The master equality polyhedron (MEP) is a canonical set that generalizes the Master Cyclic Group Polyhedron (MCGP) of Gomory. We recently characterized a nontrivial polar for the MEP, i.e., a polyhedron T such that an inequality denotes a nontrivial facet of the MEP if and only if its coefficient vector forms a vertex of T. … Read more
We extend recent work on nonlinear optimal control problems with integer restrictions on some of the control functions (mixed-integer optimal control problems, MIOCP) in two ways. We improve a theorem that states that the solution of a relaxed and convexified problem can be approximated with arbitrary precision by a solution fulfilling the integer requirements. Unlike … Read more
The Mobile Oil Recovery (MOR) unit is a truck able to pump marginal wells in a petrol field. The goal of the MOR optimization Problem (MORP) is to optimize both the oil extraction and the travel costs. We describe several formulations for the MORP using a single vehicle or a fleet of vehicles. We have … Read more
Quadratic assignment problems (QAPs) are among the hardest discrete optimization problems. Recent study shows that even obtaining a strong lower bound for QAPs is a computational challenge. In this paper, we first discuss how to construct new simple convex relaxations of QAPs based on various matrix splitting schemes. Then we introduce the so-called symmetric mappings … Read more
We consider an optimization model for determining optimal opportunistic maintenance (that is, component replacement) schedules when data is deterministic. This problem generalizes that of Dickman, Epstein, and Wilamowsky [21] and is a natural starting point for the modelling of replacement schedules when component lives are non-deterministic. We show that this basic opportunistic replacement problem is … Read more
In this work, we establish a parallel between two classes of pricing problems that have attracted the attention of researchers in economics, theoretical computer science and operations research, each community addressing issues from its own vantage point. More precisely, we contrast the problems of pricing a network or a product line, in order to achieve … Read more
If a mathematical program (be it linear or nonlinear) has many symmetric optima, solving it via Branch-and-Bound techniques often yields search trees of disproportionate sizes; thus, finding and exploiting symmetries is an important task. We propose a method for automatically finding the formulation group of any given Mixed-Integer Nonlinear Program, and reformulating the problem so … Read more
In model-based nonlinear optimal control switching decisions that can be optimized often play an important role. Prominent examples of such hybrid systems are gear switches for transport vehicles or valves in chemical engineering. Optimization algorithms need to take the discrete nature of the variables that model these switching decisions into account. Unnecessarily, for many applications … Read more
A common way to produce a convex relaxation of a Mixed Integer Quadratically Constrained Program (MIQCP) is to lift the problem into a higher dimensional space by introducing variables $Y_{ij}$ to represent each of the products $x_i x_j$ of variables appearing in a quadratic form. One advantage of such extended relaxations is that they can … Read more
We study minimizing the sum of weighted completion times in a concurrent open shop. We give a primal-dual 2-approximation algorithm for this problem. We also show that several natural linear programming relaxations for this problem have an integrality gap of 2. Finally, we show that this problem is inapproximable within a factor strictly less than … Read more