Objective 3 · 13–22%

Decision Modeling & Optimization

Data, Models & Decisions (Bertsimas & Freund) Ch 5, 7, 8, 9 + Deciding How to Decide + DICE. This is the fastest objective to learn, but it's worth about 10–20 points, and almost every sitting has one genuinely hard formulate-and-solve question. The skill that gets tested: read a messy business story → recognize the model type → write decision variables, objective and constraints correctly → interpret the output in business terms.

DMD overview: recognize the problem typeData, Models & Decisions — all chapters (XP key points)

What you must get out of it: On the exam they do not tell you "this is a binary problem." Spot the signals in the wording, choose linear / nonlinear / discrete, formulate it cleanly, and interpret the results (including shadow prices) to make a recommendation. You should also be able to critique a model and explain when you'd use each tool.

Decision guide: which model is this?

Q1. Are you choosing values to optimize something, under constraints? If no (you're estimating the distribution of an outcome driven by several random inputs) → Simulation (Ch 5). A simulation evaluates the policy you give it. It does not optimize.

Q2. Must any decision be a whole number or yes/no? (build / don't build, choose project, open plant, number of trucks, fixed setup cost, "either…or", "if…then", "at most k") → Discrete: integer / binary / mixed (Ch 9)

Q3. Is anything in the objective or constraints non-linear? (decision variables multiplied together, price × quantity where demand depends on price, squared terms, variance/covariance, distances √(Δx²+Δy²), ratios of variables) → Nonlinear (Ch 8)

Q4. Otherwise (every term is a constant × a decision variable, summed) → Linear optimization (Ch 7). Are there uncertain future states with probabilities and decisions after they're revealed? → LP under uncertainty (two-stage)

Linear (Ch 7)

Production mix, blending, sourcing, staffing, transport
Objective & constraints = Σ (constant × variable)
Optimum at a corner of the polygon feasible region
Shadow prices valid over an allowable range

Nonlinear (Ch 8)

Portfolio: min variance (w_iw_jσ_ij) for a target return
Pricing/production: (P − c)·D(P) with demand depending on price
Location: minimize weighted √ distances
Optimum can be interior; there may be local optima

Discrete (Ch 9)

Binary = on/off: select projects, open sites
Integer: whole units (planes, trucks, staff)
Mixed: binary + integer + continuous (fixed-charge)
Solved by branch-and-bound; much harder than LP

Simulation (Ch 5)

Several random variables combined (price × demand × yield)
Output = distribution, P(event), mean, sd
Run once per candidate strategy, then compare
No optimizing ability

Memory hook"S-D-N-L": ask in this order. Simulate? (no optimizing, just uncertainty) → Discrete? (whole/yes-no) → Nonlinear? (variables multiply, square or root) → else Linear.

How it gets tested

Formulate from a long description (spot that a binary is needed; spot a sunk cost that must be left out)
Solve small problems by hand or graphically (no Excel Solver in the exam)
Interpret solver output and shadow prices → make a recommendation
Critique a colleague's model (missing constraint, wrong type, sunk cost included, linear when it should be nonlinear)
The DMD case modules are on the syllabus too

Self-test: classify these 5 situations

An airline chooses fares for two cabins, and demand in each cabin falls linearly with its fare. → Nonlinear (revenue = P × (a − bP) is quadratic).
An insurer picks which 3 of 8 IT projects to fund within a $5M budget. → Binary.
A coffee chain decides pounds of beans to buy from 4 suppliers to meet a blend-quality average at min cost. → Linear (quality % constraint can be linearized).
A tire maker wants the distribution of next year's profit given random rubber price, demand and FX. → Simulation.
Decide whether to open each of 3 warehouses (fixed cost if open) and how many units to ship from each. → Mixed-integer (binary open/close + continuous shipments, x ≤ M·y).

Ch 5 — Simulation Modeling: Concepts & PracticeBertsimas & Freund, Ch 5

What you must get out of it: why we simulate (combinations of random variables rarely have a closed-form distribution), how to generate draws from a discrete or continuous distribution with uniform random numbers, how to build a small simulation by hand and interpret output (Example 5.8 style) to make a well-justified recommendation.

