We consider a version of the knapsack problem in which an item size is random and revealed only when the decision maker attempts to insert it. After every successful insertion the decision maker can choose the next item dynamically based on the remaining capacity and available items, while an unsuccessful insertion terminates the process. We … Read more
When using the standard McCormick inequalities twice to convexify trilinear monomials, as is often the practice in modeling and software, there is a choice of which variables to group first. For the important case in which the domain is a nonnegative box, we calculate the volume of the resulting relaxation, as a function of the … Read more
Sequencing activities over time is a fundamental optimization problem. The problem can be modeled using a directed network in which activities are represented by nodes and pairs of activities that can be performed consecutively are represented by arcs. A sequence of activities then corresponds to a path in the directed network, and an optimal sequence … Read more
In this paper, we address a new version of the Uncapacitated Single Allocation p-Hub Median Problem (USApHMP) in which transportation costs on each edge are given by piecewise constant cost functions. In the classical USApHMP, transportation costs are modelled as linear functions of the transport volume, where a fixed discount factor on hub-hub connections is … Read more
The pooling problem is a nonconvex nonlinear programming problem (NLP) with applications in the refining and petrochemical industries, but also the coal mining industry. The problem can be stated as follows: given a set of raw material suppliers (inputs) and qualities of the supplies, find a cost-minimising way of blending these raw materials in intermediate … Read more
We propose a formulation for the pickup and delivery problem with time windows, based on a novel modeling strategy that allows the assignment of vehicles to routes explicitly in two-index flow formulations. It leads to an effective compact formulation that can benefit OR practitioners interested in solving the problem by general-purpose optimization software. Computational experiments … Read more
We introduce a-posteriori and a-priori error bounds for optimality and feasibility of a point generated as the rounding of an optimal point of the NLP relaxation of a mixed-integer nonlinear optimization problem. Our analysis mainly bases on the construction of a tractable approximation of the so-called grid relaxation retract. Under appropriate Lipschitz assumptions on the … Read more
We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function, which allows to model risk-aversion in a very individual way. We address this class of convex mixed-integer minimization problems … Read more
A variety of formulations for the Travelling Salesman Problem as Mixed Integer Program have been proposed. They contain either non-binary variables or the number of constraints and variables is large. We want to give a new formulation that consists solely of binary variables; the number of variables and the number of constraints are of order … Read more
We present pure-integer Gomory cuts in a way so that they are derived with respect to a “dual form” pure-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex algorithm. The input integer problem is not in standard form, and so the cuts are derived a bit differently. In … Read more