There's no relation between cumulative lead time and quoted lead time. There is however a contest

Cumulative lead time is the lead time it takes to build a product from scratch if we have no inventory anywhere in the system. Quoted lead time is what we tell the customer it will take to get them their order from the time they place the order until it ships. There actually is a relationship between cumulative lead time and quoted lead time. The closer we decide to carry inventory to the finished goods level the quicker we can respond to the customer demand. Conversely, the closer we carry inventory to the raw materials level, the longer we need to respond to a customers demand. (Although we may gain some flexibility in the use of the raw materials elsewhere if we hold it at a lower level in the bill of materials).

A great example of the problem we face

The point I want to make is we usually set a quoted lead time to the customer based on carrying inventory at some level and then through changes in time and various other reasons and initiatives, we forget why we quoted the lead time and it gets lost in the mysteries of time!! Then the contest begins.

I wonder which is Sales and which is Supply Chain

Sales barks we can never respond to the customer fast enough. “We have it on our quote how long its to take!” Operations usually responds with a comment like, “Yeah that’s true if we carried some inventory but the customer blew past the forecast and isn’t willing to make any material commitments and I’m tired of getting yelled at by Finance for low inventory turns!”

Process and Policy

What this whole thing means is we need to document the commitments we made and why, and on an ongoing basis, review them for where we’re at for inventory levels to support our quoted lead times. What I mean for review is looking at forecast vs. consumption and let people know what it’s going to take to support the quoted lead time and make sure it’s bought into. If not it isn’t going to work