In this paper, we study deterministic dynamic lot-sizing problems with service level constraints on the total number of periods in which backorders can occur over the finite planning horizon. We give a natural mixed integer programming formulation for the single item problem (LS-SL-I) and study the structure of its solution. We show that an optimal … Read more
Dantzig-Wolfe decomposition is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs) in practice. However, the method is not part of any state-of-the-art MIP solver: it needs tailoring to the particular problem; the typical bordered block-diagonal matrix structure determines the decomposition; the resulting column generation subproblems need to be solved efficiently; … Read more
Proportional symbol maps are a cartographic tool to assist in the visualization and analysis of quantitative data associated with specific locations, such as earthquake magnitudes, oil well production, and temperature at weather stations. As the name suggests, symbol sizes are proportional to the magnitude of the physical quantities that they represent. We present two novel … Read more
The feasibility pump (FP) [5,7] has proved to be a successful heuristic for finding feasible solutions of mixed integer linear problems (MILPs). FP was improved in [1] for finding better quality solutions. Briefly, FP alternates between two sequences of points: one of feasible so- lutions for the relaxed problem (but not integer), and another of … Read more
The lift-and-project closure is the relaxation obtained by computing all lift-and-project cuts from the initial formulation of a mixed integer linear program or equivalently by computing all mixed integer Gomory cuts read from all tableau’s corresponding to feasible and infeasible bases. In this paper, we present an algorithm for approximating the value of the lift-and-project … Read more
In this paper we consider a relaxation of the corner polyhedron introduced by Andersen et al., which we denote by RCP. We study the relative strength of the split and triangle cuts of RCP’s. Basu et al. showed examples where the split closure can be arbitrarily worse than the triangle closure under a `worst-cost’ type … Read more
The cutting plane tree (CPT) algorithm provides a finite disjunctive programming procedure to obtain the solution of general mixed-integer linear programs (MILP) with bounded integer variables. In this paper, we present our computational experience with variants of the CPT algorithm. Because the CPT algorithm is based on discovering multi-term disjunctions, this paper is the first … Read more
This article extends a previous work focused on a mixed integer programming (MIP) based heuristic approach, aimed at solving non-standard three-dimensional problems with additional conditions. The paper that follows considers a mixed integer non-linear (MINLP) reformulation of the previous model, to improve the former heuristic, based on linear relaxation. The approach described herewith is addressed, … Read more
Geometric random walks have been proposed and analyzed for solving optimization problems. In this paper we report our computational experience with generating feasible integer solutions of mixed-integer linear programs using geometric random walks, and a random ray approach. A feasibility pump is used to heuristically round the generated points. Computational results on MIPLIB2003 and COR@L … Read more
We address a 1-dimensional cutting stock problem where, in addition to trim-loss minimization, we require that the set of cutting patterns forming the solution can be sequenced so that the number of stacks of parts maintained open throughout the process never exceeds a given $s$. For this problem, we propose a new integer linear programming … Read more