The objective of this paper is to derive the theoretical relationship between demand uncertainty and the optimal facility location in one-dimensional space, when we describe the demand uncertainty by letting the weights to be random variables. First we derive the probability distribution of the minisum point and the density distribution of the average travel distance. Then we analyze the theoretical relationship between the standard deviation of the weight and those distributions. Second, defining six decision criteria, which include the concept of regret, we show the relationship between the demand uncertainty and the optimal facility location decided by those decision criteria.
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