To be successful in a competitive environment, contractors have to prepare their bids wisely. The two main decisions they have to make are the project selection decision and the markup selection decision. This paper proposes a new optimization model that combines these two main decisions. It also takes into account the importance of eminence and previous works as the most important non-monetary evaluation criterion used by owners for evaluating bids. These factors combined with the two decisions make this model complex and nonlinear. To solve this model, a customized Genetic Algorithm is developed. Using Monte Carlo simulation, the result of the model is compared to the results of conventional models that only consider bidding markups. The comparison shows that considering eminence can increase the expected profit of the contractor to more than 25% under some evaluation criteria mindsets of the owner.