In December 2010 President Obama signed the child nutrition bill, reauthorizing $4.5 billion for the expansion of free school lunch programs for low-income public school students. The bill was notable because it was the first piece of legislation linking federally subsidized school meals to nutrition standards — standards that will bring higher prices for middle-income students whose families pay for their school lunches. While the increases are small, ranging from 10 to 25 cents per meal depending on the school district, and prices have held steady for years, they represent a sizable increase in the current average of $2.46 per meal.
The nation’s school districts could look to Professors Marcelo Olivares and Gabriel Weintraub for help controlling overall costs. A decade ago the Chilean government was purchasing its school meals at high prices and receiving a poor product in return. School meal service is a complex logistical operation that typically includes everything from purchasing bulk food to transporting food to schools, employing cooks, and purchasing utensils. At that time, Weintraub and several Chilean colleagues developed a combinatorial auction that reduced school lunch prices by 25 percent, allowing Chilean schools to feed 300,000 more school children while improving food service and quality.
A combinatorial auction allows each vendor to place multiple bids to provide a product or service in a variety of combinations. Any vendor could put in a bid to service region A, another bid to service region B, and a third bid to service both regions. Combining bids should, in theory, surface economies of scale that reduce the average per-meal costs of providing the service for both territories. If the bid regions are located nearby one another, economies of density should further reduce prices because transportation costs decrease. Bidders benefit because they no longer risk winning a contract for a single unit at a loss in cases where they don’t win their most cost-effective or profitable combinations. Buyers benefit because with the reduced risk comes more aggressive bidding — in short, lower prices.
The auction’s longevity gave Olivares and Weintraub access to ten years of data, allowing them to conduct the first empirical research project in a large-scale combinatorial auction, along with Rafael Epstein (one of the auction’s architects) and Daniel Yung of the University of Chile. Overall, the researchers’ analysis shows that the auctions are valuable to all users, revealing strong cost synergies that can be traced directly to economies of scale and density. They also make suggestions to improve the design of these auctions even further.
Auctioneers must take care in the design and execution of their combinatorial auctions. “It’s not a no-brainer to run these auctions,” Weintraub cautions. “They are complicated and can actually hurt the auctioneer if not carried out well or when they are not appropriate.” For example, a bidder could potentially take advantage of the flexibility offered by combination bids by strategically placing bids, and winning units for which he is not the most cost efficient provider, increasing overall prices. One answer is for buyers to ban some combinations in bidding and only permit bids among units that exhibit sufficiently high cost synergies. Olivares and Weintraub perform an empirical analysis to identify these combinations.
In addition, auctioneers must be attuned to the trade-offs between short-run cost efficiency and long-run competition. “It might be cheaper today to give all contracts to a few large suppliers that can exploit their size and economy of scale and therefore afford to bid low,” Olivares says. “But when smaller suppliers that may cost a bit more get priced out of the market and don’t survive to participate in the next auction, pricing will be far less competitive in the long run.”
To address this issue, buyers could also place some parameters on allowable combinations, such as prohibiting any single firm from securing more than 20 percent of the entire allocation. The researchers found that such constraints are beneficial because cost synergies that pass on competitive prices to the auctioneers can only be gained up to a certain point.
Olivares and Weintraub’s paper is being used to evaluate changes under a new Chilean government, and other applications run from transportation to communications. The London Bus Authority uses combinatorial auctions with private contractors to increase the efficiency of its routes. The FCC has considered running combinatorial auctions to allocate the broadcast spectrum around the United States. Several private companies use combinatorial auctions as part of their procurement efforts.
While complex, combinatorial auctions offer flexibility for suppliers and competitive pricing for buyers. “Despite the upfront investment,” Weintraub says, “if well-run, the auctions are worth the cost and effort.”
Marcelo Olivares is associate professor of decision, risk, and operations and a senior scholar at the Jerome A. Chazen Institute of International Business at Columbia Business School.
Gabriel Weintraub is associate professor of decision, risk, and operations and a senior scholar at the Jerome A. Chazen Institute of International Business at Columbia Business School.