Integer Programming

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

    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

    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

    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

    Exact Logit-Based Product Design

  • İrem Akçakuş
  • Velibor Mišić
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Marketing

    The share-of-choice product design (SOCPD) problem is to find the product, as defined by its attributes, that maximizes market share arising from a collection of customer types or segments. When customers follow a logit model of choice, the market share is given by a weighted sum of logistic probabilities, leading to the logit-based share-of-choice product … Read more

    SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs

  • Carlos Nohra
  • Arvind U. Raghunathan
  • Nikolaos Sahinidis
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Tags , , , ,

    We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class of convex quadratic relaxations which are derived via quadratic cuts. To construct these quadratic cuts, we solve a separation problem involving a linear matrix inequality with a special structure that allows the use of … Read more

    The Graphical Traveling Salesperson Problem has no Integer Programming Formulation in the Original Space

  • Matthias Walter
    • Categories (Mixed) Integer Linear Programming, Graphs and Matroids

    The Graphical Traveling Salesperson Problem (GTSP) is the problem of assigning, for a given weighted graph, a nonnegative number x_e to each edge e such that the induced multi-subgraph is of minimum weight among those that are spanning, connected and Eulerian. Naturally, known mixed-integer programming formulations use integer variables x_e in addition to others. Denis … Read more

    Cardinality Minimization, Constraints, and Regularization: A Survey

  • Daniel Bienstock
  • Andrea Lodi
  • Andreas M. Tillmann
  • Alexandra Schwartz
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization Tags , , , , , , ,

    We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and give concrete examples from diverse application fields such as signal and image processing, portfolio selection, or machine learning. The paper discusses general-purpose modeling techniques and … Read more

    New Valid Inequalities and Formulation for the Static Chance-constrained Lot-Sizing Problem

  • Chuanhou Gao
  • James R. Luedtke
  • Zeyang Zhang
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , ,

    We study the static chance-constrained lot sizing problem, in which production decisions over a planning horizon are made before knowing random future demands, and the backlog and inventory variables are then determined by the demand realizations. The chance constraint imposes a service level constraint requiring that the probability that any backlogging is required should be … Read more

    Alternative Regularizations for OA Algorithms for Convex MINLP

  • David E. Bernal Neira
  • Ignacio E. Grossmann
  • Jan Kronqvist
  • Zedong Peng
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming, Nonsmooth Optimization

    In this work, we extend the regularization framework from Kronqvist et al. (https://doi.org/10.1007/s10107-018-1356-3) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance-metrics and Lagrangean approximations, used in the projection problem for finding new … Read more