In the present research paper, two types of models are discussed for linear programming problems. Models are determining the work of the employee in day-to-day life. The first is Staff Scheduling for Bhopal-Dewas Corr...
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In the present research paper, two types of models are discussed for linear programming problems. Models are determining the work of the employee in day-to-day life. The first is Staff Scheduling for Bhopal-Dewas Corridor Toll Plaza and second is worker scheduling for Aqua sure Aquagurad Water Purifiers drinking water Company(Rukmani Beverages Pvt. Ltd.). (C) 2018 Elsevier Ltd. All rights reserved.
We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavio...
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ISBN:
(纸本)9783959770545
We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavior of acellular slime mold Physarum polycephalum, and more recently considered as a method to solve LP instances. We study the convergence time of the continuous Physarum dynamics in the context of the linear programming problem, and derive a new time bound to approximate optimality that depends on the relative entropy between projected versions of the optimal point and of the initial point. The bound scales logarithmically with the LP cost coefficients and linearly with the inverse of the relative accuracy, establishing the efficiency of the dynamics for arbitrary LP instances with positive costs.
In this paper, we are interested in the performance of the logarithmic barrier type of interior point method to solve a linear programming problem. We present a new alternative allowing to easily compute the step of d...
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In this paper, we are interested in the performance of the logarithmic barrier type of interior point method to solve a linear programming problem. We present a new alternative allowing to easily compute the step of displacement and without line search. This purpose is confirmed by numerical tests showing the efficiency of this approach versus classical line search methods.
linear programming is the optimization of a linear function under constraints of linear equations or inequalities. Since much of the information in the real world is unknown, linear programming does not produce accept...
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Mismatch filters are generally used to reduce the range sidelobes when phase coded waveforms are used. It is shown that such mismatch filters can be designed with linear programming techniques. This particular formula...
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ISBN:
(纸本)9781728168135
Mismatch filters are generally used to reduce the range sidelobes when phase coded waveforms are used. It is shown that such mismatch filters can be designed with linear programming techniques. This particular formulation allows a trade between the degree of sidelobe suppression and the loss to the main peak sensitivity.
In this study, we consider a particular version of the hybrid flexible flow shop (HFFS) scheduling problem, inspired from a real-life application in a printing industry. The considered problem is a variation of the cl...
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In this study, we consider a particular version of the hybrid flexible flow shop (HFFS) scheduling problem, inspired from a real-life application in a printing industry. The considered problem is a variation of the classical Flow shop problem, in which specific constraints are jointly considered, such as non-identical parallel machines, sequence-dependent setups on machines, machine eligibility, and precedence constraints among jobs, in order to minimize the total tardiness time. After a problem description, a mathematical model, in form of mixed integer linear programming (MILP) model, that incorporates these aspects is developed and evaluated using ILOG Cplex software.
Following the breakthrough work of Tardos (Oper. Res. '86) in the bit-complexity model, Vavasis and Ye (Math. Prog. '96) gave the first exact algorithm for linear programming in the real model of computation w...
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ISBN:
(纸本)9781450369794
Following the breakthrough work of Tardos (Oper. Res. '86) in the bit-complexity model, Vavasis and Ye (Math. Prog. '96) gave the first exact algorithm for linear programming in the real model of computation with running time depending only on the constraint matrix. For solving a linear program (LP) max c(T)x, Ax = b, x >= 0, A is an element of R-mxn, Vavasis and Ye developed a primal-dual interior point method using a 'layered least squares' (LLS) step, and showed that O(n(3.5) log((chi) over bar (A) + n)) iterations suffice to solve (LP) exactly, where (chi) over bar (A)* is a condition measure controlling the size of solutions to linear systems related to A. Monteiro and Tsuchiya (SIAM J. Optim. '03), noting that the central path is invariant under rescalings of the columns of A and c, asked whether there exists an LP algorithm depending instead on the measure (chi) over bar (A)*, defined as the minimum (chi) over bar (AD) value achievable by a column rescaling AD of A, and gave strong evidence that this should be the case. We resolve this open question affirmatively. Our first main contribution is an O(m(2)n(2) + n(3)) time algorithm which works on the linear matroid of A to compute a nearly optimal diagonal rescaling D satisfying (chi) over bar (AD) <= n((chi) over bar*)(3). This algorithm also allows us to approximate the value of (chi)over bar>(A) up to a factor n((chi) over bar*)(2). This result is in (surprising) contrast to that of Tuncel (Math. Prog. '99), who showed NP -hardness for approximating (chi) over bar (A) to within 2(poly(rank(A))). The key insight for our algorithm is to work with ratios g(i)/g(j) of circuits of A-i.e., minimal linear dependencies Ag = 0 which allow us to approximate the value of (chi) over bar (A)* by a maximum geometric mean cycle computation in what we call the 'circuit ratio digraph' of A. While this resolves Monteiro and Tsuchiya's question by appropriate preprocessing, it falls short of providing either a truly scaling i
In the framework of free flight, there can be no intersection between the protected areas of two planes. The traditional conflict resolution methods allow generally the aircraft to change the speed alone or to change ...
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ISBN:
(纸本)9781728158556
In the framework of free flight, there can be no intersection between the protected areas of two planes. The traditional conflict resolution methods allow generally the aircraft to change the speed alone or to change angle alone. Starting from the method of linear programming and based on solving some special problems, this article presents a method that can change the speed and angle of aircraft in the same time. Finally, some tests verify the feasibility of the method.
The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one consid...
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The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendency, spread, skewness and extreme values for the purpose of risk analysis. This enables risk analysis and business analytics, emerging topics in education and preparation for the knowledge economy.
When solving a linear programming model, the coefficients should be fixed at specific values in advance. In practice, however, data overwhelmingly lack precision and this affects the model's optimal solution. Amon...
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When solving a linear programming model, the coefficients should be fixed at specific values in advance. In practice, however, data overwhelmingly lack precision and this affects the model's optimal solution. Among other theories including fuzzy set and intuitionistic fuzzy set theories, the neutrosophic set theory is considered a generalization of the two theories mentioned and is shown to be very powerful in assimilating inaccurate, vague, and maladjusted data. In this study, we deal with neutrosophic linear programming models where all coefficients are represented by triangular neutrosophic numbers. Maximization, minimization, and all types of constraints are considered. A novel parametric-based approach is introduced to solve this type of model and a few numerical examples are provided. Results show that the presented approach yields more realistic solutions. Finally, we conclude that the proposed approach is efficient, flexible, and capable of solving neutrosophic linear programming models.
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