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In my opinion quality, schedule and keeping promises are more important than price.So I will reject the offer.
Of couse if supplier's manager's mother has died and because of this reason his offer has been delayed and you know this for sure, it is a different story and for the sake of humanity you can make an exception.
Re-do the evaluation sheet and conclude this offer.
Not all who was a lowest bidder is a good deal.specially if the bidder estimate is much lower than your cost estimate. You have to evaluate carefully perhaps they missed big quantity of materials, pricing etc. You are looking for trouble if you get the service of Lowest bidder having estimate lower that your cost estimate.
If you have public bidding late submission is not acceptable. In a sealed bidding late submission is in consideration.
Usually late submissions are not considered, however once you get lower price, then you negotiate with the winner (but not with the late submitter) of the contract to decrease prices, and I think it is not necessary to reorganize the whole process as it is waste of time and resources.