Ibrahim Muter

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

    Bin Packing Problem with Time Dimension: An Application in Cloud Computing

  • Nursen Aydin
  • Ş. İlker Birbil
  • Ibrahim Muter
    • Categories Applications - OR and Management Sciences Tags , , , ,

    Improving energy efficiency and lowering operational costs are the main challenges faced in systems with multiple servers. One prevalent objective in such systems is to minimize the number of servers required to process a given set of tasks under server capacity constraints. This objective leads to the well-known bin packing problem. In this study, we … Read more

    Algorithms for the One-Dimensional Two-Stage Cutting Stock Problem

  • Ibrahim Muter
  • Zeynep Sezer
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Production and Logistics

    In this paper, we consider the two-stage extension of the one-dimensional cutting stock problem which arises when technical requirements inhibit the cutting of large stock rolls to demanded widths of finished rolls directly. Therefore, the demands on finished rolls are fulfilled through two subsequent cutting processes, in which the rolls produced in the former are … Read more

    Benders Decomposition and Column-and-Row Generation for Solving Large-Scale Linear Programs with Column-Dependent-Rows

  • Ş. İlker Birbil
  • Kerem Bülbül
  • Ibrahim Muter
    • Categories Linear Programming

    In a recent work, Muter et al. (2013a) identified and characterized a general class of linear programming (LP) problems – known as problems with column-dependent-rows (CDR-problems). These LPs feature two sets of constraints with mutually exclusive groups of variables in addition to a set of structural linking constraints, in which variables from both groups appear … Read more

    Simultaneous Column-and-Row Generation for Large-Scale Linear Programs with Column-Dependent-Rows

  • Ş. İlker Birbil
  • Kerem Bülbül
  • Ibrahim Muter
  • Guvenc Sahin
    • Categories Linear Programming

    In this paper, we develop a simultaneous column-and-row generation algorithm that could be applied to a general class of large-scale linear programming problems. These problems typically arise in the context of linear programming formulations with exponentially many variables. The defining property for these formulations is a set of linking constraints, which are either too many … Read more