Integrated Vehicle Routing and Service Scheduling under Time and Cancellation Uncertainties with Application in Non-Emergency Medical Transportation

  • Siqian Shen
  • Huizhu Wang
  • Xian Yu
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences

    In this paper, we consider an integrated vehicle routing and service scheduling problem for serving customers in distributed locations who need pick-up, drop-off or delivery services. We take into account the random trip time, non-negligible service time and possible customer cancellations, under which an ill-designed schedule may lead to undesirable vehicle idleness and customer waiting. … Read more

    Solving the Home Service Assignment, Routing, and Appointment Scheduling (H-SARA) problem with Uncertainties

  • Syu-Ning Johnn
  • Yiran Zhu
  • Andrés Miniguano-Trujillo
  • Akshay Gupte
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming, Transportation Tags , , , ,

    The Home Service Assignment, Routing, and Appointment scheduling (H-SARA) problem integrates the strategical fleet-sizing, tactical assignment, operational vehicle routing and scheduling subproblems at different decision levels, with a single period planning horizon and uncertainty (stochasticity) from the service duration, travel time, and customer cancellation rate. We propose a two-stage stochastic mixed-integer linear programming model for … Read more

    A Fixed Point Approach with a New Solution Concept for Set-valued Optimization

  • Shengjie Li
  • Christiane Tammer
  • Chaoli Yao
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization

    We present a fixed point approach to find the whole solution set of a set-valued optimization problem though a parametric problem, in which the height of the level set of the objective function is regarded as the parameter. First, the solution concept based on the vector approach is considered in this method. Then, we propose … Read more

    Rank computation in Euclidean Jordan algebras

  • Michael Orlitzky
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    Euclidean Jordan algebras are the abstract foundation for symmetriccone optimization. Every element in a Euclidean Jordan algebra has a complete spectral decomposition analogous to the spectral decomposition of a real symmetric matrix into rank-one projections. The spectral decomposition in a Euclidean Jordan algebra stems from the likewise-analogous characteristic polynomial of its elements, whose degree is … Read more

    An Efficient Retraction Mapping for the Symplectic Stiefel Manifold

  • Rafael Herrera
  • Harry Oviedo
    • Categories Constrained Nonlinear Optimization Tags , , ,

    This article introduces a new retraction on the symplectic Stiefel manifold. The operation that requires the highest computational cost to compute the novel retraction is a matrix inversion of size $2p$–by–$2p$, which is much less expensive than those required for the available retractions in the literature. Later, with the new retraction, we design a constraint … Read more

    FISTA and Extensions – Review and New Insights

  • Weiwei Kong
  • Jefferson Gonçalves Melo
  • Renato D.C. Monteiro
    • Categories Convex Optimization, Nonsmooth Optimization Tags , ,

    The purpose of this technical report is to review the main properties of an accelerated composite gradient (ACG) method commonly referred to as the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). In addition, we state a version of FISTA for solving both convex and strongly convex composite minimization problems and derive its iteration complexities to generate iterates … Read more

    A Penalty Branch-and-Bound Method for Mixed-Binary Linear Complementarity Problems

  • Marianna De Santis
  • Sven de Vries
  • Martin Schmidt
  • Lukas Winkel
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Complementarity and Variational Inequalities Tags , , , ,

    Linear complementarity problems (LCPs) are an important modeling tool for many practically relevant situations but also have many important applications in mathematics itself. Although the continuous version of the problem is extremely well studied, much less is known about mixed-integer LCPs (MILCPs) in which some variables have to be integer-valued in a solution. In particular, … Read more

    Conic optimization: a survey with special focus on copositive optimization and binary quadratic problems

  • Mirjam Dür
  • Franz Rendl
    • Categories Linear, Cone and Semidefinite Programming

    A conic optimization problem is a problem involving a constraint that the optimization variable be in some closed convex cone. Prominent examples are second order cone programs (SOCP), semidefinite problems (SDP), and copositive problems. We survey recent progress made in this area. In particular, we highlight the connections between nonconvex quadratic problems, binary quadratic problems, … Read more

    A new stopping criterion for Krylov solvers applied in Interior Point Methods

  • Jacek Gondzio
  • Filippo Zanetti
    • Categories Convex Optimization Tags , , , ,

    A surprising result is presented in this paper with possible far reaching consequences for any optimization technique which relies on Krylov subspace methods employed to solve the underlying linear equation systems. In this paper the advantages of the new technique are illustrated in the context of Interior Point Methods (IPMs). When an iterative method is … Read more

    Designing an optimal sequence of non-pharmaceutical interventions for controlling COVID-19

  • Laurent Alfandari
  • Debajyoti Biswas
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Biomedical Applications

    The COVID-19 pandemic has had an unprecedented impact on global health and the economy since its inception in December, 2019 in Wuhan, China. Non-pharmaceutical interventions (NPI) like lockdowns and curfews have been deployed by affected countries for controlling the spread of infections. In this paper, we develop a Mixed Integer Non-Linear Programming (MINLP) epidemic model … Read more