For stochastic programs with complete (linear) recourse we present easily verifiable sufficient conditions for the strong convexity of the expected-recourse function. Both, programs with random right-hand side and wit...
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For stochastic programs with complete (linear) recourse we present easily verifiable sufficient conditions for the strong convexity of the expected-recourse function. Both, programs with random right-hand side and with random technology matrix are considered. Among the implications of strong convexity those with respect to the stability of stochastic programs are worked out in detail. In this way, former results on the quantitative stability of optimal solutions are extended.
A general model for Fuzzy linearprogramming problem is studied. Fuzzy numbers generated by an homogeneous linear fuzzy function have been used for representing the imprecision of the parameters. A solution method is ...
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A general model for Fuzzy linearprogramming problem is studied. Fuzzy numbers generated by an homogeneous linear fuzzy function have been used for representing the imprecision of the parameters. A solution method is proposed using fuzzy numbers ranking procedures.
We propose a principal pivoting method for solving the one-parametriclinear complementarity problem where all the coefficients are linear functions of the parameter K and the matrix of the problem is sufficient for a...
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In this paper a new method for generating the set of efficient extreme-points for the three-objective linearprogramming problem is presented. This method successfully exploits the fact that vectors that are strictly ...
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In this paper a new method for generating the set of efficient extreme-points for the three-objective linearprogramming problem is presented. This method successfully exploits the fact that vectors that are strictly efficient in associated multi-objective problems of lower dimensions are also efficient in the full multi-objective problem.
This paper describes procedures for computing the tightest possible best-case and worst-case bounds on the variance of a discrete, bounded, random variable when lower and upper bounds are available for its unknown pro...
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This paper describes procedures for computing the tightest possible best-case and worst-case bounds on the variance of a discrete, bounded, random variable when lower and upper bounds are available for its unknown probability mass function. An example from the application of the Monte Carlo method to the estimation of network reliability illustrates the procedures and, in particular, reveals considerable tightening in the worst-case bound when compared to the trivial worst-case bound based exclusively on range.
This paper provides several useful support tools of power system scheduling and planning. First, we propose a fast method, which is used to evaluate the generating units and transmission capability of power system, an...
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This paper provides several useful support tools of power system scheduling and planning. First, we propose a fast method, which is used to evaluate the generating units and transmission capability of power system, and calculate the optimal reserve of each demand side, based on two-step linearprogramming technique. Then, a new support tool of power system planning is described by using the parametric linear programming. The proposed support tool does not only fast give a optimal reserve curve of the system, but also provides some diagnosis information of system weak location for the expansion planning and maintenance scheduling decision of transmission lines or generating units. Third, we take into account the outages of generators and transmission lines, and show a possible method to estimate the reliability(LOLP) of multi-area power system by making use of linearprogramming. Several examples have been used to verify the proposed methodology and illustrate the application. The results show that our approaches are very simple, fast and efficient for the generation and transmission capability evaluation or the contingency test of power system as support tools.
Many classes of mathematical programming problems can be formulated as a linear program with a parametric objective function. Gass and Saaty developed in the early 1950's a parametricprogramming procedure for sol...
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Many classes of mathematical programming problems can be formulated as a linear program with a parametric objective function. Gass and Saaty developed in the early 1950's a parametricprogramming procedure for solving the latter problem. This procedure is relevant to solution strategies for many problem types but is underutilized, often because the relationship of the procedure to the relevant problem class is not recognized. In this paper five recent applications of the parametricprogramming procedure are presented.
In the general regression model y(i) = x(i)'-beta + e(i), for i = 1, ..., n and beta epsilon R(p), the "regression quantile" beta triple-overdot (theta) estimates the coefficients of the linear regressio...
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In the general regression model y(i) = x(i)'-beta + e(i), for i = 1, ..., n and beta epsilon R(p), the "regression quantile" beta triple-overdot (theta) estimates the coefficients of the linear regression function parallel to x(i)'-beta and roughly lying above a fraction theta of the data. As introduced by Koenker and Bassett [Econometrica, 46 (1978), pp. 33-50], these regression quantiles are analogous to order statistics and provide a natural and appealing approach to the analysis of the general linear model. Computation of beta triple-overdot (theta) can be expressed as a parametric linear programming problem with J(n) distinct extremal solutions as theta goes from zero to one. That is, there will be J(n) breakpoints {theta-j}, for j = 1, ..., J(n) such that beta triple-overdot (theta-j) is obtained from beta triple-overdot (theta-j-1) by a single simplex pivot. Each beta triple-overdot (theta-j) is characterized by a specific subset of p observations. Although no previous result restricts J(n) to be less than the upper bound (p(n)) = O(n(p)), practical experience suggests that J(n) grows roughly linearly with n. Here it is shown that, in fact, J(n) = O(n log n) in probability, where the distributional assumptions are those typical of multiple regression situations. The result is based on a probabilistic rather than combinatoric approach which should have general application to the probabilistic behavior of the number of pivots in (parametric) linearprogramming problems. The conditions are roughly that the constraint coefficients form random independent vectors, and that the number of variables is fixed while the number of constraints tends to infinity.
A review of the literature concerning the use of full fat soybeans (FFSB) in poultry diets identified the two requirements of heat treatment and milling to maximize nutrient availability in FFSB and assure performance...
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A review of the literature concerning the use of full fat soybeans (FFSB) in poultry diets identified the two requirements of heat treatment and milling to maximize nutrient availability in FFSB and assure performance in broilers (as measured by both growth and feed efficiency) equivalent to that attainable with diets including soybean meal (SBM). Two studies were reviewed that reported on economic evaluations of the use of FFSB in broiler diets. Based on the price relationship existing during the time period of one study, FFSB were deemed uneconomic as a replacement for SBM. The economic evaluation performed in this study used parametricprogramming and the technique of marginal cost mapping to determine the relative economic value of FFSB in four different specifications of broiler diets (two levels of energy requirements and two fat ingredient costs). The highest economic value obtained for FFSB occurred in a diet with high energy requirements and a high cost for fat. This demonstrates the importance of each producer evaluating the value of FFSB with their formula specifications and prices. The current price differential between FFSB and SBM with animal/vegetable fat was substantial enough to preclude the use of FFSB as a replacement for SBM in the model broiler diets used, but the marginal cost-mapping analysis revealed the full range substitution possibilities.
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