Reliability-dependent combined network design and routing optimization

The capacitated Fixed-Charge Network Design (FCND) problem deals with the simultaneous optimization of capacity installation and routing of traffic, where a fixed cost is paid for opening a link and a linear routing cost is paid for sending traffic flow on a link. The routing decision must be performed such that flows remain bounded by the installed capacities. This problem appears as a particular case of the combined network design and traffic flow routing problem with time-dependent demands as developed in this paper. This general problem can be formulated as a multi-period mixed integer optimization problem. A compact formulation based on the aggregation of flows by destination and an extended formulation, where flows are decomposed by origin-destination pairs while keeping the requirement of destination-based routing, have been proposed in [1] and [2], respectively. As these computational improvements enable to progressively overcome the limit of solving such problem when the network size and number of periods increases, we propose an extended model that accounts for different patterns of failures affecting installed arcs over time. The latter lead to consider time-variable link maintenance cost function as part of our generalized formulation. We also analyze the quality of the results for the proposed formulation with different link maintenance cost functions with the objective to derive the best arc replacement strategy.