Compare uncertain operating plans without inventing scenario probabilities

Management sometimes has defensible descriptions of low, moderate and high demand without a sound basis for assigning percentages to them. A probability-weighted average would then conceal a judgment inside apparently precise arithmetic. The alternatives can still be compared using explicit decision criteria.

ACCA's uncertainty guidance describes maximin, maximax and minimax regret as different ways to choose from a payoff table. They express different priorities and can produce different choices from exactly the same outcomes. None supplies the missing probabilities or proves that its selected scenario is likely.

State the decision timing first. The example assumes the business must select an operating arrangement before demand is known and cannot costlessly switch afterward. If it can stage or revise the commitment, those available actions belong among the alternatives rather than outside the analysis.

Suppose an invented service business is comparing flexible capacity, a limited capacity commitment and a large commitment for the same annual period. The table shows modeled operating contribution after the costs that differ between the arrangements. Common unchanged fixed costs are excluded consistently.

Under low demand, the three alternatives produce $18,000, $10,000 and a $15,000 loss. Under moderate demand, they produce $30,000, $45,000 and $35,000. Under high demand, they produce $42,000, $70,000 and $100,000. These are assumed scenarios, not observed results or estimated probability bounds.

Build each cell from a plausible operating calculation. The large commitment's downside might reflect idle paid capacity, while the flexible option's smaller upside might reflect higher delivery cost. The table is useful only if those mechanisms and the included costs can be examined.

Describe demand as the same external opportunity across the alternatives, then allow each arrangement's capacity to determine fulfilled work. Assuming identical completed sales while one option cannot deliver them would overstate that option's payoff. Include the consequence of unmet demand consistently where it changes the comparison, without treating every unserved prospect as a guaranteed lost customer.

Maximin selects the alternative with the highest minimum payoff. The worst outcomes here are $18,000, $10,000 and negative $15,000. Under that criterion, flexible capacity is preferred because its lowest modeled payoff is better than the other alternatives' lowest payoffs.

Maximax selects the alternative with the highest maximum payoff. The best outcomes are $42,000, $70,000 and $100,000, so that rule prefers the large commitment. It focuses on the largest modeled opportunity without giving weight to the size or likelihood of the downside.

Neither rule says which demand state will occur. They apply management's priority to the stated table. Presenting the choices together can expose a disagreement about protecting downside versus pursuing upside that would otherwise be disguised as an argument over forecast precision.

Regret measures how much payoff an alternative gives up compared with the best available alternative in the same state. Under low demand, the best payoff is $18,000. Flexible capacity therefore has zero regret, the limited commitment has $8,000 and the large commitment has $33,000.

Under moderate demand, the best payoff is $45,000, producing regrets of $15,000, zero and $10,000. Under high demand, the best payoff is $100,000, producing regrets of $58,000, $30,000 and zero. Calculate down each demand column; comparing each option with its own best outcome would answer a different question.

The largest regret for flexible capacity is $58,000. It is $30,000 for the limited commitment and $33,000 for the large commitment. Minimax regret therefore prefers the limited commitment because it has the smallest maximum opportunity loss across the modeled states.

Regret is a comparison with what would have been the best choice after knowing the state. The flexible option's $58,000 high-demand regret is not an invoice or an accounting expense. That option still produces $42,000 of contribution in the high-demand case.

The large option's $33,000 low-demand regret includes both its $15,000 loss and the $18,000 positive result it forgoes relative to flexibility. A cash-survival decision must therefore examine actual cash outcomes separately. A small maximum regret does not guarantee that every outcome is fundable.

For a table of costs rather than payoffs, construct regret by subtracting the lowest attainable cost in each state from the option's cost. Preserve the orientation of the measure. Applying the payoff subtraction unchanged to costs would reverse the interpretation.

Each criterion depends on the scenarios included. Adding a credible severe downside can change the maximin or regret choice. An unsupported extreme can dominate the result just as easily. Review whether the states capture the material uncertainties relevant to the commitment.

A low, moderate and high label does not establish equally likely outcomes. Averaging the three columns assigns equal weights whether or not the report admits it. If management uses that convention, describe it as an assumption and test how it affects the decision.

Consider whether one alternative is inferior across every relevant state. Such an alternative may be removable if no omitted quality, timing or strategic benefit justifies it. Conversely, identify feasible changes to the arrangements, such as a smaller initial commitment, before concluding that the original three choices exhaust the options.

The example produces three different preferred arrangements because the rules protect different objectives. Management should choose and explain its criterion alongside constraints on liquidity, service and commitments. The analyst's role is to make that tradeoff visible, not quietly select the rule that supports a favored contract.

Keep the payoff calculations, scenario evidence and decision date with the approval. If reliable new evidence supports probabilities or changes the available actions, revisit the analysis. An explicit criterion provides a reviewable decision while acknowledging what the current information cannot establish.