(Mixed) Integer Linear Programming

New exact approaches for the combined cell layout problem and extensions of the multi-bay facility layout problem

  • Mirko Dahlbeck
  • Anja Fischer
  • Philipp Hungerländer
  • Kerstin Maier
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design Tags , , , ,

    In this paper we consider the Combined Cell Layout Problem (CCLP), the Multi-Bay Facility Layout Problem (MBFLP) and several generalizations of the MBFLP, which have wide applications, e.g., in factory planning, heavy manufacturing, semiconductor fabrication and arranging rooms in hospitals. Given a set of cells of type single-row or directed-circular and a set of one-dimensional … Read more

    Why there is no need to use a big-M in linear bilevel optimization: A computational study of two ready-to-use approaches

  • Thomas Kleinert
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities, Cutting Plane Approaches Tags , , , , ,

    Linear bilevel optimization problems have gained increasing attention both in theory as well as in practical applications of Operations Research (OR) during the last years and decades. The latter is mainly due to the ability of this class of problems to model hierarchical decision processes. However, this ability makes bilevel problems also very hard to … Read more

    Feasible rounding approaches for equality constrained mixed-integer optimization problems

  • Christoph Neumann
  • Oliver Stein
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , , , ,

    A feasible rounding approach is a novel technique to compute good feasible points for mixed-integer optimization problems. The central idea of this approach is the construction of a continuously described inner parallel set for which any rounding of any of its elements is feasible in the original mixed-integer problem. It is known that this approach … Read more

    Short-Term Inventory-Aware Equipment Management in Service Networks

  • Natashia Boland
  • Alan L. Erera
  • Martin Savelsbergh
  • Yassine Ridouane
    • Categories (Mixed) Integer Linear Programming, Production and Logistics, Transportation

    Logistics companies often operate a heterogeneous fleet of equipment to support their service network operations. This introduces a layer of planning complexity as facilities need to maintain appropriate levels of equipment types to support operations throughout the planning horizon. We formulate an optimization model that minimizes the cost of executing a load plan, assuming knowledge … Read more

    Distributionally Robust Facility Location with Bimodal Random Demand

  • Karmel S. Shehadeh
  • Ece Sanci
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design, Stochastic Programming Tags , , , ,

    In this paper, we consider a decision-maker who wants to determine a subset of locations from a given set of candidate sites to open facilities and accordingly assign customer demand to these open facilities. Unlike classical facility location settings, we focus on a new setting where customer demand is bimodal, i.e., display, or belong to, … Read more

    Optimal Residential Users Coordination Via Demand Response: An Exact Distributed Framework

  • Natalia Alguacil Conde
  • Michael David de Souza Dutra
    • Categories (Mixed) Integer Linear Programming, Energy Tags , , ,

    This paper proposes a two-phase optimization framework for users that are involved in demand response programs. In a first phase, responsive users optimize their own household consumption, characterizing not only their appliances and equipment but also their comfort preferences. Subsequently, the aggregator exploits in a second phase this preliminary noncoordinated solution by implementing a coordination … Read more

    Solving the Time Dependent Minimum Tour Duration and Delivery Man Problems with Dynamic Discretization Discovery

  • Mike Hewitt
  • Duc Minh Vu
  • Duc D. Vu
    • Categories (Mixed) Integer Linear Programming, Scheduling, Transportation Tags , , , ,

    In this paper, we present exact methods for solving the Time Dependent Minimum Duration Problem (TDMTDP) and the Time Dependent Delivery Man Problem (TD-DMP). Both methods are based on a Dynamic Discretization Discovery (DDD) approach for solving the Time Dependent Traveling Salesman Problem with Time Windows (TD-TSPTW). Unlike the TD-TSPTW, the problems we consider in … Read more

    Affinely Adjustable Robust Linear Complementarity Problems

  • Christian Biefel
  • Frauke Liers
  • Martin Schmidt
  • Jan Hendrik Rolfes
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities, Robust Optimization Tags , , , ,

    Linear complementarity problems are a powerful tool for modeling many practically relevant situations such as market equilibria. They also connect many sub-areas of mathematics like game theory, optimization, and matrix theory. Despite their close relation to optimization, the protection of LCPs against uncertainties – especially in the sense of robust optimization – is still in … Read more

    Approximate Submodularity and Its Implications in Discrete Optimization

  • Temitayo Ajayi
  • Andrew J. Schaefer
  • Taewoo Lee
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization Tags , , ,

    Submodularity, a discrete analog of convexity, is a key property in discrete optimization that features in the construction of valid inequalities and analysis of the greedy algorithm. In this paper, we broaden the approximate submodularity literature, which so far has largely focused on variants of greedy algorithms and iterative approaches. We define metrics that quantify … Read more

    An Exact Cutting Plane Method for hBcsubmodular Function Maximization

  • Simge Küçükyavuz
  • Qimeng Yu
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Polyhedra

    A natural and important generalization of submodularity—$k$-submodularity—applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In this paper, we study maximization problems with $k$-submodular objective functions. We propose valid linear inequalities, namely the $k$-submodular inequalities, for the hypograph of any $k$-submodular … Read more