Introduction

IntroductionIntroduction

Body of KnowledgeBody of Knowledge Problem Solving and Decision Problem Solving and Decision

MakingMaking Quantitative Analysis and Decision Quantitative Analysis and Decision

MakingMaking Quantitative AnalysisQuantitative Analysis Models of Cost, Revenue, and ProfitModels of Cost, Revenue, and Profit Management Science TechniquesManagement Science Techniques

Body of KnowledgeBody of Knowledge The body of knowledge involving quantitative The body of knowledge involving quantitative

approaches to decision making is referred to as approaches to decision making is referred to as • Management ScienceManagement Science• Operations ResearchOperations Research• Decision ScienceDecision Science

It had its early roots in World War II and is It had its early roots in World War II and is flourishing in business and industry due, in part, flourishing in business and industry due, in part, to:to:• numerous methodological developments (e.g. numerous methodological developments (e.g.

simplex method for solving linear simplex method for solving linear programming problems)programming problems)

• a virtual explosion in computing powera virtual explosion in computing power

7 Steps of 7 Steps of Problem SolvingProblem Solving

(First 5 steps are the process of (First 5 steps are the process of decision makingdecision making))

1. Identify and define the problem.1. Identify and define the problem.

2. Determine the set of alternative solutions.2. Determine the set of alternative solutions.

3. Determine the criteria for evaluating 3. Determine the criteria for evaluating alternatives.alternatives.

4. Evaluate the alternatives.4. Evaluate the alternatives.

5. Choose an alternative (make a decision).5. Choose an alternative (make a decision).

------------------------------------------------------------------------------------------------------------------------------------------

6. Implement the selected alternative.6. Implement the selected alternative.

7. Evaluate the results.7. Evaluate the results.

Problem Solving and Problem Solving and Decision MakingDecision Making

Quantitative Analysis Quantitative Analysis and Decision Makingand Decision Making

DefineDefinethethe

ProblemProblem

DefineDefinethethe

ProblemProblem

IdentifyIdentifythethe

AlternativesAlternatives



DetermineDeterminethethe

CriteriaCriteria

DetermineDeterminethethe

CriteriaCriteria





ChooseChooseanan

AlternativeAlternative

ChooseChooseanan

AlternativeAlternative

Structuring the ProblemStructuring the ProblemStructuring the ProblemStructuring the Problem Analyzing the ProblemAnalyzing the ProblemAnalyzing the ProblemAnalyzing the Problem

Decision-Making Decision-Making ProcessProcess

Analysis Phase of Decision-Making ProcessAnalysis Phase of Decision-Making Process QualitativeQualitative Analysis Analysis

• based largely on the manager’s judgment based largely on the manager’s judgment and experienceand experience

• includes the manager’s intuitive “feel” for includes the manager’s intuitive “feel” for the problemthe problem

• is more of an art than a scienceis more of an art than a science


Analysis Phase of Decision-Making ProcessAnalysis Phase of Decision-Making ProcessQuantitativeQuantitative Analysis Analysis• analyst will concentrate on the quantitative analyst will concentrate on the quantitative

facts or data associated with the problemfacts or data associated with the problem• analyst will develop mathematical analyst will develop mathematical

expressions that describe the objectives, expressions that describe the objectives, constraints, and other relationships that exist constraints, and other relationships that exist in the problemin the problem

• analyst will use one or more quantitative analyst will use one or more quantitative methods to make a recommendationmethods to make a recommendation



Potential Reasons for a Quantitative Potential Reasons for a Quantitative Analysis Approach to Decision MakingAnalysis Approach to Decision Making The problem is The problem is complexcomplex.. The problem is very The problem is very importantimportant.. The problem is The problem is newnew.. The problem is The problem is repetitiverepetitive..

