A number of MOLP-algorithms have been developed to establish the set of non-dominated solutions, using a number of different approaches and theorems that may be non-trivial to the non-expert user. This article present...
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A number of MOLP-algorithms have been developed to establish the set of non-dominated solutions, using a number of different approaches and theorems that may be non-trivial to the non-expert user. This article presents a simplified MOLP-algorithm (MOLP-S), based on a straightforward extension of the simplex-method of linearprogramming, to trace out the set of non-dominated solutions. The proposed methodology exhibits computational characteristics that may render the method more efficient as compared to other algorithms currently in use. The proposed method is tested on a number of problems from the literature which exhibit varying degrees of complexity.
AbstractThis paper describes a procedure for determining if constrained transportation problems (i.e., transportation problems with additional linear constraints) can be transformed into equivalent pure transportation...
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AbstractThis paper describes a procedure for determining if constrained transportation problems (i.e., transportation problems with additional linear constraints) can be transformed into equivalent pure transportation problems by a linear transformation involving the node constraints and the extra constraints. Our results extend procedures for problems in which the extra constraints consist of bounding certain partial sums of variables.
Recently, mathematical methods of the theory of linearprogramming have come to be widely used to solve problems of optimal control of the spatial energy distribution in nuclear reactors. In this work, as the first st...
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Recently, mathematical methods of the theory of linearprogramming have come to be widely used to solve problems of optimal control of the spatial energy distribution in nuclear reactors. In this work, as the first step toward solving the problem of three-dimensional stabilization of the spatial energy distribution by mathematical-programming methods, a method is proposed for calculating the optimal displacements of the control rods (CR), on the basis of introducing into the simplex-method algorithm additional constraints.
A modification of the revised simplex algorithm is considered where every step involves O ( m 2 ) arithmetical operations. The error analysis and the bit-complexity estimates presented show very strong stability of th...
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A modification of the revised simplex algorithm is considered where every step involves O ( m 2 ) arithmetical operations. The error analysis and the bit-complexity estimates presented show very strong stability of the modified algorithm. The same modification can be included into some other linear algebra algorithms.
CRASH is the name given to procedures appearing in the majority of commercial mathematical programming packages. Their purpose is to create quickly a good starting basis for the revised simplex algorithm. The method...
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CRASH is the name given to procedures appearing in the majority of commercial mathematical programming packages. Their purpose is to create quickly a good starting basis for the revised simplex algorithm. The methods employed in different packages vary, but are all heuristic and use simple good ideas. Most CRASHing procedures deliver a starting basis which is better than the all-logical basis, but which is usually unfeasible. An attempt is made to obtain a feasible basis as a starting point. The dual of Fourier-Motzkin elimination is described and illustrated by means of a numerical example. If carried to completion, all extreme solutions of the original model are generated. If the generation of columns is restricted, only some of the extreme solutions will be produced. The best feasible basis generated in this way can be utilized as a starting basis for the simplex algorithm. This restricted method can thus be regarded as a CRASHing procedure. Ways to adapt the method for improved computational efficiency are suggested.
A complete analysis and explicit solution is presented for the problem of linear fractional programming with interval programming constraints whose matrix is of full row rank. The analysis proceeds by simple transform...
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A complete analysis and explicit solution is presented for the problem of linear fractional programming with interval programming constraints whose matrix is of full row rank. The analysis proceeds by simple transformation to canonical form, exploitation of the Farkas-Minkowski lemma and the duality relationships which emerge from the A. Charnes-W. W. Cooper linearprogramming equivalent for general linear fractional programming. The formulations as well as the proofs and the transformations provided by general linear fractional programming theory are here employed to provide a substantial simplification for this class of cases. The augmentation developing the explicit solution is presented, for clarity, in an algorithmic format.
In 1781 the French mathematician G. Monge gave an optimality criterion and a greedy-like procedure for solving specially structured transportation problems. Here we present a ‘new’ approach for solving assignment pr...
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In 1781 the French mathematician G. Monge gave an optimality criterion and a greedy-like procedure for solving specially structured transportation problems. Here we present a ‘new’ approach for solving assignment problems which builts upon Monge's observation. The basic idea is to transform an arbitrary assignment problem into an ‘equivalent’ one where Monge's condition is fulfilled.
We consider here stochastic linear programs with simple recourse when all the elements of the technology matrix and the resource vector have certain specific distributions. The distributions considered are the Normal,...
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We consider here stochastic linear programs with simple recourse when all the elements of the technology matrix and the resource vector have certain specific distributions. The distributions considered are the Normal, Exponential and Erlang. For the first two instances we extend the equivalent deterministic program to include the variance of the recourse. Finally, a simple example is given to illustrate the application of the formulas for the Erlang case.
Integer programming is widely applicable to problems in industry and business. A special type of integer program, the binary knapsack problem, is examined. The binary knapsack problem is of major importance because ...
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Integer programming is widely applicable to problems in industry and business. A special type of integer program, the binary knapsack problem, is examined. The binary knapsack problem is of major importance because it is a subproblem that must be repeatedly solved in the solution of more general mathematical programs, such as vehicle scheduling and routing. Of the several efficient algorithms for the solution of binary knapsack problems that have appeared in the literature, the direct descent algorithm suggested by Zoltners (1978) is generally considered one of the most efficient. Zoltners' direct descent algorithm is improved through a more general fathom and backtrack methodology and stronger reduction tests. The improvements result in substantially, often dramatically, shortened solution times. The efficiency of these improvements is verified via extensive computational testing.
The decision by university libraries to order new journals or cancel existing subscriptions depends on multiple conflicting factors. The faculty's need for a journal, the adjudged rating of the journal, the availa...
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The decision by university libraries to order new journals or cancel existing subscriptions depends on multiple conflicting factors. The faculty's need for a journal, the adjudged rating of the journal, the availability of the journal in other libraries, and budget constraints are among the many conflicting criteria that can be considered in the decision process. Traditional methods used by libraries to select journals for new subscriptions or for their cancellation do not consider all of these conflicting factors objectively. The purpose of this paper is to demonstrate how goal programming (GP) can be used to solve the journal selection and cancellation problem. In addition, this paper discusses the decision and modeling processes necessary to apply GP as a library science aid in the journal selection and cancellation problem.
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