In this paper, we provide a characterization of the expected value of monotone submodular set functions with $n$ pairwise independent random inputs. Inspired by the notion of “correlation gap”, we study the ratio of the maximum expected value of a function with arbitrary dependence among the random inputs with given marginal probabilities to the maximum … Read more
For many developing countries, COVID-19 vaccination roll-out programs are not only slow but vaccination centers are also exposed to the risk of natural disaster, like flooding, which may slow down vaccination progress even further. Policy-makers in developing countries therefore seek to implement strategies that hedge against distribution risk in order for vaccination campaigns to run … Read more
This paper describes a local-control method for multicommodity flow problem. Both the capacity constraints and the flow conservation constraints are relaxed. If the flow exceeds the capacity on an edge, the edge would have a congestion cost. If the flow into a vertex is not equal to that out of the vertex, the vertex would … Read more
Problem definition: We present our collaboration with the OCP Group, one of the world’s largest producers of phosphate and phosphate-based products, in support of a green initiative designed to reduce OCP’s carbon emissions significantly. We study the problem of decarbonizing OCP’s electricity supply by installing a mixture of solar panels and batteries to minimize its … Read more
\(\) A class of strong lower bounds on the solution value of a Linearized Integer Programming (LIP) reformulation is introduced for the binary quadratic optimization model to assign origin and destination nodes to strip and stack doors, resp., in a cross-dock infrastructure, whose goal is to minimize the transportation cost of the commodities to be … Read more
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades. On the one hand, we prove that when the rank of the positive semidefinite matrix in the decomposition … Read more
Bike-sharing systems have been implemented in multiple major cities, offering a low-cost and environmentally friendly transportation alternative to vehicles. Due to the stochastic nature of customer trips, stations are often unbalanced, resulting in unsatisfied demand. As a remedy, operators employ trucks to rebalance bikes among unbalanced stations. Given the complexity of the dynamic rebalancing planning, … Read more
We propose a novel approach to solve K-adaptability problems with convex objective and constraints and integer first-stage decisions. A logic-based Benders decomposition is applied to handle the first-stage decisions in a master problem, thus the sub-problem becomes a min-max-min robust combinatorial optimization problem that is solved via a double-oracle algorithm that iteratively generates adverse scenarios … Read more
Column generation is a popular method to solve large-scale linear programs with an exponential number of variables. Several important applications, such as the vehicle routing problem, rely on this technique in order to be solved. However, in practice, column generation methods suffer from slow convergence (i.e. they require too many iterations). Stabilization techniques, which carefully … Read more
In G. Haeser, A. Ramos, Constraint Qualifications for Karush-Kuhn-Tucker Conditions in Multiobjective Optimization, JOTA, Vol.~187 (2020), 469-487, a generalization of the normal cone from single objective to multiobjective optimization is introduced, along with a weakest constraint qualification such that any local weak Pareto optimal point is a weak Kuhn-Tucker point. We extend this approach to … Read more