dsci 3870 chapter 1 introduction additional reading material

1 1 Slide

Slide

© 2008 Thomson South-Western. All Rights Reserved© 2008 Thomson South-Western. All Rights Reserved

DSCI 3870 Chapter 1

INTRODUCTIONAdditional Reading Material

2 2 Slide

Slide


Chapter 1 – IntroductionChapter 1 – IntroductionAdditional Reading MaterialAdditional Reading Material

A Project Scheduling ExampleA Project Scheduling Example Austin Auto Auctions: A Pricing Model Austin Auto Auctions: A Pricing Model

ExampleExample Ponderosa Development: A Breakeven Point Ponderosa Development: A Breakeven Point

ExampleExample

3 3 Slide

Slide


Example: Project SchedulingExample: Project Scheduling

Consider 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.).

4 4 Slide

Slide



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 could additional resources be purchased? How could management science be used to solve this management science be used to solve this problem?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 and time based on the activities' normal times and then based on the activities' expedited then based on the activities' expedited (reduced) times.(reduced) times.

5 5 Slide

Slide



Question:Question:

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

6 6 Slide

Slide



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.

7 7 Slide

Slide



Question:Question:

Is the model deterministic or stochastic?Is the model deterministic or stochastic? Answer:Answer:

StochasticStochastic. Activity completion times, . Activity completion times, both normal and expedited, are uncertain and both normal and expedited, are uncertain and subject to variation. Activity expediting costs subject to variation. Activity expediting costs are uncertain. The number of activities and are uncertain. The number of activities and their precedence relationships might change their precedence relationships might change before the project is completed due to a project before the project is completed due to a project design change. design change.

8 8 Slide

Slide



Question:Question:

Suggest assumptions that could be made Suggest assumptions that could be made to simplify the model.to simplify the model.

Answer:Answer:

Make the model deterministic by Make the model deterministic by assuming normal and expedited activity times assuming normal and expedited activity times are known with certainty and are constant. The are known with certainty and are constant. The same assumption might be made about the same assumption might be made about the other stochastic, uncontrollable inputs.other stochastic, uncontrollable inputs.

9 9 Slide

Slide


Example: Austin Auto AuctionExample: Austin Auto Auction

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

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

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

10 10 Slide

Slide



Question:Question:

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

11 11 Slide

Slide


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 ))


12 12 Slide

Slide



Question:Question:

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

Answer:Answer:

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

13 13 Slide

Slide



Question:Question:

The model is based on what The model is based on what assumptions? 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!)

14 14 Slide

Slide


Example: Ponderosa Development Corp.Example: Ponderosa 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 Land for each house costs $55,000 and lumber, 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.

15 15 Slide

Slide



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

per month. The cost of supplies, utilities, andper month. The cost of supplies, utilities, and

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 commissioncommission

of $2,000 on the sale of each house. PDC has of $2,000 on the sale of each house. PDC has sevenseven

permanent office employees whose monthly permanent office employees whose monthly salariessalaries

are given on the next slide.are given on the next slide.

16 16 Slide

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

17 17 Slide

Slide



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.

18 18 Slide

Slide


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

Question:Question:

Write the monthly cost function Write the monthly cost function c c ((xx), ), revenue revenue function function r r ((xx), and profit function ), and profit 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 - 40,000 - 40,000

19 19 Slide

Slide



Question:Question:

What is the breakeven point for monthly What is the breakeven point for monthly salessales

of the houses?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.

20 20 Slide

Slide



Question:Question:

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

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

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

21 21 Slide

Slide



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

nd

s 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

22 22 Slide

Slide


End of Chapter 1End of Chapter 1

dsci 3870 chapter 1 introduction additional reading material

Documents