It's always the prime's responsibility to manage the schedule. Boeing has gotten particularly bad at managing extremely large activities, but that might be a symptom of projects being too large for anyone to manage adequately. Additionally, the problems appear to a combination of the mundane, lack of fasteners, and possibly more systemic, with the major subs tasked with jobs larger than they have experience and infrastructure for, since Boeing subcontracted major subsections of the plane to their suppliers.
When such large subsystems are subbed out, there's no room for second sourcing, and there's less visibility into any possible problems. Had the plane's 2nd tier assemblies been assigned to the main Boeing production line, many of the current problems would have been apparent sooner, and possibly solved sooner.
Unfortunately, such is the nature of large programs today. The level of complexity is substantially higher, which means that the prime's program manager and project engineers are essentially an extra layer away from potential problems and solutions.
It's not really clear that there is any solution. It used to be that a single chief engineer could understand and encompass the totality of an aircraft development and production. Today, each major system of an aircraft, or military vehicle, is so complex that chief engineers at the 2nd or even 3rd tiers have trouble coordinating the engineering activities, just because there's so many of them.
Just consider the most advanced landing gear. They used to be simply a bunch of mechanical components that were assembled together. Now, they have electronics, sensors, processors, actuators, etc. Some landing gear will even have motors to spin up the wheels prior to touchdown, to lessen the friction induced tire ruptures. These motors then act as brakes when the plane slows down. All this requires engineers versed in mechanics, physics, materials, electronics, control systems, sensors, etc., not just mechanics and materials.
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FAQ731-376