Incorporation dynamic aspects and uncertainty in 1-median location problems

In this paper we present several 1-median formulations on a tree network which incorporate dynamic evolution and/or uncertainty of node demands and transportation costs over a planning horizon. Dynamic evolution is modeled using linear demand functions for the nodes and linear length functions for the edges. Uncertainty is modeled with the use of multiple scenarios, where a scenario is a complete specification of the uncertain node demands and/or edge lengths. We formulate our objective using minimax regret like criteria. We use two different criteria, namely, robust deviation and relative robustness. We discuss what motivated the introduction of these objectives, as well as their relation to existing literature and decision making practices. For all of the models presented, we provide low-order polynomial time algorithms.