the network design problem (ndp) is one of the important problems in combinatorial optimization. among the network design problems, the multicommodity capacitated network design (mcnd) problem has numerous applications in transportation, logistics, telecommunication, and production systems. the mcnd problems with splittable flow variables are np-hard, which means they require exponential time t...

The Network Design Problem (NDP) is one of the important problems in combinatorial optimization. Among the network design problems, the Multicommodity Capacitated Network Design (MCND) problem has numerous applications in transportation, logistics, telecommunication, and production systems. The MCND problems with splittable flow variables are NP-hard, which means they require exponential time t...

We study the polyhedra of splittable and unsplittable single arc{set relaxations of multicommodity ow capacitated network design problems. We investigate the optimization problems over these sets and the separation and lifting problems of valid inequalities for them. In particular, we give a linear{time separation algorithm for the residual capacity inequalities 19] and show that the separation...

We study the polyhedra of splittable and unsplittable single arc–set relaxations of multicommodity flow capacitated network design problems. We investigate the optimization problems over these sets and the separation and lifting problems of valid inequalities for them. In particular, we give a linear–time separation algorithm for the residual capacity inequalities [19] and show that the separat...

The Network Design Problem (NDP) is one of the important problems in combinatorial optimization. Among the network design problems, the Multicommodity Capacitated Network Design (MCND) problem has numerous applications in transportation, logistics, telecommunication, and production systems. The MCND problems with splittable flow variables are NP-hard, which means they require exponential time t...

We study the polyhedra of splittable and unsplittable arc sets of multicommodity ow capac-itated network design problems. We investigate the optimization problems over these polyhedra and the separation and lifting problems of valid inequalities for them. In particular, we give a linear-time separation algorithm for the residual capacity inequalities (Magnanti et al., 1993) and show that the se...

We study 0-1 reformulations of the multicommodity capacitated network design problem, which is usually modeled with general integer variables to represent, design decisions on the number of facilities to install on each arc of the network. The reformulations are based on the multiple choice model, a generic approach to represent piecewise linear costs using 0-1 variables. This model is improved...

In this paper, we propose a capacity scaling heuristic using a column generation and row generation technique to address the multicommodity capacitated network design problem. The capacity scaling heuristic is an approximate iterative solution method for capacitated network problems based on changing arc capacities, which depend on flow volumes on the arcs. By combining a column and row generat...