Quantitative AnalysisQuantitative Analysis

Quantitative Analysis ProcessQuantitative Analysis Process Model DevelopmentModel Development Data PreparationData Preparation Model SolutionModel Solution Report GenerationReport Generation

Model DevelopmentModel Development ModelsModels are representations of real objects are representations of real objects

or situationsor situations Three Three forms of modelsforms of models are: are:

Iconic modelsIconic models - physical replicas (scalar - physical replicas (scalar representations) of real objectsrepresentations) of real objects

Analog modelsAnalog models - physical in form, but do not - physical in form, but do not physically resemble the object being modeledphysically resemble the object being modeled

Mathematical modelsMathematical models - represent real world - represent real world problems through a system of mathematical problems through a system of mathematical formulas and expressions based on key formulas and expressions based on key assumptions, estimates, or statistical analysesassumptions, estimates, or statistical analyses

Advantages of ModelsAdvantages of Models

Generally, experimenting with models Generally, experimenting with models (compared to experimenting with the real (compared to experimenting with the real situation):situation): requires requires less timeless time is is less expensiveless expensive involves involves less riskless risk

The more closely the model represents the real The more closely the model represents the real situation, the accurate the conclusions and situation, the accurate the conclusions and predictions will be.predictions will be.

Mathematical ModelsMathematical Models Objective FunctionObjective Function – a mathematical expression – a mathematical expression

that describes the problem’s objective, such as that describes the problem’s objective, such as maximizing profit or minimizing costmaximizing profit or minimizing cost

ConstraintsConstraints – a set of restrictions or limitations, – a set of restrictions or limitations, such as production capacitiessuch as production capacities

Uncontrollable InputsUncontrollable Inputs – environmental factors – environmental factors that are not under the control of the decision that are not under the control of the decision makermaker

Decision VariablesDecision Variables – controllable inputs; – controllable inputs; decision alternatives specified by the decision decision alternatives specified by the decision maker, such as the number of units of Product maker, such as the number of units of Product X to produceX to produce

Mathematical ModelsMathematical Models

Cost/benefit considerationsCost/benefit considerations must be made in must be made in selecting an appropriate mathematical model. selecting an appropriate mathematical model.

Frequently a less complicated (and perhaps less Frequently a less complicated (and perhaps less precise) model is more appropriate than a more precise) model is more appropriate than a more complex and accurate one due to cost and ease complex and accurate one due to cost and ease of solution considerations.of solution considerations.

Transforming Model Transforming Model Inputs into OutputInputs into Output

Uncontrollable InputsUncontrollable Inputs(Environmental Factors)(Environmental Factors)

Uncontrollable InputsUncontrollable Inputs(Environmental Factors)(Environmental Factors)

ControllableControllableInputsInputs

(Decision(DecisionVariables)Variables)

ControllableControllableInputsInputs

(Decision(DecisionVariables)Variables)

OutputOutput(Projected(Projected Results)Results)

OutputOutput(Projected(Projected Results)Results)

MathematicalMathematicalModelModel

MathematicalMathematicalModelModel

Example: Project Example: Project SchedulingSchedulingConsider the construction of a 250-unit Consider the construction of a 250-unit

apartmentapartment

complex. The project consists of hundreds of complex. The project consists of hundreds of activitiesactivities

involving excavating, framing,involving excavating, framing,

wiring, plastering, painting, land-wiring, plastering, painting, land-

scaping, and more. Some of thescaping, and more. Some of the

activities must be done sequentiallyactivities must be done sequentially

and others can be done at the sameand others can be done at the same

time. Also, some of the activitiestime. Also, some of the activities

can be completed faster than normalcan be completed faster than normal

by purchasing additional resources (workers, by purchasing additional resources (workers, equipment, etc.). equipment, etc.).

Example: Project Example: Project SchedulingScheduling Question:Question:

What is the best schedule for the What is the best schedule for the activities and for which activities should activities and for which activities should additional resources be purchased? How additional resources be purchased? How could management science be used to solve could management science be used to solve this problem?this problem?

Answer:Answer:

Management science can provide a Management science can provide a structured, quantitative approach for structured, quantitative approach for determining the minimum project completion determining the minimum project completion time based on the activities' normal times time based on the activities' normal times and then based on the activities' expedited and then based on the activities' expedited (reduced) times.(reduced) times.

Example: Project Example: Project SchedulingScheduling

Question:Question:

What would be the uncontrollable What would be the uncontrollable inputs?inputs?

Answer:Answer: Normal and expedited activity completion Normal and expedited activity completion

timestimes Activity expediting costsActivity expediting costs Funds available for expeditingFunds available for expediting Precedence relationships of the activitiesPrecedence relationships of the activities

Example: Project Example: Project SchedulingScheduling Question:Question:

What would be the decision variables of What would be the decision variables of the mathematical model? The objective the mathematical model? The objective function? The constraints?function? The constraints?

