We consider several formulations of two-dimensional two-stage constrained cutting, where the number of variables is polynomial. Some new models with variable strip widths are developed. Symmetries in the search space are eliminated by lexicographic constraints which are already known from the literature. However, previously known models with fixed strip widths are shown to be more effective. Th...

We present a new branch-and-cut algorithm for the capacitated vehicle routing problem (CVRP). The algorithm uses a variety of cutting planes, including capacity, framed capacity, generalized capacity, strengthened comb, multistar, partial multistar, extended hypotour inequalities, and classical Gomory mixed-integer cuts. For each of these classes of inequalities we describe our separation algor...

In this paper the Min-Max version of the Windy Rural Postman Problem with several vehicles is introduced. For this problem, in which the objective is to minimize the length of the longest tour in order to find a set of balanced tours for the vehicles, we present here an ILP formulation and study its associated polyhedron. Based on its partial description, a branch-and-cut algorithm has been imp...

In this paper we study the Multi-period Vehicle Routing Problem with Due dates (MVRPD), where customers have to be served between a release and a due date. Customers with due dates exceeding the planning period may be postponed at a cost. A fleet of capacitated vehicles is available to perform the distribution in each day of the planning period. The objective of the problem is to find vehicle r...

In this paper we deal with the polyhedral description and the resolution of the Directed General Routing Problem (DGRP) and the Stacker Crane Problem (SCP). The DGRP, in which the service activity occurs both at some of the nodes and at some of the arcs of a directed graph, contains a large number of important arc and node routing problems as special cases, including the SCP. Here, large famili...

After thirty years of doing other things, I am once again doing some research on integer programming. It has been interesting and exciting for me to see what has changed during those thirty years. The practical side of integer programming has developed far more than I would have ever anticipated. Problems of a size and complexity that we would never have thought of attempting thirty years ago a...

Absact Network loading problems occur in the design of telecommunication networks, in many different settings. The polyhedral structure of this problem is important in developing solution methods for the problem. In this paper we investigate the polytope of the problem restricted to one edge of the network (the edge capacity problem). We describe classes of strong valid inequalities for the edg...

The Traveling Salesman Problem with Pickup and Delivery (TSPPD) is defined on a graph containing pickup and delivery vertices between which there exists a one-toone relationship. The problem consists of determining a minimum cost tour such that each pickup vertex is visited before its corresponding delivery vertex. In this paper, the TSPPD is modeled as an integer linear program and its polyhed...

This paper deals with a variant of the well-known Cluster Editing Problem (CEP), more precisely, the p-CEP, in which a given input graph should be edited by adding and/or removing edges in such a way that p vertex-disjoint cliques (clusters) are generated with the minimum number of editions. We introduce several valid inequalities where some of them turned out to be very effective when implemen...

In the Traveling Salesman Problem with Pickup and Delivery (TSPPD) a single vehicle must serve a set of customer requests, each defined by an origin location where a load must be picked up, and a destination location where the load must be delivered. The problem consists of determining a shortest Hamiltonian cycle through all locations while ensuring that the pickup of each request is performed...