Although Branch and Bound (BnB) methods are among the most widely used techniques for solving hard problems, it is still a challenge to make these methods smarter. In this paper, we investigate iterative patching, a technique in which a fixed patching procedure is applied at each node of the BnB...

In this paper we deal with a pseudo-Boolean representation of the simple plant location problem. We define instances of this problem that are equivalent, in the sense that each feasible solution has the same goal function value in all such instances. We further define a collection of polytopes...

In this paper we consider stochastic discrete optimization problems (DOP) in which feasible solutions remain feasible irrespective of the randomness of the problem parameters. We introduce the concept of the risk associated with a solution and define optimal solution in terms of having least...

In a general class of discrete optimization problems with min-sum objective function, some of the elements may have random costs associated with them. In such a situation, the notion of optimality needs to be suitably modified. We define an optimal solution to be a feasible solution with the...

Given a set of elements, each having a profit and cost associated with it, and a budget, the 0-1 knapsack problem finds a subset of the elements with maximum possible combined profit subject to the combined cost not exceeding the budget. In this paper we study a stochastic version of the problem...

In this paper we introduce a concept of skewness and suggest its measure among a class of unimodal distributions. The measure is built on the lack of symmetry of the density function around the the mode of the distribution. It is shown to satisfy all standard properties expected from a measure...