integer programming

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

    Parallel Dual Dynamic Integer Programming for Large-Scale Hydrothermal Unit-Commitment

  • Bruno Colonetti
  • Erlon Finardi
  • Victor M. Zavala
  • Samuel Brito
    • Categories Dynamic Programming, Parallel Algorithms, Scheduling Tags , , ,

    Unit commitment has been at the center of power system operation for well over 50 years. Yet, this problem cannot be considered solved due to its size and complexity. Today, operators rely on off-the-shelf optimization solvers to tackle this challenging problem, and often resort to simplifications to make the problem more tractable and solvable in … Read more

    Solving a Multi-product, Multi-period, Multi-modal Freight Transportation Problem Using Integer Linear Programming

  • Anoop K.P.
  • Meenarli Sharma
    • Categories Applications - OR and Management Sciences, Transportation Tags , , ,

    We consider a real-world multimodal freight transportation problem that arises in a food grain organization in India. This problem aims to satisfy the demand for a set of warehouses for different types of food grains from another set of warehouses with surplus quantities over multiple periods of time by rail and road, while minimizing the … Read more

    A prediction-based approach for online dynamic radiotherapy scheduling

  • Tu-San Pham
  • Antoine Legrain
  • Patrick De Causmaecker
  • Louis-Martin Rousseau
    • Categories Applications - OR and Management Sciences Tags , , ,

    Patient scheduling is a difficult task as it involves dealing with stochastic factors such as an unknown arrival flow of patients. Scheduling radiotherapy treatments for cancer patients faces a similar problem. Curative patients need to start their treatment within the recommended deadlines, i.e., 14 or 28 days after their admission while reserving treatment capacity for … Read more

    Facets of the Total Matching Polytope for bipartite graphs

  • Luca Ferrarini
    • Categories 0-1 Programming, Combinatorial Optimization, Cutting Plane Approaches Tags , , ,

    The Total Matching Polytope generalizes the Stable Set Polytope and the Matching Polytope. In this paper, we give the perfect formulation for Trees and we derive two new families of valid inequalities, the balanced biclique inequalities which are always facet-defining and the non-balanced lifted biclique inequalities obtained by a lifting procedure, which are facet-defining for … Read more

    Recognizing Integrality of Weighted Rectangles Partitions

  • Paul Deuker
  • Ulf Friedrich
    • Categories (Mixed) Integer Linear Programming Tags , , ,

    Given a grid of active and inactive pixels, the weighted rectangles partitioning (WRP) problem is to find a maximum-weight partition of the active pixels into rectangles. WRP is formulated as an integer programming problem and instances with an integral relaxation polyhedron are characterized by a balanced problem matrix. A complete characterization of these balanced instances … Read more

    An Overview of Nested Decomposition for Multi-Level Optimization Problems

  • Stephen J. Maher
  • Ibrahim Muter
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Integer Programming Tags , , , ,

    Nested multi-level structures are frequently encountered in many real-world optimization problems. Decomposition techniques are a commonly applied approach used to handle nested multi-level structures; however, the typical problem-specific focus of such techniques has led to numerous specialized formulations and solution methods. This lack of generalized results for nested multi-level optimization problems is addressed in this … Read more

    An Integrated Rolling Horizon and Adaptive-Refinement Approach for Disjoint Trajectories Optimization

  • Benno Hoch
  • Frauke Liers
    • Categories Applications - OR and Management Sciences Tags , , , ,

    Planning of trajectories, i.e. paths over time, is a challenging task. Thereby, the trajectories for involved commodities often have to be considered jointly as separation constraints have to be respected. This is for example the case in robot motion or air traffic management. Involving these discrete separation constraints in the planning of best possible continuous … Read more

    A Theoretical and Computational Analysis of Full Strong-Branching

  • Santanu S. Dey
  • Yatharth Dubey
  • Marco Molinaro
  • Prachi Shah
    • Categories Branch and Cut Algorithms, Integer Programming Tags , , ,

    Full strong-branching (henceforth referred to as strong-branching) is a well-known variable selection rule that is known experimentally to produce significantly smaller branch-and-bound trees in comparison to all other known variable selection rules. In this paper, we attempt an analysis of the performance of the strong-branching rule both from a theoretical and a computational perspective. On … Read more