Suggest how the below NEGOTIATION could be improved using the steps below and why?

Preparation

Team Selection

Information Exchange

Developing Strategy

Deal Making

At the beginning of this fiscal year, I was tasked to lead a project to acquire new technology equipment. The task includes finding the technology that best suits the requirement and finding at least three suppliers. As a standard operating procedure, the company has a formal process for choosing suppliers that requires completing a bidding form and conflict of interest declaration for transparency and to make sure that the business is not influenced by someone else. Looking at the three different suppliers, the team decided to go with the company with the lowest offer. After a few e-mails exchanged with the supplier, we've set up a virtual meeting to discuss and negotiate pricing and delivery. Joining the meeting is the director of our department and me and acting as a specialist, and the other party consists of those whom we don't know until they introduce themselves during the meeting, except one which is the account manager, whom we initially had communicated to. The meeting started with us discussing the delivery time, as this is the most important aspect of this deal for us. The other party confirmed that they can deliver according to our requirements. The next is the price; without even negotiating, we have agreed with their pricing, considering that this fall within our budget. The meeting concluded with everyone satisfied with the deal.