How do you prove who pays for a delay?

[AndrewwTait]

A small contractor finished a school build seven months late. The owner said the delay was the contractor's fault and refused to pay the final bill. The contractor said the real problem was late approvals and bad weather. Both sides had different numbers and no clear proof. They hired a neutral expert to do a quantum analysis. The expert looked at timesheets, material invoices, and daily site records. The final report showed exactly which delays cost money and who should pay. The two sides settled in weeks. How does your team track delay costs on big projects?