Why simulate?

Forecast the consequences of management decisions before making them
Combining random variables (sum, product…) rarely gives a convenient distribution. The exception is a sum of normals, which is still normal
Uses: manufacturing operations, service queues (banking, air travel, food service), pricing complex derivatives
Textbook example: random fish price × demand at the port

What it gives you (and doesn't)

✔ Estimated shape of the distribution of quantities of interest
✔ Estimated probabilities of events (e.g. P(loss))
✔ Means and standard deviations
✘ No optimal-decision capability, unlike a decision tree. With several strategies, run a simulation for each and compare

Generating sample data

Discrete distribution (3 steps)

Divide [0,1] into non-overlapping intervals, one per possible value, width = probability
Generate uniform U(0,1) random numbers
Assign each U the value whose interval contains it

Continuous distribution (inverse CDF)

Generate U ~ Uniform(0,1)
Solve F(y) = P(Y ≤ y) = U for y, and use y as the draw

Normal y = μ + σ · Φ⁻¹(U)

e.g. U = 0.8413 → Φ⁻¹ = 1 → y = μ + σ. (Exam on paper: use the normal table. XP flags the p.210 normal example as exam-like.)

Mini demo: map random numbers to a discrete distribution

Values (comma-separated) Probabilities

Uniform random numbers U

Normal inverse-CDF draw

μσU

Interpreting simulation output (Example 5.8 style)

Asked for	How to get it from n simulated trials
Expected value	sample mean x̄
Variability / risk	sample std dev s, percentiles, histogram shape (skew, fat tails)
P(event), e.g. P(profit < 0)	(# trials where event occurred) / n
Precision of the mean estimate	95% CI ≈ x̄ ± 1.96 · s / √n (more trials → narrower)
Which strategy is better?	Compare each strategy's mean and risk (sd, P(loss), worst percentile) against management's objective and risk appetite

Confidence interval for the simulated mean x̄ ± 1.96 · s√n

Gaining managerial confidence in a simulation model depends on 3 things

A good understanding of the underlying management problem
Using probability and statistics correctly
Communicating these concepts effectively

Memory hook"Simulation describes, optimization prescribes." Interval widths equal probabilities, like slicing a 0–1 ruler.

How it gets tested

Build and quickly calculate a simple simulation by hand from given random numbers (past exams have done this)
2-point "interpret this output" question: P(event), mean, recommend a strategy
Outline how you would set up a simulation: which variables are random, what distributions, what output you'd track, how many trials
Applied to case-study style businesses (queues, operations, pricing)

Traps

Claiming the simulation "found the optimal strategy." It didn't. You compared the strategies you ran
Using the average of each input and plugging it in once. The average of a function ≠ function of averages (this is exactly why you simulate)
Ignoring correlation between inputs (e.g. price and demand)
Reporting only the mean when the question is about risk

Self-test: Demand is 10 (p=.3), 20 (p=.5), 30 (p=.2). Price per unit is N(5, 1). U_demand = 0.25, 0.62, 0.91. U_price = 0.5, 0.8413, 0.1587. Simulate revenue.

Intervals: 10 → [0, .3), 20 → [.3, .8), 30 → [.8, 1).

Trial	U_d → Demand	U_p → Φ⁻¹ → Price	Revenue
1	.25 → 10	.5 → 0 → 5	50
2	.62 → 20	.8413 → 1 → 6	120
3	.91 → 30	.1587 → −1 → 4	120

Sample mean revenue = 96.7. With 3 trials this is far too few to rely on, so say so and recommend more trials (and a CI).

Self-test: 1,000 trials of strategy A give mean profit 2.1M, s = 1.5M, and 180 trials with a loss. Strategy B gives mean 1.8M, s = 0.6M, 40 losses. Recommend.

P(loss): A = 18%, B = 4%. 95% CI for A's mean: 2.1 ± 1.96·1.5/√1000 = 2.1 ± 0.09. A has a higher expected profit (~+0.3M, statistically meaningful) but much higher risk. Recommendation depends on risk appetite: a capital-constrained or risk-averse firm (e.g. one near a solvency threshold) should choose B. A well-capitalized firm maximizing expected value might choose A. State the trade-off explicitly and tie it to the company in the question.

