MGMT90280 Managerial Decision Analytics

How MGMT90280 is assessed

What MGMT90280 covers

The whole subject → one exam-ready map, from optimisation to simulation to forecasting. Each topic links to its free chapter guide and to the recurring exam question it feeds.

It runs across three strands: prescriptive optimisation (linear, integer and nonlinear programming with Excel Solver and sensitivity analysis), decision-making under uncertainty (probability distributions and Monte Carlo simulation), and data analytics (cluster analysis, association rules, regression, time-series forecasting and classification trees, largely in Excel with the Analysis ToolPak and Analytic Solver Basic).

Assessment in Managerial Decision Analytics is a timed Assignment 1 (20%), a group Assignment 2 report (25%) with a short presentation (5%), and a dominant final exam (50%). This free guide mirrors MGMT90280 Managerial Decision Analytics as taught at the University of Melbourne and maps every topic to the 50% open-book final; the full study bible then works each method end to end.

Confirm exact dates, weights and rules for your cohort on Moodle / the LMS.

Worked example · free

Nonlinear programming: two-plant profit maximisation

Key terms

Decision variable

An unknown a model solves for — e.g. hours to assign or units to produce. A linear program has a linear objective (Max or Min) in the decision variables, linear constraints (≤, =, ≥) and non-negativity (variables ≥ 0).

Shadow price (dual value)

The change in the optimal objective value per one-unit increase in a constraint’s right-hand side, valid only within the allowable increase/decrease range. A binding constraint (slack 0) generally has a non-zero shadow price; a non-binding constraint (slack > 0) has a shadow price of 0.

Binding vs non-binding constraint

A constraint is binding when it holds with equality at the optimum (slack/surplus = 0) and non-binding when there is slack left over. Relaxing a non-binding constraint does not change the optimum — the exam’s classic sensitivity read.

LP relaxation

Dropping the integer/binary requirement from an integer program. Because it enlarges the feasible region, for a maximisation its optimum is an upper bound on the integer optimum (a lower bound for a minimisation); used to bound and prune the search.

Monte Carlo simulation

Automated what-if analysis under uncertainty: each uncertain input is a random draw from its distribution, and many iterations (≥1,000) build an output distribution for risk analysis. It handles many uncertain variables but does not guarantee an optimum.

Inverse-transform sampling

Turning a uniform random number RN from RAND() into a sample: Uniform(a,b) via a+(b−a)·RN, Normal via NORM.INV(RN,μ,σ), and a discrete distribution by mapping RN through the cumulative-probability cutoffs.

R² and adjusted R²

R² = SSR/SST is the fraction of variation in y a regression explains (0–1). R² only rises as predictors are added, so adjusted R² = 1 − (1−R²)(n−1)/(n−p−1) penalises weak predictors and is the fair yardstick when comparing models.

Overall F-test vs coefficient t-test

The overall F = MSR/MSE (upper-tailed, df p and n−p−1) tests H₀: all slopes = 0 — is the model any good? Each coefficient t = bₖ/SE(bₖ) (two-tailed, df n−p−1) tests H₀: βₖ = 0 — does that predictor matter? Regression uses t/F, not z, because σ is estimated by MSE.

p-value reject-rule

Reject H₀ when the p-value < α (typically 0.05); otherwise fail to reject. “Fail to reject” means insufficient evidence, not proof the effect is zero. A 95% confidence interval for a coefficient that excludes 0 is equivalent to rejecting H₀ at 5%.

Confidence and lift (association rules)

For a rule “if A then C”: confidence = support(A∪C)/support(A) = P(C∣A); lift = confidence ÷ (support(C)/N). Lift > 1 means the rule beats random (useful), = 1 means independent, < 1 worse than random — so always check lift, not confidence alone.

Euclidean distance & standardisation

The straight-line distance d = √Σ(uⱼ−vⱼ)² between two observations, used to assign a point to its nearest cluster centroid. Because it is scale-sensitive, standardise each variable to a z-score first so no single unit dominates.

Confusion matrix metrics

From counts of TN, FP, FN, TP: accuracy = 1 − overall error; sensitivity (recall) = TP/(TP+FN); specificity = TN/(TN+FP); precision = TP/(TP+FP); F1 = 2·TP/(2·TP+FP+FN). ROC plots sensitivity vs 1−specificity; a larger AUC means a better classifier.

Overfitting

When a model fits the training data far better than it generalises — the symptom is training error much lower than validation error. Data is partitioned into training, validation and test sets, and a classification tree is pruned on the validation set to reduce it.

MGMT90280 FAQ

Questions students ask in each MGMT90280 chapter

Why must percentage rules be linearised before Solver can use them?

A rule like 'x₁ must be at least 40% of x₁+x₂' written as x₁/(x₁+x₂) ≥ 0.40 is a ratio, which is non-linear, so Simplex LP cannot handle it. Multiply both sides by the (non-negative) denominator and move every variable to one side: x₁ − 0.40(x₁+x₂) ≥ 0, i.e. 0.60x₁ − 0.40x₂ ≥ 0. The inequality direction never flips because you multiply by a non-negative quantity, and the result is a clean linear constraint with a constant right-hand side. Chapter 01 · Introduction to MDA & Linear Programming (LP) + Sensitivity Analysis

Can I just round the LP-relaxation answer to get the integer solution?

