Efficient scheduling and routing of vessels are crucial in the oil and gas industries. In this paper, we consider a periodic supply vessel planning problem in which the weekly demands at multiple offshore facilities are satisfied with a fleet of heterogeneous vessels. Preemptive service at the base, variable service at facilities, and split delivery are … Read more
We propose a new method for linear second-order cone programs. It is based on the sequential quadratic programming framework for nonlinear programming. In contrast to interior point methods, it can capitalize on the warm-start capabilities of active-set quadratic programming subproblem solvers and achieve a local quadratic rate of convergence. In order to overcome the non-differentiability … Read more
We consider the portfolio optimization problem with contextual information that is available to better quantify and predict the uncertain returns of assets. Motivated by the regime modeling techniques for the finance market, we consider the setting where both the uncertain returns and the contextual information follow a Gaussian Mixture (GM) distribution. This problem is shown … Read more
Motivated by food distribution operations for non-profit organizations, we study a variant of the stochastic routing-allocation problem under demand uncertainty, in which one decides the assignment of trucks for demand nodes, the sequence of demand nodes to visit (i.e., truck route), and the allocation of food supply to each demand node. We propose three stochastic … Read more
In this paper, we consider piecewise polyhedral relaxations (PPRs) of multilinear optimization problems over axis-parallel hyper-rectangular partitions of their domain. We improve formulations for PPRs by linking components that are commonly modeled independently in the literature. Numerical experiments with ALPINE, an open-source software for global optimization that relies on piecewise approximations of functions, show that … Read more
We consider a problem from the context of energy-efficient underground railway timetabling, in which an existing timetable draft is improved by slightly changing departure and running times. In practice, synchronization between accelerating and braking trains to utilize regenerative braking plays a major role for the energy-efficiency of a timetable. Since deviations from a planned timetable … Read more
We present an inventory management solution for a non-stationary capacitated multi-echelon distribution network involving thousands of products. Assuming backlogged sales, we revisit and leverage the seminal multi-echelon inventory management results in the literature to establish the structural properties of the problem, and derive an efficient and practical solution method. In particular, we describe how the … Read more
In this paper we identify a new class of nonconvex optimization problems that can be equivalently reformulated to convex ones. These nonconvex problems can be characterized by convex functions with bilinear arguments. We describe several examples of important applications that have this structure. These include the problems with variable coefficients, the dual of robust nonlinear … Read more
Bilevel problems are used to model the interaction between two decision makers in which the lower-level problem, the so-called follower’s problem, appears as a constraint in the upper-level problem of the so-called leader. One issue in many practical situations is that the follower’s problem is not explicitly known by the leader. For such bilevel problems … Read more
This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue of dynamic sample selection in the evaluation of the gradient in conjunction with inexact solutions to the SQP subproblems. Under reasonable … Read more