We study the resource loading problem, which arises in tactical capacity planning. In this one has to plan intensity of execution a set orders minimize cost function that penalizes use above given limits and completion after their due dates. Our main contributions include novel mixed-integer linear-programming (MIP)‐based formulation, investigation polyhedra associated with feasible assignments...

Branch & Cut is today’s state-of-the-art method to solve 0/1-integer linear programs. Important for the success of this method is the generation of strong valid inequalities, which tighten the linear programming relaxation of 0/1IPs and thus allow for early pruning of parts of the search tree. In this paper we present a novel approach to generate valid inequalities for 0/1IPs which is based on ...

Branch & Cut is today’s state-of-the-art method to solve 0/1-integer linear programs. Important for the success of this method is the generation of strong valid inequalities, which tighten the linear programming relaxation of 0/1IPs and thus allow for early pruning of parts of the search tree. In this paper we present a novel approach to generate valid inequalities for 0/1-IPs which is based on...

Given a complete and undirected graph G, the Adjacent Only Minimum Spanning Tree Problem (AQMSTP) consists of finding a spanning tree that minimizes a quadratic function of its adjacent edges. The strongest AQMSTP linear integer programming formulation in the literature works in an extended variable space, using exponentially many decision variables assigned to the stars of G. In this paper, we...

Aparametric form of tabu-search is proposed for solvingmixed integer programming (MIP) problems that creates and solves a series of linear programming (LP) problems embodying branching inequalities as weighted terms in the objective function. The approach extends and modifies a parametric branch and bound procedure of Glover [Parametic branch and bound. OMEGA, The International Journal of Manag...

Cutting plane methods are exact algorithms for integer programming problems. They have proven to be very useful computationally in the last few years, especially when combined with a branch and bound algorithm in a branch and cut framework. These methods work by solving a sequence of linear programming relax-ations of the integer programming problem. The relaxations are gradually improved to gi...

This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first stage approximation is solved using a branch-and-bound tree with nodes inheriting Benders’ cuts that are valid for their ancestor nodes. In addition, we develop two closely related convexification ...

We are given a graph G=(V?T,E), with V?T the set of vertices where T is terminals and E edges. The multi-terminal vertex separator problem consists in finding subset S?V minimum size intersecting all paths between every pair terminals. In this paper we present three extended linear integer programming formulations for develop Branch-and-Price Branch-and-Cut-and-Price algorithms. For each formul...

In this paper we deal with the critical node problem, where a given number of nodes has to be removed from an undirected graph in order to maximize the disconnections between the node pairs of the graph. We propose an integer linear programming model with a non-polynomial number of constraints but whose linear relaxation can be solved in polynomial time. We derive different valid inequalities a...

Branch-and-price algorithms based on Dantzig-Wolfe decomposition have shown great success in solving mixed integer linear optimization problems (MILPs) with specific identifiable structure, such as vehicle routing and crew scheduling problems. For unstructured MILPs, the most frequently used methodology is branch-and-cut, which depends on generation of “generic” classes of valid inequalities to...