Answer:Answer: Decision variablesDecision variables: which activities to : which activities to

expedite and by how much, and when to expedite and by how much, and when to start each activitystart each activity

Objective functionObjective function: minimize project : minimize project completion timecompletion time

ConstraintsConstraints: do not violate any activity : do not violate any activity precedence relationships and do not precedence relationships and do not expedite in excess of the funds available.expedite in excess of the funds available.

Data PreparationData Preparation

Data preparation is not a trivial step, Data preparation is not a trivial step, due to the time required and the due to the time required and the possibility of data collection errors.possibility of data collection errors.

A model with 50 decision variables and A model with 50 decision variables and 25 constraints could have over 1300 25 constraints could have over 1300 data elements!data elements!

Often, a fairly large data base is needed.Often, a fairly large data base is needed. Information systems specialists might Information systems specialists might

be needed.be needed.

Model SolutionModel Solution The analyst attempts to identify the The analyst attempts to identify the

alternative (the set of decision variable alternative (the set of decision variable values) that provides the “best” output for values) that provides the “best” output for the model.the model.

The “best” output is the The “best” output is the optimal solutionoptimal solution.. If the alternative does not satisfy all of the If the alternative does not satisfy all of the

model constraints, it is rejected as being model constraints, it is rejected as being infeasibleinfeasible, regardless of the objective , regardless of the objective function value.function value.

If the alternative satisfies all of the model If the alternative satisfies all of the model constraints, it is constraints, it is feasiblefeasible and a candidate and a candidate for the “best” solution.for the “best” solution.

Model SolutionModel Solution One solution approach is trial-and-One solution approach is trial-and-

error.error. Might not provide the best solutionMight not provide the best solution Inefficient (numerous calculations required)Inefficient (numerous calculations required)

Special solution procedures have been Special solution procedures have been developed for specific mathematical developed for specific mathematical models.models. Some small models/problems can be solved Some small models/problems can be solved

by hand calculationsby hand calculations Most practical applications require using a Most practical applications require using a

computercomputer

Model SolutionModel Solution

A variety of software packages are available A variety of software packages are available for solving mathematical models. for solving mathematical models. Microsoft ExcelMicrosoft Excel The Management ScientistThe Management Scientist LINGOLINGO

Model Testing and Model Testing and ValidationValidation Often, goodness/accuracy of a model cannot be Often, goodness/accuracy of a model cannot be

assessed until solutions are generated.assessed until solutions are generated. Small test problems having known, or at least Small test problems having known, or at least

expected, solutions can be used for model expected, solutions can be used for model testing and validation.testing and validation.

If the model generates expected solutions, use If the model generates expected solutions, use the model on the full-scale problem.the model on the full-scale problem.

If inaccuracies or potential shortcomings If inaccuracies or potential shortcomings inherent in the model are identified, take inherent in the model are identified, take corrective action such as:corrective action such as: Collection of more-accurate input dataCollection of more-accurate input data Modification of the modelModification of the model

Report GenerationReport Generation A managerial report, based on the A managerial report, based on the

results of the model, should be results of the model, should be prepared.prepared.

The report should be easily The report should be easily understood by the decision maker.understood by the decision maker.

The report should include:The report should include: the recommended decisionthe recommended decision other pertinent information about the other pertinent information about the

results (for example, how sensitive the results (for example, how sensitive the model solution is to the assumptions and model solution is to the assumptions and data used in the model)data used in the model)

Implementation and Follow-Implementation and Follow-UpUp Successful implementation of model Successful implementation of model

results is of critical importance.results is of critical importance. Secure as much user involvement as Secure as much user involvement as

possible throughout the modeling possible throughout the modeling process.process.

Continue to monitor the Continue to monitor the contribution of the model.contribution of the model.

It might be necessary to refine or It might be necessary to refine or expand the model.expand the model.

Example: Austin Auto Example: Austin Auto AuctionAuction

An auctioneer has developed a simple An auctioneer has developed a simple mathematical model for deciding the starting bid mathematical model for deciding the starting bid he will require when auctioning a used he will require when auctioning a used automobile.automobile.

