Convex approximations for a class of mixed-integer recourse models

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.

On multiple simple recourse models

We consider multiple simple recourse (MSR) models, both continuous and integer versions, which generalize the corresponding simple recourse (SR) models by allowing for a refined penalty cost structure for individual shortages and surpluses. It will be shown that (convex approximations of) such MSR models can be represented as explicitly specified continuous SR models, and thus can be solved efficiently by existing algorithms.

Convex approximations for complete integer recourse models

We consider convex approximations of the expected value function of a two-stage integer recourse problem. The convex approximations are obtained by perturbing the distribution of the random right-hand side vector. It is shown that the approximation is optimal for the class of problems with totally unimodular recourse matrices. For problems not in this class, the result is a convex lower bound that is strictly better than the one obtained from the LP relaxation.

Integrated chance constraints in an ALM model for pension funds

We discuss integrated chance constraints in their role of short-term risk constraints in a strategic ALM model for Dutch pension funds. The problem is set up as a multistage recourse model, with special attention for modeling the guidelines proposed by the regulating authority for Dutch pension funds. The paper concludes with an outline of a special-purpose heuristic, which is used to approximately solve the resulting model which contains many binary decision variables.

Approximation in stochastic integer programming

Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solutions. However, efficiency in the complexity theoretical sense is usually not taken into account. Quality statements mostly remain restricted to convergence to an optimal solution without accompanying implications on the running time of the algorithms for attaining more and more accurate solutions. However, over the last twenty years also some studies on performance analysis of approximation algorithms for stochastic programming have appeared. In this direction we find both probabilistic analysis and worst-case analysis. There have been studies on performance ratios and on absolute divergence from optimality. Only recently the complexity of stochastic programming problems has been addressed, indeed confirming that these problems are harder than most combinatorial optimization problems.

Optimizing electricity distribution using two-stage integer recourse models

We consider two planning problems faced by an electricity distributor. Electricity can be ob-tained both from power plants and small generators such as hospitals and greenhouses, whereas the future demand for electricity is uncertain. The price of electricity obtained from the power plants depends on quota that are to be determined in a yearly contract, whereas the (given) contracts with small generators contain various constraints on switching them on or off.

Implementation of new regulatory rules in a multistage ALM model for Dutch pension funds

This paper discusses the implementation of new regulatory rules in a multistage recourse ALM model for Dutch pension funds. The new regulatory rules, which are called the ?Financieel Toetsingskader?, are effective as of January 2007 and have deep impact on the issues of valuation of liabilities, solvency, contribution rate, and indexation. Multistage recourse models have proved to be valuable for pension fund ALM. The ability to include the new regulatory rules would increase the practical value of these models.