If the buyer takes the position that the supplier has to sign the agreement first, if the supplier delays in signing the contract, the buyer could hire another supplier to perform the work. If the buyer signs it first, the buyer would need to provide notice to the supplier to rescind their offer. That would need to be done before the supplier signs the agreement. Since there is no notice requirement in place that would require written notice if you felt that the supplier was playing games with the signing, you could always call them with a witness listening on and ask them the status. If they say it hasn’t been signed yet, you could give them a verbal notice that you are rescinding the offer and confirm that in writing.
I have a reader that had problems with subcontractors signing their contracts within a reasonable time frame and wanting to negotiate further. When I asked for details she said they would provide a letter of intent. Since a letter of intent can be binding its not a lot different than signing the contract first. You are obligating yourself without the supplier being obligated. My suggestion to her was to simply stop using letters of intent, required the subcontractor to sign within a short period of time. If they don’t hire the next one and let the original supplier know that they didn’t get the job because they didn’t sign the agreement on time. It may cost you a little more that time, but it send a strong message that they can’t hold you up and play games.
In locations where it is legally acceptable I use counterparts language to expedite contract signing. What counterparts language does is allow copies made by any reliable means be considered to be an original. When I have counterparts language in the agreement I e-mail a PDF copy for the supplier for them to sign and require them to fax it back to me where I can sign it. I then fax that signed copy back to the supplier. Where counterparts language really works well is when you have a number of entities that need to sign the agreement where you can do the signing in parallel with all of them rather that serially having to send copies to one and have them transmit it to all others for their signatures.