Demand set

Abstract: A procedure for representing competitive and noncompetitive market structures in linear programming (LP) models is presented. The specification of the objective function follows from the choice of market form to be incorporated in the model. Development of the function yields demand and expenditure equations and an LP tableau with separable demands. In the event of two or more products that are not separable in demand, the nonlinear demand set can be linearized directly by specification of activity vectors representing points on the demand surface and by incorporating an appropriate convex combination constraint. The specification of commodity demand structures incorporates one characteristic, which makes it particularly convenient for obtaining comparative statics solutions. The demand function for any commodity group can be rotated merely by an appropriate change in the constraint value of the convex combination inequality. A representation of international trade can be incorporated by adding commodity specific importing activities as additional production activities and adding exporting activities as additional selling activities. 21 references.

Abstract: In this paper, we deal with single facility location problems in a general normed space in which the existing facilities are represented by convex sets of points. The criterion to be satisfied by the service facility is the minimization of an increasing, convex function of the distances from the service facility to the closest point of each demand set. We obtain a geometrical characterization of the set of optimal solutions for this problem. Two remarkable cases--the classical Weber problem and the minimax problem with demand sets--are studied as particular instances of our problem. Finally, for the planar polyhedral case, we give an algorithm to find the solution set of the considered problems.

Abstract: We design and analyze deterministic truthful approximation mechanisms for multi-unit Combinatorial Auctions with only a constant number of distinct goods, each in arbitrary limited supply Prospective buyers (bidders) have preferences over multisets of items, ie for more than one unit per distinct good Our objective is to determine allocations of multisets that maximize the Social Welfare Despite the recent theoretical advances on the design of truthful Combinatorial Auctions (for several distinct goods) and multi-unit auctions (for a single good), results for the combined setting are much scarser Our main results are for multi-minded and submodular bidders In the first setting each bidder has a positive value for being allocated one multiset from a prespecified demand set of alternatives In the second setting each bidder is associated to a submodular valuation function that defines his value for the multiset he is allocatedFor multi-minded bidders we design a truthful FPTAS that fully optimizes the Social Welfare, while violating the supply constraints on goods within factor (1+e) for any fixed e > 0 (ie, the approximation applies to the constraints and not to the Social Welfare) This result is best possible, in that full optimization is impossible without violating the supply constraints It also improves significantly upon a related result of Grandoni et al [SODA 2010] For submodular bidders we extend a general technique by Dobzinski and Nisan [JAIR, 2010] for multi-unit auctions, to the case of multiple distinct goods We use this extension to obtain a PTAS that approximates the optimum Social Welfare within factor (1+e) for any fixed e > 0, without violating the supply constraints This result is best possible as well Our allocation algorithms are Maximum-in-Range and yield truthful mechanisms when paired with Vickrey-Clarke-Groves payments

Abstract: A method of controlling a power generating unit or other process equipment with a slow reaction time includes creating a feedforward control signal to selectively include a fast response rate component or a slow response rate component based on the average rate at which a load demand set point signal has changed during a particular previous period of time. The method then uses the developed feedforward control signal to control the power generating equipment or other slowly reacting process equipment. In particular, a control method switches between introducing a fast or a slow response component within a feedforward control signal based on whether the change in the load demand set point over a particular period of time in the past (e.g., an average rate of change of the load demand set point signal) is greater than or less than a predetermined threshold. This method is capable of providing a relatively fast control action even if the expected load demand set point change is in a small range. In addition, this method does not require knowledge of the final or target load demand set point during the time in which the load demand set point is ramping up to a final target value and is not dependent on the ramp size, i.e., the ultimate difference between the load demand set point at the beginning of the load demand set point change and the final or target value of the load demand set point, making it more versatile than prior art systems.