MBA Decision Analytics Course Guide Template

Decision Analytics Course Guide: [Your programme and term]

A course guide for the data and decisions core of an MBA: probability, distributions, sampling and inference, hypothesis tests and A/B tests, regression, forecasting, optimisation with linear programming and Excel Solver, and Monte Carlo simulation. It is for incoming and first-year MBA students who want a map of the course, a session plan, an original mini-case with a full teaching note, and an exam plan. It links every topic to the concept cards in this library and to the academic/stats-* statistics library for depth. Source basis: primary works from Bayes (1763) to Metropolis and Ulam (1949), Dantzig (1951) and Holt (1957, reprinted 2004), written up in original words; every number was computed in Python and is shown with its Excel formula. Replace every [bracketed] value and every row marked Example.

Document control

What the course is for

Managers decide under uncertainty with incomplete data. The decision analytics core teaches a disciplined way to do that: describe uncertainty with probability, learn from data with sampling and inference, test ideas with experiments, explain and predict with regression and forecasting models, choose the best plan under constraints with optimisation, and stress-test plans with simulation. The point is not to make you a statistician. It is to make you the person in the room who asks the right quantitative question, builds a model that is good enough to decide, and knows where it breaks.

Competencies built (mapped to competencies common in accreditation-style programme learning goals):

Prerequisites

Session roadmap

Key concepts

Mini-case: Northfield's winter plan

Situation

This case is fictional. Names, numbers and events are invented for teaching.

On a wet Monday in late July, Imani Okafor, vice president of planning at Northfield Outdoor Co., opened the shared folder for the winter planning meeting scheduled for Friday. Northfield sells outdoor clothing and equipment through 64 stores and its own website. Winter jackets drive almost a third of the year's gross margin, and two styles matter most: the Ridge, a down jacket that sells at USD 260 against a landed cost of USD 140, and the Summit, a synthetic jacket that sells at USD 200 against a cost of USD 110.

Four questions were on Friday's agenda, and each had an owner who had sent data.

Rafael Lindqvist, head of e-commerce, had run a four-week A/B test of a new one-page checkout. Visitors were randomly assigned to the old checkout or the new one, 12,000 sessions each. He was ready to roll the new design out to all traffic. "Conversion went from 3.2 to 3.7 percent. That's a 15 percent lift," he wrote. The finance team, who remembered two earlier "wins" that vanished after launch, wanted to know whether the result was real and what it was worth.

Mei Tanaka, the demand planner, had twelve weeks of online orders for the Summit and needed a forecast for the next four weeks to set the website's stock allocation. Her current method was to use last week's orders as the forecast, smoothed a little. Orders had climbed steadily all summer, and she was tired of running short.

Kwame Mensah, who ran Northfield's small sewing facility, had to set the mix for the pre-season production run. The facility could sew both jackets but was limited by sewing hours, cutting-table hours and the supply of certified down, which only the Ridge uses. Marketing had capped Summit volume from this run at the quantity it believed the early season would absorb. Kwame's habit was to make as many Ridges as the down allowed, "because the Ridge earns more per jacket".

Finally, Imani herself owned the total Ridge buy for the season: in-house units plus a top-up from a contract manufacturer at the same landed cost. Ridge demand was uncertain. Last season's forecast error suggested a normal distribution with a mean of 4,000 units and a standard deviation of 900. Unsold jackets would go to an outlet partner at USD 70 after the season. A board member had asked, at the last meeting, why Northfield did not simply order the forecast: "If we expect 4,000, buy 4,000."

Imani wanted one page per question by Thursday night: the number, the range, the assumption that mattered most and a recommendation. She also wanted to know how the four answers fitted together, because the production run and the season buy drew on the same cash and the same down supply.

Exhibit 1: checkout A/B test (four weeks, random assignment)

Average order value USD 95; gross margin on online orders 40 percent.

Exhibit 2: weekly online orders for the Summit (units)

Exhibit 3: pre-season production run

Exhibit 4: Ridge season buy

Demand: normal, mean 4,000 units, SD 900. Price USD 260, landed cost USD 140, outlet salvage USD 70 per unsold unit. No reorder is possible once the season starts.

Discussion questions

1. Is the checkout result real? What is it worth per 100,000 sessions, and what else would you want to know before rolling it out?
2. How large should the test have been to detect a lift from 3.2 to 3.7 percent with 80 percent power?
3. Forecast Summit orders for weeks 13 to 16. Which method would you use, and how do you know it is better than Mei's current method?
4. What production mix maximises contribution? Is Kwame's rule right? What is one more sewing hour worth?
5. How many Ridges should Imani buy for the season? Answer the board member.
6. How do the four answers interact, and what would you put on Imani's one-page summary?

