TB12 - Advances in Location and Network Design

This study formulates a stochastic two-layer network design problem involving capacity decisions. Using a two-stage stochastic programming approach, we address demand and capacity uncertainties across interdependent layers. Strategic designs form the first stage, while supported-layer network design and flow decisions alongside outsourcing act as second-stage recourse mechanisms.

We study a Competitive Facility Location Problem with rank-based choice models to estimate customer behaviour. We reformulate the standard bilevel program, replacing primal assignment variables and constraints by their dual representation, to enable a Benders-inspired decomposition. Our branch-and-cut algorithm solves Quebec-inspired instances 10 times faster, on average, than baseline approaches.

We study a profit-oriented network design problem with elastic demand over arbitrary topologies. Demand is modeled via a gravity function sensitive to travel times. This results in a highly non-linear formulation. To solve it efficiently, we propose a logic-based Benders decomposition with dynamically generated secant cuts and several algorithmic enhancements.

While multi-period planning models typically assume that demand is defined independently for each time-period, multiple applications suggest that unmet demand may carry over to future time-periods and, in certain situations, even multiply. Based on applications in humanitarian logistics and facility location, we illustrate how such demand behavior can be modelled effectively, as well as the economical benefits of doing so.