A comparative study of time aggregation techniques in relation to power capacity-expansion modeling

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Comments on: A comparative study of time aggregation techniques in relation to power capacity-expansion modeling

The cg -average tree value for games on cycle-free fuzzy communication structures Abstract The main goal in a cooperative game is to obtain a fair allocation of the profit due the cooperation of the involved agents. The most known of these allocations is the Shapley value. This allocation considers that the communication among the players is complete. The Myerson value is a modification of the Shapley value considering a communication structure which determines the feasible bilateral relationships among the agents. This allocation of the profit is not always a stable solution. Another payoff allocation for games with a communication structure from the definition of the Shapley value is the average tree value. This one is a stable solution for any game using a cycle-free communication structure. Later fuzzy communication structures were introduced. In a fuzzy communication structure, the membership of the agents and the relationships among them are leveled. The Myerson value was extended in several different ways depending on the behavior of the agents. In this paper, the average tree value is extended to games with fuzzy communication structures taking one particular version: the Choquet by graphs (cg). We present an application to the management of an electrical network with an algorithmic implementation.

Existence of Nash equilibria in stochastic games of resource extraction with risk-sensitive players Abstract We consider a two-person stochastic game of resource extraction. It is assumed that players have identical preferences. A novelty relies on the fact that each player is equipped with the same risk coefficient and calculates his discounted utility in the infinite time horizon in a recursive way by applying the entropic risk measure parametrized by this risk coefficient. Under two alternative sets of assumptions, we prove the existence of a symmetric stationary Markov perfect equilibrium.

A comparative study of time aggregation techniques in relation to power capacity expansion modeling Abstract In this paper, we studied the aggregation techniques for power capacity expansion problems. Combining a growing demand for green energy with a hard constraint on demand satisfaction causes system flexibility to be a major challenge in designing a stable energy system. To determine both the need for flexibility and which technologies that could satisfy these needs at minimum cost, the system should be analyzed on an hour-by-hour scale for a long period of time. This often leads to computationally intractable problems. One way of getting more tractable models is to aggregate the time domain. Many different aggregation techniques have been developed, all with a common goal of selecting representative time slices to be used instead of the full time scale, gaining a problem size reduction in the number of variables and/or constraints. The art of aggregation is to balance the computational difficulty against the solution quality, making validation of the techniques crucial. We propose new aggregation techniques and compare these to each other and to a selection of aggregation techniques from the literature. We validate the aggregated problems against the non-aggregated problems and look into the sensitivity of the performance of the aggregation techniques to different data sets and to the selection of different element types. Our analysis shows that aggregation techniques can be used to achieve very good solutions in a short amount of time, and that simple aggregation techniques achieve good performance similar to that of techniques with higher complexity. Even though the aggregation techniques in this paper are applied to power capacity expansion models, the methodology can be used for other problems with similar time dependence, and we believe that results in agreement with the results seen here, would be achieved.

Mathematical modelling of a tollbooth system with two parallel skill-based servers and two vehicle types Abstract This paper considers a tollbooth system with two parallel heterogeneous servers and two vehicle types (say, cars and trucks), where one server collects tolls from vehicles of both types and the other only serves one type of them. With such characteristic, the system is referred to as “skill-based servers” for brevity in this paper. Meanwhile, vehicles are accommodated in a single common lane and get served on the “global First-Come-First-Served” basis. In fact, such a system and its variants are commonly encountered and their performance measures are of great significance to managers. We first develop a Quasi-Birth-Death process to explicitly model this tollbooth system. Then by applying spectral expansion technique, we derive the stationary probabilities for the computation of the system’s performance measures, such as mean queue size and the idle probability of each server. The Laplace–Stieltjes transforms of an arbitrary vehicle’s sojourn time is derived as well. Finally, numerical results are presented to show the impact of parameters’ selection upon performance measures, and they have intriguing managerial implications. The results also reveal that the tollbooth system with skill-based servers is much more efficient compared to the system with dedicated servers, which has been studied by Mélange et al. (Comput Oper Res 71:23–33, 2016), especially in rush hours.

Congress seat allocation using mathematical optimization Abstract After the 2015 Spanish general election a row erupted over the allocation of physical seats in the Congress of Deputies, with certain parties left feeling they possessed an inferior selection of seats compared to other parties. Using this as motivation, this paper considers how mathematical optimization can be used to generate seating plans for political chambers, an application that has not been considered before. As well as being in some way ‘fair’ to all parties, the seating plan should ensure that each block of seats is well-defined and compact. Two optimization models are formulated and, due to their complexity, heuristic methods are developed to find ‘good’ solutions. Analysis shows that the heuristics are able to produce visually appealing seating plans for basic cases, but problems can occur when there are additional requirements to be satisfied.