. publishing as Prentice Hall A - 54
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Solved Problem 4
White Valley Ski Resort is planning the ski lift operation for itsnew ski resort and wants to determine if one or two lifts will
be necessary. Each lift can accommodate 250 people per day
and skiing occurs 7 days per week in the 14-week season and
lift tickets cost $20 per customer per day. The table below
shows all the costs and probabilities for each alternative and
condition. Should the resort purchase one lift or two?
Alternatives Conditions Utilization Installation Operation
One lift Bad times (0.3) 0.9 $50,000 $200,000
Normal times (0.5) 1.0 $50,000 $200,000Good times (0.2) 1.0 $50,000 $200,000
Two lifts Bad times (0.3) 0.9 $90,000 $200,000
Normal times (0.5) 1.5 $90,000 $400,000
Good times (0.2) 1.9 $90,000 $400,000
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Solved Problem 4
The decision tree is shown on the following slide. The payoff($000) for each alternative-event branch is shown in the
following table. The total revenues from one lift operating at
100 percent capacity are $490,000 (or 250 customers 98 days
$20/customer-day).
0.9(490)(50 + 200) = 191
1.0(490)(50 + 200) = 240
1.0(490)(50 + 200) = 240
0.9(490)(90 + 200) = 151
1.5(490)(90 + 400) = 245
1.9(490)(90 + 400) = 441
Alternatives Economic Conditions Payoff Calculation (RevenueCost)
One lift Bad times
Normal times
Good times
Two lifts Bad times
Normal times
Good times
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Bad times [0.3]
Normal times [0.5]
Good times [0.2]
$191
$240
$240
Bad times [0.3]
Normal times [0.5]
Good times [0.2]
$151
$245
$441
One lift
Two lifts
$256.0
$225.3
$256.0
Solved Problem 4
0.3(191) + 0.5(240) +
0.2(240) = 225.3
0.3(151) + 0.5(245) +
0.2(441) = 256.0
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