### Abstract

In this paper, the definition of medians in 'classical' location problems is generalized to the cases: 1) when generated demands and travel costs are random, and 2) when the demand induced at the facilities is random because of competition. Under a particular set of assumptions, the well-known theorems on 'optimality of node locations' hold for the underlying 'probabilistic networks'. For case 1) the model is shown to be a generalization of the probabilistic and deterministic median location problem is also pointed out. For case 2) the 'competitive median location' problem is formulated, and some results presented. For the special structure of probabilistic tree networks some interesting localization properties for both medians are discussed.-from Authors

Original language | English (US) |
---|---|

Pages (from-to) | 917-932 |

Number of pages | 16 |

Journal | Environment and Planning A |

Volume | 14 |

Issue number | 7 |

State | Published - 1982 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Environmental Science (miscellaneous)
- Geography, Planning and Development

### Cite this

*Environment and Planning A*,

*14*(7), 917-932.

**Probabilistic demands and costs in facility location problems.** / Mirchandani, Pitu; Oudjit, A.

Research output: Contribution to journal › Article

*Environment and Planning A*, vol. 14, no. 7, pp. 917-932.

}

TY - JOUR

T1 - Probabilistic demands and costs in facility location problems.

AU - Mirchandani, Pitu

AU - Oudjit, A.

PY - 1982

Y1 - 1982

N2 - In this paper, the definition of medians in 'classical' location problems is generalized to the cases: 1) when generated demands and travel costs are random, and 2) when the demand induced at the facilities is random because of competition. Under a particular set of assumptions, the well-known theorems on 'optimality of node locations' hold for the underlying 'probabilistic networks'. For case 1) the model is shown to be a generalization of the probabilistic and deterministic median location problem is also pointed out. For case 2) the 'competitive median location' problem is formulated, and some results presented. For the special structure of probabilistic tree networks some interesting localization properties for both medians are discussed.-from Authors

AB - In this paper, the definition of medians in 'classical' location problems is generalized to the cases: 1) when generated demands and travel costs are random, and 2) when the demand induced at the facilities is random because of competition. Under a particular set of assumptions, the well-known theorems on 'optimality of node locations' hold for the underlying 'probabilistic networks'. For case 1) the model is shown to be a generalization of the probabilistic and deterministic median location problem is also pointed out. For case 2) the 'competitive median location' problem is formulated, and some results presented. For the special structure of probabilistic tree networks some interesting localization properties for both medians are discussed.-from Authors

UR - http://www.scopus.com/inward/record.url?scp=0020436532&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020436532&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0020436532

VL - 14

SP - 917

EP - 932

JO - Environment and Planning A

JF - Environment and Planning A

SN - 0308-518X

IS - 7

ER -