New PDF release: Decision Making with Dominance Constraints in Two-Stage

By Uwe Gotzes

Two-stage stochastic programming versions are regarded as beautiful instruments for making optimum judgements less than uncertainty. usually, optimality is formalized by way of utilising statistical parameters resembling the expectancy or the conditional price in danger to the distributions of aim values.

Uwe Gotzes analyzes an method of account for danger aversion in two-stage versions dependent upon partial orders at the set of actual random variables. those stochastic orders let the incorporation of the features of entire distributions into the choice technique. The revenue or price distributions needs to cross a benchmark try out with a given applicable distribution. hence, extra ambitions could be optimized. For this new classification of stochastic optimization difficulties, effects on constitution and balance are confirmed and a adapted set of rules to take on huge challenge cases is constructed. the results of the modelling historical past and numerical effects from the appliance of the proposed set of rules are validated with case experiences from strength buying and selling.

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Additional info for Decision Making with Dominance Constraints in Two-Stage Stochastic Integer Programming

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The sign of these variables indicates the flow direction. Since decisions on pool transactions are short-term decisions depending on the forward portfolio and on the actual demands, these variables carry the scenario identifier . 4 Client Demand We consider that the retailer has the potential to supply energy to a set of clients divided into NE groups (here we implemented three groups: industrial, commercial and residential customers). Each group e is characterized by consumption patterns and its response to the selling price.

1 Decision Framework We consider the problem of an electricity retailer that has to decide the forward contracting purchases and the selling prices offered to potential clients at the beginning of the year. In the course of the year, the retailer participates in the pool to supply proportions of it’s clients demands or to sell excessive energy previously contracted in the futures market. At the beginning of the year, future pool prices and client demands are unknown for the retailer. Thus the retailer has to decide on the forward contracting portfolio and on selling prices with incomplete information.

XL 17 . This, however, would lead to a Lagrangean 17 “Nonanticipativity” H1 ... HL = ∈ {−1, 0, 1}((L−1)·dim X)×(L·dim X) , with e. , ¯ cf. 4) and (H1 )• j := (0¯ (dim X·( j−1)) , 1¯ (dim X) , 0¯ (dim X·(L− j−1)) ) (1¯ is defined analogously to 0, (Hi )• j := (0¯ (dim X·( j−1)+i−2) , −1, 0¯ (dim X·(L− j)−i+1) ) , i = 2, . . , L 52 4 Decomposition Method dual in dimension (L − 1) · dim X, which quickly can become several tens or even hundreds of thousands. Therefore, we leave it at working with the copies x in our lower bounding scheme at first, striking a compromise between computational effort and quality of bounds.

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