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Optimal set partitioning, matchings and lagrangian duality

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  • George L. Nemhauser
  • Glenn M. Weber

Abstract

We formulate the set partitioning problem as a matching problem with simple side constraints. As a result we obtain a Lagrangian relaxation of the set partitioning problem in which the primal problem is a matching problem. To solve the Lagrangian dual we must solve a sequence of matching problems each with different edge‐weights. We use the cyclic coordinate method to iterate the multipliers, which implies that successive matching problems differ in only two edge‐weights. This enables us to use sensitivity analysis to modify one optimal matching to obtain the next one. We give theoretical and empirical comparisons of these dual bounds with the conventional linear programming ones.

Suggested Citation

  • George L. Nemhauser & Glenn M. Weber, 1979. "Optimal set partitioning, matchings and lagrangian duality," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(4), pages 553-563, December.
    • Handle: RePEc:wly:navlog:v:26:y:1979:i:4:p:553-563
    DOI: 10.1002/nav.3800260401
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