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Setting a bid markup strategy is a very difficult task. Nevertheless, it is important to construction firms or consulting engineering companies because the development of successful bidding strategies is a key factor to their survival in business. Based on the two bidding criteria of the conditional profit ratio and the work force continuity, this short paper first presents the explicit expression of an equilibrium bid markup strategy in procurement auctions. However, the two bidding criteria conflict with each other and tradeoffs must be made. To make tradeoffs between the two bidding criteria, a new bid markup selection making model is then developed by Cobb-Douglas utility function. The model generalizes the classical expected profit model in the sense that the latter's objective function is only a special case of the former. The result shows that the relative importance of a bidding criterion to another has significant effect on the selection of the equilibrium bid markup strategy.