In this paper, we derive new families of piecewise linear facet-defining inequalities for the finite group problem and extreme inequalities for the infinite group problem using approximate lifting. The new valid inequalities for the finite group problem are twoand three-slope facet-defining inequalities as well as the first family of four-slope facet-defining inequalities. The new valid inequal...

We improve the mixed-integer programming formulation of the multicommodity capacitated fixed-charge network design problem by incorporating valid inequalities into a cutting-plane algorithm. We use five classes of valid inequalities: the strong, cover, minimum cardinality, flow cover, and flow pack inequalities. The first class is particularly useful when a disaggregated representation of the c...

L.A. Wolsey * A class of strong valid inequalities is described for the single-item uncapacitated economic lot-sizing problem with start-up costs. It is shown that these inequalities yield a complete polyhedral characterization of the problem. The corresponding separation problem is formulated as a shortest path problem. Finally, a reformulation as a plant location problem is shown to imply the...

We propose in this paper a tour of the symmetric traveling salesman polytope, focusing on inequalities that can be deened on sets. The most known inequalities are all of this type. Many papers have appeared which give more and more complex valid inequalities for this polytope, but no intuitive idea on why these inequalities are valid has ever been given. In order to help in understanding these ...

Flow cover inequalities are among the most effective valid inequalities for solving capacitated fixed-charge network flow problems. These valid inequalities are implications on the flow quantity on the cut arcs of a two-partitioning of the network, depending on whether some of the cut arcs are open or closed. As the implications are only on the cut arcs, flow cover inequalities can be modeled b...

We consider the single item capacitated lot–sizing problem, a well-known production planning model that often arises in practical applications, and derive new classes of valid inequalities for it. We first derive new, easily computable valid inequalities for the continuous 0–1 knapsack problem, which has been introduced recently and has been shown to provide a useful relaxation of mixed 0-1 int...

In this paper, we consider the problem of scheduling on two-machine permutation flowshop with minimal time lags between consecutive operations of each job. The aim is to find a feasible schedule that minimizes the total tardiness. This problem is known to be NP-hard in the strong sense. We propose two mixed-integer linear programming (MILP) models and two types of valid inequalities which aim t...

An explicit description of the convex hull of solutions to the uncapacitated lot-sizing problem with backlogging, in its natural space of production, setup, inventory and backlogging variables, has been an open question for many years. In this paper, we identify valid inequalities that subsume all previously known valid inequalities for this problem. We show that these inequalities are enough t...

In this paper our primary concern is with the establishment of weighted Hardy inequalities in L(Ω) and Rellich inequalities in L(Ω) depending upon the distance to the boundary of domains Ω ⊂ R with a finite diameter D(Ω). Improved constants are presented in most cases.