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.

Stochastic programming with recourse usually assumes uncertainty to be exogenous. Our work presents modelling and application of decision-dependent uncertainty in mathematical programming including a taxonomy of stochastic programming recourse models with decision-dependent uncertainty. The work includes several ways of incorporating direct or indirect manipulation of underlying probability distributions through decision variables in two-stage stochastic programming problems. Two-stage models are formulated where prior probabilities are distorted through an affine transformation or combined using a convex combination of several probability distributions. Additionally, we present models where the parameters of the probability distribution are first-stage decision variables. The probability distributions are either incorporated in the model using the exact expression or by using a rational approximation. Test instances for each formulation are solved with a commercial solver, BARON, using selective branching.

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The network for transport of natural gas on the Norwegian Continental Shelf, with 7,800 km of subsea pipelines, is the world's largest offshore pipeline network. The gas flowing through this network represents approximately 15 percent of European consumption, and the system has a capacity of 120 billion standard cubic meters (bcm) a year. In a network of interconnected pipelines, system effects are prevalent, and the network must be analyzed as a whole to determine the optimal operation. SINTEF has developed a decision support tool, GassOpt, which is based on a mixed-integer program, to optimize the network configuration and routing for the main Norwegian shipper of natural gas, StatoilHydro, and the independent network operator, Gassco. GassOpt allows users to graphically model their network and run optimizations to find the best solutions quickly. StatoilHydro and Gassco use it to evaluate the current network and possible network extensions. Both companies use operations research (OR) methods in the departments that are responsible for transport planning and security of supply. Several new OR projects have grown out from this cooperation. StatoilHydro estimates that its accumulated savings related to the use of GassOpt were approximately US$2 billion in the period 1995–2008.

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