OPERATIONS MANAGEMENTOPERATIONS MANAGEMENTfor MBAsfor MBAs

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Topic 5: Decision Making, Strategic Allocation of Resources, & Simulation

OutlineOutline 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 AnalysisBreak-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 AnalysisBreak-Even AnalysisBreak-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 AnalysisBreak-Even Analysis

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Finding the Break-Even Finding the Break-Even QuantityQuantity

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 Finding the Break-Even QuantityQuantity

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Break-Even AnalysisBreak-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 AnalysisBreak-Even Analysis

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Preference MatrixPreference MatrixA 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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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?

Evaluating an AlternativeEvaluating an Alternative

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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Preference Matrix Preference Matrix ExampleExample

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Weight Score

Decisions Under CertaintyDecisions Under Certainty

Example: New product introduction. Build a large or small facility?

Possible Future Demand

Low High

Build Small 200 270

Build Large 160 800

A manager knows with certainty which event or outcome will occur. Pick the alternative with the best payoff for the known outcome.

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Decision Making Under Decision Making Under UncertaintyUncertainty

Maximin Maximax Laplace

Possible Future Demand

Low High

Build Small 200 270

Build Large 160 800

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Decisions Under RiskDecisions 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 ConceptExpected Value Concept(Used in Decision Trees)(Used in Decision Trees)

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Decision TreesDecision 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

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Analyzing a Decision TreeAnalyzing a Decision Tree$200

$223

$270

$40

$800

$20

$220

Don’t expand

Expand

Low demand [0.4]

High demand

[0.6]

2

Low dem

and

[0.4]

High demand [0.6]

3

Do nothing

Advertise

Modest response [0.3]

Sizable response [0.7]

Smal

l fac

ility

Large facility

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Strategic Allocation of ResourcesStrategic Allocation of Resources(Linear Programming)(Linear Programming)

Applications IncludeApplications 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 ProblemThe Maximization Problem

Bags Tents ResourceAvailability

Cutting 2 1 14

Sewing 5 5 40

Waterproofing 1 3 18

Profit $50 $30

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The Maximization ProblemThe Maximization Problem

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The Maximization ProblemThe Maximization Problem

P R TotalChanging Cells 6.00 2.00 Min Cost/Max Profit $50.00 $30.00 $360.00

Resources >= Min Rqmt/ Surplus/Used <= Capacity Avail. Slack

Constraint1 2 1 14.00 <= 14 0.00Constraint2 5 5 40.00 <= 40 0.00Constraint3 1 3 12.00 <= 18 6.00

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The Minimization ProblemThe Minimization Problem

Grain 1 Grain 2 ResourceRequirement

Carbos 24 4 128

Proteins 14 7 168

Fructose 8 32 120

Cost $7 $2

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The Minimization ProblemThe Minimization Problem

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The Minimization ProblemThe Minimization Problem

G1 G2 TotalChanging Cells 2.00 20.00 Min Cost/Max Profit $7.00 $2.00 $54.00

Resources >= Min Rqmt/ Surplus/Used <= Capacity Avail. Slack

Constraint1 24 4 128.00 >= 128 0.00Constraint2 14 7 168.00 >= 168 0.00Constraint3 8 32 656.00 >= 120 536.00

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Example-Transportation Example-Transportation ProblemProblem

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?

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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

ExampleExample

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ExampleExample 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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ExampleExampleLP Formulation:

ST

capacity

barley

hops

2:1 ratio

minimum P requirement

minimum L requirement

maximum requirement

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ExampleExampleP R L Variable4 Variable5 Variable6 Variable7 Variable8 Total

Changing Cells 4000.00 9761.90 4880.95 Min Cost/Max Profit $3.00 $2.70 $2.80 $52,023.81

Resources >= Min Rqmt/ Surplus/Used <= Capacity Avail. Slack

Constraint1 1 1 1 18642.86 27000 8357.14Constraint2 3.5 2.9 2.6 55000.00 55000 0.00Constraint3 1.1 0.8 0.6 15138.10 20000 4861.90Constraint4 0 1 -2 0.00 0 0.00Constraint5 1 0 0 4000.00 4000 0.00Constraint6 0 1 0 9761.90 4000 5761.90Constraint7 1 0 1 8880.95 12000 3119.05Constraint8 0 0 0

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Simulation in Decision MakingSimulation in Decision MakingRisk & UncertaintiesRisk & Uncertainties

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Simulation – Flip 3 Coins

10 32 54 76 8

3H$20

2H$10

1H$2

0H$0

0.934040.812520.551330.881120.564260.987640.092120.312340.695950.765520.171330.974120.647730.073690.701400.443270.419950.523750.373950.759530.311220.625120.853430.919910.925940.577310.268080.758370.03453

0.000 0.125 0.500 0.875 1.000

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Net

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Sim1

Sim2

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?

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 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

a. If Octane submits a bid of $750,000, what is the probability they will win?b. If Octane wants to be at least 80% sure they will win, what should they bid?c. Provide a short managerial description of your simulation results.

LP #1LP #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 #2LP #22. 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 #3LP #33. 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 #4LP #44. 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 #5LP #55. 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

Monthly Warehouse

Requirement (cases)9,000 9,000 12,000 10,000

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 DM #1#1

DM DM #2#2

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DM DM #3#3

DM #4DM #4A 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 #5DM #5Refer 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 #6DM #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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