Essentially, he sets the starting bid at seventy Essentially, he sets the starting bid at seventy percent of what he predicts the final winning bid percent of what he predicts the final winning bid will (or should) be. He predicts the winning bid will (or should) be. He predicts the winning bid by starting with the car's original selling price and by starting with the car's original selling price and making two deductions, one based on the car's making two deductions, one based on the car's age and the other based on the car's mileage. age and the other based on the car's mileage.

The age deduction is $800 per year and the The age deduction is $800 per year and the mileage deduction is $.025 per mile.mileage deduction is $.025 per mile.


Question:Question:

Develop the mathematical Develop the mathematical model that will give the starting bid model that will give the starting bid ((B B ) for a car in terms of the car's ) for a car in terms of the car's original price (original price (P P ), current age (), current age (AA) ) and mileage (and mileage (M M ). ).

Answer:Answer:

The expected winning bid can be The expected winning bid can be expressed as:expressed as:

PP - 800( - 800(AA) - .025() - .025(M M ))

The entire model is:The entire model is:

BB = .7(expected winning bid) = .7(expected winning bid)

BB = .7( = .7(PP - 800( - 800(AA) - .025() - .025(M M ))))

BB = .7( = .7(P P )- 560()- 560(AA) - .0175() - .0175(M M ))



Question:Question:

Suppose a four-year old car with Suppose a four-year old car with 60,000 miles on the odometer is being 60,000 miles on the odometer is being auctioned. If its original price was auctioned. If its original price was $12,500, what starting bid should the $12,500, what starting bid should the auctioneer require? auctioneer require?

Answer:Answer:

BB = .7(12,500) - 560(4) = .7(12,500) - 560(4) - .0175(60,000) = $5,460- .0175(60,000) = $5,460

Example: Austin Auto Example: Austin Auto AuctionAuction Question:Question:

The model is based on what assumptions? The model is based on what assumptions? Answer:Answer:

The model assumes that the only factors The model assumes that the only factors influencing the value of a used car are the influencing the value of a used car are the original price, age, and mileage (not condition, original price, age, and mileage (not condition, rarity, or other factors). rarity, or other factors).

Also, it is assumed that age and mileage Also, it is assumed that age and mileage devalue a car in a linear manner and without devalue a car in a linear manner and without limit. (Note, the starting bid for a very old car limit. (Note, the starting bid for a very old car might be negative! )might be negative! )

Example: Iron Works, Example: Iron Works, Inc.Inc.Iron Works, Inc. manufactures twoIron Works, Inc. manufactures two

products made from steel and just receivedproducts made from steel and just received

this month's allocation of this month's allocation of bb pounds of steel. pounds of steel.

It takes It takes aa11 pounds of steel to make a unit of product 1 pounds of steel to make a unit of product 1

and and aa22 pounds of steel to make a unit of product 2. pounds of steel to make a unit of product 2.

Let Let xx11 and and xx22 denote this month's production level of denote this month's production level of

product 1 and product 2, respectively. Denote by product 1 and product 2, respectively. Denote by pp11 and and

pp22 the unit profits for products 1 and 2, respectively. the unit profits for products 1 and 2, respectively.

Iron Works has a contract calling for at least Iron Works has a contract calling for at least m m units units ofof

product 1 this month. The firm's facilities are such that atproduct 1 this month. The firm's facilities are such that at

most most uu units of product 2 may be produced monthly. units of product 2 may be produced monthly.

Example: Iron Works, Example: Iron Works, Inc.Inc. Mathematical ModelMathematical Model

The total monthly profit = The total monthly profit =

(profit per unit of product 1) (profit per unit of product 1)

x (monthly production of product x (monthly production of product 1) 1)

+ (profit per unit of product 2) + (profit per unit of product 2)

x (monthly production of product 2) x (monthly production of product 2)

= = pp11xx11 + + pp22xx22

We want to maximize total monthly profit:We want to maximize total monthly profit:

Max Max pp11xx11 + + pp22xx22

Example: Iron Works, Example: Iron Works, Inc.Inc. Mathematical Model (continued)Mathematical Model (continued)

The total amount of steel used during The total amount of steel used during monthly production equals: monthly production equals:

(steel required per unit of product 1) (steel required per unit of product 1)

x (monthly production of product 1)x (monthly production of product 1)

+ (steel required per unit of product 2) + (steel required per unit of product 2)

x (monthly production of product 2) x (monthly production of product 2)

