MGMT20005 Cheatsheet · Business Decision Analysis

0 · Exam map course facts

“This is an open-book exam, which means you can bring 2 pages handwritten or typed notes related to the subject to the exam venue.” (MGMT20005 assessments information, 2026)

1 · Choose the method W1–W7

Exam move Before arithmetic: name objective, controllable choices, uncertainty/information, units and requested output.

1b · Model-answer spine course FAQ

1. Recognise: identify the model from the information structure, not from a keyword alone.
2. Represent: draw the table/tree/hierarchy/LP; label symbols and units.
3. Calculate: keep intermediate joints, node values, corners or report ranges visible.
4. Check: probability totals, reciprocity, feasibility, domains and allowable ranges.
5. Recommend: action + computed basis + assumption or material downside.

2 · No probabilities W1

profit regretrᵢⱼ = maxᵢ(payoffᵢⱼ) − payoffᵢⱼ
Choose i with minᵢ[maxⱼ(rᵢⱼ)]

cost regretrᵢⱼ = costᵢⱼ − minᵢ(costᵢⱼ)
Regrets must be ≥ 0.

Representation test

Payoff table: one choice across common states. Tree: timing, conditional events or later choices. Influence diagram: compact dependency picture, not a rollback calculation.

Trap Never invent equal probabilities. Put PROFIT or COST above the table before any max/min.

2b · Rule execution W1 FAQ

1. Confirm one objective and one common unit/time horizon.
2. List actions in rows and uncontrollable states in columns.
3. For maximax/maximin, write the relevant row summary beside every action before selecting.
4. For regret, write the best state benchmark above each column; subtract in the direction that keeps regret non-negative.
5. Take each row's maximum regret, then choose the smallest of those maxima.

Why answers differ: each rule optimises a different summary. None predicts the realised state. State the criterion and decisive value; do not call one rule universally “best”.

3 · Trees & expected value W2

chance nodeEV = Σ pⱼvⱼ, with Σpⱼ = 1

path probabilityP(A then B) = P(A) × P(B | A)

1. Draw time left → right; distinguish squares and circles.
2. Put probability on every chance branch; siblings are mutually exclusive and collectively exhaustive.
3. Put all local costs/benefits into terminal payoffs.
4. Roll back right → left: average at circles; select best objective branch at squares.
5. Mark the retained contingent strategy; then form its risk profile.

Node check If you maximise at a circle or average at a square, the rollback is wrong.

3b · Tree audit & risk W2 FAQ

A risk profile is the probability distribution of terminal payoffs generated by the retained strategy. Combine identical payoffs by adding probabilities of mutually exclusive paths; verify the final probabilities sum to one. Compare downside, spread or liquidity exposure without changing the EV arithmetic.

Conditional-path rule: multiply when every event on the same path must occur. Add only mutually exclusive paths when finding a report probability, a repeated payoff probability, or a complete total.

Close “Choose [branch] under expected value because EV=… versus …; however, the strategy still exposes the business to [specific endpoint].”

4 · Information & Bayes W3

BayesP(Sᵢ∩R)=P(Sᵢ)P(R|Sᵢ)
P(R)=ΣᵢP(Sᵢ∩R)
P(Sᵢ|R)=P(Sᵢ∩R)/P(R)

perfect informationEVwPI = Σⱼ pⱼ[maxᵢ payoffᵢⱼ]
EVPI = EVwPI − maxᵢ EVᵢ ≥ 0

sample informationFor each report r: update → choose best action.
EVwSI = ΣᵣP(r)[best conditional EV after r]
EVSI = EVwSI − best EV without information

Fee: compare fee with gross EVSI, or deduct it once from EVwSI. Information can have zero value even if probabilities move: if every report leaves the same action best, there is no decision improvement.

4b · Information workflow W3

1. For each report separately, calculate every state–report joint and the report marginal.
2. Divide joints by that report's marginal; posterior states under the report sum to one.
3. Recalculate action EVs using those posteriors; choose locally.
4. Weight those locally best EVs by report probabilities; report probabilities also sum to one.

Sanity chain: EVwPI ≥ EVwSI ≥ best EV without information; hence EVPI ≥ EVSI ≥ 0. If the chain fails, check whether the action was optimised within each report and whether the fee was deducted twice.

