Optimal Allocation Without Money: An Engineering Approach

• Published in: Management science Vol. 62; no. 4; pp. 1078 - 1097
• Main Authors: Ashlagi, Itai, Shi, Peng
• Format: Journal Article
• Language: English
• Published: Linthicum INFORMS 01.04.2016; Institute for Operations Research and the Management Sciences
• Subjects: Approximation; assignment; Customer services; Economic aspects; Engineering; Engineering research; Finite element analysis; large-market approximation; market design; Methods; Money; optimal design; priors; Public schools; Resource allocation; school choice; Transfer of funds; Welfare
• ISSN: 0025-1909; 1526-5501
• DOI: 10.1287/mnsc.2015.2162

We study the allocation of heterogeneous services to agents with incomplete information and without monetary transfers. Agents have private, multidimensional utilities over services, drawn from commonly known priors. The social planner’s goal is to maximize a potentially complex public objective. For tractability, we take an “engineering” approach, in which we solve a large-market approximation, and convert the solution into a feasible finite-market mechanism that still yields good results. We apply this framework to real data from Boston to design a mechanism that assigns students to public schools, in order to maximize a linear combination of utilitarian and max-min welfare, subject to capacity and transportation constraints. We show how to optimally solve a large-market formulation with more than 868 types of students and 77 schools, and we translate the solution into a finite-market mechanism that significantly outperforms the baseline plan chosen by the city in terms of efficiency, equity, and predictability. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2015.2162 . This paper was accepted by Martin Lariviere, operations management.