= = aa11xx11 + a + a22xx22

This quantity must be less than or This quantity must be less than or equal to the allocated equal to the allocated bb pounds of steel: pounds of steel:

aa11xx11 + + aa22xx2 2 << bb

Example: Iron Works, Example: Iron Works, Inc.Inc. Mathematical Model (continued)Mathematical Model (continued)

The monthly production level of product The monthly production level of product 1 must be greater than or equal to 1 must be greater than or equal to m m ::

xx11 >> mm The monthly production level of product The monthly production level of product

2 must be less than or equal to 2 must be less than or equal to u u ::

xx22 << uu However, the production level for However, the production level for

product 2 cannot be negative: product 2 cannot be negative:

xx22 >> 0 0

Example: Iron Works, Example: Iron Works, Inc.Inc.

Mathematical Model SummaryMathematical Model Summary

Max Max pp11xx11 + + pp22xx22

s.t. s.t. aa11xx11 + + aa22xx22 << bb

xx11 >> mm

xx22 << uu

xx22 >> 0 0

ObjectivObjectivee

FunctionFunction

““Subject Subject to”to”

ConstrainConstraintsts


Question:Question:

Suppose Suppose bb = 2000, = 2000, aa11 = 2, = 2, aa22 = = 3, 3, mm = 60, = 60, uu = 720, = 720, pp11 = 100, = 100, pp22 = 200. Rewrite the model with = 200. Rewrite the model with these specific values for the these specific values for the uncontrollable inputs.uncontrollable inputs.


Answer:Answer:

Substituting, the model is:Substituting, the model is:

Max 100Max 100xx11 + 200 + 200xx22

s.t. 2s.t. 2xx11 + 3 + 3xx22 << 2000 2000

xx11 >> 60 60

xx22 << 720 720

xx22 >> 0 0

Example: Iron Works, Example: Iron Works, Inc.Inc. Question:Question:

The optimal solution to the current model The optimal solution to the current model is is xx11 = 60 and = 60 and xx22 = 626 2/3. If the product = 626 2/3. If the product were engines, explain why this is not a true were engines, explain why this is not a true optimal solution for the "real-life" problem. optimal solution for the "real-life" problem.

Answer:Answer:

One cannot produce and sell 2/3 of an One cannot produce and sell 2/3 of an engine. Thus the problem is further restricted engine. Thus the problem is further restricted by the fact that both by the fact that both xx11 and and xx22 must be integers. must be integers. (They could remain fractions if it is assumed (They could remain fractions if it is assumed these fractions are work in progress to be these fractions are work in progress to be completed the next month.)completed the next month.)

Example: Iron Works, Example: Iron Works, Inc.Inc.Uncontrollable InputsUncontrollable InputsUncontrollable InputsUncontrollable Inputs

$100 profit per unit Prod. 1$100 profit per unit Prod. 1$200 profit per unit Prod. 2$200 profit per unit Prod. 22 lbs. steel per unit Prod. 12 lbs. steel per unit Prod. 13 lbs. Steel per unit Prod. 23 lbs. Steel per unit Prod. 2

2000 lbs. steel allocated2000 lbs. steel allocated60 units minimum Prod. 160 units minimum Prod. 1

720 units maximum Prod. 2720 units maximum Prod. 20 units minimum Prod. 20 units minimum Prod. 2

$100 profit per unit Prod. 1$100 profit per unit Prod. 1$200 profit per unit Prod. 2$200 profit per unit Prod. 22 lbs. steel per unit Prod. 12 lbs. steel per unit Prod. 13 lbs. Steel per unit Prod. 23 lbs. Steel per unit Prod. 2

2000 lbs. steel allocated2000 lbs. steel allocated60 units minimum Prod. 160 units minimum Prod. 1

720 units maximum Prod. 2720 units maximum Prod. 20 units minimum Prod. 20 units minimum Prod. 2

60 units Prod. 160 units Prod. 1626.67 units Prod. 2626.67 units Prod. 2

60 units Prod. 160 units Prod. 1626.67 units Prod. 2626.67 units Prod. 2

Controllable InputsControllable InputsControllable InputsControllable Inputs

Profit = $131,333.33Profit = $131,333.33Steel Used = 2000Steel Used = 2000

Profit = $131,333.33Profit = $131,333.33Steel Used = 2000Steel Used = 2000

OutputOutputOutputOutput

Mathematical ModelMathematical ModelMathematical ModelMathematical Model

Max 100(60) + 200(626.67)Max 100(60) + 200(626.67)s.t. 2(60) + 3(626.67) s.t. 2(60) + 3(626.67) << 2000 2000 60 60 >> 60 60 626.67 626.67 << 720 720 626.67 626.67 >> 0 0