Ch 7 — Linear OptimizationBertsimas & Freund, Ch 7 (incl. sensitivity & LP under uncertainty)

What you must get out of it: formulate an LP from words (variables, objective, constraints, non-negativity), solve 2-variable problems graphically, identify binding constraints, and use shadow prices correctly within their allowable range to recommend actions. Also be able to build a two-stage LP under uncertainty.

Vocabulary

Objective

What to optimize (min cost, max profit)

Decision variables

The unknowns you control (tons of coal from each mine). State units.

Objective function

Objective written in terms of decision variables

Constraints

Limits on the variables (≤, ≥, =). Put the variables on the LHS

Non-negativity

x ≥ 0. Easy to forget!

Feasible / optimal solution

Feasible = satisfies all constraints. Optimal = feasible with the best objective value

Binding vs non-binding

Binding = holds with equality at the optimum (line passes through it). Non-binding = has slack

Special outcomes

Multiple optima (isoquant parallel to a binding edge), unbounded (objective → ∞), infeasible (no point satisfies everything → relax constraints)

Formulation rules of thumb

Variables & objective

"What decisions must I make?" → one variable per decision
Typical objective: max revenue − cost, or min cost − revenue
Count every cost and revenue exactly once
Leave out sunk and fixed costs: they don't change with the decision (unless a binary decides whether the cost is incurred)
There is often no unique formulation. Equality vs inequality takes judgment

4 constraint types

Resource: can't use more steel or labor than is available
Capacity: plant can make at most N units
Quality: average content must meet a standard (linearize it! see below)
Policy: a management rule, e.g. ≥ 50% of coal from union mines

Linearizing a % / quality constraint (p.366) 0.02x₁ + 0.05x₂x₁ + x₂ ≤ 0.03 ⇒ 0.02x₁ + 0.05x₂ ≤ 0.03x₁ + 0.03x₂ ⇒ −0.01x₁ + 0.02x₂ ≤ 0

Multiply through by the (positive) denominator so the constraint stays linear. Policy constraints like "at least 50% from union mines" work the same way: x_U ≥ 0.5(x_U + x_N).

Graphical method: 5 steps (2 variables only)

1Plot non-negativity (x, y ≥ 0)

2Plot each constraint line + shade the feasible side

3Feasible region = intersection (a polygon)

4Draw objective isoquants (parallel lines)

5Slide the isoquant in the improving direction, and the last corner touched is optimal

Worked example

Max profit 30x + 40y (x = chairs, y = tables). Labor 2x + 4y ≤ 40 hrs · Machine 3x + 2y ≤ 36 hrs · Demand x ≤ 10 · x, y ≥ 0

Corner	How found	Profit
(0, 0)	origin	0
(10, 0)	demand ∩ y=0	300
(10, 3)	demand ∩ machine	420
(8, 6)	labor ∩ machine	480 ★
(0, 10)	labor ∩ x=0	400

Binding: labor (2·8 + 4·6 = 40 ✓) and machine (3·8 + 2·6 = 36 ✓). Non-binding: demand (x = 8 < 10, slack 2), so its shadow price = 0.

Fast exam trick: just evaluate the objective at every corner of the feasible polygon. The LP optimum is always at one (simplex walks corner to corner, "pivoting" to a better one until no better neighbor exists).

Sensitivity analysis & shadow prices

Definition Shadow price = change in optimal objective value per +1 unit of a constraint's RHS, all else fixed = ∂ (optimal objective)∂ RHS

1One per constraintEvery constraint has a shadow price

2Unitsobjective units ÷ constraint units (e.g. $ / labor-hr)

3Decision-usefulOften very valuable to management

4Marginal valueOf the resource in that constraint (most you'd pay for one more unit)

5A derivativeOf optimal objective w.r.t. RHS

Range information

Solver output gives an allowable increase / decrease for each RHS. The shadow price holds only within that range. Beyond it, the binding set changes and you must re-solve.

