When constructing political districting plans, prominent criteria include population balance, contiguity, and compactness. The compactness of a districting plan, which is often judged by the “eyeball test,” has been quantified in many ways, e.g., Length-Width, Polsby-Popper, and Moment-of-Inertia. This paper considers the number of cut edges, which has recently gained traction in the redistricting literature … Read more
This work proposes to create a tool for support for cost reduction in wagon maintenance through the distribution of the annual plan in workshops. The distribution depends on the type of wagon, the scope of the maintenance service that each workshop serves, and the capacity that is supported by the workshops. This plan is a … Read more
The Barvinok-Pataki bound provides an upper bound on the rank of extreme points of a spectrahedron. This bound depends solely on the number of affine constraints of the problem, i.e., on the algebra of the problem. Specifically, the triangular number of the rank r is upper bounded by the number of affine constraints. We revisit … Read more
In this paper, we study a retailer price optimization problem which includes the practical constraints: maximum number of price changes and minimum amount of price change (if a change is recommended). We provide a closed-form formula for the Euclidean projection onto the feasible set defined by these two constraints, based on which a simple gradient … Read more
A new business opportunity beckons with the emergence of prosumers. This article proposes an innovative business model to harness the potential of aggregating behind-the-meter residential storage in which the aggregator compensates participants for using their storage system on an on-demand basis. A bilevel optimization model is developed to evaluate the potential of this proposed business … Read more
We consider the problem of laying out several objects in an equal number of pre-defined positions. Objects are allowed finitely many orientations, can overlap each other, and must be arranged contiguously. We are particularly interested in the case when the evaluation of the dimensions of the objects requires computational or physical effort. We develop a … Read more
In this paper, we present the online tool salaplanejada.unifesp.br developed to assist the layout planning of classrooms considering the social distance in the context of the COVID-19 pandemic. We address both the allocation problem in rooms where seats are fixed as well as the problem in rooms where seats can be moved freely. For the … Read more
Two-echelon distribution systems are often considered in city logistics to maintain economies of scale and satisfy the emission zone requirements in the cities. In this work, we formulate the two-echelon vehicle routing problem with stochastic demands as a chance-constrained stochastic optimization problem, where the total demand of the customers in each second-echelon route should fit … Read more
We present FrankWolfe.jl, an open-source implementation of several popular Frank-Wolfe and Conditional Gradients variants for first-order constrained optimization. The package is designed with flexibility and high-performance in mind, allowing for easy extension and relying on few assumptions regarding the user-provided functions. It supports Julia’s unique multiple dispatch feature, and interfaces smoothly with generic linear optimization … Read more
In this paper we study numerically solving optimal control problems with bang-bang control functions. We present a formal Lagrangian approach for solving the optimal control problem, and address difficulties encountered when numerically solving the state and adjoint equations by using the immersed interface method. We note that our numerical approach does not approximate the discontinuous … Read more