We consider here the problem of finding a non-negative solution to a set of linear equations which minimizes a bottleneck type objective. Two algorithms are described for the general problem and a single algorithm for...
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We consider here the problem of finding a non-negative solution to a set of linear equations which minimizes a bottleneck type objective. Two algorithms are described for the general problem and a single algorithm for the bottleneck transportation problem.
Preemptive linear-goal programming and its related simplex-based algorithm is too restrictive in its ability to search out an acceptable solution and imposes an unrealistic burden on the decision maker by requiring a ...
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Preemptive linear-goal programming and its related simplex-based algorithm is too restrictive in its ability to search out an acceptable solution and imposes an unrealistic burden on the decision maker by requiring a statement of strict preemptive priorities. Also, the question of goal norming has little importance in terms of the basic problem -- finding a suitable set of objective-function weights that can be applied to the over- and under-achievement deviation variables. An approach for solving large-scale goal problems is described. For problems of special structure, the weighted objective method can utilize efficient computer codes directly, whereas the preemptive approach cannot.
An algorithm for the bicriteria linearprogramming problem is presented. The algorithm determines the set of efficient extreme points in objective function space and involves solving a sequence of single criteria line...
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An algorithm for the bicriteria linearprogramming problem is presented. The algorithm determines the set of efficient extreme points in objective function space and involves solving a sequence of single criteria linearprogramming problems and can thus be used with any LP package.
Many students find the translation of a verbal description of a problem into the appropriate mathematical model a difficult task. We describe how semantic networks can be used to assist in the structuring of complicat...
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Many students find the translation of a verbal description of a problem into the appropriate mathematical model a difficult task. We describe how semantic networks can be used to assist in the structuring of complicated models and thereby facilitate the modeling process.
Multilevel programming models partition control over decision variables among ordered levels within a hierarchical structure. A planner at one level of the hierarchy may have his objective function and set of feasible...
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Multilevel programming models partition control over decision variables among ordered levels within a hierarchical structure. A planner at one level of the hierarchy may have his objective function and set of feasible decisions determined, in part, by decisions at other levels. However, his control instruments may allow him to influence, rather than dictate, the policies at other levels and thereby improve his own objective function. The greatest barrier to the effective use of these concepts has been the lack of efficient algorithmic procedures to solve the resulting mathematical programming problems. This paper has developed and implemented promising procedure for solving three-level linearprogramming problem.
The purpose of this paper is to investigate different preprocessing procedures for stochastic linear programs. The procedures are meant to be of use mostly for the modeler, but there are important computational implic...
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The purpose of this paper is to investigate different preprocessing procedures for stochastic linear programs. The procedures are meant to be of use mostly for the modeler, but there are important computational implications as well. We discuss how to check if the problem under investigation is overspecified, i.e. have options (columns) that can never be in an optimal solution, if the problem is tight or loose in terms of feasibility, and we demonstrate how to achieve relatively complete recourse in a number of cases. Computational results are detailed.
The running of benchmarks to assess the performance/costs of computing on a particular system is a common practice in data processing. One problem that arises is the selection of a particular set of runs that can be s...
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The running of benchmarks to assess the performance/costs of computing on a particular system is a common practice in data processing. One problem that arises is the selection of a particular set of runs that can be said to adequately represent the workload that is being considered. The basic problem is: given a set of computer runs, how to select a subset in terms of a linear combination that best fits the user profile (or work load) as measured on an existing system over a period of time. This study describes an application of linearprogramming as a tool in the selection process.
The incremental linear constraint satisfaction problem consists of repeatedly solving the satisfiability problem for a growing set of linear constraints. This problem is important to constraint logic programming syste...
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The incremental linear constraint satisfaction problem consists of repeatedly solving the satisfiability problem for a growing set of linear constraints. This problem is important to constraint logic programming systems where constraints are discovered one at a time and added to a current constraint set, and the satisfiability of this constraint set must be known at all times. Implicit equalities of a system of constraints are inequality constraints that are satisfied as an equality in all solutions of the system of constraints. Detecting implicit equalities is important in determining the minimal (canonical) representation of a system of linear constraints. In incremental constraint solving systems detecting implicit equalities provides information that can simplify further constraint solving. We present an algorithm which efficiently solves the incremental linear constraint satisfaction problem and detects all the implicit equalities present in the constraints. The algorithm forms a basis for the inequality constraint solver in the CLP (R) system.
The simplex method, under its various pivoting rules, is not a ″good algorithm″ in the sense of J. Edmonds, i. e. , the number of pivots needed to solve a given linearprogramming problem by this method cannot be bo...
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The simplex method, under its various pivoting rules, is not a ″good algorithm″ in the sense of J. Edmonds, i. e. , the number of pivots needed to solve a given linearprogramming problem by this method cannot be bounded by a polynomial function of the number of rows and columns defining it. V. Klee, G. J. Minty and R. G. Jerosolow have developed methods for constructing examples of such linear programs on polytopes. The aim of this paper is to extend these constructions to abstract polytopes.
This is an interactive system to aid in the analysis of linearprogramming models and, optionally, their solution. It is an enhancement of the earlier ANALYZE, featuring natural language explanations of the model plus...
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This is an interactive system to aid in the analysis of linearprogramming models and, optionally, their solution. It is an enhancement of the earlier ANALYZE, featuring natural language explanations of the model plus enriched analysis aids. Explicit query includes tabular or pictorial output, simple and flexible delineation of any portion of the matrix, and blocking. Analysis aids include path tracing, model reducing, infeasibility diagnosis and rates of substitution. The micro-computer version can typically support 1,000 rows, 2,000 columns and 15,000 non-zeros. Mainframe versions can support any size that will fit in core memory (using supersparse data structure).
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