Non-binding ⇒ shadow price = 0

There's already slack, so more of that resource adds nothing. The reverse needs care: a binding constraint usually has a non-zero shadow price.

Sensitivity report for the worked example
Constraint	Final LHS	RHS	Shadow price	Allow. increase	Allow. decrease
Labor (hrs)	40	40	$7.50 / hr	32	8
Machine (hrs)	36	36	$5.00 / hr	4	16
Demand (chairs)	8	10	$0	∞	2

Check: 7.5×40 + 5×36 + 0×10 = 480 = optimal profit. (Duals solve 2a+3b = 30, 4a+2b = 40.) Labor stays valid while the binding intersection stays feasible: 32 ≤ L ≤ 72. Machine: 20 ≤ M ≤ 40.

Self-test: interpret the sensitivity report (3 management proposals)

Hire 10 temp labor hours at $6/hr? 10 ≤ allowable increase 32, so the shadow price holds: gain 10 × 7.50 = $75 vs cost $60 → +$15, do it. Breakeven wage = $7.50/hr.
Rent 8 extra machine hours at $7/hr? Shadow price $5 < $7 → each hour loses money, so no. Also, only the first 4 hours are covered by the $5 shadow price. Beyond 4, re-solve (the marginal value drops, here to $0 once demand x≤10 binds).
Marketing campaign to raise chair demand to 14? Demand is non-binding (shadow price 0) → no profit gain. Capacity, not demand, is the bottleneck. Spend on labor instead.

Linear optimization under uncertainty (two-stage)

Think of it as a decision tree inside an LP: today's decisions, then one set of recourse variables per future state, and the objective is the expected value across states.

1Split decisions: stage 1 (now) vs stage 2 (after uncertainty resolves)

2Enumerate future states, their data & probabilities

3Variables: one per stage-1 decision + one per stage-2 decision per state

4Write constraints for each state

5Objective = stage-1 contribution + Σ p_s × stage-2 contribution in state s

Self-test: formulate. Buy capacity K now at $4/unit. Next year demand is 100 (p=0.6) or 60 (p=0.4). Each unit sold earns $10 margin; you can't sell more than K or than demand.

Variables: K = capacity bought now (stage 1). s_H, s_L = units sold in high/low demand state (stage 2).

Max −4K + 0.6(10 s_H) + 0.4(10 s_L)

s.t. s_H ≤ K, s_H ≤ 100, s_L ≤ K, s_L ≤ 60, K, s_H, s_L ≥ 0.

Solution logic: capacity from 0–60 is used in both states (marginal value 10 − 4 = +6). Capacity from 60–100 is used only in the high state (0.6×10 − 4 = +2 > 0). → K = 100, expected profit = −400 + 600 + 240 = 440. If the cost were $7, the 60–100 tranche would be worth 6 − 7 < 0 → K = 60.

Memory hookShadow price = "what's one more unit worth, and for how long?" The value is the price. The allowable range is how long it lasts.

How it gets tested

Turn a complex case paragraph into an LP (often with a policy or quality % constraint)
Graph and solve a 2-variable LP quickly
High-cognitive: apply shadow-price data to a specific proposal (buy more resource? at what price? how much?) — XP: "a classic high-cognitive level question"
Practice: Example 7.2, Section 7.5.4 / Table 7.8 (explain every shadow price), Q&A p.364, quality constraint p.366

Traps

Forgetting non-negativity
Including sunk costs (already-paid leases, past R&D) in the objective
Using a shadow price outside its allowable range
Leaving a ratio constraint non-linear instead of multiplying through
Double-counting costs (e.g. per-unit cost and also total cost)
Saying a non-binding resource is "valuable." Its shadow price is 0

Ch 8 — Nonlinear OptimizationBertsimas & Freund, Ch 8

What you must get out of it: recognize and formulate the 3 classic nonlinear problems (portfolio, production/pricing, facility location). Know that the optimum may be interior and may be only a local optimum. Know when local = global (convex min / concave max). Know that shadow prices hold only for small changes.