Not reliably. If the relaxation already comes out whole, it also solves the ILP. Otherwise rounding can be infeasible (it breaks a constraint) or feasible but sub-optimal (a better integer point lies at a different corner). The relaxation value is only a bound — an upper bound for a max, a lower bound for a min — so you should re-solve with the integer or binary requirement in Solver rather than round. Chapter 02 · Integer Linear Programming (ILP)

Do I need calculus, or is Excel Solver enough?

Both. The exam rewards the by-hand method — write Profit = Revenue − Cost, set the derivative(s) to zero, run the feasibility check, and substitute on the binding boundary if needed — and you should be able to reproduce or check the answer with Excel Solver's GRG Nonlinear engine. A final number with no working scores little. Chapter 03 · Nonlinear Programming (NLP)

When do I use the binomial versus the Poisson?

Use the binomial when you have a fixed number of trials n, each a success/failure with the same probability p, and you count successes (e.g. how many of 15 applications are declined). Use the Poisson when you count events over an interval at an average rate μ with no fixed number of trials (e.g. calls per hour); its giveaway is that the mean equals the variance. Chapter 04 · Probability Distributions

Why do you need at least about 1,000 iterations?

A handful of iterations — what you can do by hand in an exam — only illustrates the method; the simulated output is still very noisy. Running many iterations (≥ 1,000) lets the output distribution settle so the average, spread and probabilities are stable enough to base a decision on. Whenever you draw a conclusion from a short hand-run, say explicitly that a real study needs many more iterations. Chapter 05 · Monte Carlo Simulation

When should I use Jaccard instead of the matching coefficient?

Use Jaccard when a joint absence (both records showing 0) is not genuine similarity. For one-hot-encoded categories or market-basket flags, almost every pair of records shares many 0s, so the matching coefficient inflates similarity through those joint absences; Jaccard removes the 0-0 positions from the denominator, giving the honest score. Use matching only when a shared 0 really is meaningful agreement. Chapter 06 · Descriptive Data Mining: Cluster Analysis

Is association-rule mining on the MGMT90280 final exam?

Yes. In the past papers the final is five compulsory 20-mark questions, and descriptive data mining is one of them — bundling similarity coefficients, hierarchical clustering and association rules. The association-rule part is a formula-driven block: compute support, confidence and lift from given support counts, then state the lift-greater-than-1 verdict. The final is worth 50% and is open-book (Casio FX-82, unrestricted student notes); confirm the exact structure and the ~November 2026 exam date on the LMS. Chapter 07 · Descriptive Data Mining: Association Rules

When do I reject the null hypothesis in a regression test?

Use one consistent rule: reject H₀ when the p-value is less than α (typically 0.05), and fail to reject when it is not. The overall F-test is upper-tailed (a large F, small p, means the model explains real variation). Each coefficient t-test is two-tailed with df = n−p−1, testing βₖ = 0 against βₖ ≠ 0. 'Fail to reject' means there is not enough evidence that the coefficient differs from zero — it is not proof the effect is exactly zero. Equivalently, a 95% confidence interval for a coefficient that excludes 0 corresponds to rejecting H₀ at the 5% level. Chapter 08 · Regression Modelling

When do I use smoothing versus regression forecasting?

Plot the series first. If it is roughly horizontal — fluctuating around a constant mean with no drift — use a moving average or exponential smoothing. If it drifts (trend) and/or repeats within the year (seasonal), fit a regression with a trend term and seasonal dummies, because a moving average cannot climb a trend or bend with a season. Chapter 09 · Time Series Analysis & Forecasting

What is the difference between precision and sensitivity (recall)?

They share the true-positive count but use different denominators. Sensitivity / recall = n11/(n11+n10) reads across the actual-positive row: of everyone who truly is positive, what fraction did the model catch? Precision = n11/(n11+n01) reads down the predicted-positive column: of everyone the model flagged, what fraction truly is positive? Optimise recall when missing a positive (a false negative) is costly, and precision when acting on a false alarm (a false positive) is costly. Chapter 10 · Predictive Data Mining: Classification Trees & Performance Measures

How to study for the exam

Treat MGMT90280 Managerial Decision Analytics as a method-selection subject: the University of Melbourne final is open-book, so marks come from naming the right tool, doing one clean calculation and writing the explicit decision — not from memorising formulas.

Because the exam is 50% and spans the whole unit, keep up week to week and build a one-page menu that links each cue to its method: percentage rules → linearise the LP and read the shadow price/slack; quadratic profit → set ∂Z/∂Q = 0 then check the binding bound; “probability that” → the right distribution and Excel function; “simulate” → inverse-transform sampling; “if…then” → confidence and lift; “significant?” → F-test then t-tests with the reject rule p < α; “forecast” → regression with trend and seasonal dummies, compared on adjusted R²/MSE.

Pace by the marks at about 1.2 minutes per mark (a 20-mark question ≈ 24 minutes) and never leave a question blank — bank the part-marks for a model, a labelled table or a stated hypothesis. Rehearse with the re-authored practice set, then use SWOTVAC to close gaps; a strong final protects your WAM because it is half the subject. Confirm the exam date, permitted materials and any hurdle on Moodle.

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