In this paper we introduce a new formulation of the VRPTW involving only binary variables associated with the arcs in the underlying digraph. The new formulation is based on the formulation of the ATSPTW by Ascheuer et al. [1] and has the advantage of avoiding additional variables and linking constraints. In the new formulation of the VRPTW time windows are modeled using path inequalities. The ...

— In this paper an algorithm for obtaining a Hamiltonian path from a shortest spanning tree ofa complete weighted graph isproposed. As a conséquence, two inequalities between the costs ofa shortest Hamiltonian path and a shortest spanning tree Tin the symmetrie EucUdean case are proposed. These inequalities involve the diameter of T or the number of terminal vertices of T and they become equali...

We develop the theory of twisted L-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on H(M, R) and they generalize the standard notions. A new feature of the twisted L-cohomology theory is that in addition to satisfying the standard L Morse inequalities, they also satisfy certain asymptotic L Morse inequalities. These...

We consider most of the known classes of valid inequalities for the graphical travelling salesman polyhedron and compute the worst-case improvement resulting from their addition to the subtour polyhedron. For example, we show that the comb inequalities cannot improve the subtour bound by a factor greater than ~. The corresponding factor for the class of clique tree inequalities is 8, while it i...

Path-block-cycle inequalities are valid, and sometimes facet-defining, inequalities for polytopes in connection with graph partitioning problems and corresponding multicut problems. Special cases of the inequalities were introduced by De Souza & Laurent (1995) and shown to be facet-defining for the equicut polytope. Generalizations of these inequalities were shown by Ferreira et al. (1996) to b...

The new concepts of repelling inequalities, repelling paths, and prime analytic centers are introduced. A repelling path is a generalization of the analytic central path for linear programming, and we show that this path has a unique limit. Furthermore, this limit is the prime analytic center if the set of repelling inequalities contains only those constraints that ‘‘shape’’ the polytope. Becau...

The fixed-charge transportation problem is an interesting problem in its own right. This paper further motivates its study by showing that it is both a special case and a strong relaxation of the big-bucket multi-item lot-sizing problem. We then provide a polyhedral analysis of the polynomially solvable special case in which the associated bipartite graph is a path. We give a O(n 3)-time optimi...

Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the BakryEmery curvature condition, the subordinate semigroup with power α satisfies a dimension-free Harnack inequality provided α ∈ ` 1 2 , 1 ́ , and it satisfies the log-Harnack inequality for all α ∈ (0, 1). Some infinite-dimensional examples are also presen...