## Abstract

We introduce and study a generalization of the classic sequential testing problem, asking to identify the correct state of a given series system that consists of independent stochastic components. In this setting, costly tests are required to examine the state of individual components, which are sequentially tested until the correct system state can be uniquely identified. The goal is to propose a policy that minimizes the expected testing cost, given a-priori probabilistic information on the stochastic nature of each individual component. Unlike the classic setting, where variables are tested one after the other, we allow multiple tests to be conducted simultaneously, at the expense of incurring an additional set-up cost. The main contribution of this article consists in showing that the batch testing problem can be approximated in polynomial time within factor 6.829 + ϵ, for any fixed ϵ ∈ (0,1). In addition, we explain how, in spite of its highly nonlinear objective function, the batch testing problem can be formulated as an approximate integer program of polynomial size, while blowing up its expected cost by a factor of at most 1 + ϵ. Finally, we conduct extensive computational experiments, to demonstrate the practical effectiveness of these algorithms as well as to evaluate their limitations.

Original language | English |
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Pages (from-to) | 275-286 |

Number of pages | 12 |

Journal | Naval Research Logistics |

Volume | 63 |

Issue number | 4 |

DOIs | |

State | Published - 1 Jun 2016 |

### Bibliographical note

Publisher Copyright:© 2016 Wiley Periodicals, Inc.

## Keywords

- approximation algorithms
- function evaluation
- integer programming
- sequential testing

## ASJC Scopus subject areas

- Modeling and Simulation
- Ocean Engineering
- Management Science and Operations Research