Beale, E. M. L., Mathematical Programming in Practice. ... Charnes, A., and W. W. Cooper, The Stepping Stone Method of Explaining Linear Programming Calculations in Transportation Problems. ... Scheduling for a Manufacturing Firm.
Author: Sven Dano
Publisher: Springer Science & Business Media
Category: Technology & Engineering
A. Planning Company Operations: The General Problem At more or less regular intervals, the management of an industrial enter prise is confronted with the problem of planning operations for a coming period. Within this category of management problems falls not only the overall planning of the company's aggregate production but problems of a more limited nature such as, for example, figuring the least-cost combina tion of raw materials for given output or the optimal transportation schedule. Any such problem of production planning is most rationally solved in two stages: (i) The first stage is to determine the feasible alternatives. For example, what alternative production schedules are at all compatible with the given capacity limitations? What combinations of raw materials satisfy the given quality specifications for the products? etc. The data required for solving this part of the problem are largely of a technological nature. (ii) The second is to select from among these alternatives one which is economically optimal: for example, the aggregate production programme which will lead to maximum profit, or the least-cost combination of raw materials. This is where the economist comes in; indeed, any economic problem is concerned with making a choice be.tween alternatives, using some criterion of optimal utilization of resources.
___ Leontief InputModelScheduling War —Production (1940) Mechanization (1947)-<------- LinearProgramming (1947)- Model (1948) Economic—Industrial Output (1936) ' ^ Model(1937) Theory Theory Fourier (1823) Gauss (1826) WalrasianSystem ...
Author: George Dantzig
Publisher: Princeton University Press
In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered. George Dantzig is properly acclaimed as the "father of linear programming." Linear programming is a mathematical technique used to optimize a situation. It can be used to minimize traffic congestion or to maximize the scheduling of airline flights. He formulated its basic theoretical model and discovered its underlying computational algorithm, the "simplex method," in a pathbreaking memorandum published by the United States Air Force in early 1948. Linear Programming and Extensions provides an extraordinary account of the subsequent development of his subject, including research in mathematical theory, computation, economic analysis, and applications to industrial problems. Dantzig first achieved success as a statistics graduate student at the University of California, Berkeley. One day he arrived for a class after it had begun, and assumed the two problems on the board were assigned for homework. When he handed in the solutions, he apologized to his professor, Jerzy Neyman, for their being late but explained that he had found the problems harder than usual. About six weeks later, Neyman excitedly told Dantzig, "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." Dantzig had no idea what he was talking about. He later learned that the "homework" problems had in fact been two famous unsolved problems in statistics.
In 1959 , Greene , Chatto , Hicks , and Cox [ 34 ] described an application of a " product mix ” formulation for the packing industry . But the first industrial application of linear programming was described in the Journal of ...
Author: Mordecai Avriel
Publisher: CRC Press
Setting out to bridge the gap between the theory of mathematical programming and the varied, real-world practices of industrial engineers, this work introduces developments in linear, integer, multiobjective, stochastic, network and dynamic programing. It details many relevant industrial-engineering applications.;College or university bookstores may order five or more copies at a special student price, available upon request from Marcel Dekker, Inc.
The present volume is intended to serve a twofold purpose.
Author: Sven Dano
Publisher: Springer Science & Business Media
The present volume is intended to serve a twofold purpose. First, it provides a university text of Linear Programming for students of economics or operations research interested in the theory of production and cost and its practical applications; secondly, it is the author's hope that engineers, business executives, managers, and others responsible for the organization and planning of industrial operations may find the book useful as an introduction to Linear Programming methods and techniques. Despite the different backgrounds of these categories of potential readerR, their respective fields overlap to a considerable extent; both are concerned with economic optimization problems, and the use of Linear Programming to problems of production planning is simply applied theory of production. The non-economist reader may, but should not, pass over Chapter IV in which the linear production model is linked up with the economic theory of production. Without being an advanced text, the book aims at covering enough ground to make the reader capable of detecting, formulating, and solving such linear planning problems as he may encounter within his particular field. No heavy demands are made on the reader's mathematical profi ciency; except for the proofs in the Appendix-which may be skipped if desired-the mathematical exposition is purely elementary, involving only simple linear relations. In the author's experience, the pedagogical advantages of thi;:; approach, as compared with the use of matrix algebra, amply justify the sacrifice of mathematical elegance and typographical simplicity, particularly in explaining the simplex method.
