An algorithm for the separation of two-row cuts

We consider the question of finding deep cuts from a model constructed with two rows of a simplex tableau. To do that, we show how to reduce the complexity of setting up the polar of such model from a quadratic number of integer hull computations to a linear number of integer hull computations. Furthermore we … Read more

Designing AC Power Grids using Integer Linear Programming

Recent developments have drawn focus towards the efficient calculation of flows in AC power grids, which are difficult to solve systems of nonlinear equations. The common linearization approach leads to the well known and often used DC formulation, which has some major drawbacks. To overcome these drawbacks we revisit an alternative linearization of the AC … Read more

On n-step MIR and Partition Inequalities for Integer Knapsack and Single-node Capacitated Flow Sets

Pochet and Wolsey [Y. Pochet, L.A. Wolsey, Integer knapsack and flow covers with divisible coefficients: polyhedra, optimization and separation. Discrete Applied Mathematics 59(1995) 57-74] introduced partition inequalities for three substructures arising in various mixed integer programs, namely the integer knapsack set with nonnegative divisible/arbitrary coefficients and two forms of single-node capacitated flow set with divisible … Read more

Improving the LP bound of a MILP by dual concurrent branching and the relationship to cut generation methods

In this paper branching for attacking MILP is investigated. Under certain circumstances branches can be done concurrently. By introducing a new calculus it is shown there are restrictions for certain dual values and reduced costs. As a second unexpected result of this study a new class of cuts for MILP is found, which are defined … Read more

Solution Methods for the Multi-trip Elementary Shortest Path Problem with Resource Constraints

We investigate the multi-trip elementary shortest path problem (MESPPRC) with resource constraints in which the objective is to find a shortest path between a source node and a sink node such that nodes other than the specified replenishment node are visited at most once and resource constraints are not violated. After each visit to the … Read more

A Chance-Constrained Model & Cutting Planes for Fixed Broadband Wireless Networks

In this paper, we propose a chance-constrained mathematical program for fixed broadband wireless networks under unreliable channel conditions. The model is reformulated as integer linear program and valid inequalities are derived for the corresponding polytope. Computational results show that by an exact separation approach the optimality gap is closed by 42 % on average. ArticleDownload … Read more

A Dynamic Inequality Generation Scheme for Polynomial Programming

Hierarchies of semidefinite programs have been used to approximate or even solve polynomial programs. This approach rapidly becomes computationally expensive and is often tractable only for problems of small size. In this paper, we propose a dynamic inequality generation scheme to generate valid polynomial inequalities for general polynomial programs. When used iteratively, this scheme improves … Read more

Lifted Inequalities for 0−1 Mixed-Integer Bilinear Covering Sets

In this paper, we study 0-1 mixed-integer bilinear covering sets. We derive several families of facet-defining inequalities via sequence-independent lifting techniques. We then show that these sets have polyhedral structures that are similar to those of certain fixed-charge single-node flow sets. As a result, we obtain new facet-defining inequalities for these sets that generalize well-known … Read more

Recoverable Robust Knapsack: the Discrete Scenario Case

Admission control problems have been studied extensively in the past. In a typical setting, resources like bandwidth have to be distributed to the different customers according to their demands maximizing the profit of the company. Yet, in real-world applications those demands are deviating and in order to satisfy their service requirements often a robust approach … Read more

Recoverable Robust Knapsacks: $\GammahBcScenarios

In this paper, we investigate the recoverable robust knapsack problem, where the uncertainty of the item weights follows the approach of Bertsimas and Sim (2003,2004). In contrast to the robust approach, a limited recovery action is allowed, i.e., upto k items may be removed when the actual weights are known. This problem is motivated by … Read more