On two-stage minimax problems

Minimax flow tree problems

We examine a class of problems which seeks to find tree-structured networks which minimize the maximum cost among a subset of nodes in a graph. The cost metric is characterized by a series of parameters which can represent distance, flow volume, and delivery deadlines. Derived through variations in problem parameters, we present 17 different problems and discuss their worst-case complexity. Fou...

A Note on the Minimax Solution for the Two-Stage Group Testing Problem.

Group testing is an active area of current research and has important applications in medicine, biotechnology, genetics, and product testing. There have been recent advances in design and estimation, but the simple Dorfman procedure introduced by R. Dorfman in 1943 is widely used in practice. In many practical situations, the exact value of the probability p of being affected is unknown. We pre...

On Minimax Theory in Two Hilbert Spaces

Two-stage flexible-choice problems under uncertainty

A significant input-data uncertainty is often present in practical situations. One approach to coping with this uncertainty is to describe the uncertainty with scenarios. A scenario represents a potential realization of the important parameters of the problem. In this paper we apply a recent approach, called flexibility, to solving two-stage flexible-choice problems. The first stage represents ...

Robust recoverable and two-stage selection problems

In this paper the following selection problem is discussed. A set of n items is given and we wish to choose a subset of exactly p items of the minimum total cost. This problem is a special case of 0-1 knapsack in which all the item weights are equal to 1. Its deterministic version has a trivial O(n)-time algorithm, which consists in choosing p items of the smallest costs. In this paper it is as...