Final answer:
In the Design-Bid-Build project delivery method, the owner is usually responsible for cost overruns because this method involves separate contracts for design and construction, thus making the owner financially responsible for any additional costs beyond the initial bid.
Step-by-step explanation:
The question pertains to the types of project delivery methods and their respective disadvantages with cost overruns. The delivery method where the owner is responsible for cost overruns is most closely associated with the Design-Bid-Build method. In this traditional delivery approach, the project is divided into multiple distinct phases: first the design is completed by an architect or engineer, then the project is bid on by contractors, and lastly, the winning contractor builds the project. One of the key drawbacks of this method is that any additional costs that arise beyond the original bid amounts typically become the owner's responsibility to finance, as the contractor's obligations are typically limited to the terms set forth in the original contract.