## Abstract

A population of items is said to be "group-testable", (i) if the items can be classified as "good" and "bad", and (ii) if it is possible to carry out a simultaneous test on a batch of items with two possible outcomes: "Success" (indicating that all items in the batch are good) or "failure" (indicating a contaminated batch). In this paper, we assume that the items to be tested arrive at the group-testing centre according to a Poisson process and are served (i.e., group-tested) in batches by one server. The service time distribution is general but it depends on the batch size being tested. These assumptions give rise to the bulk queueing model M/G^{(m,M)}/1, where m and M(>m) are the decision variables where each batch size can be between m and M. We develop the generating function for the steady-state probabilities of the embedded Markov chain. We then consider a more realistic finite state version of the problem where the testing centre has a finite capacity and present an expected profit objective function. We compute the optimal values of the decision variables (m, M) that maximize the expected profit. For a special case of the problem, we determine the optimal decision explicitly in terms of the Lambert function.

Original language | English |
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Pages (from-to) | 226-237 |

Number of pages | 12 |

Journal | European Journal of Operational Research |

Volume | 183 |

Issue number | 1 |

DOIs | |

State | Published - 16 Nov 2007 |

## Keywords

- Applied probability
- Quality control
- Queueing

## ASJC Scopus subject areas

- Computer Science (all)
- Modeling and Simulation
- Management Science and Operations Research
- Information Systems and Management