ISE 540:338 Probabilistic Models in OR
Assignment #1: Introduction to OR
Due: Electronic submission, September 10th, 2024 at 5:00pm
**Fill in this Template with a different color: All HWs must be “typed” NOT manually written**
[25 pts]
a. [3 pts] According to George Box: “All models are wrong, but some are useful.” A model is defined as
A simplification of a real-world system. A model that is used to optimize bus schedules, for instance,
should
capture
important
details
like
bus station location
Consumer demand,but leaves out minor details like color of the bus
and
. In contrast to
deterministic models, probabilistic models invoke probability distributions to solve OR problems.
b. [3 pts] In class, we have discussed how the battle of Great Britain was one of the real-world challenges
that led to the creation and development of the field of Operations Research (OR). Another application of
OR in World War II is the Battle of the Atlantic (or Battle of the North Atlantic). Describe in 3-4 lines about
how OR sciences helped the Allied forces win the Battle of the North Atlantic? In your view, what were the
decision variables, objective function, and parameters in this problem?
The Battle of the North Atlantic was an OR problem, with the objective function being the maximization of
Acis forces destroyed and the minimization of Allied forces lost. The decision variables were the route,
speed, and resources of a convoy. The parameters with the environment, the cost of artillery and vessels,
and the routes the enemies could take.
c. [2 pts] You may have been following the emerging and rapid developments in Artificial Intelligence (AI),
especially with the increase in the size and volume of data and how AI can harness this data to extract
meaningful information. In light of the constituents of an OR model (objective function, parameters, decision
variables), where do you think AI can help in developing better OR models, and hence, reaching better
decisions? Give at least one example to clarify your answer. Limit your response to 4-5 lines.
AI could be used to extract large data that humans would never have the time to analyze in their OR
models. AI would be able to see patterns that may not be caught be even the most experienced data
scientists. AI would also be able access past OR models and apply their successful elements to the model,
while making sure to avoid their failures.
d. [3 pts] You are trying to find the optimal capacity of your company’s warehouse which offers storage
services to the manufacturing industry. Fill in below to describe this as an OR problem, by stating the decision
variables, parameters, and objective function. (You do not have to “mathematically” formulate the problem
– just fill in plain English). Concise answers (no more than 2-3 lines per row).
Objective Function
Find the optimal capacity of the warehouse that maximizes profits and minimizes costs
Decision Variables
Price charged, capacity used
Parameters
Cost, demand for storage, maximum capacity
e. [4 pts] Give an example of how OR can be used to transform an existing business/industry that you regularly
interact with [you may use Google and other relevant resources, if needed, but rephrase in your own words]?
State what would be the decision variables, parameters, and objective function. You can fill in the below
table. (You do not have to “mathematically” formulate the problem – just fill in plain English). Concise
answers (no more than 2-3 lines per row).
Problem Statement
(1-2 lines describing
Ensure that Door Dashers receive orders that are closest to them
the problem in English)
Objective Function
Decision Variables
Parameters
f.
Measure the distance between the most recent order and the Door Dasher
Order assignment
Customer order, dasher availability, demand of area
[5 pts] Each year, INFORMS organizes a prestigious competition, called: “Franz Edelman competition,”
wherein the goal is to demonstrate the contributions of operations research and analytics in both the profit
and non-profit sectors. Go to this link (https://www.informs.org/Recognizing-Excellence/INFORMSPrizes/Franz-Edelman-Award/Franz-Edelman-Academy), select a year, then scroll through the winners and
finalists. Pick the one that you feel is the most interesting to you (you may want to click on some of the
links in the “Related Content” in the bottom of the page for more information). Fill in below to
describe the problem, and state what would be the decision variables, parameters, and objective function.
Explain why this problem in particular appeals to you. (You do not have to “mathematically” formulate the
problem – just fill in plain English). Concise answers (no more than 2-3 lines per row).
Problem Statement
(1-2 lines describing
A ferry company in Denmark was having trouble predicting passengers and vehicles to board their
ferries, making them late for departures
the problem in English)
Objective Function
Create and AI Decision making model to predict how many passengers and vehicles would buy
tickets on a given day
Decision Variables
Parameters
Pasenger ticket price, vehicle ticket price, listed departure time
Actual departure time, number of vehicles, number of passengers
Why This Problem
appeals to you?
I never knew the ferry industry was as large as the aviation industry, so this problem stood out to
me.
g. [5 pts] Go to this paper: “Petropoulos, Fotios, Gilbert Laporte, Emel Aktas, Sibel A. Alumur, Claudia Archetti,
Hayriye Ayhan, Maria Battarra et al. "Operational research: Methods and applications," (2023). After
reading the paper, go to section 3 (Applications), pick one application that is most interesting to you. Now,
either use the article or any online resources to find a problem that lies under this type of application. Fill in
below to describe the problem, and state what would be the decision variables, parameters, and objective
function. Explain why this problem in particular appeals to you. (You do not have to “mathematically”
formulate the problem – just fill in plain English). Concise answers (no more than 2-3 lines per row).
Problem Statement
(1-2 lines describing
Creating a basketball team
the problem in English.
Mention the application
in the paper under
which this problem lies)
Objective Function
Decision Variables
Parameters
Why This Problem
appeals to you?
Creating a basketball team with the highest possible win rate
Salaries, Players signed and sold
Market of players, player performance, income of team
I love basketball and always wondered what it would be like to start a team