Robust 1-Median Location Problems: Dynamic Aspects and Uncertainty

Abstract

In Chapter 2, Example 9, we introduced the robust 1-median location on a tree problem, and later in the same chapter we introduced a variation of this problem referred to as the dynamically robust 1-median location on a tree. The robust 1-median on a tree problem, as introduced in Chapter 2, addresses the location of a single facility on a tree network in the presence of significant uncertainty in the node weights (node demands) and edge lengths (transportation cost). 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. The dynamically robust 1-median location problem, as introduced in Example 10 of Chapter 2, uses again multiple data scenarios, however the multiplicity of scenarios is not caused by parameter uncertainty but by the dynamic evolution of the parameters of the location decision model (i.e., dynamic evolution of node demands and/or transportation costs). The purpose of this chapter is to propose a unifying approach for incorporating dynamic aspects (i.e., variation over time) and/or uncertainty of important input data (i.e., parameters of the decision model) in the location decision making process. The problem under consideration is a 1-median problem on a tree. All points of the network, nodes or not, are eligible for locating the facility. The weights (demands) of the various nodes are either of a dynamic nature or uncertain.