Two rules of a sealed ceiling bid and their analysis by mathematical programming techniques

Two rules of a sealed ceiling bid for a contract that a firm offering this contract can set are proposed. The rules are such that they encourage the bidders to submit their prices for the contract within a range desirable by the firm so that these prices not to exceed the (unknown to the bidders) price of the bid (the ceiling). It is shown that under certain natural assumptions on the behavior of the bidders, evaluating chances of a firm to award the contract at a price within such a desirable range as a result of the bid conducted in line with the rules is reducible to solving mathematical programming problems on polyhedral sets. It is also shown that under additional assumptions of the same kind, under the proposed rules, the maximum probability to win the bid at a price within the range is higher for each bidder than that under the rule of awarding the contract to a bidder nominated the lowest price. Thus, while serving the interests of the firm, the proposed rules make the bid more attractive to the potential bidders. (c) 2006 Elsevier Ltd. All rights reserved.