Abstract
Inspired by a case study, this paper reports a successful application of VNS to the production planning and scheduling problem that arises in the glass container industry. This is a multi-facility production system, where each facility has a set of furnaces where the glass paste is produced in order to meet the demand, being afterwards distributed to a set of parallel molding machines. Since the neighborhoods used are not nested, they are not ordered by increasing sizes, but by means of a new empirical measure to assess the distance between any two solutions. Neighborhood sizes decrease significantly through-out the search thus suggesting the use of a scheme in which efficiency is placed. over effectiveness in a first step, and the opposite in a second step. We test this variant as well as other two with a real-world problem instance from our case study.

Abstract
Game theory has traditionally used real-valued utility functions in decision-making problems. However, the real information available to assess these utility functions is normally uncertain, suggesting the use of uncertainty distributions for a more realistic modelling. In this sense, utilities results or pay-offs have been normally modelled with probability distributions, assuming random uncertainty. However, when statistical information is unavailable, probability may not be the most adequate paradigm, and can lead to very large execution times when some real complex problems are addressed. In this article possibility distributions are used to model the uncertainty of utility functions when the strategies are probability distributions (mixed strategies) over a set of original and discrete strategies (pure strategies). Two dual approaches to solve the resulting non-cooperative fuzzy games are proposed: modelling players' risk aversion, and thus providing realistic conservative strategies. Two examples show the robustness of the strategies obtained with the proposed approaches.

Abstract

Abstract
It is widely known and accepted that Nash equilibrium suitably models agents' behavior in electricity markets, since it is coherent with the common sense of their simultaneous profits maximisation. In the literature, these approaches are usually addressed using deterministic representations, despite the fact that electricity markets are highly conditioned by the uncertainty in demand or in agents' bidding strategies. Only some equilibrium-modelling approaches under uncertainty can be found in the literature, most of them using probability distributions. However, probability approaches may lead to very complex formulations and generally require restrictive assumptions (such as normality or independence) that can hardly be verified in real complex problems. A conjectured-price-response equilibrium model that uses LR-possibility distributions to represent the uncertainty of the residual demand curves faced by the participant agents is proposed. Modelling the risk-aversion attitudes of the agents, the resulting possibilistic equilibrium is transformed into a simplified deterministic one, which is solved with a new globally convergent algorithm for variational inequalities problems. Some interesting results for a real-size electricity system show the robustness of this new approach when compared with other risk-neutral approaches.

Abstract

Abstract