Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe sampling and computational requirements on classical solution methods that render them impractical. This work proposes a novel sampling-free method for solving … Read more
We establish and analyze a service center location model with a simple but novel decision-dependent demand induced from a maximum attrac- tion principle. The model formulations are investigated in the distributionally- robust optimization framework. A statistical model that is based on the max- imum attraction principle for estimating customer demand and utility gain from service … Read more
Cardinality-constrained optimization problems are notoriously hard to solve both in theory and practice. However, as famous examples such as the sparse portfolio optimization and best subset selection problems show, this class is extremely important in real-world applications. In this paper, we apply a penalty alternating direction method to these problems. The key idea is to … Read more
Generation expansion planning (GEP) is a classical problem that determines an optimal investment plan for existing and future electricity generation technologies. GEP is a computationally challenging problem, as it typically corresponds to a very large-scale problem that contains several sources of uncertainties. With the advent of demand response (DR) as a reserved capacity in modern … Read more
Online restaurant aggregators have experienced significant sales growth in recent years, driving demand for meal delivery in the US. Meal delivery logistics is quite challenging, primarily due to the difficulty in managing the supply of delivery resources to satisfy dynamic and uncertain customer demand under very tight time constraints. In this paper, we study several … Read more
We consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In this paper we carry out a polyhedral study for the cubic integer programming formulation by establishing the dimension of the integer hull … Read more
We give simple iterative methods for computing approximately optimal primal and dual solutions for the problem of maximizing a linear functional over a convex set $K$ given by a separation oracle. In contrast to prior work, our algorithms directly output primal and dual solutions and avoid a common requirement of binary search on the objective … Read more
Uncertainty in classical stochastic programming models is often described solely by independent random parameters, ignoring their dependence on multidimensional features. We describe a novel contextual chance-constrained programming formulation that incorporates features, and argue that solutions that do not take them into account may not be implementable. Our formulation cannot be solved exactly in most cases, … Read more
In this paper, we focus on the cost-sharing problem for ride-sharing that determines how to allocate the total ride cost between the driver and the passengers. We identify the properties that a desirable cost-sharing mechanism should have and develop a general framework which can be used to create specific cost-sharing mechanisms. We propose specific mechanisms … Read more
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this (simple) approximation using mixed-integer programming (MIP). Notably, the number of constraints, binary variables, and auxiliary continuous variables used in this formulation grows logarithmically in … Read more