Cite as:

Mirchandani P B, Oudjit A, 1982, "Probabilistic demands and costs in facility location problems" *Environment and Planning A* **14**(7) 917 – 932

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**Probabilistic demands and costs in facility location problems**

**P B Mirchandani, A Oudjit**

Received 17 March 1981, in revised form 3 August 1981

**Abstract. **When deterministic assumptions in 'classical' location problems are relaxed some new theoretical and algorithmic problems arise. In this paper, the definition of *medians *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 problems on networks. The relationship of the model to a multicommodity location problem is also pointed out. Additionally, within the framework of the problem formulation, certain parallels with multiobjective location problems are drawn. 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 the 1-median and 2-median are discussed.

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