Section: New Results

Network Design Problems

The delivery of freight from manufacturing platforms to demand zones is often managed through one or more intermediate locations where storing, merging, transshipment and consolidation activities are performed. In [15], we design a Two-Echelon Distribution Network that helps synchronize different flows of product. Under demand uncertainty, our model integrates decisions on the locations and the size of second echelon facilities an decisions on the flows assignment between the echelons, and on delivery routes to serve the demand zones.

In [8], we study the $k$-edge-connected $L$-hop-constrained network design problem. Given a weighted graph $G=(V,E)$, a set $D$ of pairs of nodes, two integers $L\ge 2$ and $k\ge 2$, the problem consists in finding a minimum weight subgraph of $G$ containing at least $k$ edge-disjoint paths of length at most $L$ between every pair $\{s,t\}\in D$. We consider the problem in the case where $L=2$, 3 and $\left|D\right|\ge 2$. We first discuss integer programming formulations introduced in the literature. Then, we introduce new integer programming formulations for the problem that are based on the transformation of the initial undirected graph into directed layered graphs. We present a theoretical comparison of these formulations in terms of LP-bound. Finally, these formulations are tested using CPLEX and compared in a computational study for $k=3,4,5$.