Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure

Scenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program. Most approaches to scenario generation are distribution-driven, that is, they attempt to construct a random vector which captures well in a probabilistic sense the uncertainty. On the other hand, a problem-driven approach may be able to exploit the structure of a problem to provide a more concise representation of the uncertainty. In this paper we propose an analytic approach to problem-driven scenario generation. This approach applies to stochastic programs where a tail risk measure, such as conditional value-at-risk, is applied to a loss function. Since tail risk measures only depend on the upper tail of a distribution, standard methods of scenario generation, which typically spread their scenarios evenly across the support of the random vector, struggle to adequately represent tail risk. Our scenario generation approach works by targeting the construction of scenarios in areas of the distribution corresponding to the tails of the loss distributions. We provide conditions under which our approach is consistent with sampling, and as proof-of-concept demonstrate how our approach could be applied to two classes of problem, namely network design and portfolio selection. Numerical tests on the portfolio selection problem demonstrate that our approach yields better and more stable solutions compared to standard Monte Carlo sampling

Optimal Fleet Size When National Quotas Can Be Traded

Assuming stochastic quotas for a fish stock that is shared between two nations, we find the optimal fleet size for one of them by maximizing expected profit under the assumption that national quotas can be traded and that stable national quotas is a political goal. As an example we use the Norwegian purse seiner fleet and the summer capelin fishery in the Barents Sea.Environmental Economics and Policy, International Development, International Relations/Trade, Resource /Energy Economics and Policy,

Stochastic programming in energy

We give the reader a tour of good energy optimization models that explicitly deal with uncertainty. The uncertainty usually stems from unpredictability of demand and/or prices of energy, or from resource availability and prices. Since most energy investments or operations involve irreversible decisions, a stochastic programming approach is meaningful. Many of the models deal with electricity investments and operations, but some oil and gas applications are also presented. We consider both traditional cost minimization models and newer models that reflect industry deregulation processes. The oldest research coincides with the birth of linear programming, and most models within the market paradigm have not yet found their final form.stochastic programming, energy, regulated markets, deregulation, uncertainty, electricity, natural gas, oil

Problem-driven scenario generation:an analytical approach for stochastic programs with tail risk measure

Scenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program. Most approaches to scenario generation are distribution-driven, that is, they attempt to construct a random vector which captures well in a probabilistic sense the uncertainty. On the other hand, a problem-driven approach may be able to exploit the structure of a problem to provide a more concise representation of the uncertainty. There have been only a few problem-driven approaches proposed, and these have been heuristic in nature. In this paper we propose what is, as far as we are aware, the first analytic approach to problem-driven scenario generation. This approach applies to stochastic programs with a tail risk measure, such as conditional value-at-risk. Since tail risk measures only depend on the upper tail of a distribution, standard methods of scenario generation, which typically spread there scenarios evenly across the support of the solution, struggle to adequately represent tail risk well

The impact of design uncertainty in engineer-to-order project planning

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.acceptedVersio

Rock varnish evidence for a Younger Dryas wet period in the Dead Sea basin

Rock varnish from 14.6 to 13.2 ka recessional shorelines of late glacial Lake Lisan and fan delta surfaces between 280 and 365 m bmsl (meters below mean sea level) along the western margins of the Dead Sea contains replicable layering patterns, characterized by a low Mn and Ba orange/yellow surface layer and a high Mn and Ba dark basal layer. The deposition of the dark basal layers immediately after the lake recession represents a wet period coinciding with the Younger Dryas (YD) cooling (12.9–11.6 ka), manifesting the influence of midlatitude westerly winds in the eastern Mediterranean-central Levant (EM-CL). In contrast, varnish from the distal base of fan deltas contains only orange/yellow surface layers, diagnostic of the Holocene relatively dry climate. The absence of the dark basal layers in the varnish further indicates a YD high stand at ~365 m bmsl and a lake level rise of at least 100 m from its Bølling-Ållerød lowstand. This rise stands in contrast to the abrupt drop of the lake level during the Heinrich (H1) cold event, illustrating the opposite response of the EM-CL climate to changes in the North Atlantic climate. The YD wet event most likely reflects a southward shift of the Atlantic meridional overturning circulation-modulated midlatitude westerly wind belt in the EM-CL region

The impact of wind uncertainty on the strategic valuation of distributed electricity storage

The intermittent nature of wind energy generation has introduced a new degree of uncertainty to the tactical planning of energy systems. Short-term energy balancing decisions are no longer (fully) known, and it is this lack of knowledge that causes the need for strategic thinking. But despite this observation, strategic models are rarely set in an uncertain environment. And even if they are, the approach used is often inappropriate, based on some variant of scenario analysis—what-if analysis. In this paper we develop a deterministic strategic model for the valuation of electricity storage (a battery), and ask: “Though leaving out wind speed uncertainty clearly is a simplification, does it really matter for the valuation of storage?”. We answer this question by formulating a stochastic programming model, and compare its valuation to that of its deterministic counterpart. Both models capture the arbitrage value of storage, but only the stochastic model captures the battery value stemming from wind speed uncertainty. Is the difference important? The model is tested on a case from Lancaster University’s campus energy system where a wind turbine is installed. From our analysis, we conclude that considering wind speed uncertainty can increase the estimated value of storage with up to 50 % relative to a deterministic estimate. However, we also observe cases where wind speed uncertainty is insignificant for storage valuation

Synergy of smart grids and hybrid distributed generation on the value of energy storage

In smart grids, demand response and distributed energy systems aim to provide a higher degree of flexibility for load-shifting operations and the leverage to control intermittent wind supply. In this more dynamic energy system, deployment of energy storage at the site of consumption is envisioned to create synergies with the local distributed generation (DG) system. From a large end-user perspective, this paper contributes to the practical understanding of smart grids by modelling the impact of real-time pricing schemes (smart grids) on a hybrid DG system (mixed generation for heating and electricity loads) coupled with storage units. Specifically, we address: How does the portfolio of DG units affect the value of energy storage? and, what is the value of energy storage when assessing different designs of demand response for the end-user? To this end, we formulate a dynamic optimization model to represent a real-life urban community’s energy system composed of a co-generation unit, gas boilers, electrical heaters and a wind turbine. We discuss the techno-economic benefits of complementing this end-user’s energy system with storage units (thermal storage and battery devices). The paper analyses the storages policy strategies to simultaneously satisfy heat and electricity demand through the efficient use of DG units under demand response mechanisms. Results indicate that the storage units reduce energy costs by 7–10% in electricity and 3% in gas charges. In cases with a large DG capacity, the supply–demand mismatch increases, making storage more valuable

Sensitivity Analysis in Stochastic Second Order Cone Programming for Mobile Ad Hoc Networks

AbstractIn this paper sensitivity analysis is adopted in order to understand the randomness of a stochastic second order cone program for mobile ad hoc networks [3]. The algorithm looks for a destination node and sets up a route by means of the expected zone, the region where the sender node expects to find the destination node and the requested zone defined by the sender node for spreading the route request to the destination node. Sensitivity analysis is performed by considering different costs of flooding and latency penalty. Evaluation of EVPI and VSS [2]-[4] allows us to find the range of values in which it is safe to save time by using a deterministic approach instead of a stochastic one