Max 100(60) + 200(626.67)Max 100(60) + 200(626.67)s.t. 2(60) + 3(626.67) s.t. 2(60) + 3(626.67) << 2000 2000 60 60 >> 60 60 626.67 626.67 << 720 720 626.67 626.67 >> 0 0

Example: Ponderosa Example: Ponderosa Development Corp.Development Corp.

Ponderosa Development CorporationPonderosa Development Corporation

(PDC) is a small real estate developer that (PDC) is a small real estate developer that buildsbuilds

only one style house. The selling price of the only one style house. The selling price of the house ishouse is

$115,000.$115,000.

Land for each house costs $55,000 and lumber, Land for each house costs $55,000 and lumber,

supplies, and other materials run another supplies, and other materials run another $28,000 per$28,000 per

house. Total labor costs are approximately house. Total labor costs are approximately $20,000 per$20,000 per

house.house.


Ponderosa leases office space for Ponderosa leases office space for $2,000$2,000

per month. The cost of supplies, utilities, per month. The cost of supplies, utilities, andand

leased equipment runs another $3,000 per leased equipment runs another $3,000 per month. month.

The one salesperson of PDC is paid a The one salesperson of PDC is paid a commission of $2,000 on the sale of each commission of $2,000 on the sale of each house. PDC has seven permanent office house. PDC has seven permanent office employees whose monthly salaries are given employees whose monthly salaries are given on the next slide.on the next slide.


EmployeeEmployee Monthly SalaryMonthly Salary

President President $10,000$10,000

VP, Development 6,000VP, Development 6,000

VP, Marketing VP, Marketing 4,500 4,500

Project Manager Project Manager 5,500 5,500

Controller Controller 4,000 4,000

Office Manager Office Manager 3,000 3,000

Receptionist Receptionist 2,000 2,000


Question:Question:

Identify all costs and denote the marginal Identify all costs and denote the marginal cost and marginal revenue for each house.cost and marginal revenue for each house.

Answer:Answer:

The monthly salaries total $35,000 and The monthly salaries total $35,000 and monthly office lease and supply costs total monthly office lease and supply costs total another $5,000. This $40,000 is a monthly another $5,000. This $40,000 is a monthly fixed cost. fixed cost.

The total cost of land, material, labor, The total cost of land, material, labor, and sales commission per house, $105,000, is and sales commission per house, $105,000, is the marginal cost for a house. the marginal cost for a house.

The selling price of $115,000 is the The selling price of $115,000 is the marginal revenue per house.marginal revenue per house.


Question:Question:

Write the monthly cost function Write the monthly cost function c c ((xx), revenue ), revenue function function r r ((xx), and profit ), and profit function function p p ((xx).).

Answer:Answer:

c c ((xx) = variable cost + fixed cost = ) = variable cost + fixed cost = 105,000105,000xx + 40,000 + 40,000

r r ((xx) = 115,000) = 115,000xx

p p ((xx) = ) = r r ((xx) - ) - c c ((xx) = 10,000) = 10,000xx - - 40,00040,000


Question:Question:

What is the breakeven point for What is the breakeven point for monthly sales of the houses?monthly sales of the houses?

Answer:Answer:

r r ((x x ) = ) = c c ((x x ) )

115,000115,000xx = 105,000 = 105,000xx + 40,000 + 40,000

Solving, Solving, xx = 4. = 4.


