In this chapter we begin with a brief explanation of linear programming (LP) since integer
programming (IP) is usually regarded as an extension of LP. Also most practical methods of …

Stochastic dominance constraints allow a decision maker to manage risk in an optimization
setting by requiring his or her decision to yield a random outcome which stochastically …

For many decision-making problems under uncertainty, it is crucial to develop risk-averse
models and specify the decision makers' risk preferences based on multiple stochastic …

In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic
dominance provides a theoretically sound approach to comparing uncertain quantities, but …

We propose a new class of stochastic integer programs whose special features are
dominance constraints induced by mixed-integer linear recourse. For these models, we …

We introduce stochastic integer programs with second-order dominance constraints induced
by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to …

For stochastic optimization problems with second order stochastic dominance constraints we
develop a new form of the duality theory featuring measures on the product of the probability …

Purpose: To describe a fast projection algorithm for optimizing intensity modulated proton
therapy (IMPT) plans and to describe and demonstrate the use of this algorithm in …

This paper considers a multiperiod emergency medical services (EMS) location problem
and introduces two two-stage stochastic programming formulations that account for …

The geometric-mean argument and the recently developed Almost Stochastic Dominance
criterion have been employed to make the case for “stocks for the long run”. We show that …