Teaching note

Question 1: the A/B test

Two-proportion z-test: pooled rate $\hat{p} = 828/24{,}000 = 0.0345$,

$SE = \sqrt{\hat{p}(1-\hat{p})\left(\tfrac{1}{12{,}000} + \tfrac{1}{12{,}000}\right)} = 0.00236, \qquad z = \frac{0.0370 - 0.0320}{0.00236} = 2.12, \qquad p = 0.034$

The 95% CI for the difference (unpooled SE 0.00236) runs from 0.04 to 0.96 percentage points. Excel: =(444/12000-384/12000)/SQRT(0.0345*(1-0.0345)*(2/12000)) for $z$, and =2*(1-NORM.S.DIST(2.1221,TRUE)) for $p$.

The difference is statistically significant at 5 percent, but the interval is wide: the true lift could be almost zero or almost one point. The relative lift is 15.6 percent. Value at the point estimate: $0.005 \times 100{,}000 \times 95 \times 0.40$ = USD 19,000 of contribution per 100,000 sessions. Before rollout ask: was the duration fixed in advance (no peeking and stopping when significant)? Did the test run over full weekly cycles? Is order value unchanged? Does the lift hold on mobile and desktop? Recommend rollout with a holdout group of 5 to 10 percent of traffic to confirm the effect, which also answers finance's concern about past "wins" that vanished (regression to the mean and the winner's curse).

Question 2: sample size

For 80 percent power and a two-sided 5 percent test, the classical formula

$n = \frac{\left(z_{0.975}\sqrt{2\bar{p}(1-\bar{p})} + z_{0.80}\sqrt{p_A(1-p_A) + p_B(1-p_B)}\right)^2}{(p_B - p_A)^2}$

gives about 20,900 sessions per arm (20,914 by the formula, 20,889 with the arcsine method in statsmodels). The test ran 12,000 per arm, so it was underpowered: it had little chance of detecting the true lift if the lift is near 0.5 points, and significant results from underpowered tests tend to overstate the effect. See academic/stats-power-sample-size.

Question 3: forecasting

Trend line: orders $= 304.20 + 8.14 \times$ week, $R^2$ = 0.964. Excel: =FORECAST.LINEAR(13,B2:B13,A2:A13) returns 410.0; smoothing: =0.3*B3+0.7*C3 copied down. Simple smoothing lags a trending series every week, which is exactly why Mei runs short. Use a trend method. Do not compare the regression's in-sample error with the smoothing methods' one-step-ahead errors: a fair comparison holds out the last weeks and forecasts them (see academic/stats-time-series-arima and Hyndman and Athanasopoulos, open text). Add a seasonal model once there is more than one year of data.

Question 4: the production mix (linear programming)

Decision variables: Ridge units $R$, Summit units $S$. Maximise $120R + 90S$ subject to $1.5R + 1.0S \le 9{,}000$ (sewing), $0.5R + 0.6S \le 4{,}200$ (cutting), $0.3R \le 1{,}500$ (down), $S \le 6{,}000$, $R, S \ge 0$.

At the optimum, sewing and cutting are binding; down (600 kg slack) and the Summit cap (1,500 units slack) are not. Shadow prices: USD 67.50 per sewing hour and USD 37.50 per cutting hour (re-solving with 100 more sewing hours gives 771,750, exactly 100 times 67.50). Down has a shadow price of zero: buying more of it is worthless in this run. Kwame's rule loses USD 30,000 because it ranks products by contribution per unit instead of contribution per unit of the scarce resource: per sewing hour the Summit earns 90 against the Ridge's 80.

Excel Solver set-up: decision cells B2:C2; objective =SUMPRODUCT(B2:C2,B3:C3), Max; constraints =SUMPRODUCT($B$2:$C$2,B5:C5)<=D5 for each resource row; tick "Make Unconstrained Variables Non-Negative"; method Simplex LP; then ask for the Sensitivity Report to read shadow prices and allowable ranges. Python check:

from scipy.optimize import linprog
res = linprog(c=[-120, -90],
              A_ub=[[1.5, 1.0], [0.5, 0.6], [0.3, 0.0], [0, 1]],
              b_ub=[9000, 4200, 1500, 6000], method="highs")
print(res.x, -res.fun, res.ineqlin.marginals)
# [3000. 4500.] 765000.0 [-67.5 -37.5  -0.   -0. ]

linprog minimises, so the model maximises contribution by minimising its negative; the marginals are therefore negative, and their absolute values (67.5 and 37.5) are the shadow prices.

