If one of your team members insisted on his/her opinion regarding the best way to achieve a result. How would you deal with this situation?

Ask him/here to transfer his/here opinion to monatory values and estimate the risk related to this opinion in terms of Time and Cost :)

First of all make him/her realize that you value his opinion/solution and ask him why he thinks it is the best. Show him the comparison of his opinion with others by comparing pros and cons of different options.. Explain to him why you don't choose his opinion at this time..

If he is one of my team then I beleive in him...but for value to my customer & company...best is some thing objective..so simply he should turn it his idea to be benefit for the company & the customer then I beleive I'll support him to do it. 

Listen to him/her infront of all the team members who have a word in every decision made and trying to find the best possible solution from every opinion