Elisabetta Allevi

Bounds in Multistage Linear Stochastic Programming

Multistage stochastic programs, which involve sequences of decisions over time, are usually hard to solve in realistically sized problems. Providing bounds for optimal solution may help in evaluating whether it is worth the additional computations for the stochastic program vs. simplified approaches. In this paper we generalize measures from the two-stage case, based on different levels of available information, to the multistage stochastic programming problems. A set of theorems providing chains of inequalities among the new quantities are proved. Numerical results on a case study related to a simple transportation problem illustrate the described relationships.

The proximal point method for nonmonotone variational inequalities

We consider an application of the proximal point method to variational inequality problems subject to box constraints, whose cost mappings possess order monotonicity properties instead of the usual monotonicity ones. Usually, convergence results of such methods require the additional boundedness assumption of the solutions set. We suggest another approach to obtaining convergence results for proximal point methods which is based on the assumption that the dual variational inequality is solvable. Then the solutions set may be unbounded. We present classes of economic equilibrium problems which satisfy such assumptions.

The steel industry: A mathematical model under environmental regulations

In this work, a spatial equilibrium problem is formulated for analyzing the impact of the application of the EU-ETS on the steel industry that has historically seen Europe as one of its major producers. The developed model allows us to simultaneously represent the interactions of several market players, to endogenously determine output and steel prices and to analyze the investment in the Carbon Capture and Storage (CCS) technology. In addition, the proposed model supports the evaluation of the CO2 emission costs on the basis of Directive 2009/29/EC, the “20-20-20” targets, and the Energy Roadmap 2050. In this light, two main processes for steelmaking have to be considered: integrated mills (BOF) and Electric Arc Furnace (EAF) in minimills.

Monotonic bounds in multistage mixed-integer stochastic programming

Multistage stochastic programs bring computational complexity which may increase exponentially with the size of the scenario tree in real case problems. For this reason approximation techniques which replace the problem by a simpler one and provide lower and upper bounds to the optimal value are very useful. In this paper we provide monotonic lower and upper bounds for the optimal objective value of a multistage stochastic program. These results also apply to stochastic multistage mixed integer linear programs. Chains of inequalities among the new quantities are provided in relation to the optimal objective value, the wait-and-see solution and the expected result of using the expected value solution. The computational complexity of the proposed lower and upper bounds is discussed and an algorithmic procedure to use them is provided. Numerical results on a real case transportation problem are presented.

Generalized Nash equilibrium and market coupling in the European power system

“Market Coupling” is currently seen as the most advanced market design in the restructuring of the European electricity market. Market coupling, by construction, introduces what is generally referred to as an incomplete market: it leaves several constraints out of the market and hence avoids pricing them. This may or may not have important consequences in practice depending on the case on hand. Quasi-Variational Inequality problems and the associated Generalized Nash Equilibrium can be used for representing incomplete markets. Recent papers propose methods for finding a set of solutions of Quasi-Variational Inequality problems. We apply one of these methods to a subproblem of market coupling namely the coordination of counter-trading. This problem is an illustration of a more general question encountered for instance in hierarchical planning in production management. We first discuss the economic interpretation of the Quasi-Variational Inequality problem. We then apply the algorithmic approach to a set of stylized case studies in order to illustrate the impact of different organizations of counter-trading. The paper emphazises the structuring of the problem. A companion paper considers the full problem of market coupling and counter-trading and presents a more extensive numerical analysis.

A mixed integer nonlinear optimization model for gas sale company

In this paper the authors propose an optimisation model, called OMoGaS (Optimisation Modelling for Gas Seller), to assist companies dealing with gas retail commercialisation. The model takes into account the limits on price imposed by law on small consumers as well as the gas company policies in order to explore the commercial consequences of different policies. The GAMS framework is used for the optimisation of the defined MINLP model where the profit function is based on the number of contracts with the final consumers, on the tipology of consumers and on the cost supported to meet the final demand while the constraints include information on a maximum daily gas consumption, on yearly maximum and minimum comsumption in order to avoid penalties and on consumption profiles. A case study is presented.

Evaluating the effects of environmental regulations on a closed-loop supply chain network: a variational inequality approach

Global climate change has encouraged international and regional adoption of pollution taxes and carbon emission reduction policies. Europe has taken the leadership in environmental regulations by introducing the European Union Emissions Trading System (EU-ETS) in 2005 and by promoting a set of policies destined to lower carbon emissions from energy, industrial, and transport sectors. These environmental policies have significantly affected the production choices of these European sectors. Considering this framework, the objective of this paper is to evaluate the effects of the application of environmental policies in a multitiered closed-loop supply chain network where raw material suppliers, manufacturers, consumers, and recovery centers operate. In particular, we assume that manufacturers are subject to the EU-ETS and a carbon tax is imposed on truck transport. In this way, the developed model captures carbon emission regulations, recycling, transportation and technological factors within a unified framework. In particular, it allows for evaluating the impacts of the considered environmental regulations on carbon emissions, product flows, and prices. The proposed model is optimized and solved by using the theory of variational inequalities. Our analysis shows that the combined application of the EU-ETS at the manufacturers’ tier and the carbon tax on truck transport implies additional costs for producers that reduce their good provisions. On the other side, this has a positive outcome for the environment since

A Spatial Competitive Analysis: The Carbon Leakage Effect on the Cement Industry Under the European Emissions Trading Scheme

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