Question 5: the season buy (newsvendor and Monte Carlo)

Underage cost $c_u$ = 260 - 140 = 120 (margin lost per unit short); overage cost $c_o$ = 140 - 70 = 70 (loss per unsold unit). Critical ratio $c_u/(c_u + c_o)$ = 120/190 = 0.6316, so $Q^* = 4{,}000 + 900 \times z_{0.6316} = 4{,}000 + 900 \times 0.3360 \approx$ 4,300 units. Excel: =NORM.INV(120/190,4000,900) returns 4,302.

Monte Carlo check (100,000 demand draws, seed 2026):

import numpy as np
rng = np.random.default_rng(2026)
D = np.maximum(rng.normal(4000, 900, 100_000), 0)
for Q in [3500, 4000, 4300, 4500, 5000]:
    sold = np.minimum(D, Q)
    profit = 260 * sold + 70 * (Q - sold) - 140 * Q
    print(Q, round(profit.mean()), round(np.percentile(profit, 5)), round(np.mean(D <= Q), 4))
# 3500 389087 234527 0.2898
# 4000 411901 199527 0.4992
# 4300 415688 178527 0.63
# 4500 414193 164527 0.7104
# 5000 398626 129527 0.868

The table rounds the last column to two decimals. The analytic expected profits agree to within 0.1 percent (for example 415,526 at 4,300). In Excel, put =MAX(0,NORM.INV(RAND(),4000,900)) in a demand cell, compute profit from it, and replicate 5,000 times with a one-way data table.

Answer to the board member: buying the forecast (4,000) is not optimal, because a missed sale costs more (USD 120) than an unsold jacket (USD 70); ordering about 4,300 adds about USD 3,800 of expected profit. Also, "profit at the average demand" is not "average profit": with 4,000 units and exactly 4,000 demand, profit would be USD 480,000, but the expected profit is USD 411,901, because shortfalls and leftovers both cost money. This is the flaw of averages (Savage 2009). The higher order also widens the downside (5th percentile falls from 199,527 to 178,527), so a risk-averse board might stop slightly lower.

Question 6: putting it together

The production LP makes 3,000 Ridges in-house, so about 1,300 of the 4,300-unit season buy comes from the contract manufacturer. The in-house run leaves 600 kg of down unused; the contract buy needs only 390 kg for 1,300 jackets, so if the contract maker uses Northfield's certified down, the slack covers it. The binding resource is sewing time, worth USD 67.50 an hour: overtime or a second shift below that rate pays. The checkout rollout raises online conversion, which raises Summit demand: Mei's forecast should be re-based if the new checkout launches. The one-page summary: one row per decision with the number, the range, the key assumption and the next check.

Typical assignments and how they are graded

Exam preparation plan

Rules that consistently help: answer before you look (retrieval practice), space the sessions, mix topics, and redo worked examples from a blank sheet rather than re-reading them (Dunlosky et al. 2013). Use mba/mba-exam-prep for the full plan and mba/mba-concept-flashcards for spaced review of definitions.

Common struggles

1. Bayes' rule feels backwards. Always build the joint-probability table; never apply the formula from memory.
2. p-values read as the probability the hypothesis is true. A p-value is the probability of data at least this extreme if the null hypothesis were true (Wasserstein and Lazar 2016).
3. Regression read as causation. Write the causal story and the confounders before interpreting a coefficient.
4. Forecast accuracy measured in-sample. Hold out the latest periods.
5. Solver set-up errors. Forgetting non-negativity, mixing units across constraints, or choosing GRG Nonlinear for a linear model and getting no sensitivity report with shadow prices.
6. Simulation with too few draws or a fixed random number. Use enough replications and report the spread.
7. Spreadsheets nobody else can audit. Separate inputs, calculations and outputs; colour-code inputs.
8. Time. Exams reward a correct set-up done quickly. Practise set-ups without computing.

