Accurate cost estimates for an incoming order are critical in formulating the optimal bidding strategy. When a firm is approaching its resource capacity, adding a new job into the system in the short-run may cause violations of the due date requirements, thus penalty costs arise. Failure to obtain an accurate estimate of the penalty costs often leads to sub-optimal bids. In this paper, we propose a two-stage model and procedure for optimal bidding under explicit resource constraints. The computational results indicate that our model and solution approach is both effective and efficient for the proposed problem.