Piecewise Step Isolation
GMAT glossary · Playbook
Definition
In Counterfactual Optimization, isolate which discrete fee/tax/rate branch a counterfactual hits instead of smoothing a step function into one line.
Piecewise Step Isolation in plain English
Pull Piecewise Step Isolation for Counterfactual Optimization whenever a pricing, fee, tax, or rate rule changes at discrete thresholds and the stem asks what happens under an alternative schedule. Structural clues: for the first n, then, bracket, tier, piecewise, what if instead. Blueprint: (1) locate the boundary multiples that clear the actual rule; (2) run only the units past that boundary through the alternative (counterfactual) rule; (3) compare totals branch by branch. Why it beats the long way: treating a step function as one smooth line misprices every Counterfactual Optimization tier and invents a fake continuous cost. Micro-example: Fee $5 for the first 10 units, then $2 each. For 18 units: 5+8· 2=21. If the counterfactual were $3 flat after 10, only the 8 overflow units change (5+8· 3=29). Isolate the branch; do not redraw the whole schedule as one slope.
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