Reading list

Classic works (primary sources):

• Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370-418.
• Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd.
• Neyman, J., and Pearson, E. S. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London, Series A, 231, 289-337.
• von Neumann, J., and Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press.
• Metropolis, N., and Ulam, S. (1949). The Monte Carlo method. Journal of the American Statistical Association, 44(247), 335-341.
• Dantzig, G. B. (1951). Maximization of a linear function of variables subject to linear inequalities. In T. C. Koopmans (Ed.), Activity Analysis of Production and Allocation, 339-347. Wiley.
• Holt, C. C. (2004). Forecasting seasonals and trends by exponentially weighted moving averages. International Journal of Forecasting, 20(1), 5-10. (Reprint of a 1957 Office of Naval Research memorandum.)
• Winters, P. R. (1960). Forecasting sales by exponentially weighted moving averages. Management Science, 6(3), 324-342.
• Raiffa, H. (1968). Decision Analysis: Introductory Lectures on Choices under Uncertainty. Addison-Wesley.
• Wasserstein, R. L., and Lazar, N. A. (2016). The ASA statement on p-values: context, process, and purpose. The American Statistician, 70(2), 129-133.
• Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., and Willingham, D. T. (2013). Improving students' learning with effective learning techniques. Psychological Science in the Public Interest, 14(1), 4-58.

Textbooks and practitioner books (further reading, by name only): Albright and Winston, Business Analytics: Data Analysis and Decision Making; Clemen and Reilly, Making Hard Decisions; Kohavi, Tang and Xu, Trustworthy Online Controlled Experiments (2020); Savage, The Flaw of Averages (2009); Wooldridge, Introductory Econometrics.

Open resources: Hyndman and Athanasopoulos, Forecasting: Principles and Practice (OTexts, free online); OpenStax, Introductory Statistics 2e (CC BY-NC-SA 4.0); OpenIntro, OpenIntro Statistics (free online).

Self-test questions

1. A fraud screen flags 90 percent of fraudulent orders and 5 percent of legitimate ones; 2 percent of orders are fraudulent. What share of flagged orders is fraudulent?
2. Defects occur independently in 5 percent of units. In a batch of 20, what is the probability of 3 or more defects? Give the Excel formula.
3. Customer calls arrive at an average of 3 per minute (Poisson). What is the probability of no call in a minute?
4. A survey of 36 customers has a sample SD of 30. What is the standard error of the mean and the approximate 95% margin of error?
5. What is $P(Z > 1.5)$ for a standard normal variable? Give the Excel formula.
6. Explain in one sentence why the A/B test in Exhibit 1 was underpowered, and what that does to significant results.
7. In Exhibit 3, why is down's shadow price zero?
8. Why did simple exponential smoothing under-forecast Summit orders every week?
9. State the newsvendor critical ratio and explain why $Q^*$ is above mean demand in Exhibit 4.
10. Give one situation where you would use a decision tree rather than a Monte Carlo simulation, and one where you would do the opposite.

Answer key

1. $0.02 \times 0.90 / (0.02 \times 0.90 + 0.98 \times 0.05) = 0.018/0.067 = 0.2687$: only about 27 percent of flags are fraud, because legitimate orders vastly outnumber fraudulent ones (base rate).
2. $1 - P(X \le 2) = 0.0755$. Excel =1-BINOM.DIST(2,20,0.05,TRUE).
3. $e^{-3} = 0.0498$. Excel =POISSON.DIST(0,3,FALSE).
4. $SE = 30/\sqrt{36} = 5.0$; margin about $1.96 \times 5 = 9.8$ (with $t_{35}$ = 2.03 the margin is about 10.2).
5. 0.0668. Excel =1-NORM.S.DIST(1.5,TRUE).
6. Detecting a 0.5-point lift with 80 percent power needs about 20,900 sessions per arm and the test had 12,000; when an underpowered test does come out significant, its estimated effect tends to be inflated (winner's curse).
7. It is not binding: the optimum uses 900 kg of the 1,500 kg available, so one more kg does not change the plan.
8. It forecasts a weighted average of past levels, so on a rising series the forecast always trails the actual; a trend term (Holt) removes the lag.
9. $c_u/(c_u + c_o)$ = 120/190 = 0.6316. Because a lost sale costs more than an unsold unit, the optimal service level is above 50 percent, so $Q^*$ lies above the mean.
10. Tree: a few discrete uncertainties with sequential decisions and information to buy (test market, then launch). Simulation: many continuous, interacting inputs (demand, price, cost, exchange rate) where you need the full distribution of profit.

Revision history

Standard and licence note

Structure aligned with the data and decisions core commonly taught in leading international MBA programmes and with accreditation-style learning goals for analytical reasoning and technology use; content based on the primary works listed in the reading list. The text, mini-case, data, exercises and teaching note are original and fictional; no published case, textbook or course material was copied or paraphrased. This template is not affiliated with or endorsed by any business school, accreditor, publisher or software vendor. Check your own syllabus and the current documentation of Excel Solver and your statistics software. Template licence: MIT.