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In this paper, we apply the minimum information theory to the uncapacitated  p- median facility location problem to determine the most probable allocation solution. Indeed, we investigate the  bi -level  p -median model introduced by [TRANSPORT RES B-METH. 123 (2019) 1–20] in the case that facilities have unlimited capacities. At the upper level, minimizing the cost of establishing facilities and allocating demands is considered, while the most probable allocation solution in the customers’ point of view is determined through the lower level. By adding the Karush-Kuhn-Tucker optimality conditions of the lower-level problem to the upper-level constraints, the  bi -level model is reduced to a one-level linear mixed integer problem. Some numerical examples are provided to verify the added value of the proposed model and its solution method.

The minimum information approach to the uncapacitated p -median facility location problem