Infrastructure-planning models are challenging because of their combination of different time scales: while planning and building the infrastructure involves strategic decisions with time horizons of many years, one needs an operational time scale to get a proper picture of the infrastructure's performance and profitability. In addition, both the strategic and operational levels are typically subject to significant uncertainty, which has to be taken into account. This combination of uncertainties on two different time scales creates problems for the traditional multistage stochasticprogramming formulation of the problem due to the exponential growth in model size.In this paper, we present an alternative formulation of the problem that combines the two time scales, using what we call a multi-horizon approach, and illustrate it on a stylized optimization model. We show that the new approach drastically reduces the model size compared to the traditional formulation and present two real-life applications from energy planning.

We examine the stability of a portfolio management model based on the conditional value-at-risk (CVaR) measure; the model controls risk exposure of international investment portfolios. We use a moment-matching method to generate discrete distributions (scenario sets) of asset returns and exchange rates so that their statistical properties match corresponding values estimated from historical data. First, we establish that the scenario generation procedure does not bias the results of the optimization program, and we determine the required number of scenarios to attain stable solutions. We then investigate the sensitivity of the CVaR model to mis-specifications in the statistics of stochastic parameters: mean, standard deviation, skewness, kurtosis, as well as correlations. The results are most sensitive to estimation errors in the means of the stochastic parameters (asset returns and currency exchange rates). Mis-specifications in the standard deviation, skewness and correlations of the random parameters also have considerable impact on the solutions. The effect of mis-specifications in the values of kurtosis, although less than that of the other statistics, is still not negligible.Portfolio management, Stability analysis, Impact of higher-order moments, Estimation errors, Conditional value-at-risk,

A major driver of planning complexity in engineer-to-order (ETO) projects is design uncertainty far into the engineering and production processes. This leads to uncertainty in technical information and will typically lead to a revision of parts of the project network itself. Hence, this uncertainty is different from standard task completion uncertainty. We build a stochastic program to draw attention to, and analyse, the engineering-design planning problem, and in particular, to understand what role design flexibility plays in hedging against such uncertainty. The purpose is not to devise a general stochastic dynamic model to be used in practice, but to demonstrate by the use of small model instances how design flexibility actually adds value to a project and what, exactly, it is that produces this value. This will help us understand better where and when to develop flexibility and buffers, even when not actually solving stochastic models.

Stochastic programming, Scenario generation, Copulas,

in: Computational Management Science. See also B T E X entry below. This paper presents a new heuristic for generating scenarios for two-stage stochastic programs. The method uses copulas to describe the dependence between the marginal distributions, instead of the more common correlations. The heuristic is then tested on a simple portfolio-selection model, and compared to two other scenario-generation methods. B T E X: