A Combinational Auction Improves School Meals in Chile

Chileȧs school system is using mathematical modeling to assign catering contracts in a singleround sealed-bid combinational auction. The Chilean state spends around US$180 million a year to feed 1,300,000 students from low income families, making this one of the largest state auctions. To improve the quality of the assignment in the auction process, we constructed an integer linear programming model to decide contract awards optimally among different concession holders. The model completely changed the nature of the process in three crucial aspects. First, it gave transparency and objectivity to the complete process, generating competition among firms. Second, it allowed the companies to build flexible territorial bids to include their scale economies, leading to efficient resource allocation. Finally, the model indeed found an optimal solution, which is not easy because the assignment problem was NP-complete with more than 10,000 binary variables. This new methodology improved the price-quality ratio of the meals with yearly savings of around US$40 million—equivalent to the cost of feeding 300,000 children during one year.