Transcript OPERATIONS MANAGEMENT for MBAs Topic 5: Decision Making, Strategic Allocation of

OPERATIONS MANAGEMENT
for MBAs
Topic 5: Decision Making, Strategic Allocation of
Resources, & Simulation
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Outline

About the best alternative under various outcome scenarios.

Break Even Analysis

Preference Matrix

Certainty

Uncertainty

Risk

Expected Value

Decision Trees

Strategic Allocation of Resources

Simulation

Homework
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Break-Even Analysis

Evaluating Services or Products
◦ Is the predicted sales volume of the service or
product sufficient to break even (neither earning
a profit nor sustaining a loss)?
◦ How low must the variable cost per unit be to
break even, based on current prices and sales
forecasts?
◦ How low must the fixed cost be to break even?
◦ How do price levels affect the break-even
quantity?
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Break-Even Analysis
Break-even analysis is based on the assumption that all
costs related to the production of a specific service or
product can be divided into two categories: variable costs
and fixed costs
 Variable cost, c, is the portion of the total cost that varies
directly with volume of output
 If Q = the number of customers served or units produced
per year, total variable cost = cQ
 Fixed cost, F, is the portion of the total cost that remains
constant regardless of changes in levels of output

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Break-Even Analysis
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Finding the Break-Even Quantity
EXAMPLE
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.
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Finding the Break-Even Quantity
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Break-Even Analysis
Community
Fixed Costs (F)
c
A
$150,000
$62
B
$300,000
$38
C
$500,000
$24
D
$600,000
$30
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Break-Even Analysis
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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
same scale 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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Evaluating an Alternative
EXAMPLE
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?
Performance Criterion
Weighted Score (A  B)
Weight (A)
Score (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
5
4
20
Project risk
Weighted score =
750
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Preference Matrix Example
Weight
Score
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Decisions Under Certainty

A manager knows with certainty which event or outcome will occur.

Pick the alternative with the best payoff for the known outcome.
Example: New product introduction. Build a large or small facility?
Possible Future Demand
Low
High
Build Small
200
270
Build Large
160
800
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Decision Making Under Uncertainty



Maximin
Maximax
Laplace
Possible Future Demand
Low
High
Build Small
200
270
Build Large
160
800
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Decisions Under Risk

Similar to Laplace technique, but we use estimated probabilities
(not equal) for the outcomes.
Possible Future Demand
Low
High
Build Small
200
270
Build Large
160
800
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Expected Value Concept
(Used in Decision Trees)
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Decision Trees
Model of alternatives along with potential consequences.
Square Nodes – decision points.
Circular Nodes – chances/probabilities that must sum to one.
Branches – represent alternatives or different possibilities.
Payoffs
Payoffs
EV
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Analyzing a Decision Tree
Low demand [0.4]
$200
Don’t expand
$223
2
Expand
$270
1
Do nothing
$40
3
Modest response [0.3]
$20
Advertise
Sizable response [0.7]
$220
High demand [0.6]
$800
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Strategic Allocation of Resources
(Linear Programming)
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Applications Include

Strategic Product or Service Mix Planning

Financial Portfolios

Choosing the Right Mix (ingredients, diet)

