QBUS2310 Management Science
The Complete Exam Bible · Semester 2 2026QBUS2310 Overview
- The University of Sydney
- Semester 2 2026
- Level 2
- Mathematical optimisation
Management Science studies how to turn complex operational choices into mathematical models that can be solved and checked. The unit begins with prescriptive analytics: define the decision variables, separate parameters from choices, state an objective, and describe every operational limit as an equation or inequality.
- Core method Define choices, goal, limits and domains
- Verification Check feasibility and an independent certificate
- Assessment mix Assignments, written test and final exam
- Tools Python, Gurobi and RSOME support modelling
How QBUS2310 is assessed
| Component | Weight | Format |
|---|---|---|
| Final exam Written exam | 40% | Written exam in the formal exam period, two hours |
| Assignment 0 A written assignment submitted through Canvas. | 8% | Practical skill Early Feedback Task in Week 03 |
| Mid-Semester Test A mid-semester test | 20% | Written test in Week 07, one and a half hours |
| Assignment 1 A written assignment submitted through Canvas. | 12% | Practical skill task in Week 07 |
| Assignment 2 A written assignment submitted through Canvas. | 20% | Practical skill task in Week 13 |
What QBUS2310 covers
The unit moves from mathematical decision models and linear optimisation through geometry, modelling, duality, integer decisions, networks, and optimisation under uncertainty. Each chapter pairs formulation with a verification method so the result remains connected to the management decision.
Optimisation Decisions and Linear Models
Decision variables, objectives, constraints, feasibility and linear model conventions02Linear Algebra, Convexity and Model Structure
Vectors, matrices, linear independence, convex combinations and convex functions03Feasible Geometry and Basic Solutions
Halfspaces, active constraints, vertices, basic feasible solutions and standard form04Building Linear Optimisation Models
Resource, transport, staffing, inventory and cash-flow formulations05Linearisation and Piecewise Objectives
Epigraph variables, maximum functions, absolute values and concave maximisation06Duality, Certificates and Shadow Prices
Weak duality, complementary slackness, infeasibility certificates and sensitivity07Zero-Sum Games as Linear Programs
Mixed strategies, guaranteed payoff, equalisation and maximin formulations08Integer Models and Branch-and-Bound
Binary decisions, logical links, LP relaxations, integrality gaps and branching09Network Flow and Assignment Models
Conservation, capacities, shortest paths, assignment and max-flow duality10Optimisation Under Uncertainty and Risk
Worst-case models, expected value, recourse framing, VaR and CVaRLinear optimisation then provides the core language for resource allocation, capacity planning, production, transportation, workforce coverage, inventory, and short-term financing. Geometry links halfspaces, active constraints, vertices, and basic feasible solutions. Algebra and convexity explain why those pictures generalise beyond two variables.
Later topics use duality to produce bounds and certificates, shadow prices to interpret local resource value, and linearisation to represent finite piecewise-linear objectives. Discrete decisions require integer and binary variables, LP relaxations, integrality-gap reasoning, and branch-and-bound. Network structure brings conservation, capacity, shortest-path, assignment, and max-flow ideas into one family.
A zero-sum game becomes a maximin linear program over probabilities. Uncertain decisions introduce expected value, worst-case protection, recourse framing, Value at Risk, and Conditional Value at Risk. Throughout, the important habit is verification: a solver output matters only when the formulation is correct, the candidate is feasible, and an independent bound or structural check supports the conclusion.
The recurring discipline is to connect each model family to its own proof obligation. A linear candidate needs feasibility and a bound; a network needs conservation at every node; a mixed strategy needs probabilities that sum to one and a guarantee against every response; an integer incumbent needs comparison with a valid relaxation bound; and a tail-risk calculation needs an explicit loss and probability convention.
Inequality direction carries meaning: capacity commonly uses total use ≤ availability, while service or nutrition requirements commonly use delivery ≥ need. A good written solution also distinguishes an exact reformulation from an approximation, states the conditions behind an extreme-point or integrality claim, and limits sensitivity conclusions to the range where the active structure remains unchanged.
These checks make the result reproducible even when software is used for the final solve.
Resource allocation with a dual certificate
- +1Enumerate the feasible vertices: (0,0), (4,0), (3,2), and (0,5).
- +1Evaluate the objective at each vertex to obtain 0, 12, 13, and 10.
- +1Choose (3,2), which is feasible and has the largest vertex value, 13.
- +1Use dual multipliers u=v=1. They are feasible and give 5u+8v=13, matching the primal value.
Key terms
- Optimisation Model
- A mathematical representation of choices, goals, and operational limits.
- Feasible Solution
- A choice that satisfies every constraint and variable-domain rule.
- Linear Program
- An optimisation model with a linear objective, linear constraints, and continuous variables.
- Basic Feasible Solution
- A feasible point determined by enough independent active constraints.
- Duality
- A relationship between a primal model and a companion bounding model.
- Shadow Price
- A local marginal value associated with changing a constraint bound.
- Integer Program
- A model requiring selected decision variables to take integer values.
- Flow Conservation
- A balance requiring inflow and outflow to match at a transshipment node.
- Mixed Strategy
- A probability distribution over actions in a game.
- Conditional Value at Risk
- The average loss in a specified worst tail.
QBUS2310 FAQ
What does Management Science teach?
It teaches how to formulate decisions as optimisation models, solve or bound those models, and interpret the result. The course connects linear and integer programming with geometry, duality, network flows, strategic games, and uncertainty, while emphasising assumptions and critical evaluation.
How is the unit assessed?
The official Semester 2 offering uses three written practical assignments, a mid-semester written test, and a final written exam. The published weights are 8%, 12%, 20%, 20%, and 40%, which total 100%. Check the current unit page for operational dates and instructions.
Do I need to know programming?
The unit uses optimisation software and Python-based tools, but mathematical formulation comes first. The published mid-semester format is written and has no programming component. Software should be used to solve a model you can define, audit, and explain.
What should I check after a solver returns an answer?
Check variable units, constraint directions, feasibility, objective value, and the solver status. Then find an independent certificate where possible, such as vertex comparison, a matching dual value, flow conservation, or a relaxation bound.
How should I prepare for the written tests?
Practise translating new stories into variables, objectives, and constraints without looking at a solution. Follow each formulation with a verification pass and a short managerial interpretation. Keep handwritten revision notes aligned with the current assessment instructions.
How to study for the exam
Learn by alternating modelling and auditing. On one day, formulate a new production, transport, inventory, or risk problem from prose. On the next, inspect a finished formulation and locate a deliberate defect in its units, indices, timing, or inequality direction. Keep a compact glossary of theorem conditions and a separate error log.
Recompute small examples by hand before using software, because geometry, conservation, and primal-dual bounds reveal mistakes that a status message cannot explain. For assessment preparation, practise complete written solutions: define variables, state the objective, list constraints and domains, solve or reason to a candidate, verify it independently, and translate the result back into the decision context.
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