Previously I have discussed an automated optimization method for designing a fast four lens refrative objective that uses symmetrically manufactured lenses (you can read about it from here). The original development model used glass from Schott, but next I will discuss how it won't make much difference which glass manufacturer one uses.
In addition to the most famous glass manufacturers such as Schott from Germany and Ohara from the US, there are such as LZOS from Russia and CDGM from China, and many others. Manufacturers have their preferences, and it is a good designer practice to include alternative glasses to the lens ISO drawings, as every maker has their own N-BK7's and S-FPL53's. Sometimes though, a small amount of redesign after the glass manufacturer change is indeed necessary due to minute differences in manufacturing processes. Sometimes these changes could result in improved chromatic correction, but the main advantage of deciding glass manufacturer is to secure, simplify and tender glass sourcing for manufacture of lenses.
Next I will demonstrate that an optical design can be quickly re-optimized to accommodate change of glass manufacturer. First example is the original development of the above mentioned four lens symmetrical refractor using exclusively Schott glasses.
The next is the same design, optimized for Ohara glass. The demerit function is the same, but gives greatly deteriorated value due to radii not having being optimized for the alternate glasses yet. The demerit function hasn't changed, so the optimization landscape is also still the same, and the local minimum is still in the vicinity. One optimization round locates the local minimum.
The third example is optimized for Russian Lzos glass. Again demerit function is the same and so is the landscape. The local minimum is quickly found.
In conclusion, all glass manufacturers do have their special features, but as a rule of thumb they all follow the same glass map shape. Therefore the glass manufacturer can basically be pre-determined freely, should the manufacturer have preferences or if geopolitical trends seem to bother the supply.