We define and study two versions of the bipartite matching problem in the framework of two-stage stochastic optimization with recourse. In one version the uncertainty is in the second stage costs of the edges, in the other version the uncertainty is in the set of vertices that needs to be matched. We prove lower bounds, and analyze efficient strategies for both cases. These problems model real-...

We consider two-stage stochastic programming problems with integer recourse. The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition. Nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques. Finite convergence of...

Stochastic linear programs have been rarely used in practical situations largely because of their complexity. In evaluating these problems without finding the exact solution, a common method has been to find bounds on the expected value of perfect information. In this paper, we consider a different method. We present bounds on the value of the stochastic solution, that is, the potential benefit...

In this paper, we consider a new formulation with recourse for a class of stochastic nonlinear complementarity problems. We show that the new formulation is equivalent to a smooth semi-infinite program that no longer contains recourse variables. We then propose a combined Monte Carlo sampling and penalty method for solving the problem in which the underlying sample space is assumed to be compac...

The capacitated vehicle routing problem with stochastic demands can be modelled using either the chance-constrained approach or the recourse approach. In previous works, we extended the former approach to address the case where uncertainty on customer demands is represented by belief functions, that is where customers have so-called evidential demands. In this paper, we propose an extension of ...

This paper studies Lebesgue integral of a fuzzy closed set-valued stochastic process with respect to the time t. Firstly, a progressively measurable fuzzy closed set-valued stochastic process is discussed and an almost everywhere problem in the former Aumann type Lebesgue integral of the level-set process is pointed out. Secondly, a new definition of the Lebesgue integral by decomposable closur...

In this paper we present a parallel method for solving two-stage stochastic linear programs with restricted recourse. The mathematical model considered here can be used to represent several real-world applications, including ®nancial and production planning problems, for which signi®cant changes in the recourse solutions should be avoided because of their diculty to be implemented. Our paralle...

We propose a new variant of the two-stage recourse model. It can be used e.g., in managing resources in whose supply random interruptions may occur. Oil and natural gas are examples for such resources. Constraints in the resulting stochastic programming problems can be regarded as generalizations of integrated chance constraints. For the solution of such problems, we propose a new decomposition...

The paper considers modeling of risk-averse preferences in (multi-stage) stochastic programming problems using risk measures. We utilize the axiomatic foundation of coherent risk measures and deviation measures in order to develop simple representations for these measures that facilitate their incorporation into stochastic programs. It is demonstrated that the developed representations allow fo...