5 Algorithms 8 5.1 Fourier-Motzkin Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.2 The Simplex Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.3 Seidel’s Randomized Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.4 The Ellipsoid Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.5 Using the Ellipsoid...

Sandpile group or Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. It is well known that these recurrent configurations can be characterized as optimal solution certain non-linear optimization problems. We show graph correspond to solutions some integer linear programs. More precisely, we present two new programming models, on...

This paper extends the proposed method by Jahanshahloo et al. (2004) (a method for generating all the efficient solutions of a 0–1 multi-objective linear programming problem, Asia-Pacific Journal of Operational Research). This paper considers the recession direction for a multi-objective integer linear programming (MOILP) problem and presents necessary and sufficient conditions to have unbounde...