| Course | BU 407 Quantitative Decision-Making |
|---|---|
| Unit | Unit 1 |
| Paper type | Payoff table write-up |
| Length | About 1,000 words, 6 pages |
| Format | APA 7 student paper |
| School | Herzing University |
| Program | BS in Business Analytics |
| Updated | September 2026 |
Free sample paper for BU 407 Unit 1
Four Ways to Make More Yogurt, Three Markets That Might Arrive: A Payoff Table Write-Up for a Composite Wisconsin Dairy Cooperative, Read Under Four Criteria
Student Name
Business, Herzing University
BU 407: Quantitative Decision-Making
Instructor Name
January 21, 2026
Four Ways to Make More Yogurt, Three Markets That Might Arrive: A Payoff Table Write-Up for a Composite Wisconsin Dairy Cooperative, Read Under Four Criteria
The Decision
Northwoods Dairy Cooperative is a composite farmer-owned cooperative in Wisconsin, built for this course, that processes members' milk into fluid milk, yogurt and cheese at three plants. Its yogurt line at the Eau Claire plant has run near capacity for a year, and the board must decide how to meet future yogurt demand. Four alternatives are on the table. The cooperative could install a new automated cup-filling line, expand the existing line with a second, smaller filler, contract a co-packer to produce some of its yogurt under the Northwoods label, or do nothing and keep turning away orders. The outcome depends on how the regional yogurt market develops over the next three years, which the board's planning committee summarizes in three states: weak demand, where growth stalls; steady demand, where recent growth continues; and strong demand, where a large grocery chain's interest in a store brand turns into orders.
This write-up builds the payoff table for that decision and reads it under four decision criteria that require no probabilities: maximax, maximin, minimax regret and equal likelihood. Render et al. (2018) describe this as decision making under uncertainty, where the decision maker can list the possible states but cannot yet assign them probabilities. Probabilities come in the next unit.
The Payoff Table
Each cell gives the estimated change in annual contribution, in thousands of dollars, compared with doing nothing, averaged over the three-year planning period after the cost of the investment is spread across it. Figures come from the cooperative's finance office and belong to the composite case. The automated line has the highest capacity and the highest fixed cost, so it loses money in a weak market and earns the most in a strong one. The smaller filler costs less and adds less capacity. The co-packer contract needs no investment but pays the co-packer a margin on every cup, so its gains are modest in every state. Doing nothing is the reference point at zero.
| Alternative | Weak demand | Steady demand | Strong demand |
|---|---|---|---|
| A1: New automated line | minus $180 | $220 | $640 |
| A2: Second, smaller filler | minus $40 | $260 | $410 |
| A3: Co-packer contract | $60 | $180 | $290 |
| A4: Do nothing | $0 | $0 | $0 |
Reading the Table Four Ways
Each criterion formalizes a different attitude toward uncertainty, which is why operations research texts present them side by side rather than ranking them (Hillier & Lieberman, 2015). The maximax criterion, which suits an optimistic decision maker, picks the alternative with the best of its best outcomes. A1's best is $640,000, the highest in the table, so maximax chooses the automated line.
The maximin criterion, which suits a cautious decision maker, picks the alternative with the best of its worst outcomes. The worst outcomes are minus $180,000 for A1, minus $40,000 for A2, $60,000 for A3 and $0 for A4. The best of these is A3's $60,000, so maximin chooses the co-packer contract.
The minimax regret criterion measures how much a decision maker would regret each choice once the state is known. In each state, the best payoff is $60,000 in weak demand, $260,000 in steady demand and $640,000 in strong demand. Each alternative's regret in a state is the best payoff minus its own. The largest regrets are $240,000 for A1, from a weak market; $230,000 for A2, from a strong market; $350,000 for A3, from a strong market; and $640,000 for A4. The smallest maximum regret is A2's $230,000, so minimax regret chooses the smaller filler.
The equal likelihood criterion, sometimes called the Laplace criterion, treats each state as equally probable and averages the payoffs. The averages are about $226,700 for A1, $210,000 for A2, $176,700 for A3 and $0 for A4, so equal likelihood chooses A1, narrowly ahead of A2.
| Alternative | Regret, weak | Regret, steady | Regret, strong | Maximum regret |
|---|---|---|---|---|
| A1 | $240 | $40 | $0 | $240 |
| A2 | $100 | $0 | $230 | $230 |
| A3 | $0 | $80 | $350 | $350 |
| A4 | $60 | $260 | $640 | $640 |
What the Criteria Reveal
Four criteria produced three different choices, which is the point of reading the table more than one way. The choice depends on the board's attitude toward risk, not on the numbers alone. A board that cannot afford a loss in any state would choose the co-packer contract, the only alternative that earns money even when demand stalls. A board willing to accept a loss for the chance of the largest gain would choose the automated line. The minimax regret criterion, which asks which choice the board would least regret in hindsight, lands on the smaller filler, which gives up some of the upside of the automated line in exchange for a much smaller loss if demand weakens.
Two alternatives can already be set aside. Doing nothing is dominated by the co-packer contract, which earns at least as much in every state and more in each. And the co-packer contract, though safest, gives up so much in steady and strong markets that it is attractive only to a board with no tolerance for loss. The real contest is between A1 and A2, and it turns on how likely weak and strong demand are. Raiffa (1968) argued that when criteria disagree, the decision maker should look for the information that would settle the disagreement rather than choose a criterion to suit a preferred answer. Here, that information is the probability of each state.
