Puzzle of the Week #120 - Quality Control

A company orders in a variety of pieces of metal of lengths:

7cm        17cm     18cm     19cm     25cm     37cm     44cm

46cm     63cm     65cm     82cm     83cm     90cm     100cm

The quality controller, whose task it is to check the length of the incoming parts is correct, has figured out that he can use a straight rod of a particular length, and mark a series of points on it so that all of the lengths in the above list can be measured, either between two of the marks, or from an end to one of the marks. He uses the minimum possible number of marks.

How long is the rod, how many marks were made, and where were they positioned?