integer programming

Comparing league formats from a business oriented view: the case of Argentina’s National Basketball League

  • Nicolas Garcia Aramouni
  • Juan José Miranda-Bront
    • Categories Applications - OR and Management Sciences Tags , , , ,

    During the last decades, the use of advanced optimization algorithms to generate sports timetables has caught the attention of both academics and practitioners. From a managerial standpoint, the competition’s structure and the design of the league’s schedule represent key strategic decisions with a direct impact in terms of revenue and other important indicators. Argentina’s National … Read more

    Integer Programming Models for Round Robin Tournaments

  • Jasper van Doornmalen
  • Christopher Hojny
    • Categories Scheduling Tags , , ,

    Round robin tournaments are omnipresent in sport competitions and beyond. We propose two new integer programming formulations for scheduling a round robin tournament, one of which we call the matching formulation. We analytically compare their linear relaxations with the linear relaxation of a well-known traditional formulation. We find that the matching formulation is stronger than … Read more

    Relaxations and Duality for Multiobjective Integer Programming

  • Alex Dunbar
  • Saumya Sinha
  • Andrew J. Schaefer
    • Categories Integer Programming, Multi-Criteria Optimization Tags , , , ,

    Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective func- tions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a … Read more

    Temporal Bin Packing with Half-Capacity Jobs

  • Christopher Muir
  • Luke Marshall
  • Alejandro Toriello
    • Categories (Mixed) Integer Linear Programming, Polyhedra, Scheduling Tags , , , ,

    Motivated by applications in cloud computing, we study a temporal bin packing problem with jobs that occupy half of a bin’s capacity. An instance is given by a set of jobs, each with a start and end time during which it must be processed, i.e., assigned to a bin. A bin can accommodate two jobs … Read more

    Maximizing resilience in large-scale social networks

  • Samuel Kroger
  • Hamidreza Validi
  • Illya V. Hicks
    • Categories Combinatorial Optimization, Integer Programming, Network Optimization Tags , ,

    Motivated by the importance of social resilience as a crucial element in cascading leaving of users from a social network, we study identifying a largest relaxed variant of a degree-based cohesive subgraph: the maximum anchored k-core problem. Given graph G=(V,E) and integers k and b, the maximum anchored k-core problem seeks to find a largest … Read more

    A Stochastic Optimization Approach to Energy-Efficient Underground Timetabling under Uncertain Dwell and Running Times

  • Patrick Gemander
  • Andreas Bärmann
  • Alexander Martin
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming, Transportation Tags , , , , ,

    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

    Mathematical models and decomposition methods for the two-bar charts packing problem

  • Barkel Mathijs
  • Maxence Delorme
    • Categories Combinatorial Optimization Tags , , , ,

    We consider the two-bar charts packing (2-BCPP), a recent combinatorial optimization problem whose aim is to pack a set of one-dimensional items into the minimum number of bins. As opposed to the well-known bin packing problem, pairs of items are grouped to form bar charts, and a solution is only feasible if the first and … Read more

    DiversiTree: A New Method to Efficiently Compute Diverse Sets of Near-Optimal Solutions to Mixed-Integer Optimization Problems

  • Izuwa Ahanor
  • Hugh R. Medal
  • Andrew C. Trapp
    • Categories Applications - Science and Engineering, Integer Programming, Other Topics Tags , , ,

    While most methods for solving mixed-integer optimization problems compute a single optimal solution, a diverse set of near-optimal solutions can often lead to improved outcomes. We present a new method for finding a set of diverse solutions by emphasizing diversity within the search for near-optimal solutions. Specifically, within a branch-and-bound framework, we investigated parameterized node … Read more

    Exact solution methods for the Resource Constrained Project Scheduling Problem with a flexible Project Structure

  • T. Van der Beek
  • J.T. Van Essen
  • J. Pruyn
  • Karen I. Aardal
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , , ,

    The Resource Constrained Project Scheduling Problem with a flexible Project Structure (RCPSP-PS) is a generalization of the Resource Constrained Project Scheduling Problem (RCPSP). The objective of the RCPSP-PS is to find a minimal makespan schedule subject to precedence and resource constraints, while only having to execute a subset of all activities. We present a general … Read more

    Benders-type Branch-and-Cut Algorithms for Capacitated Facility Location with Single-Sourcing

  • Dieter Weninger
  • Laurence A. Wolsey
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Facility Planning and Design Tags , , , ,

    We consider the capacitated facility location problem with (partial) single-sourcing (CFLP-SS). A natural mixed integer formulation for the problem involves 0-1 variables x_j indicating whether faclility j is used or not and y_{ij} variables indicating the fraction of the demand of client i that is satisfied from facility j. When the x variables are fixed, … Read more