① Portfolio (risk vs return)

Min Var = Σ_iΣ_j w_iw_jσ_ij = Σ w_i²σ_i² + 2Σ_i<j w_iw_jσ_ij

s.t. Σ w_i = 1 · Σ w_iμ_i ≥ target (e.g. 11%) · w_i ≥ 0 (+ extra policy limits, e.g. ≥ x% tech)

Re-solve for many targets → the efficient frontier (lowest risk for each return).

② Production & pricing

Max (P_W − c_W)·W + (P_P − c_P)·P

where demand depends on price, e.g. W ≤ 565 − 0.5·P_W and P ≤ 325 − 0.25·P_P, plus capacity constraints.

Price × quantity gives a quadratic objective. Optimum is often interior.

③ Facility location

Min Σ_i 2 · n_i · √((x − a_i)² + (y − b_i)²)

n_i = daily trips to site i, 2 = there and back, (a_i, b_i) = site coordinates, s.t. allowed-zone constraints on (x, y).

Graphical insights

The optimum need not be at a corner, nor even on the boundary
If it's on the boundary, it's where the feasible region just touches the best isoquant (tangency)
Isoquants can be circles (distance), ellipses (variance)…

Local vs global

Local optimum: best among nearby feasible points, but maybe not the global best
Calculus-based solvers usually find only a local optimum
General NLPs can be very hard even with a computer. Try several starting points
Book picture: "kidney" (XP: "baby seal") shaped region, local min A, global min B

When does local = global? (the easy classes)

	Convex minimization	Concave maximization
Objective	Convex (∪ bowl) to be minimized	Concave (∩ hill) to be maximized
Equality constraints	must be linear
"≤" constraints	must be convex functions
"≥" constraints	must be concave functions
Result	every local optimum is a global optimum. Linear constraints always qualify (linear is both convex and concave)

Portfolio variance (min) is convex, so portfolio problems are easy. Revenue P·(a − bP) is concave, so the max-pricing problem is easy.

Memory hookconVex looks like a V (bowl), so you minimize it: drop a marble and it rolls to the one bottom. ConCAVE is a cave roof (hill), so you maximize it. Constraints: "≤ convex, ≥ concave, = linear."

How it gets tested

Recognize that a case situation is nonlinear and formulate it (use the 3 patterns as templates)
Explain why the solver's answer might not be the true optimum, and what you'd do
Interpret NLP shadow prices with caution
Practice: Examples 8.1–8.3, Exercise 8.6 (XP video)

Traps

Assuming the NLP optimum is at a corner (that's LP only)
Using NLP shadow prices for large changes. They're valid only for very small Δ
Forgetting Σw = 1 or w ≥ 0 (no shorting unless allowed) in portfolio problems
Writing a variance without the covariance (cross) terms

Self-test: single product, demand D = 200 − 2P, unit cost 20. Optimal price?

Profit = (P − 20)(200 − 2P) = −2P² + 240P − 4000, which is concave, so the local max is the global max. dπ/dP = −4P + 240 = 0 → P = 60, D = 80, profit = 40 × 80 = 3,200. If capacity were 60 units, the constraint binds: D = 60 → P = 70, profit = 3,000 (on the boundary, not at the unconstrained optimum).

Ch 9 — Discrete OptimizationBertsimas & Freund, Ch 9 (special constraints pp.455–456)

What you must get out of it: when variables must be integer or binary, how to model logical conditions with binary variables (the trickiest exam skill here), and the logic of branch-and-bound.

ℤ

Integer model

All variables integer (linear objective & constraints). Small production runs where you can't make 2.4 planes.

0/1

Binary model

All variables 0 or 1: on/off switches. Project selection, site opening.

mix

Mixed-integer

Binary + integer + continuous. Fixed-charge / setup-cost problems.