Question:Question:

What is the monthly profit if 12 What is the monthly profit if 12 houses perhouses per

month are built and sold?month are built and sold? Answer:Answer:

p p (12) = 10,000(12) - 40,000 = (12) = 10,000(12) - 40,000 = $80,000 monthly profit$80,000 monthly profit


00

200200

400400

600600

800800

10001000

12001200

00 11 22 33 44 55 66 77 88 99 1010Number of Houses Sold (x)Number of Houses Sold (x)

Th

ousa

nds

of

Dolla

rsTh

ousa

nds

of

Dolla

rs

Break-Even Point = 4 HousesBreak-Even Point = 4 Houses

Total Cost Total Cost = = 40,000 + 40,000 + 105,000x105,000x

Total Total Revenue =Revenue = 115,000x115,000x

Management Science Management Science TechniquesTechniques

Linear ProgrammingLinear Programming Integer Linear Integer Linear

ProgrammingProgramming PERT/CPMPERT/CPM Inventory ModelsInventory Models Waiting Line ModelsWaiting Line Models SimulationSimulation

Decision AnalysisDecision Analysis Goal ProgrammingGoal Programming Analytic Hierarchy Analytic Hierarchy

ProcessProcess ForecastingForecasting Markov-Process Markov-Process

ModelsModels Dynamic Dynamic

ProgrammingProgramming

The Management The Management ScientistScientist Software Software

12 Modules12 Modules

Using Excel for Using Excel for Breakeven AnalysisBreakeven Analysis

A A spreadsheet software packagespreadsheet software package such as such as MicrosoftMicrosoft ExcelExcel can be used to perform a can be used to perform a quantitative analysis of Ponderosa quantitative analysis of Ponderosa Development Corporation.Development Corporation.

We will enter the We will enter the problem dataproblem data in the top in the top portion of the spreadsheet.portion of the spreadsheet.

The bottom of the spreadsheet will be used for The bottom of the spreadsheet will be used for model developmentmodel development..


Formula SpreadsheetFormula SpreadsheetA B

1 PROBLEM DATA2 Fixed Cost $40,0003 Variable Cost Per Unit $105,0004 Selling Price Per Unit $115,0005 MODEL6 Sales Volume7 Total Revenue =B4*B68 Total Cost =B2+B3*B69 Total Profit (Loss) =B7-B8


QuestionQuestion

What is the monthly profit if 12 What is the monthly profit if 12 houses are built and sold per month?houses are built and sold per month?


Spreadsheet SolutionSpreadsheet Solution

A B1 PROBLEM DATA2 Fixed Cost $40,0003 Variable Cost Per Unit $105,0004 Selling Price Per Unit $115,0005 MODEL6 Sales Volume 127 Total Revenue $1,380,0008 Total Cost $1,300,0009 Total Profit (Loss) $80,000


Question:Question:

What is the breakeven point for monthly sales What is the breakeven point for monthly sales of the houses?of the houses?

Spreadsheet Solution:Spreadsheet Solution: One way to determine the break-even point using One way to determine the break-even point using

a spreadsheet is to use the a spreadsheet is to use the Goal SeekGoal Seek tool. tool. Microsoft ExcelMicrosoft Excel ‘s Goal Seek tool allows the user ‘s Goal Seek tool allows the user

to determine the value for an to determine the value for an input cellinput cell that will that will cause the cause the output celloutput cell to equal some specified to equal some specified value.value.

In our case, the goal is to set Total Profit to zero In our case, the goal is to set Total Profit to zero by seeking an appropriate value for Sales Volume.by seeking an appropriate value for Sales Volume.


Spreadsheet Solution: Goal Seek ApproachSpreadsheet Solution: Goal Seek Approach

Using Using Excel Excel ’s ’s Goal SeekGoal Seek Tool Tool

Step 1:Step 1: Select the Select the ToolsTools menu menu

Step 2:Step 2: Choose the Choose the Goal SeekGoal Seek option option

Step 3:Step 3: When the When the Goal Seek Goal Seek dialog box appears:dialog box appears:

Enter B9 in the Enter B9 in the Set cellSet cell box box

Enter 0 in the Enter 0 in the To valueTo value box box

Enter B6 in the Enter B6 in the By changing cellBy changing cell box box

Click Click OKOK


Spreadsheet Solution: Goal Seek Spreadsheet Solution: Goal Seek Approach Approach

Completed Goal Seek Completed Goal Seek Dialog BoxDialog Box


Spreadsheet Solution: Goal Seek Spreadsheet Solution: Goal Seek ApproachApproach

A B1 PROBLEM DATA2 Fixed Cost $40,0003 Variable Cost Per Unit $105,0004 Selling Price Per Unit $115,0005 MODEL6 Sales Volume 47 Total Revenue $460,0008 Total Cost $460,0009 Total Profit (Loss) $0

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