Given a set of n items with profits and weights and a knapsack capacity C, we study the problem of finding a maximal knapsack packing that minimizes the profit of selected items. We propose for the first time an effective dynamic programming (DP) algorithm which has O(nC) time complexity and O(n+C) space complexity. We demonstrate … Read more
In this paper we study integer linear programming models and develop branch-and-cut algorithms to solve the Black-and-White Traveling Salesman Problem (BWTSP) (Bourgeois et al., 2003) which is a variant of the well known Traveling Salesman Problem (TSP). Two strategies to model the BWTSP have been used in the literature. The problem is either modeled on … Read more
We introduce bi-objective models for ring tree network design with a focus on network reliability within telecommunication applications. Our approaches generalize the capacitated ring tree problem (CRTP) which asks for a partially reliable topology that connects customers with different security requirements to a depot node by combined ring and tree graphs. While the CRTP aims … Read more
We study the one-warehouse multi-retailer (OWMR) problem under deterministic dynamic demand and concave batch order costs, where order batches have an identical capacity and the order cost function for each facility is concave within the batch. Under appropriate assumptions on holding cost structure, we obtain lower bounds via a decomposition that splits the two-echelon problem … Read more
A path-block cycle is a graph that consists of several cycles that all intersect in a common subset of nodes. The associated 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) … Read more
A proper edge-coloring of a given undirected graph with natural numbers identified with colors is an interval (or consecutive) coloring if the colors of edges incident to each vertex form an interval of consecutive integers. Not all graphs admit such an edge-coloring and the problem of deciding whether a graph is interval colorable is NP-complete. … Read more
Physical properties of materials are seldom studied in the context of packing problems. In this work we study the behavior of semifluids: materials with particular characteristics, that share properties both with solids and with fluids. We describe the importance of some specific semifluids in an industrial context, and propose methods for tackling the problem of … Read more
We consider the 0-1 Knapsack Problem with Setups (KPS). Items are grouped into families and if any items of a family are packed, this induces a setup cost as well as a setup resource consumption. We introduce a new dynamic programming algorithm which performs much better than a previous dynamic program and turns out to … Read more
We consider, for complete bipartite graphs, the convex hulls of characteristic vectors of matchings, extended by a binary number indicating whether the matching contains two specific edges. This polytope is associated to the quadratic matching problem with a single linearized quadratic term. We provide a complete irredundant inequality description, which settles a conjecture by Klein … Read more
The multiple traveling salesmen problem with moving targets (MT-SPMT) is a generalization of the classical traveling salesmen problem (TSP), where the targets (cities or objects) are moving over time. Additionally, for each target a visibility time window is given. The task is to find routes for several salesmen so that each target is reached exactly … Read more