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QBUS2310 Management Science

创建日期：2024-05-23 17:00:26

所属分类：管理Management

标签： QBUS2310

Management Science

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QBUS2310 Management Science

What is Management Science?
Management: decision-making to control an organization/entity.
Management science refers to analytical/quantitative techniques
that are used in decision-making processes for organizations (including
businesses). Examples:
▶ mathematical optimization (a.k.a. mathematical programming)
▶ game theory
▶ forecasting
▶ statistics
▶ queueing theory.
The course will focus on mathematical optimization/programming,
arguably the most fundamental tool used for quantitative
decision-making.

What is mathematical optimization?
Mathematical optimization: a framework to model quantitative
decision-making problems, taking into account:
▶ data – the information that we have;
▶ constraints – which decisions are allowed;
▶ objectives – how good are different decisions.
Optimization: we want to make some quantity as large or as small as
possible, i.e., we optimize the quantity. Examples:
▶ profits
▶ losses
▶ wasted resources
▶ utilities
▶ clashes.

Three types of analytics
Mathematical optimization falls within prescriptive analytics.

Case study: Birchbox
▶ The company: a monthly subscription service for beauty products.
Each month, subscribers get a custom box of product samples
tailored to their preferences.
▶ The problem: how to tailor boxes for customers according to
individual preferences?
▶ Complexity: millions of customers each month, 100s of different
possible samples, 5–7 samples each box.
▶ Na¨ıvely, there are ≈ 106 ×
(100
5
)
≈ 7.5× 1013 possible combinations.
▶ Impossible to solve by hand.

Case study: Birchbox
The solution (part 1):
▶ Group similar customers; from 1 million to ≈ 4000 groups.
▶ Still about ≈ 4000×
(100
5
)
≈ 3× 1011 possible combinations.
▶ More complexity: not every box combination is possible.
▶ value, weight and volume constraints for each box. Product
selections must obey these (e.g., can’t be too heavy/light).
▶ minimum/maximum number of products each box.
▶ certain pairs of products must go together (e.g., face scrub + face
cream); certain pairs of products can’t go together.
▶ certain products can’t be sent to certain groups; certain products
must be shipped to certain groups.

Case study: Birchbox
The solution (part 2): use mathematical optimize to solve Birchbox’s
assortment problem.
▶ This means we need to define the decision variables, objective and
constraints mathematically. This is called building an
optimization model.
▶ For example, let xpb = 1 if product p is part of configuration b, and
xpb = 0 otherwise; this is a decision variable.
▶ Let P be the set of all products. Then∑p∈P xpb ≤ 5 is a constraint.
▶ Once the model is built, we can solve this using software, such as
Gurobi.
▶ Note: there may be more than one way to build the model. Some
approaches are more advantageous.

When you should use optimization models
▶ There are large number of variables with complex interdependencies.
▶ The interdependencies between variables and objectives are relatively
well understood.
▶ The problem can be framed quantitatively.

What you will learn
▶ The components of an optimization model.
▶ How to build linear optimization models for common
decision-making problems.
▶ How to use state-of-the-art software to solve optimization models.
▶ How to model uncertainty and risk in decision-making problems.
Note: the course will focus on linear optimization models and its
variants. It will only briefly touch on algorithms and skip over nonlinear
models.

How you will learn
Minimum:
▶ Attend lectures and tutorials.
To do well:
▶ Actively engage with lectures, and review coding supplement.
▶ Attempt problems before tutorials, and practice more on your own.
▶ Consult suggested readings for further clarification (if needed).

Assessment
▶ Three assignments (20% each).
▶ Final exam (40%).
Collaboration policy: For assignments, you are only allowed to verbally
discuss high-level ideas with classmates. All detailed model workings and
coding should be done individually. You are not permitted to consult
resources (e.g., internet forums, websites) except for provided lecture and
tutorial content. For exams, there is strictly no collaboration of any kind.
WARNING: Breaches of this policy will be reported as academic
dishonesty to the University, and may carry severe consequences; see
more information on Canvas.
Nam Ho-Nguyen QBUS2310 Management Science
12/214
Prerequisites and software
Mathematics:
▶ Linear algebra: vector and matrix multiplication.
▶ Comfort with mathematical reasoning.
▶ Comfort with programming using Python.
Software to be used:
▶ Python – freely available.
▶ Gurobi – this is commercial-grade software (e.g., used in the
Birchbox case study), but freely available to students. Instructions
on Canvas.

Textbooks
There is no official textbook for this course. The slides are
self-contained (except for advanced mathematical proofs, which you
won’t need) and there are plenty of Jupyter demonstrations to
supplement these.

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