Transportation Problems

Staff Scheduling

Routing

Optimize an Objective Function
◦
Minimize Costs
◦
Maximize Profits
◦
Constraints
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The Maximization Problem
Bags
Tents
Resource
Availability
Cutting
2
1
14
Sewing
5
5
40
Waterproofing
1
3
18
$50
$30
Profit
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The Maximization Problem
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The Maximization Problem
Changing Cells
Min Cost/Max Profit
Constraint1
Constraint2
Constraint3
P
R
6.00
$50.00
2.00
$30.00
2
5
1
Total
$360.00
Resources
Used
1
14.00
5
40.00
3
12.00
>= Min Rqmt/
Surplus/
<= Capacity Avail.
Slack
<=
14
0.00
<=
40
0.00
<=
18
6.00
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The Minimization Problem
Grain 1
Grain 2
Resource
Requirement
Carbos
24
4
128
Proteins
14
7
168
Fructose
8
32
120
Cost
$7
$2
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The Minimization Problem
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The Minimization Problem
Changing Cells
Min Cost/Max Profit
Constraint1
Constraint2
Constraint3
G1
2.00
$7.00
G2
Total
20.00
$2.00
$54.00
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14
8
Resources
Used
4
128.00
7
168.00
32
656.00
>= Min Rqmt/
Surplus/
<= Capacity Avail.
Slack
>=
128
0.00
>=
168
0.00
>=
120
536.00
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Example-Transportation Problem
Delorian motors has 2 distribution centers (DCs) for their 3 dealerships.
Delorian automobiles are shipped from the centers to the dealerships.
The shipping cost per auto, monthly dealership requirements, and
distribution center levels are shown below. How many automobiles
should be shipped per month from each DC to each dealership to
minimize shipping costs and satisfy dealership demand?
Dealership
A
B
C
Capacity
DC1
$5.00
$6.00
$3.00
2500
DC2
$2.00
$8.00
$6.50
2500
Rqmt
1000
2000
1500
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Example
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Example
A local brewery produces three types of beer: premium, regular, and
light. The brewery has enough vat capacity to produce 27,000 gallons of
beer per month. A gallon of premium beer requires 3.6 pounds of barley
and 1.2 pounds of hops, a gallon of regular requires 2.9 pounds of barley
and .8 pounds of hops, and a gallon of light requires 2.6 pounds of barley
and .6 pounds of hops. The brewery is able to acquire only 55,000
pounds of barley and 20,000 pounds of hops next month. The brewery’s
largest seller is regular beer, so it wants to produce at least twice as much
regular beer as it does light beer. It also wants to have a competitive
market mix of beer. Thus, the brewery wishes to produce at least 4000
gallons each of light beer and premium beer, but not more than 12,000
gallons of these two beers combined. The brewery makes a profit of
$3.00 per gallon on premium beer, $2.70 per gallon on regular beer, and
$2.80 per gallon on light beer. The brewery manager wants to know how
much of each type of beer to produce next month in order to maximize
profit.
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Example
LP Formulation:
ST
capacity
barley
hops
2:1 ratio
minimum P requirement
minimum L requirement
maximum requirement
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Example
Changing Cells
Min Cost/Max Profit
Constraint1
Constraint2
Constraint3
Constraint4
Constraint5
Constraint6
Constraint7
Constraint8
P
4000.00
$3.00
1
3.5
1.1
0
1
0
1
0
R
9761.90
$2.70
1
2.9
0.8
1
0
1
0
0
L
Variable4 Variable5 Variable6 Variable7 Variable8 Total
4880.95
$2.80
$52,023.81
1
2.6
0.6
-2
0
0
1
0
Resources >= Min Rqmt/
Surplus/
Used
<= Capacity Avail.
Slack
18642.86
27000 8357.14
55000.00
55000
0.00
15138.10
20000 4861.90
0.00
0
0.00
4000.00
4000
0.00
9761.90
4000 5761.90
8880.95
12000 3119.05
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Simulation in Decision Making
Risk & Uncertainties
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Simulation – Flip 3 Coins
3H
$20
0.000 0.125
0
1
2H
$10
1H
$2
0H
$0
0.500
2
3
4
0.875
5
6
7
1.000
8
0.93404
0.81252
0.55133
0.88112
0.56426
0.98764
0.09212
0.31234
0.69595
0.76552
0.17133
0.97412
0.64773
0.07369
0.70140
0.44327
0.41995
0.52375
0.37395
0.75953
0.31122
0.62512
0.85343
0.91991
0.92594
0.57731
0.26808
0.75837
0.03453
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Net
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Sim1
The management of Maderia Manufacturing is considering the introduction of a new
product. The fixed cost to begin production of the product is $30,000. The variable cost
for the product is uniformly distributed between $16 and $24 per unit. The product will
sell for $50 per unit. Demand for the product is best described by a normal probability
distribution with a mean of 1200 units and a standard deviation of 300 units. Develop a
spreadsheet simulation to answer the following managerial issues:
a.What is the expected mean profit for the new product?
b.What is the probability the project will result in a loss for us?
c.Develop a histogram that describes the profit picture.
d.What is your recommendation concerning introduction of the new product?
Sim2
Octane Contracting is preparing a bid on a new construction project against three other
contractors bidding on the same project. Based on past bidding practices, bids from the
other contractors can be described by the distributions below:
Contractor
a.
b.
c.
Probability Distribution of Bid
A
Uniform between $600,000 and $800,000
B
Normal mean of $700,000 and standard deviation of $50,000
C
Triangular low of $500,000, most likely $600,000, and high of $900,000
If Octane submits a bid of $750,000, what is the probability they will win?
If Octane wants to be at least 80% sure they will win, what should they bid?
Provide a short managerial description of your simulation results.
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LP #1
1. The Ohio Creek Ice Cream Company is planning production for next
week. Demand for Ohio Creek premium and light ice cream continue
to outpace the company’s production capacities. Ohio Creek earns a
profit of $100 per hundred gallons of premium and $100 per hundred
