We consider mixed-integer recourse (MIR) models with a single recourse constraint. We relate the secondstage value function of such problems to the expected simple integer recourse (SIR) shortage function. This allows to construct convex approximations for MIR problems by the same approach used for SIR models.

Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of risk. From the perspective of qualitative robustness theory, we discuss sufficient conditions for continuity of the resulting objective functions with respect ...

We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a complete description of the class of probability density functions such that the objective functio...

We discuss the performance of the convex approximations introduced by Van der Vlerk [2004] for the class of integer recourse problems with totally unimodular (TU) recourse matrices. We show that the main result in Van der Vlerk [2004] needs stronger assumptions, so that a performance guarantee for the convex approximations is lacking in general. In order to obtain such a performance guarantee, ...

We consider the other direction: the 2-stage stochastic programming problem (or also called stochastic recourse problem). Conceptually one should think of the decision process taking place in two stages. In the first, values for the first stage variables x are chosen. In the second, upon a realisation of the random parameters, a recourse action is to be taken in case of infeasibilities. Costs a...

Stochastic programming deals with optimization under uncertainty. A stochastic programming problem with recourse is referred to as a two-stage stochastic problem. We consider the stochastic programming problem with simple integer recourse in which the value of the recourse variable is restricted to a multiple of a nonnegative integer. The algorithm of a dynamic slope scaling procedure to solve ...

Maternal mortality has declined considerably in Bangladesh over the past few decades. Some of that decline--though precisely how much cannot be quantified--is likely attributable to the country's menstrual regulation program,which allows women to establish nonpregnancy safely after a missed period and thus avoid recourse to unsafe abortion. Key Points. (1) Unsafe clandestine abortion persists i...