Decsion Making Powerpoint

8/10/2019 Decsion Making Powerpoint

1/58

Supplement A

Decision Making

Copyright 2013 Pearson Education, Inc. publishing as Prentice Hall A - 01


2/58

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.



3/58

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.



4/58


5/58

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



6/58

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



7/58

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)



8/58

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?

Copyright 2013 Pearson Education, Inc. publishing as Prentice Hall A -08


9/58

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



10/58

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



11/58

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



12/58

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



13/58


14/58

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?



15/58

The formula for the break-even quantity yields thefollowing:

Q=FmFbcbcm

= 19,200 salads=12,0002,400

2.01.5

Example A.3



16/58

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?


Buy

Make

Fixed costs $0 $300,000

Variable costs

$9

$7

Q =FmFbcbcm

Q =300,0000

97Q = 150,000


17/58

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.



18/58

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



19/58

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



20/58

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?


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


21/58

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



22/58

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



23/58

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



24/58

Decision Making under Uncertainty

Maximin

Maximax

Laplace

Minimax Regret



25/58

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.



26/58

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.



27/58

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



28/58

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.



29/58

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:


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)


30/58

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

A - 30Copyright 2013 Pearson Education, Inc. publishing as Prentice Hall


31/58

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.



32/58


33/58

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?


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


34/58

Application A.5

A - 34

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

Copyright 2013 Pearson Education, Inc. publishing as Prentice Hall

Arrows is the

best alternative.


35/58

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



36/58

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



37/58

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



38/58

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



1 0.3 x $20 = $6

0.7 x $220 = $154

$6 + $154 = $160



39/58

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



1

$160$160



40/58

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



1

$160$160

$270



41/58


42/58

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



1

$160$160

$270

$242

x 0.6 = $480

0.4 x $160 = $64

$544



43/58


44/58

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



45/58

Application A.6



46/58

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?



47/58

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



48/58

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



49/58

Solved Problem 1

b. Total profit contribution = Total revenueTotal cost

= pQ(F+ cQ)

= 15(10,000)[56,000 + 7(10,000)]

= $24,000



50/58

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



51/58

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



52/58

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



53/58

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



54/58

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


55/58

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



56/58

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



57/58

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



58/58

All rights reserved. No part of this publication may be reproduced,

stored in a retrieval system, or transmitted, in any form or by any

means, electronic, mechanical, photocopying, recording, or

otherwise, without the prior written permission of the publisher.

Printed in the United States of America.

Documents

Decsion Making Powerpoint