40 Questions
What is another term used for the field of Operations Research?
Management Science
Which of the following models assumes all data are known with certainty?
Deterministic Models
What is the primary goal of Stochastic Models?
To estimate system performance
When did Operations Research begin in a systematic way?
In the late 1930s
Who is credited with the development of Scientific Management?
Frederick Taylor
What is the term used to describe the combination of Operations Research and Management Science in the U.S.?
ORMS
Which of the following is an example of a Deterministic Model?
Linear Programming
What is the term used to describe the study of waiting lines?
Queuing Theory
What is the age deduction per year in the Austin Auto Auction model?
$800
What is the mileage deduction per mile in the Austin Auto Auction model?
$0.025
What is the expression for the expected winning bid in the Austin Auto Auction model?
P - 800(A) - 0.025(M)
What is the assumption behind the Austin Auto Auction model regarding the factors influencing the value of a used car?
Only the age and mileage of the car affect its value.
What is crucial for the successful implementation of model results?
User involvement throughout the modeling process
What should a managerial report include?
The recommended decision and other pertinent information
What is the purpose of the Austin Auto Auction model?
To determine the starting bid of a car in an auction.
What is the variable x1 in the Iron Works, Inc. model?
The production level of product 1 this month.
What is the purpose of a what-if analysis in an OR-based decision support system?
To test the sensitivity of the model solution to different assumptions and data
What is an example of OR application in the field of logistics?
All of the above
What is the contract requirement for product 1 in the Iron Works, Inc. model?
At least m units of product 1 must be produced this month.
What is the primary goal of an OR-based decision support system?
To support decision-making with data-driven insights
What is the unit profit of product 2 in the Iron Works, Inc. model?
p2
What is the purpose of providing training sessions during the workday?
To increase user involvement and understanding of the model
What is the auctioneer's strategy in the Austin Auto Auction example?
To set the starting bid at seventy percent of the predicted final winning bid
What is a component of an OR-based decision support system?
All of the above, including what-if analysis
What is the objective of the mathematical model in Iron Works, Inc?
Maximize the total monthly profit
What is the constraint on the total amount of steel used during monthly production?
a1x1 + a2x2 < b
What is the constraint on the monthly production level of product 1?
x1 > m
What is the constraint on the monthly production level of product 2?
x2 < u
What is the profit per unit of product 1 in the given example?
100
What is the allocated amount of steel in the given example?
2000
What is the constraint on the production level of product 2 in the given example?
x2 < 720
What is the steel required per unit of product 2 in the given example?
3
What is the total cost of land, lumber, supplies, and labor for each house?
$105,000
What is the monthly fixed cost for Ponderosa Development Corp?
$40,000
What is the marginal revenue per house for Ponderosa Development Corp?
$115,000
What is the variable cost per house for Ponderosa Development Corp?
$105,000
What is the breakeven point for monthly sales of the houses?
4 houses
What is the monthly profit if 12 houses per month are built and sold?
$80,000
What is the total monthly salary of the employees in Ponderosa Development Corp?
$35,000
What is the revenue function for Ponderosa Development Corp?
r(x) = 115,000x
Study Notes
Operations Research
- Also known as Management Science (MS) or Decision Science (DS)
- Combines Operational Research (OR) and Management Science (MS) in the US, referred to as OR/MS or ORMS
Operations Research Models
- Deterministic Models: assume all data is known with certainty
- Examples:
- Linear Programming
- Network Optimization
- Integer Programming
- Nonlinear Programming
- Inventory Models
- Examples:
- Stochastic Models: explicitly represent uncertain data via random variables or stochastic processes
- Examples:
- Discrete-Time Markov Chains
- Continuous-Time Markov Chains
- Queuing Theory (waiting lines)
- Decision Analysis
- Game Theory
- Inventory models
- Simulation
- Examples:
History of Operations Research
- A relatively new discipline, only 70 years old
- Developed from mathematics, physics, and engineering in the late 1930s
- Key contributors:
- Frederick Taylor (Scientific Management)
- Henry Gannt (Project Scheduling)
- F.W.Harris (Inventory Theory)
- William Shewart (Control Charts)
- Andrey A. Markov (Markov Processes)
- E.K. Erlang (Queuing Theory)
- H. Dodge and H. Roming (Quality Theory)
Implementation and Follow-Up
- Successful implementation of model results is critical
- Secure user involvement throughout the modeling process
- Continue to monitor the contribution of the model and refine or expand as necessary
Report Generation
- Prepare a managerial report based on model results
- Include:
- Recommended decision
- Pertinent information about results (e.g., sensitivity to assumptions and data)
Components of OR-Based Decision Support System
- Data base (e.g., nurse profiles, external resources, rules)
- Graphical User Interface (GUI)
- Algorithms, pre- and post-processor
- What-if analysis
- Report generators
Examples of OR Applications
- Rescheduling aircraft in response to groundings and delays
- Planning production for printed circuit board assembly
- Scheduling equipment operators in mail processing and distribution centers
- Developing routes for propane delivery
- Adjusting nurse schedules in light of daily fluctuations in demand
Austin Auto Auction Example
- Auctioneer uses a simple mathematical model to decide starting bid
- Model takes into account car's original price, age, and mileage
- Starting bid is 70% of expected winning bid
Iron Works, Inc. Example
- Manufacturer produces two products from steel
- Wants to maximize total monthly profit
- Constraints:
- Limited steel allocation
- Minimum production level for product 1
- Maximum production level for product 2
- Non-negativity constraint for product 2
Ponderosa Development Corp. Example
- Builds one style house in the valley
- Costs include land, labor, and sales commission
- Selling price is $115,000
- Identify all costs and denote marginal cost and marginal revenue for each house
- Write monthly cost function, revenue function, and profit function
Introduction to Operations Research, also known as Management Science or Decision Science, including its different models such as deterministic and stochastic models.
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