Dynamic location under uncertainty

The authors consider an uncapacitated dynamic location problem. Given a set of customers and a set of possible locations, they want to decide when and where to install facilities and, for each time period, how to assign customers to the installed facilities. For each time period there is a variable production and distribution cost associated to every customer-location pair, and a fixed installation cost connected to every location. These costs are uncertain. With limited information about the uncertainty, it may be appropriate to generate scenarios with different weights (e.g. probabilities) connected to them to reflect their relative importance. The present objective is to minimize the expected present value of total costs. This stochastic problem gives rise to a large and complex mixed-integer-model. The authors use the scenario and policy aggregation developed by Rockafellar and Wets for the case of continuous variables to find implementable solutions, i.e. policies that do not depend on hindsight. Under the scenario and policy aggregation scheme, they solve the stochastic problem by solving perturbed scenario-problems. Given a scenario the problem can be viewed as a deterministic dynamic location problem. The authors have tested the algorithm on a set of small test problems and it seems to converge nicely in spite of the problem at hand being a mixed-integer-problem.