## Abstract

We consider the following optimal selection problem: There are n identical assets which are to be sold, one at a time, to coming bidders. The bids are i.i.d. where there are only two possible bid-values, with known probabilities. The stream of bidders constitutes a general renewal process, and rewards are continuously discounted at a constant rate. The objective is to maximize the total expected discounted revenue from the sale of the n assets. The optimal policy here is stationary, where the decision in question is only whether to accept a low bid or not; the answer is affirmative depending on a critical number n * of remaining assets. In this paper we derive an explicit formula for n *, being a function of the Laplace transform of the renewal distribution evaluated at the discount rate, the probability for a low bid, and the ratio between the two bid-values. We also specify the pertinent value functions. Applications of the model are discussed in detail, and extensions are made to include holding costs and to allow for optimal pricing.

Original language | English |
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Pages (from-to) | 576-584 |

Number of pages | 9 |

Journal | European Journal of Operational Research |

Volume | 110 |

Issue number | 3 |

DOIs | |

State | Published - 1 Nov 1998 |

## Keywords

- Asset selling
- Dynamic programming
- Pricing
- Secretary problems

## ASJC Scopus subject areas

- General Computer Science
- Modeling and Simulation
- Management Science and Operations Research
- Information Systems and Management