A fifth criterion, the Hurwicz criterion, blends maximax and maximin with a coefficient of optimism between 0 and 1. With a coefficient of 0.6, A1 scores 0.6 times $640,000 plus 0.4 times minus $180,000, or $312,000, while A2 scores 0.6 times $410,000 plus 0.4 times minus $40,000, or $230,000, and A3 scores $198,000. A board that leans optimistic would again choose A1, but the result depends entirely on a coefficient the board would have to choose, which is why this write-up treats it as a check rather than a separate answer.
Handing the Decision Forward
The payoff table narrows the choice to the automated line and the smaller filler. The next unit will ask the planning committee for probabilities of weak, steady and strong demand, compare the two finalists on expected value and estimate how much a perfect forecast of the market would be worth before the board commits. The cooperative, its plants and its figures are invented for teaching.
References
Hillier, F. S., & Lieberman, G. J. (2015). Introduction to operations research (10th ed.). McGraw-Hill Education.
Raiffa, H. (1968). Decision analysis: Introductory lectures on choices under uncertainty. Addison-Wesley.
Render, B., Stair, R. M., Jr., Hanna, M. E., & Hale, T. S. (2018). Quantitative analysis for management (13th ed.). Pearson.
The Herzing BU 407 Unit 1 instructions
The first unit of BU 407 asks students to set up a payoff table for a business decision and apply decision criteria that do not require probabilities. Most versions want the decision described, the alternatives and states of nature listed, a table of payoffs with a stated source and unit, and each criterion applied with its working shown: usually maximax, maximin, minimax regret and equal likelihood, sometimes Hurwicz. Many rubrics ask what each criterion's choice reveals about the decision maker's attitude toward risk. Instructors look for clearly derived cell values and visible calculations rather than bare answers. The case is often supplied, though composite figures work when their basis is explained. Plan on two to three pages with the payoff table and a regret table, cited in APA 7 with the course text, and state which alternatives survive for the next unit.
Inside the BU 407 Unit 1 example
The sample opens by describing the cooperative, its capacity problem and the four alternatives, then defines the three demand states. The payoff table section explains what each cell measures and why the alternatives behave differently across states. Four criteria are then applied one at a time, each with its arithmetic and its choice, and a regret table shows the full calculation behind minimax regret. The interpretation section explains which risk attitude each criterion represents, adds a Hurwicz check with a stated coefficient and points out that doing nothing is dominated. A short final section hands the two finalists to the next unit, where probabilities will be added to separate them.
Where the points sit in the BU 407 Unit 1 rubric
Herzing's grading for the payoff table unit usually weighs the setup of the table, the correct application of each criterion, the interpretation and presentation. Setup earns full points when alternatives, states and cell values are clearly defined with a unit and source. Application is judged by accurate calculations shown step by step, especially the regret table, which many submissions get wrong by subtracting in the wrong direction. Interpretation earns top marks when each criterion's choice is read as a statement about risk attitude and dominated alternatives are named, as in the sample. Instructors also credit a sensible conclusion about what information would resolve disagreement among criteria. Tables that are easy to read and correct citations complete the grade, and a note on which alternatives go forward shows the student sees the course as connected.
BU 407 Unit 1 help before you submit
The most common Unit 1 mistake is presenting one criterion's answer as the decision, without explaining that other criteria disagree. Another is computing regret incorrectly, for example by comparing each payoff with the row maximum instead of the column maximum. Students often leave cell values unexplained, so an instructor cannot tell whether they are profits, costs or changes. Some papers include probabilities, which belong to the next unit. Others miss dominated alternatives that could be removed immediately. Finally, keep the decision maker in view; the criteria are models of different attitudes toward risk, and the most useful conclusion says which attitude fits the organization and why.
Get a BU 407 Unit 1 example written to your instructions
Forward the Unit 1 instructions and the rubric your BU 407 classroom posts, plus the scenario if one is attached. We build a custom example that fixes alternatives and states first, sources every payoff, runs each criterion separately and defends one at the close. First custom sample free, back in 24 to 48 hours.
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BU 407 Unit 1 questions, answered
Do I need probabilities for this assignment?
Only where the instructions supply them. A decision under uncertainty is defined by their absence, and that is what makes maximax, maximin and regret the available tools. If your unit gives likelihoods for each state, the work shifts to expected value and the criteria above become a comparison rather than the answer. Read the prompt closely, because sections split on this.
How many alternatives should the table hold?
Enough that the criteria can actually disagree, which usually means three or four. Two options often produce the same winner under every rule and leave nothing to discuss. Where the instructions name a count, meet it exactly. Where they do not, add an option that looks weak on one criterion and strong on another, since that is the row the analysis will earn its marks on.
Can I use figures from my own workplace?
Costs, margins and volumes held in an employer's system are the employer's, and a coursework table is not the place for them. Build the case instead: choose amounts that behave the way your industry behaves, say in a line that the firm is composite, and keep the ratios sensible. Graders in many sections care that the arithmetic is traceable rather than that the numbers are real.
Where can I find a free BU 407 Unit 1 sample paper?
The full BU 407 Unit 1 payoff table write-up is published above for free, with both tables and margin notes. If your case uses different alternatives or states, send the prompt and your figures, and a free custom write-up will be prepared around them, usually within two days.
Do I need probabilities for BU 407 Unit 1?
Usually not. The first unit applies criteria that work without probabilities, such as maximax, maximin and minimax regret. The sample adds probabilities only in the next unit, when expected value is used to choose between the two finalists.