TY - JOUR

T1 - Approximation algorithms for sequential batch-testing of series systems

AU - Daldal, Rebi

AU - Gamzu, Iftah

AU - Segev, Danny

AU - Ünlüyurt, Tonguç

N1 - Publisher Copyright:
© 2016 Wiley Periodicals, Inc.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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.

AB - 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.

KW - approximation algorithms

KW - function evaluation

KW - integer programming

KW - sequential testing

UR - http://www.scopus.com/inward/record.url?scp=84980048123&partnerID=8YFLogxK

U2 - 10.1002/nav.21693

DO - 10.1002/nav.21693

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AN - SCOPUS:84980048123

SN - 0894-069X

VL - 63

SP - 275

EP - 286

JO - Naval Research Logistics

JF - Naval Research Logistics

IS - 4

ER -