Graphical view

Feasible region = a set of discrete points, not a polygon
No "corner points". Border points needn't be where two constraints meet
Rounding the LP answer can be infeasible or sub-optimal

Solvability

Much harder than LP
No system of linear equations whose solution is the optimum
Solved by branch-and-bound

Binary modelling cheat table

Condition (in words)	Constraint (x_i ∈ {0,1})
If project A is chosen then B must be chosen	x_B ≥ x_A (i.e. x_B − x_A ≥ 0). Book: "if 4 then 3" → x₃ ≥ x₄
A only if both B and C	x_A ≤ x_B and x_A ≤ x_C
A and B are mutually exclusive (at most one)	x_A + x_B ≤ 1
Exactly one of A, B, C	x_A + x_B + x_C = 1
At most k of n / at least k of n	Σ x_i ≤ k / Σ x_i ≥ k
A and B together or not at all	x_A = x_B
Budget	Σ cost_i x_i ≤ Budget
Fixed charge / setup cost: pay F only if you produce any x	Objective: … − F·y − c·x Constraint: x ≤ M·y, y ∈ {0,1} (M = max possible x, e.g. capacity)
If produced, at least m units (minimum batch)	m·y ≤ x ≤ M·y
Either constraint 1 or constraint 2 must hold	g₁(x) ≤ b₁ + M·z and g₂(x) ≤ b₂ + M(1 − z)
Open warehouse j before shipping from it	Σ_i ship_ij ≤ Cap_j·y_j

Branch-and-bound (binary model)

1 RelaxSolve the LP with 0 ≤ x ≤ 1. If all binary → done

2 BranchPick a fractional variable and make two child LPs (x = 0 and x = 1). Label them active

3 PruneA node becomes inactive if: its solution is binary · it's infeasible · its LP value is no better than the best binary found (bound)

4 RepeatUntil no active nodes remain. The best binary is optimal

Max problem, root LP relaxation = 27.5 (x2 = 0.4) ← upper bound ├─ x2 = 0 → LP = 24.0, all binary ★ incumbent = 24 (inactive: binary) └─ x2 = 1 → LP = 26.2 (x3 = 0.7) still active (26.2 > 24) ├─ x3 = 0 → LP = 23.1 inactive: 23.1 ≤ incumbent 24 (bounded) └─ x3 = 1 → infeasible inactive Optimal binary solution = 24 (the x2 = 0 branch)

Memory hookBranch-and-bound = "Relax, Branch, Bound": relax 0/1 to [0,1], branch on fractions, bound (prune) anything that can't beat the incumbent. For logic constraints, "if A then B → B ≥ A" (the consequence is at least as big as the trigger).

How it gets tested

Formulate a project-selection / site-selection problem with logical conditions and a budget
Recognize a fixed cost needs a binary linked to a continuous variable (big-M)
Explain branch-and-bound at a high level (XP isn't sure B&B calculations will be asked)
Practice: Examples 9.1–9.3 (9.3 uses several variable types and is a great final review), Exercise 9.4 (XP video), pp.455–456

Traps

Writing "if A then B" backwards (x_A ≥ x_B)
Rounding the LP relaxation and calling it optimal
Forgetting to link a fixed cost to the quantity (x ≤ M·y), which lets the model produce without paying setup
Including a sunk cost of a project already started

Self-test: formulate. 5 projects with NPV v_i and cost c_i, budget $10M. At most 2 of projects 1–3. Project 5 requires project 2. Projects 3 and 4 can't both be done.

x_i = 1 if project i is undertaken, 0 otherwise.

Max Σ v_ix_i s.t. Σ c_ix_i ≤ 10 · x₁+x₂+x₃ ≤ 2 · x₂ ≥ x₅ · x₃ + x₄ ≤ 1 · x_i ∈ {0,1}.

(If NPV already nets out money spent to date on any project, don't also subtract it. It's sunk.)

Self-test: product needs a $5,000 setup if made at all, $12 margin/unit, capacity 800, and you must make ≥ 100 if you make any.

x = units (continuous/integer), y = 1 if produced. Max 12x − 5000y s.t. 100y ≤ x ≤ 800y, y ∈ {0,1}, x ≥ 0. (Produce only if 12x > 5000, i.e. x > 417.)

The Hard Side of Change Management (DICE), quick reminderCP311-101-25, listed under Objectives 1 & 3. Full treatment: Objective 1 → DICE

What you must get out of it: score a change program on D, I, C1, C2, E (1–4 each), compute the score, place it in a zone, and justify each score from the facts given.

