Vol.6 No.3 2014
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Research paper : A proposal for setting electric power saving rate to avoid risk of electric power shortage occurrence (I. ARIZONO et al.)−143−Synthesiology - English edition Vol.6 No.3 (2013) probability inequality is a pessimistic evaluation, more effective policy decision-making is enabled by devising a higher-performance probability inequality which gives tighter probability. Here, we give some explanations concerning the probability inequalities adopted in this paper. Because the electricity shortage should not happen, the electricity shortage outbreak probability has to be evaluated as a relatively small value. Therefore, some probability inequalities with the feature of giving a pessimistic evaluation have been adopted in this paper. Concretely, we employ three probability inequalities of one-sided Chebychev, Bennett and Hoeffding probability inequalities. The one-sided Chebychev probability inequality[6] which is a well-known and basic probability inequality, gives an evaluation based on the information about the expectation and variance of the random variable. Both the Bennett and Hoeffding probability inequalities need the information about the range in addition to the expectation and variance of the random variable. This information is observable in actuality. The device to give the range using the expectation and variance is presented in this paper. Talagrand[12] and Bentku[13] have mentioned that the Hoeffding probability inequality is extremely useful among the existing probability inequalities evaluated under the same conditions. The Bennett probability inequality is the basis of the derivation of the Hoeffding probability inequality. Therefore, both the Bennett and Hoeffding probability inequalities are also employed in this paper.There are other probability inequalities not adopted in this paper, for example, the Markov probability inequality, the Chernoff probability inequality and another Hoeffding probability inequality. Although the Markov probability inequality[9] is a basic probability inequality shown in various textbooks about the probability theory, evaluation by the Markov probability inequality based on information of the lower limit and expectation of the random variables is not exactly practical. There is another Hoeffding probability inequality[8] which can evaluate by using the information on only the range of random variables. However, since this Hoeffding probability inequality gives a larger value than the Hoeffding probability inequality in this paper, this Hoeffding probability inequality has not been employed here. There is the Chernoff probability inequality which is considered a well-known probability inequality. The Chernoff probability inequality uses information of probability distributions of random variables.[14][15] Therefore, in the situation considered in this paper, it is not suitable to adopt this Chernoff probability inequality.Although there may be some critical comments, we consider that the system proposed in this paper is presently of a certain completed form under the available information in order to evaluate the electricity shortage outbreak probability. However, it is important to improve the performance of the probability inequalities. By deriving probability inequalities with better performance, we can make more fruitful decisions. In this sense, the authors would like to pursue the improvement of probability inequality.The results of this paper are summarized as follows:1.An electricity shortage outbreak probability evaluation system under the worst-case scenario has been constructed by using probability inequality in the case where limited information about the expectation and variance of electricity supplies and demand is only given.2.The fact that the disclosure of the past data for the electricity demand and supply is not necessarily enough has been explained. At the same time, if this past data is disclosed, in order to use it effectively, the development of the estimation method of the expectation and variance of the electricity demand and supply is needed and is a future subject to be explored. 3.It has been exhibited that the performance improvement of probability inequality is a subject for more effective and efficient decision-making in using the proposed system based on probability inequality.From the above, authors pray that this proposed evaluation system is supplemented and upgraded by more researchers to meet social requests. For example, there are many young and energetic researchers in the field of data analysis. If the electric power companies disclose more information, a method for estimating precisely the expectation, variance and range might be developed by such researchers. The proposed evaluation system satisfies the requirements to be at the least a basic system, and it has been suggested with this intention.References[1]The Asahi Shimbun: The Tokyo Electric Power Company, Inc., toward the re-operation of thermal plants, the morning newspaper on March 18 (2011) (in Japanese).[2]The Asahi Shimbun: The trying winter with no electricity supply from nuclear power plants is coming soon, the morning newspaper on December 18 (2011) (in Japanese).[3]S. Yamamoto: Electricity shortage and Japanese economy affected by the East Japan Great Earthquake disaster - influence on production/employment caused by electricity savings and electricity supply reduction by sign restriction VAR -, Discussion Paper of the Graduate School of Economics, Kobe University, 1119, 1-13 (2011) (in Japanese).[4]Y. Takemoto, F. Iwamoto and I. Arizono: Proposal of reorder point satisfying allowable shortage rate under limited demand information, Journal of Japan Industrial Management Association, 62 (1), 21-24 (2011) (in Japanese).[5]T. Shinzato and I. Kaku: Large deviation approach for safety stock management for correlated demands, Journal of Japan Industrial Management Association, 62 (4), 164-173 (2011) (in Japanese).[6]J. R. Birge and F. Louveaux: Introduction to Stochastic Programming, Springer (1997).

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