THE RAY-METHOD: THEORETICAL BACKGROUND AND COMPUTATIONAL RESULTS

In our talk we present an algorithm for determining initial bound for the Branch and Bound (B&B) method. The idea of the algorithm is based on the use of the "ray" introduced in the "ray-method" developed for solving integer programming problems [13], [14]. Instead of solving a common integer programming problem we use the main idea of the ray-method to find an integer feasible solution of integer linear programming (ILP) problem along the ray as close to optimal solution of relaxation problem, as possible. Objective value obtained in this way may be used as an initial bound for B&B method. The algorithm has been implemented in the frame of educational package WinGULF [3] for linear and linear-fractional programming and has been tested on various ILP problems. Then inspired by the results obtained we implemented the method using the so-called callable library of CPLEX package by IBM. omputational experiments with the algorithm proposed show that such preprocessing procedure in many cases results an integer feasible solution very close to the solution of relaxation problem. Initial bound for branch and bound method determined in this way often can significantly decrease the size of the binary tree to be searched and in this manner can improve performance of the B&B method

Taxes, subsidies and unemployment - a unified optimization approach

Like a linear programming (LP) problem, linear-fractional programming (LFP) problem can be usefully applied in a wide range of real-world applications. In the last few decades a lot of research papers and monographs were published throughout the world where authors (mainly mathematicians) investigated different theoretical and algorithmic aspects of LFP problems in various forms. In this paper we consider these two approaches to optimization (based on linear and linear-fractional objective functions on the same feasible set), compare results they lead to and give interpretation in terms of taxes, subsidies and manpower requirement. We show that in certain cases both approaches are closely connected with one another and may be fruitfully utilized simultaneously

THE RAY-METHOD: THEORETICAL BACKGROUND AND COMPUTATIONAL RESULTS

In our talk we present an algorithm for determining initial bound for the Branch and Bound (B&B) method. The idea of the algorithm is based on the use of the "ray" introduced in the "ray-method" developed for solving integer programming problems [13], [14]. Instead of solving a common integer programming problem we use the main idea of the ray-method to find an integer feasible solution of integer linear programming (ILP) problem along the ray as close to optimal solution of relaxation problem, as possible. Objective value obtained in this way may be used as an initial bound for B&B method. The algorithm has been implemented in the frame of educational package WinGULF [3] for linear and linear-fractional programming and has been tested on various ILP problems. Then inspired by the results obtained we implemented the method using the so-called callable library of CPLEX package by IBM. omputational experiments with the algorithm proposed show that such preprocessing procedure in many cases results an integer feasible solution very close to the solution of relaxation problem. Initial bound for branch and bound method determined in this way often can significantly decrease the size of the binary tree to be searched and in this manner can improve performance of the B&B method