At my seminars people often mention how difficult it is to compete against incumbents. Usually they want to know effective ways of overcoming the advantage incumbents have.
Well, there's good news – the single most important thing is to ensure you are known by the purchaser before you make your submission! Say an incumbent has an 80% advantage going in (which is a figure commonly quoted), you only have a 20% chance to start with which almost reduces to nothing if the purchaser has never heard of you. I know some companies who make a rule that they will not bid under these circumstances. If you seriously want the business make sure you identify companies you want to work with and approach them before a tender comes out.
Of course, incumbents don't necessarily win 80% of the business. Purchasers have told me the principle reason is "arrogance" – incumbents often presume that their relationship is enough to retain the business and don't put a good submission in. So, to even up the odds make sure you answer every question carefully; attach all the requested documents and follow the order and format required. Do this and the odds are much more in your favour.