Optimization Letters

, Volume 12, Issue 7, pp 1503–1521 | Cite as

Solving 0–1 semidefinite programs for distributionally robust allocation of surgery blocks

  • Yiling Zhang
  • Siqian Shen
  • S. Ayca Erdogan
Original Paper


We allocate surgery blocks to operating rooms (ORs) under random surgery durations. Given unknown distribution of the duration of each block, we investigate distributionally robust (DR) variants of two types of stochastic programming models using a moment-based ambiguous set. We minimize the total cost of opening ORs and allocating surgery blocks, while constraining OR overtime via chance constraints and via an expected penalty cost in the objective function, respectively in the two types of models. Following conic duality, we build equivalent 0–1 semidefinite programming (SDP) reformulations of the DR models and solve them using cutting-plane algorithms. For the DR chance-constrained model, we also derive a 0–1 second-order conic programming approximation to obtain less conservative solutions. We compare different models and solution methods by testing randomly generated instances. Our results show that the DR chance-constrained model better controls average and worst-case OR overtime, as compared to the stochastic programming and DR expected-penalty-based models. Our cutting-plane algorithms also outperform standard optimization solvers and efficiently solve 0–1 SDP formulations.


Distributionally robust optimization Chance-constrained programming Stochastic programming 0–1 Semidefinite programming Cutting-plane algorithm 0–1 Second-order conic programming 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial and Operations EngineeringUniversity of MichiganAnn ArborUSA
  2. 2.Department of Industrial and Systems EngineeringSan Jose State UniversitySan JoseUSA

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