In this paper we conduct an empirical investigation of a large-scale combinatorial auction (CA)—the Chilean auction for school meals in which the government procures half a billion dollars worth of meal services every year. Our empirical study is motivated by two fundamental aspects in the design of CAs: (1) which packages should bidders be allowed to bid on and (2) diversifying the supplier base to promote competition. We use bidding data to uncover important aspects of the firms’ cost structure and their strategic behavior, both of which are not directly observed by the auctioneer; these estimates inform the auction design. Our results indicate that package bidding that allows firms to express their cost synergies due to economies of scale and density seems appropriate. However, we also found evidence that firms can take advantage of this flexibility by discounting package bids for strategic reasons and not driven by cost synergies. Because this behavior can lead to inefficiencies, it may be worth evaluating whether to prohibit certain specific combinations in the bidding process. Our results also suggest that market share restrictions and running sequential auctions seem to promote competition in the long run, without significantly increasing the short-run cost for the government due to unrealized cost synergies. Our results highlight that the simultaneous consideration of the firms’ operational cost structure and their strategic behavior is key to the successful design of a CA. More broadly, our paper is the first to provide an econometric study of a large-scale CA, providing novel and substantive insights regarding bidding behavior in this type of auction.