The trade-off between the median and range of assigned demand in facility location models

In this paper, we present an extension of the classic p-median facility location model. The new formulation allows the user to trace the trade-off between the demand-weighted average distance (the traditional p-median objective) and the range in assigned demand. We extend the model to incorporate additional constraints that significantly reduce the computation time associated with the model. We also outline a genetic algorithm-based approach for solving the problem. The paper shows that significant reductions in the range in assigned demand are possible with relatively minor degradations in the average distance metric. The paper also shows that the genetic algorithm does very well at identifying the approximate trade-off curve. The model and algorithms were tested on real-life data-sets ranging in size from 33 nodes to 880 nodes.

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