gallons of light ice cream. Two resources used in ice cream
production are in short supply for next week: the capacity of the
mixing machine and the amount of high-grade milk. After accounting
for required maintenance time, the mixing machine will be available
140 hours next week. A hundred gallons of premium ice cream
requires .3 hours of mixing and a hundred gallons of light ice cream
requires .5 hours of mixing. Only 28,000 gallons of high-grade milk
will be available for next week. A hundred gallons of premium ice
cream requires 90 gallons of milk and a hundred gallons of light ice
cream requires 70 gallons of milk.
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LP #2
2. The Sureset Concrete Company produces concrete in a
continuous process. Two ingredients in the concrete are sand,
which Sureset purchases for $6 per ton, and gravel, which costs
$8 per ton. Sand and gravel together must make up exactly 75%
of the weight of the concrete. Furthermore, no more than 40% of
the concrete can be sand, and at least 30% of the concrete must
be gravel. Each day 2,000 tons of concrete are produced.
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LP #3
3. A ship has two cargo holds, one fore and one aft. The fore cargo
hold has a weight capacity of 70,000 pounds and a volume capacity
of 30,000 cubic feet. The aft hold has a weight capacity of 90,000
pounds and a volume capacity of 40,000 cubic feet. The shipowner
has contracted to carry loads of packaged beef and grain. The total
weight of the available beef is 85,000 pounds; the total weight of the
available grain is 100,000 pounds. The volume per mass of the beef
is 0.2 cubic foot per pound, and the volume per mass of the grain is
0.4 cubic foot per pound. The profit for shipping beef is $0.35 per
pound, and the profit for shipping grain is $0.12 per pound. The
shipowner is free to accept all or part of the available cargo; he
wants to know how much meat and grain to accept in order to
maximize profit.
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LP #4
4. The White Horse Apple Products Company purchases apples from
local growers and makes applesauce and apple juice. It costs $0.60
to produce a jar of applesauce and $0.85 to produce a bottle of
apple juice. The company has a policy that at least 30% but not
more than 60% of its output must be applesauce.
The company wants to meet but not exceed the demand for
each product. The marketing manager estimates that the demand
for applesauce is a maximum of 5,000 jars, plus an additional 3 jars
for each $1 spent on advertising. The maximum demand for apple
juice is estimated to be 4,000 bottles, plus an additional 5 bottles for
every $1 spent to promote apple juice. The company has $16,000
to spend on producing and advertising applesauce and apple juice.
Applesauce sells for $1.45 per jar; apple juice sells for $1.75 per
bottle. The company wants to know how many units of each to
produce and how much advertising to spend on each in order to
maximize profit.
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LP #5
5. MadeRite, a manufacturer of paper stock for copiers and printers, produces cases of
finished paper stock at Mills 1, 2, and 3. The paper is shipped to Warehouses A, B, C,
and D. The shipping cost per case, the monthly warehouse requirements, and the
monthly mill production levels are:
Monthly Mill
Destination
Production
A
B
C
D (cases)
Mill 1
$5.40
$6.20
$4.10
$4.90
15,000
Mill 2
4.00
7.10
5.60
3.90
10,000
Mill 3
4.50
5.20
5.50
6.10
15,000
Requirement (cases)9,000
9,000
12,000
10,000
Monthly Warehouse
How many cases of paper should be shipped per month from each mill to each warehouse
to minimize monthly shipping costs?
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DM #1
DM #2
48
DM #3
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DM #4
A firm must decide whether to construct a small, medium, or large stamping plant. A consultant’s
report indicates a .20 probability that demand will be low and a .80 probability that
demand will be high.
If the firm builds a small facility and demand turns out to be low, the net present value will be
$42 (million). If demand turns out to be high, the firm can either subcontract and realize
a NPV of $42 or expand greatly for an NPV of $48.
The firm could build a medium size facility as a hedge: If demand turns out to be low, its NPV is
estimated at $22; if demand turns out to be high, the firm could do nothing and realize a
NPV of $46, or it could expand and realize a NPV of $50.
If the firm builds a large facility and demand is low, the NPV will be -$20, whereas high demand
will result in a NPV of $72.
Analyze this issue using a decision tree.
What would be the maximin alternative?
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DM #5
Refer to Problem #15 (DM #3) in the textbook. Suppose after a certain amount of discussion,
management is able to assess the probabilities of demand as follows:
P(low)=.40
P(moderate)=.40
P(high)=.20
Determine the expected profit of each alternative.
Which alternative is best?
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DM #6
A firm is trying to decide whether to sell one of its plants next year or do a
feasibility study on expanding the plant. If it sells the plant next year, the
firm estimates that it will get $3 million (net present value) if the economy is
good or $1 million (npv) if the economy is bad. There is a 60% probability
for a good economy next year. A feasibility study would cost $1 million, and
there is only a 30% chance that the feasibility study will be favorable. If the
study is unfavorable then the firm can at that point sell the plant for
$500,000 (npv). If the study is favorable, then the firm can sell the plant for
$4 million (npv) or expand the plant. If the plant is expanded and the future
economic outlook is high, the firm would receive a net present value of $7
million, and if the outlook Is low the firm would receive a npv of $2 million.
There is a 60% chance that the future economic outlook at that point will be
high. Draw a decision tree for this problem and show all expected values.
Explain what the firm should do at each decision node.
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