Linear programming is useful for solving many problems involving choice . What specific information does the planner require for optimal area development ? He or she wishes to know : ( 1 ) which industries are optimal for the area ...
The firms are subsets of the more aggregated 4 - digit Standard Industrial Classification ( SIC ) manufacturing industries , some of which are included and some of which are not included , in a rural multicounty , linear programming ...
Gilmore, P. C., and R. E. Gomory: A Linear-Programming Approach to the CuttingStock Problem—Part II, Operations Research, ... Catchpole, A. R.: The Application of Linear Programming to Integrated Supply Problems in the Oil Industry, ...
Author: Saul I. Gass
Publisher: Courier Corporation
Comprehensive, well-organized volume, suitable for undergraduates, covers theoretical, computational, and applied areas in linear programming. Expanded, updated edition; useful both as a text and as a reference book. 1995 edition.
Only the early applications are mentioned here and the exercises at the end of this chapter give additional example applications of linear programming. One of the early industrial applications of linear programming was made in the ...
Author: Singiresu S. Rao
Publisher: John Wiley & Sons
Technology/Engineering/Mechanical Helps you move from theory to optimizing engineering systems in almost any industry Now in its Fourth Edition, Professor Singiresu Rao's acclaimed text Engineering Optimization enables readers to quickly master and apply all the important optimization methods in use today across a broad range of industries. Covering both the latest and classical optimization methods, the text starts off with the basics and then progressively builds to advanced principles and applications. This comprehensive text covers nonlinear, linear, geometric, dynamic, and stochastic programming techniques as well as more specialized methods such as multiobjective, genetic algorithms, simulated annealing, neural networks, particle swarm optimization, ant colony optimization, and fuzzy optimization. Each method is presented in clear, straightforward language, making even the more sophisticated techniques easy to grasp. Moreover, the author provides: Case examples that show how each method is applied to solve real-world problems across a variety of industries Review questions and problems at the end of each chapter to engage readers in applying their newfound skills and knowledge Examples that demonstrate the use of MATLAB® for the solution of different types of practical optimization problems References and bibliography at the end of each chapter for exploring topics in greater depth Answers to Review Questions available on the author's Web site to help readers to test their understanding of the basic concepts With its emphasis on problem-solving and applications, Engineering Optimization is ideal for upper-level undergraduates and graduate students in mechanical, civil, electrical, chemical, and aerospace engineering. In addition, the text helps practicing engineers in almost any industry design improved, more efficient systems at less cost.
The discovery of linear programming started a new age of optimization. George B. Dantzig who first proposed the simplex method to solve linear programming in 1947 stated in his article Linear Programming: The Story About How It Began; ...
Author: Panos M. Pardalos
Publisher: Springer Science & Business Media
Optimization from Human Genes to Cutting Edge Technologies The challenges faced by industry today are so complex that they can only be solved through the help and participation of optimization ex perts. For example, many industries in e-commerce, finance, medicine, and engineering, face several computational challenges due to the mas sive data sets that arise in their applications. Some of the challenges include, extended memory algorithms and data structures, new program ming environments, software systems, cryptographic protocols, storage devices, data compression, mathematical and statistical methods for knowledge mining, and information visualization. With advances in computer and information systems technologies, and many interdisci plinary efforts, many of the "data avalanche challenges" are beginning to be addressed. Optimization is the most crucial component in these efforts. Nowadays, the main task of optimization is to investigate the cutting edge frontiers of these technologies and systems and find the best solutions for their realization. Optimization principles are evident in nature (the perfect optimizer) and appeared early in human history. Did you ever watch how a spider catches a fly or a mosquito? Usually a spider hides at the edge of its net. When a fly or a mosquito hits the net the spider will pick up each line in the net to choose the tense line? Some biologists explain that the line gives the shortest path from the spider to its prey.