Concave objective functions which are both piecewise linear and separable are often encountered in a wide variety of management science problems. Provided the constraints are linear, problems of this kind are normally...
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Concave objective functions which are both piecewise linear and separable are often encountered in a wide variety of management science problems. Provided the constraints are linear, problems of this kind are normally forced into a linear programming mould and solved using the simplex method. This paper takes another look at the associated linear programs and shows that they have special structural features which are not exploited by the simplex algorithm. It suggests that their variables can be divided into special ordered sets which can then be used to guide the pivoting strategies of the simplex algorithm with a resultant reduction in basis changes.
A linear programming (LP) method for security dispatch and emergency control calculations on large power systems is presented. The method is reliable, fast, flexible, easy to program, and requires little computer stor...
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A linear programming (LP) method for security dispatch and emergency control calculations on large power systems is presented. The method is reliable, fast, flexible, easy to program, and requires little computer storage. It works directly with the normal power-system variables and limits, and incorporates the usual sparse matrix techniques. An important feature of the method is that it handles multi-segment generator cost curves neatly and efficiently.
In the planning and design of a high-voltage transmission network it is sometimes desirable to install controllable kilovar ar capacity at several locations to support bus voltages during emergencies. This problem ari...
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In the planning and design of a high-voltage transmission network it is sometimes desirable to install controllable kilovar ar capacity at several locations to support bus voltages during emergencies. This problem arises when transmission line or generation outages cause bus voltage magnitudes to decrease below desirable limits. The problem of selecting where and how much kilovar capacity is required has many feasible solutions which satisfy the conditions imposed. A method for locating that solution with the minimum total installed capacity is presented. This nonlinear programming problem will be solved by using a linear approximation, solving the linear programming problem, and then correcting the linear approximation through the use of differences between the linear and nonlinear results. The method is illustrated by an application to a portion of a large high-voltage network.
In this correspondence, we describe an approach for the identification of good distance spectra for possibly existing binary linear block codes based on linear programming and the MacWilliams-Delsarte identities. Spec...
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In this correspondence, we describe an approach for the identification of good distance spectra for possibly existing binary linear block codes based on linear programming and the MacWilliams-Delsarte identities. Specifically, the linear program is defined by an expression characterizing the performance of a potential code in terms of its distance spectrum and constraints imposed by the MacWilliams-Delsarte identities. Using the union bound to characterize performance, our results suggest that the best distance spectrum is not a function of signal-to-noise ratio (SNR) above the cutoff rate SNR and also suggest the existence of several unknown, good codes. Characterizing the performance using the maximum spectral error component of the union bound suggests spectral thinning with decreasing. SNR.
Approaches to the solution of the l 1 estimation problem have a long history, going back to at least Edgeworth in the nineteenth century. Modern solution approaches have been of two types: (i) descent methods and (ii)...
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Approaches to the solution of the l 1 estimation problem have a long history, going back to at least Edgeworth in the nineteenth century. Modern solution approaches have been of two types: (i) descent methods and (ii) primal or dual LP methods. Simplex based algorithms have a standard geometric interpretation, but occasionally much more tangible geometric insights are available. For example, in the capacitated transhipment problem the workings of the LP solution algorithms can be interpreted on the underlying network. In this paper we develop geometric insight into the solution process directly in the space where the problem originates - the space of observations .
This article presents a method for solving linear programming problems in which elements of the tableau are stochastic. Using least-cost poultry rations as an example, the authors demonstrate the procedure developed. ...
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This article presents a method for solving linear programming problems in which elements of the tableau are stochastic. Using least-cost poultry rations as an example, the authors demonstrate the procedure developed. Sufficiently accurate results are obtained with less time and complexity than required by alternative methods. The authors conclude that the largest obstacle to examining related problems is in the limitations imposed by lack of data, in this case with regard to biological minima.
The inverse method of images is a relatively easy way to find approximate solutions to first-passage time problems. We extend the method in several ways: We use a linear program instead of a system of linear equations...
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The inverse method of images is a relatively easy way to find approximate solutions to first-passage time problems. We extend the method in several ways: We use a linear program instead of a system of linear equations;we utilize asymptotic information in addition to values at finite points;and we use a larger palette of approximating functions. These techniques enhance the scope, flexibility and accuracy of the method.
In this paper linear programming problems with fuzzy constraints and fuzzy coefficients in both matrix and right hand side of the constraint set are considered. Because of fuzzy coefficients in both members of each co...
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In this paper linear programming problems with fuzzy constraints and fuzzy coefficients in both matrix and right hand side of the constraint set are considered. Because of fuzzy coefficients in both members of each constraint, ranking methods for fuzzy numbers must be considered. The diversity of such methods provides a lot of different models of conventional linear programming problems from which fuzzy solutions to the former problem can be obtained.
When operating hybrid desalination plants combining multistage flash (MSF) and reverse osmosis (RO) processes, it is crucial to determine the blend ratios of water produced by these two processes. These blend ratios m...
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When operating hybrid desalination plants combining multistage flash (MSF) and reverse osmosis (RO) processes, it is crucial to determine the blend ratios of water produced by these two processes. These blend ratios must take economic and environmental aspects of the hybrid plant's sustainability into consideration, and must enable the plant to meet constraint conditions with respect to water demand, energy consumption savings, and saline content. We mathematically resolve this issue by formulating it as a linear programing problem and by computing that problem's solutions. Permissible solutions occur as an area in a triangle in the MSF-RO blend ratio diagram, and the most desirable solutions occur at (1) the intersection point between the water demand limit line and salinity limit line and at (2) the intersection point between the water demand limit line and the energy savings limit line.
State estimation plays an important role in real time security monitoring and control of power systems. There are many problems in the implementation of state estimator for large scale networks due to measurement erro...
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State estimation plays an important role in real time security monitoring and control of power systems. There are many problems in the implementation of state estimator for large scale networks due to measurement errors, weights given and the numerical ill-conditioning associated with the solution techniques. In this paper a new formulation using linear programming approach is presented. The formulation is devoid of weights and errors associated with the measurements are taken care of in constraints. The non linear problem is linearized at previous operating state and constraints are set up using flow mismatches. The implementation of the formulation exploits sparse features of the network matrices and avoids matrix inversions. Upper bound optimization technique is employed to solve the linear programming problem. Illustration of the proposed approach on sample 3-bus and 6-bus systems and a practical Indian Southern grid 72 bus equivalent system are presented.
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