DICE score (lower = better) D + 2·I + 2·C₁ + C₂ + E → 7–14 win zone · 15–16 risks rising · 17+ worry zone

DDurationtime between milestone reviews: <2 mo = 1 · 2–4 = 2 · 4–8 = 3 · >8 = 4

I ×2Integrityteam capability: respected leader, skilled, ≥50% time = 1 … lacking all = 4

C1 ×2Senior commitmentclearly visible = 1 · neutral = 2–3 · reluctant = 4

C2Local commitmenteager = 1 · willing = 2 · reluctant = 3–4

EEffortextra work: <10% = 1 · 10–20% = 2 · 20–40% = 3 · >40% = 4

How it gets testedFall 2022 had a lot of points on DICE, which had never been tested before. If you can't recall the exact bands, give the direction and a reason ("reviews only every 6 months → high D, ~3") and you'll get most of the marks.

Deciding How to DecideCP311-111-26 (Courtney, Lovallo & Clarke, HBR), also in Objective 4

What you must get out of it: most firms over-rely on DCF and simple scenarios. Diagnose the decision with two questions (+ is the information centralized?), then match the tool. Know the 5 tool families, the 4 information-aggregation tools, the 5 McDonald's situations and the 5 complicating factors.

Q1 · Do I know what it takes to succeed?

Do you have a causal model, i.e. which critical success factors and economic conditions, in what combination, lead to success? Test: can you confidently write "if-then" statements ("If the new process cuts cost X% and we win Y% share, then invest")? Do you know the metrics that must be met, almost a recipe?

Q2 · Can I predict the range of outcomes?

Single outcome with reasonable certainty? A range of outcomes with probabilities? Or can't specify the range or its probabilities with any precision?

Q3 (aggregation): Is the needed information centralized or dispersed across experts/the crowd?

The 5 decision-support tool families

Tool	What it is	Needs
Conventional capital budgeting	DCF, NPV, expected rate of return on estimated incremental cash flows	Causal model + predictable outcome; stable, well-understood setting
Quantitative multiple-scenario	Monte Carlo (repeated random sampling), decision analysis (scenarios + probabilities → best choice for an objective), real options (value of flexibility, e.g. a pilot)	Causal model + range of outcomes with probabilities
Qualitative scenario analysis	A set of representative (not exhaustive) narratives of how the present may evolve, and the decision's consequences under each	Causal model, but outcomes can't be fully specified
Case-based decision analysis ★	Collect analogous past cases, record their results, rate their similarity → choose the option maximizing the similarity-weighted average result. The authors' most-advocated, under-used tool	Works even without a causal model
Information aggregation	Gather dispersed knowledge (4 tools below)	Info is decentralized. Used largely independent of Q1/Q2

DDelphi methodExperts give views, which are aggregated and iterated → range of outcomes + probabilities

PPrediction / information markets"Wisdom of crowds": trade securities paying off on outcomes. Limitation: only works if you can specify the possible outcomes

IIncentivized estimatesPeople with diverse info estimate a key outcome, and the closest wins a reward

SSimilarity-based forecastingIndividuals rate similarity to past decisions/assets, and ratings are aggregated statistically into forecasts

The 5 McDonald's situations: diagnostic matrix

Can predict the outcome (≈ certain)

Can predict a range + probabilities

Cannot predict the range

Causal model: YES

① Capital budgetingDCF / expected rate of returnLocate a new U.S. restaurant (traffic, demographics, calibrated revenue/cost models)

② Quantitative multiple scenarioMonte Carlo, decision analysis, real optionsLaunch a new U.S. sandwich: demand & cannibalization uncertain; a pilot = a real option

③ Qualitative scenarios + case-basedEnter an emerging market for the first time: same store economics, unknown customers/competitors/suppliers/regulation

Causal model: NO

—(not one of the five)

④ Case-based decision analysisNew business model, e.g. food-service process consulting: learn from other firms that added a new model

⑤ Case-based decision analysisRespond to the obesity backlash: lawsuits, research, legislation unforecastable. Use analogies (others repositioning as "healthy")

Overlay information aggregation on any cell where the knowledge is dispersed. As uncertainty rises (moving right/down), shift from quantitative tools to analogies and, ultimately, iterative experimentation.

