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Two Dimensional Optimal Mechanism Design for a Sequencing Problem

  • Conference paper
Integer Programming and Combinatorial Optimization (IPCO 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7801))

Abstract

We propose an optimal mechanism for a sequencing problem where the jobs’ processing times and waiting costs are private. Given public priors for jobs’ private data, we seek to find a scheduling rule and incentive compatible payments that minimize the total expected payments to the jobs. Here, incentive compatible refers to a Bayes-Nash equilibrium. While the problem can be efficiently solved when jobs have single dimensional private data, we here address the problem with two dimensional private data. We show that the problem can be solved in polynomial time by linear programming techniques, answering an open problem in [13]. Our implementation is randomized and truthful in expectation. The main steps are a compactification of an exponential size linear program, and a combinatorial algorithm to decompose feasible interim schedules. In addition, in computational experiments with random instances, we generate some more insights.

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Authors and Affiliations

  1. Dept. Applied Mathematics, University of Twente, P.O. Box 217, 7500AE, Enschede, The Netherlands

    Ruben Hoeksma & Marc Uetz

Authors
  1. Ruben Hoeksma
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  2. Marc Uetz
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Editor information

Editors and Affiliations

  1. Massachusetts Institute of Technology, 77 Massachusetts Ave., 02139, Cambridge, MA, USA

    Michel Goemans

  2. Universidad de Chile, Santiago, Chile

    José Correa

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Hoeksma, R., Uetz, M. (2013). Two Dimensional Optimal Mechanism Design for a Sequencing Problem. In: Goemans, M., Correa, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2013. Lecture Notes in Computer Science, vol 7801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36694-9_21

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  • DOI: https://doi.org/10.1007/978-3-642-36694-9_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36693-2

  • Online ISBN: 978-3-642-36694-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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