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Political Science
Public Policy

Solving multiple scenarios in a combinatorial auction

Profile image of Cristian MartinezCristian Martinez

2009, Computers & Operations Research

https://doi.org/10.1016/J.COR.2008.12.006
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7 pages

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Abstract

As part of its social policy, the government of Chile provides more than 1.8 million meals daily to public schoolchildren under the authority of Junta Nacional de Auxilio Escolar y Becas (JUNAEB), the state agency responsible for the program, at an annual cost of 360 million dollars. The service is provided by private firms chosen through an annual public auction. In order to capture economies of scale, a combinatorial auction design is implemented, allowing suppliers to bid on different sets of geographical units within the country. The bid evaluation process must solve multiple scenarios of a difficult combinatorial optimization model. To date, more than 2 billion dollars have been awarded under this methodology. In this paper, we describe the 2006 auction process and report that solution times can be significantly improved if the scenarios are solved in an appropriate order and the optimal solution to one scenario is employed as the initial solution of another. Results reflecting these improvements are given for real instances of the 2006 auction.

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A combinatorial auction improves school meals in Chile: a case of OR in developing countries
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Chile's 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 NPcomplete with more than 10,000 binary variables. This new methodology improved the pricequality ratio of the meals with yearly savings of around US$40 million-equivalent to the cost of feeding 300,000 children during one year. (Games/group decisions: bidding/auctions. Government: agencies.) EPSTEIN, HENRÍQUEZ, CATALÁ N, WEINTRAUB, AND MARTÍNEZ

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Related topics

  • Applied Mathematics
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  • Combinatorial Auction
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