5 complicating factors

1. Executives don't know what they don't know

The diagnosis depends on judging the uncertainty correctly, and most underestimate it

2. Cognitive bias creeps in

Biased assessment of uncertainty points to the wrong tool

3. Organizational processes get in the way

Need general decision protocols, because politics and behavioral pitfalls are rife when money or power is at stake

4. Reliance on a single tool

Usually conventional capital budgeting. Big decisions often need a combination

5. Not considering the option to delay

"Deciding when to decide is as important as deciding how." In very uncertain settings, use learning-based, iterative experimentation

Memory hookTwo questions: "Recipe? Range?" Recipe + point → DCF. Recipe + range → Monte Carlo/real options. Recipe, no range → qualitative scenarios (+ cases). No recipe → cases. Spread-out info → D-P-I-S aggregation ("Delphi Picks Incentivized Similarities").

How it gets tested

Given a case-company decision (e.g. a new country, a new product, a disruptive regulation): diagnose causal model / outcome predictability, then recommend and justify tool(s)
Critique management for using only DCF in a highly uncertain context
Recommend an aggregation tool and note its limits (prediction markets need a specifiable outcome set; confidentiality)

Traps

Recommending NPV alone for a new business model
Forgetting that a pilot = real option (situation 2)
Saying "prediction market" when the outcomes can't even be enumerated
Not justifying with the two diagnostic questions applied to the facts

Self-test: a life insurer (think case-study Darwin/Snappy) is considering launching a fully digital, AI-underwritten product in a new country. Which tools?

Causal model: partly. Insurance economics are understood (mortality, expenses, lapse), but digital distribution + new-country customer behavior + regulation are not. Outcomes: can't credibly put probabilities on take-up or regulatory response. → Closest to situation 3 (or 4 for the new digital model): qualitative scenario analysis (take-up, competitor, regulator scenarios) + case-based analysis of analogous digital launches. Use information aggregation (Delphi with local distribution and regulatory experts) because the knowledge is dispersed. Consider a pilot (real option) and the option to delay/stage the investment. DCF alone would understate uncertainty.

Exam playbook for DMD questionsXP answering-skills guidance + standard formulation discipline

What you must get out of it: a repeatable template that scores the formulation marks even if you run out of time to solve.

1 · ClassifySimulation / LP / NLP / IP? Say why in one line ("revenue = price × demand(price) → nonlinear")

2 · VariablesDefine each with units & time period ("x_j = tons bought from mine j per week")

3 · ObjectiveMax/min, all relevant revenues and costs once, no sunk costs

4 · ConstraintsResource, capacity, quality (linearized), policy, logical (binary), non-negativity / integrality

5 · Solve / interpretCorners, shadow prices within range → a business recommendation

Time management

XP: students struggle to finish DMD solving in time. Budget time in proportion to the points (exam minutes ÷ total points) and stick to it
Short on time? Explain HOW you would solve (e.g. "evaluate the objective at each corner of the feasible region; the max is optimal") for big part marks
Formulation marks usually come before solution marks, so write them first

Interpretation = marks

Translate numbers into the case's language ("an extra pilot hour is worth $X up to Y hours, so hire contractors below $X")
Name binding constraints (the bottlenecks) and slack resources
Flag model limitations (data quality, linearity, uncertainty → suggest sensitivity, simulation or scenarios)
Book guidance: think through the issues, good data is essential, study the data, make many "what-if" runs

Most common lost marks

No non-negativity · sunk cost included · undefined variables/units · a shadow price applied beyond its range · "optimal" claimed from a simulation · answering a different question than asked (e.g. formulating when asked to critique)

Final-week practice list (XP)Ex 5.8 & the p.210 normal example · Ex 7.2 · §7.5.4 Table 7.8 + p.364 Q&A · p.366 quality constraint · Ex 8.1–8.3 · Ex 9.1–9.3 (esp. 9.3) · pp.455–456 constraints · Ch 10 examples (if available) · case modules · past SOA DMD questions under a time limit.