5 · Scoring & AHP W4

1. Build A: aᵢᵢ=1 and aⱼᵢ=1/aᵢⱼ.
2. Sum each column; divide each entry by its column total.
3. Average each normalised row → priority w; check Σw=1.
4. Using original A: compute Aw; ratios (Aw)ᵢ/wᵢ; average → λmax.
5. Compute CI and CR. Only then combine local priorities.

consistencyCI = (λmax − n)/(n − 1)
CR = CI/RIₙ
Course rule: CR < 0.10 acceptable; CR > 0.10 revise.

Reporting Preserve decimals until the final rank; if scores are close, name the contribution or contested weight that could reverse them.

5b · Combine priorities W4

overall AHP priorityOverall priority of alternative i = Σⱼ(criterion priorityⱼ × local priorityᵢⱼ)

Weighted scoring: multiply each given weight × rating, then sum across criteria. AHP: derive priorities from reciprocal comparisons, test consistency, then synthesise.

Reciprocity: if item A is 3 times item B, reverse entry = 1/3. Fill one triangle, reflect reciprocals, keep diagonal entries 1. Rounding can slightly disturb totals; retain at least four decimals until the final result.

6 · LP + sensitivity W5–W7

generic LPChoose xⱼ (meaning + unit + period).
Max/min z = Σⱼcⱼxⱼ
s.t. Σⱼaᵢⱼxⱼ ≤, = or ≥ bᵢ; domains.

Validity checks

Linear means fixed coefficient × one variable: no variable products, powers or nonlinear functions. Substitute a proposed solution into every constraint; feasibility is not optimality. Binding: LHS=RHS. Slack: RHS−LHS for ≤. Infeasible = no common point; unbounded = no finite improving limit—first audit signs, directions and missing bounds.

local RHS changeΔz = shadow price × ΔRHS, only inside RHS range.

Re-solve Outside a range; unsupported simultaneous change; changed constraint coefficient; or changed structure.

7 · Flow applications W7

Opening inventoryₜ + Productionₜ = Demandₜ + Ending inventoryₜ
Opening inventoryₜ₊₁ = Ending inventoryₜ

W1 · Launch rules W1 worked

Regret matrix

State benchmarks: weak = 42; strong = 138.

Answer: National under maximax; Pilot under maximin with protected payoff 42; Regional under minimax regret with worst regret 46.

Trap Regret benchmarks are column-by-column states, never row-by-row alternatives.

Fast recall · cost W1

Optimistic cost: choose smallest row minimum. Protective cost: choose smallest row maximum. Regret: cost − state minimum; minimise maximum regret.

Validation: profit-regret entries equal state maximum minus payoff; cost-regret entries equal cost minus state minimum. Every regret is zero for at least one action in each state and never negative. The selected action minimises its maximum regret, not its sum.

Representation choice: use a payoff table for one present decision across common states. Move to a tree when later decisions depend on earlier events, probabilities attach to sequential branches, or timing changes the available strategy.

W2 · Beta vs national W2 worked

EV(Beta)=.45(38)+.55(24)=17.10+13.20=30.30

EV(National)=.45(105)+.55(−27)=47.25−14.85=32.40

Decision: National under EV because 32.40 exceeds 30.30 by 2.10. The risk profile still contains 105 (.45) and −27 (.55); 32.40 is not a realised payoff.

Write “Under an expected-value criterion …” if the manager could reasonably reject the higher EV because of downside or survival constraints.

Tree construction marks W2

Distinct node shapes · chronological branches · conditional labels · probabilities · full terminal payoffs · chance-node EVs · retained branches · final contingent strategy.

Risk profile: after retaining the strategy, list each terminal payoff and its path probability. If different paths end at the same payoff, add their mutually exclusive probabilities. The profile—not the EV alone—supports discussion of downside, liquidity or survival risk.

Timing discipline: a decision branch can depend only on information observed before that decision. A tree that lets management choose after learning an unobserved state overstates value and behaves like perfect information.

Final check: name the retained strategy, its root EV and one material endpoint from its risk profile.

Audit backwards Trace any unexpected root value from terminal payoff → chance-node arithmetic → retained decision branch.

