38 Questions
What is the last step in the 7 steps of problem solving?
Evaluate the results
Who is associated with the development of Linear Programming?
George Dantzig
What is the primary reason for using a Quantitative Analysis approach to decision making?
The problem is complex
Who is associated with the development of Integer Programming?
Ralph Gomory
What is the primary focus of Game Theory?
Decision making under uncertainty
What is the name of the organization that was formed in 2006?
INFORMS
What is the minimum number of units of Product 1 that Iron Works, Inc. must produce?
60 units
What is the optimal solution to the Iron Works, Inc. problem?
x1 = 60 and x2 = 626 2/3
What are the key inputs required to build a mathematical model for project scheduling?
Normal and expedited activity completion times, funds available for expediting, and precedence relationships of the activities
What is the objective function of the mathematical model in project scheduling?
Minimize project completion time
What is the mathematical model that gives the starting bid (B) for a car in terms of the car's original price (P), current age (A) and mileage (M)?
B = .7(P - 800(A) - .025(M))
What is the purpose of solving the mathematical model in project scheduling?
To identify the values of the decision variables that provide the best output for the model
What type of model is used in project scheduling?
Stochastic model
Why is the optimal solution x1 = 60 and x2 = 626 2/3 not a true optimal solution for the 'real-life' problem?
Because it assumes production of fractions of units
What is the age deduction per year in the Austin Auto Auction model?
$800
What is the maximum number of units of Product 2 that Iron Works, Inc. can produce?
720 units
What is the assumption of the Austin Auto Auction model regarding the factors influencing the value of a used car?
The model assumes that the only factors influencing the value of a used car are the original price, age, and mileage.
What are the decision variables in the mathematical model for project scheduling?
Which activities to expedite and by how much, and when to start each activity
What is the outcome of solving the mathematical model in project scheduling?
Best course of action
What is the monthly rent paid by Ponderosa Development Corporation for its building?
$2,000
What is the total monthly cost of Ponderosa Development Corporation?
$6,000
What is an example of a tool used to solve the mathematical model in project scheduling?
Read nurse profiles and demand requirements
What is the total monthly salary cost of the seven permanent employees of Ponderosa Development Corporation?
Not given
What is the mileage deduction per mile in the Austin Auto Auction model?
$0.025
What approach can be used to solve the mathematical model in project scheduling?
Trial-and-error approach
What is the monthly cost of supplies, utilities, and leased equipment for Ponderosa Development Corporation?
$3,000
What is the linear manner of devaluation assumed in the Austin Auto Auction model?
Age and mileage decrease the value of a car in a linear manner.
What is the unit profit for product 1 in the Iron Works, Inc. model?
p1
What is the minimum number of units of product 1 required in the Iron Works, Inc. contract?
m
How many pounds of steel are required to make a unit of product 1 in the Iron Works, Inc. model?
a1
What was the primary goal of Merrill Lynch's Management Science Group?
To evaluate the total revenue at risk
What was the outcome of introducing two new products at Merrill Lynch?
A revenue gain of $80 million
What was the primary challenge faced by NBC's sales staff?
Manually developing sales plans for advertisers
What was the primary objective of Ford Motor's prototype vehicle testing?
To reduce costs on prototype development
What was the benefit of Merrill Lynch's Management Science Group's simulation of client-choice behavior?
Evaluation of total revenue at risk and assessment of pricing schedules
What was the outcome of NBC's use of optimization models?
Improved sales-force productivity and revenue management
What was the common goal of the three companies mentioned?
To increase revenue through optimization and simulation
What was the outcome of NBC's optimization of ad sales?
A revenue gain of $200 million
Study Notes
History of Operations Research
- Operations Research originated in the 1940s with contributions from L.H. Kuhn, A.Tucker, Jon Von Neumann, George Dantzig, and Oscar Morgenstern
- Key developments: Queuing Theory, Non-Linear Programming, Linear Programming, Game Theory, Simulation, Dynamic Programming, and Integer Programming
Timeline of Operations Research
- 1970: Microcomputer, H.Karmarkar's work on Linear Programming, and the introduction of Spreadsheet Packages
- 1980: Personal computer, OR/MS Softwares, and the establishment of INFORMS
- 1990: Advancements in OR/MS Softwares and simulations
- 2006: You are here
Problem Solving and Decision Making
- 7 Steps of Problem Solving: • Identify and define the problem • Determine the set of alternative solutions • Determine the criteria for evaluating the alternatives • Evaluate the alternatives • Choose an alternative • Implement the chosen alternative • Evaluate the results
- The first 5 steps are the process of decision making
Quantitative Analysis and Decision Making
- Reasons for using a Quantitative Analysis Approach: • The problem is complex • The problem is very important • The problem is new • The problem is repetitive
Project Scheduling
- Example: Project Scheduling
- Decision variables: which activities to expedite and by how much, and when to start each activity
- Objective function: minimize project completion time
- Constraints: do not violate any activity precedence relationships and do not expedite in excess of the funds available
Model Solution
- Involves identifying the values of the decision variables that provide the "best" output for the model
- One approach is trial-and-error
Examples and Case Studies
- Austin Auto Auction: Develop a mathematical model to determine the starting bid for a car based on its original price, age, and mileage
- Iron Works, Inc.: Determine the optimal production levels for two products made from steel, considering the original price, age, and mileage
- Ponderosa Development Corporation: Determine the optimal production levels for two products, considering the monthly salaries of employees, leased equipment, and supplies
- Merrill Lynch: Simulate client-choice behavior to evaluate the total revenue at risk and assess the impact of various pricing schedules
- NBC's Optimization of Ad Sales: Use optimization models to reduce labor time and improve pricing of ad spots, increasing revenue by over $200 million
- Ford Motor Prototype Vehicle Testing: Reduce costs on developing prototypes for new cars and modified products
This quiz covers the key figures and developments in the history of operations research, including notable mathematicians, algorithms, and methodologies.
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