ISSN:0160-5682    

DOI:10.1057/jors.1985.62

出版商:Taylor&Francis    

年代:1985

数据来源: Taylor

摘要:

AbstractLinear programming and its variants have been used for over 30 years, and during this time there have been technological and theoretical developments which have given the modeller enormous computer power and flexibility. Have these been matched in application—are the models being used?This paper attempts to look at the overall applied nature of linear programming—what has happened, what is happening and what is likely to happen. It draws on evidence from many sources including surveys, the literature and informal comments. The results indicate the growth in real application and power of the latest computer packages. However, there are still some problems remaining, and an attempt is made to highlight barriers to implementation.

ISSN:0160-5682    

DOI:10.1057/jors.1985.63

出版商:Taylor&Francis    

年代:1985

数据来源: Taylor

摘要:

AbstractComputer programs to solve linear programming problems by the simplex method have existed since the early 1950s. They remain the central feature of today's mathematical programming systems. There has been a steady increase in the size of problem that can be solved: this has been due as much to a better understanding of how to exploit sparseness as to larger and faster computers. There has been a steady increase in the type of problem that can be solved: this has been due as much to new concepts, such as separable programming, integer variables and special ordered sets, as to new algorithms. There has been a steady increase in the extent to which the application of mathematical programming has become more automatic. This applies both to the use of computerized matrix generators and report writers and to the mathematical formulation itself, in that we rely less on the user producing a well-scaled linear programming problem and are starting on the process of automatically sharpening the formulation of integer programming problems.Important new work is being done on all these aspects of computational mathematical programming.

ISSN:0160-5682    

DOI:10.1057/jors.1985.64

出版商:Taylor&Francis    

年代:1985

数据来源: Taylor

摘要:

AbstractEarly attempts to utilize linear algebraic (L.P.) techniques in financial planning met with little success. This was probably due to a misunderstanding of the process by which financial and corporate plans were formulated. The planning process is now better understood and the use of computer-based models is well accepted. However current modelling systems perform only simple arithmetic evaluations. There is aprima faciecase for re-examining linear algebraic methods to exploit the considerable amount of information which is available within a plan. This paper describes the work done in the South of Scotland Electricity Board to develop an interactive financial modelling system.

ISSN:0160-5682    

DOI:10.1057/jors.1985.65

出版商:Taylor&Francis    

年代:1985

数据来源: Taylor

摘要:

AbstractMathematical programming techniques are designed to optimize a selected criterion in the context of constraints. Modelling activity is often directed at an exploration of alternatives, where measurement of solution merit involves the consideration of several criteria, some of which may not be expressed or expressable in formal terms and therefore outwith the model.In a descriptive rather than formal manner, a presentation is given of two methods which allow a decision-maker or analyst to explore the solutions to underdetermined linear systems through the use of control variables. Such variables need not be controllable in reality, but do provide a powerful‘what if?’facility. The two methods stem from the application of (i) the generalized inverse and (ii) partitioning techniques to linear equations. Some of the underlying algebra is displayed, but the key features of the methods (and their common elements) are developed in the context of a small example.In a section on implementation the superiority of the partitioning techniques is established.

ISSN:0160-5682    

DOI:10.1057/jors.1985.66

出版商:Taylor&Francis    

年代:1985

数据来源: Taylor

摘要:

AbstractWe present experimental results on some new formulations of problems as mixed integer programmes.On a family of small problems involving‘either/or’constraints, the newer formulations performed distinctly better than does a‘textbook formulation’, with an advantage that increases with problem size. On a second set of small problems involving separable programmes with fixed charges imposed on a piecewise-linear functions, the advantage of the newer formulations was again evident.

ISSN:0160-5682    

DOI:10.1057/jors.1985.67

出版商:Taylor&Francis    

年代:1985

数据来源: Taylor

摘要:

AbstractWe consider Newton-like line search descent methods for solving non-linear least-squares problems. The basis of our approach is to choose a method, or parameters within a method, by minimizing a variational measure which estimates the error in an inverse Hessian approximation. In one approach we consider sizing methods and choose sizing parameters in an optimal way. In another approach we consider various possibilities for hybrid Gauss-Newton/BFGS methods. We conclude that a simple Gauss-Newton/BFGS hybrid is both efficient and robust and we illustrate this by a range of comparative tests with other methods. These experiments include not only many well known test problems but also some new classes of large residual problem.

ISSN:0160-5682    

DOI:10.1057/jors.1985.68

出版商:Taylor&Francis    

年代:1985

数据来源: Taylor

摘要:

AbstractVector programming seeks to identify efficient solutions of multiple-objective problems. It is closely related to parametric programming and three examples of this relationship, using objective weights, target (or goal) levels and weighted norms, are described. In each case, the use of the relationship to develop algorithms for determining the efficient set or to obtain characterizations of efficiency is investigated.

ISSN:0160-5682    

DOI:10.1057/jors.1985.69

出版商:Taylor&Francis    

年代:1985

数据来源: Taylor

ISSN:0160-5682    

DOI:10.1057/jors.1985.71

出版商:Taylor&Francis    

年代:1985

数据来源: Taylor

ISSN:0160-5682    

DOI:10.1057/jors.1985.72

出版商:Taylor&Francis    

年代:1985

数据来源: Taylor