W3 · Warning update W3 worked

1. Volatile∩Warning = .30(.80)=.24.
2. Stable∩Warning = .70(.20)=.14.
3. P(Warning)=.24+.14=.38.
4. P(Volatile|Warning)=.24/.38=.6316; P(Stable|Warning)=.3684.

Interpret: Warning raises volatile-demand probability from .30 to .6316, but does not establish volatility with certainty.

Direction test Inputs are P(report | state); outputs are P(state | report). Posteriors for one report must sum to 1.

Information-value order W3

Contingent strategy: calculate an action EV inside each report using that report's posterior probabilities; retain the best action locally. Then average those retained branch values using report probabilities. Using state priors at the outer layer mixes levels.

Zero-value test: if the same action stays optimal after every report, EVSI=0 even when posteriors differ. The report has changed belief but not the decision.

Ceiling test: EVSI cannot exceed EVPI. Sample information does not reveal the state perfectly, so it cannot rationally command a larger gross price than perfect information about the same uncertainty.

Keep report labels attached to every posterior and retained action so the outer expectation can be audited branch by branch.

Fee trap Keep EVSI gross through comparison; if the tree already includes the fee, do not subtract it again.

W4 · AHP matrix W4 worked

Rows R,C,S: [1,2,4], [1/2,1,2], [1/4,1/2,1].

Aw ≈ (1.7142,.8571,.4287)
(Aw)ᵢ/wᵢ = (3,3,3) → λmax=3
CI=(3−3)/(3−1)=0
RI(3)=.58 → CR=0/.58=0

Answer: Reliability > Cost > Speed. CR=0<.10, so judgments are perfectly consistent.

Matrix audit Diagonal=1; opposite cells reciprocal; priorities sum to 1. Use the original matrix for Aw.

Scoring shortcut W4

Keep criterion weights separate from performance ratings. Show each wⱼrᵢⱼ contribution; do not multiply a rating by the wrong criterion weight. For a narrow lead, report sensitivity to the contested weight.

Full AHP synthesis: repeat the pairwise-priority calculation for criteria and for alternatives under every criterion. Multiply each local alternative priority by its criterion priority; sum across criteria. Final alternative priorities should sum to one.

Consistency sequence: original A × w → weighted-sum vector; divide componentwise by w; average ratios → λmax; then CI and CR. Do not use the normalised matrix in the Aw step.

When CR is high: locate contradictory pairwise entries, ask for revised judgments, and recompute. A mathematical ranking from inconsistent judgments is not a defensible recommendation.

W5/6 · LP then what-if worked

Max z=40x+30y
s.t. 2x+y≤40; x+2y≤50; x,y≥0

Intersection: y=40−2x. Substitute into x+2y=50: x+80−4x=50 → x=10, y=20. Corners give z: 0, 800, 750, 1000. Check: 2(10)+20=40; 10+2(20)=50.

Coefficient scenario

x coefficient 40; allowable increase 10, decrease 5 → range [35,50]. New coefficient 46 is inside, so x=10,y=20 remain optimal.

znew=46(10)+30(20)=460+600=1060

RHS scenario

Packaging RHS 80; shadow price 6; allowable increase 12, decrease 20 → range [60,92]. Nine extra units give new RHS 89, inside range.

Keep scenarios separate: coefficient change → 1060; RHS change → 1054. They are one-at-a-time conclusions.

LP answer audit W5–W7

Linearity: each term is a fixed coefficient times one variable. No variable products, powers or nonlinear functions. A relative rule remains linear when written, for example, x≥.30(x + y).

Feasibility: substitute into every constraint/domain. Optimality still needs all feasible corners or a valid solve.

Application transfer: inventory links periods by carryover; portfolio decisions send cash to maturity nodes; media models preserve budget and mix. Draw the conserved flow before indexed balances.

Method chooser exam routing

Error clinic all weeks

Recommendation stem

“Using [method], choose [action/plan] because [computed comparison]. This conclusion assumes [probabilities/linearity/range]; the main limitation or risk is [specific feature].”

Last 30 seconds Units? Probabilities sum to one? Signs/directions? Range tested? Decision and objective both stated? Limitation named?

Fast definitions recall

Terminal payoff is the full path consequence. Posterior is a state probability after a report. Priority vector is derived AHP weights summing to one. Feasible region satisfies all restrictions. Extreme point is a feasible vertex.