On every job that I worked on where the general contractor ordered the material himself and hiring a separate installer, just to save money, I saw that it is not worth it. Here are the reasons why:

1-First of all you loose your single source accountability during the job.
2-You loose your single source liability after the job, when the installed material needs to perform as expected. if something goes wrong, your installer will definitely blame you about the materials.
3-You expose yourself to quantity takeoff mistakes. This can cause you extra money when you have to throw away or reorder material. Reordering material will also mean schedule delay.
4-You will have to use your own resources to quantify, order, track, process the order of materials. It is a lot of extra follow up and overhead time and paperwork for you.
5-You are responsible for the delays of the material. Usually if you hire an installer order the materials, as they are doing this all the time, they will have established order channels and will be able to deliver quicker than you can bring.
6-It is true that your installer will put a markup if you get the material through him, however for the reason explained above, they can get the material cheaper than you, because they have the advantage of mass ordering and established channels.
7-You will need to have extra supervision time to watch the installer because the material belongs to you and the waste, quality of installation will depend on the correct use of material, which you will need to ensure yourself in this case. If you had your installer supplied the materials, you only watch him for being on schedule and installing per plans and specs.
8-You are responsible for the field measurements if necessary.
9-You are responsible for the producing of the submittals - even if it is through your vendor -, not only just reviewing them.

Therefore, it is really not worth it to order the materials yourself. You should only do this if you find yourself in a situation that your subcontractor is going to delay the job.