Many firms increasingly rely on suppliers for intermediate and finished goods. Some companies (e.g., CISCO) even eliminated in-house production capabilities. While production outsourcing is often cost-effective, firms also lose some manufacturing and technical capabilities that are relevant to estimate production cost. One way to address this is creating cost models to estimate the costs of potential suppliers so that the firm can use the information to negotiate an attractive price with suppliers. However, in settings where the buyer wishes to negotiate a contract price by soliciting competitive bids from multiple suppliers, the benefit of cost modeling is not clear since the bidding competition among suppliers can itself reveal cost information. In this paper, we examine this interplay, and examine if and when cost modeling should be used prior to competitive bidding. We show that although bid competition sometimes duplicates the information gleaned by cost modeling, cost modeling can still be benefit the buyer by helping the buyer to tighten a reserve price. We then analyze under what situations the buyer can gain the most benefit through cost modeling. Specifically, we characterize which supplier(s) to learn about, which portion(s) of the costs to learn, and how deeply the buyer should learn.  We then apply these results to design the optimal learning strategy when the buyer has multiple supply bases and/or  costs are correlated. Interestingly, learning about the supplier whose cost is the most uncertain is not necessarily optimal, nor is learning about the cost portion that contributes most to the total cost. We also show that conventional intuition that the benefit of additional information has a diminishing rate of return does not always apply when it comes to cost modeling.