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The capacity constraint bound the upgrade and approval variables in its where clause, outside its sums over the substation's upgrades and requests. For each substation and investment level it therefore compared the sum of the upgrade variables times the sum of the upgrade capacities with the sum of the approval variables times the sum of the requested MW. Each upgrade's capacity and each request's MW is now weighted by its own variable. Listing InvestmentLevel in the objective's sum makes it say what the solver already computes, one term per request and level. The optimum moves from 1,579,200,000 to 1,562,600,000. The knee stays at $300M, now with 6 data centers, 1,530 MW and $252M net value: Google Metroplex and Lambda Labs at Dallas-Fort Worth are approved from $300M, and xAI Colossus at no budget. The README and runbook state the new results.
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Stage 5's substation capacity constraint compared the wrong totals, so the Pareto frontier the template prints and its docs quote solved a different problem from the one they describe.
What was wrong: the constraint bound one upgrade's and one request's variable in its
whereclause, outside its sums over the substation's upgrades and requests. For each substation and investment level it compared (sum of the upgrade variables) × (sum of the upgrade capacities) with (sum of the approval variables) × (sum of the requested MW).Fix: each upgrade's capacity and each request's MW is weighted by its own variable. Listing
InvestmentLevelin the objective's sum makes it say what the solver already computes, one term per request and level; results at 1.27.1 do not change. The README and runbook now match what the script prints.Results, from a cloud run at the template's pinned
relationalai[gnn]==1.27.1. An exhaustive search over every approval and upgrade choice reproduces both columns' approvals, MW and revenue at every budget, under the old constraint and the fixed one. Net value at $500M and $600M depends on which of several same-revenue upgrade sets the solver picks.The knee stays at $300M. xAI Colossus was approved from $300M and now never is. With both Dallas-Fort Worth upgrades the substation has 699.8 MW of headroom: xAI with Lambda Labs (700 MW) does not fit, and Google Metroplex with Lambda (600 MW, $108M/yr) earns more than xAI alone (500 MW, $105M/yr).