Title of Talk: Modeling and Computational Strategies for Optimal Offshore Oilfield Development Planning under Complex Fiscal Rules

Offshore oil and gas field development planning has received significant attention in recent years given the new discoveries of large oil and gas reserves in the last decade around the world. Therefore, there is currently a strong focus on exploration and development activities for new oil fields all around the world, specifically at offshore locations. These projects involve capital intensive decisions pertaining to the installation of exploration and production facilities, subsea structures, pipeline connections, well drilling, that must be made at the early stages of the project. However, there is a very large number of alternatives that is usually available to make these decisions under the given physical and practical restrictions. This motivates the need for optimizing the investment and operations decisions to ensure the highest return on the large investments over the given time horizon. The optimization of investment and operations planning of offshore oil and gas field infrastructure is traditionally modeled using the net present value (NPV) as the objective function, without considering the effect of fiscal rules that are associated to these development sites. These rules determine the share of the oil company and host government in the total oil produced in a given year. Therefore, the models with simple NPV objective functions may yield solutions that are optimistic, which can in fact be suboptimal after considering the impact of fiscal terms. The main goal of this paper is to extend a mixed-integer nonlinear programming (MINLP) model for NPV-based oilfield development planning to include complex fiscal rules. In particular, we consider a recently proposed multi-field site strategic planning model for offshore oil and gas fields as a basis to include generic fiscal rules with ring-fencing provisions. The proposed MINLP model is rather large as it includes many new discrete variables and additional constraints. We show that this model can be reduced to a variety of specific contracts models. Results on realistic instances show improved investment and operations decisions due to the explicit consideration of the fiscal terms during planning. Since the model becomes computationally very expensive to solve with the extension to fiscal rules, we provide several reformulation/approximation techniques and solution strategies that yield orders of magnitude reduction in the solution time. Finally, we briefly discuss the extension of the proposed model to handle uncertainties in the reservoir size and its productivity using a framework based on multi-sage stochastic programming.
This is joint work with Vijay Gupta.

Title of Talk: Aspirational preferences and their representation by risk measures

We consider choice over uncertain, monetary payoffs and study a general class of preferences. These preferences favor diversification, except perhaps on a subset of sufficiently disliked acts, over which concentration is instead preferred. This structure encompasses a number of known models (e.g., expected utility and several variants under a concave utility function). We show that such preferences share a representation in terms of a family of measures of risk and targets. Specifically, the choice function is equivalent to selection of a maximum index level such that the risk of beating the target at that level is acceptable. This representation may help to uncover new models of choice.One that we explore in detail is the special case when the targets are bounded. This case corresponds to a type of satisficing and has descriptive relevance. Moreover, the model is amenable to large-scale optimization.
This is joint work with David Brown and Enrico De Giorgi.

Title of Talk: From stochastic programming to stochastic equilibrium for capacity expansion analysis: the example of power generation

Capacity expansion in power generation was first formulated as an optimization model aimed at satisfying demand at overall minimal discounted cost. Uncertainty justifies extending the formulation to a stochastic environment and hence to resort to a stochastic programming version of the model. The primal-dual optimality conditions can be interpreted in term of a competitive market where different agents invest in order to maximize their expected profit discounted at a single cost of capital.
Competitive markets are not always perfect and one finds situations were risk exposure depends on technology and plant owner and hence assets need to be valued at different costs of capital. A first extension of the standard capacity expansion model is to insert these technology and company dependent costs of capital in the model. We explain how a particular stochastic version of the equilibrium model permits this extension and discuss computational approaches.
The follow-up question is to go beyond exogenous differentiated costs of capital and to make them endogenous. This means that cost of capital can depend on exogenous factors such as fuel cost or demand evolution, but also on the endogenous development of the generation system (different generation structures imply different risk exposures: just think of wind penetration). We first take the problem in the usual CAPM context and show that the introduction of stochastic discount rates allows one to endogenize the cost of capital in a CAPM compatible way at least as long as we only deal with systematic risk. The model can be stated as a stochastic programming problem.
Things become more complicated if one wants to deal with idiosyncratic risk. The principle of the CAPM is that this risk is priced at zero. But the notion of incomplete market suggests to go beyond that usual model and to account for non-zero idiosyncratic risk in the equilibrium model. One then extends the CAPM based equilibrium model to one where systematic risk is represented by a linear stochastic discount factor and idiosyncratic risk is modelled through a non-linear stochastic risk factor. This calls upon using convex or coherent risk functions. The model is of the stochastic equilibrium type and can become non convex.
Non-convex stochastic equilibrium problems are as annoying as non-convex optimization problems. It is thus interesting to explore the origin of the non-convexity. The CAPM with its zero pricing of idiosyncratic risk is a convex stochastic equilibrium model. A more general situation that does not rely on the CAPM assumes full risk trading (a complete market) where the price of risk is determined endogenously from a capacity optimization problem with risk function. The crucial remaining question is then to explore how incomplete risk trading can affect investment in a stochastic equilibrium model. We sketch a possible way to handle that problem using a (simpler) stochastic equilibrium model with an incomplete market for risk hedging when capacities are fixed.
This is joint work with Gauthier de Maere d’Aertrycke, Andreas Ehrenmann and Daniel Ralph.

Title of Talk: Understanding stochastic (mixed) integer programs

On one hand, most cases of industrial-sized stochastic (mixed) integer programs are numerically unsolvable. On the other hand, the problems exist and deserve our attention. This talk focuses on a series of papers investigating different network design problems. We investigate the relationship between the stochastic and deterministic versions of the design problems, and in particular ask if the deterministic solutions can be useful even if the Value of the Stochastic Solution is high. The goal is to understand what stochastics does to these problems and how it affects the optimal solutions. By better understanding what stochastics does we are in a position to develop better heuristics and also to communicate better with users, even when we do not solve the relevant models.