1,315 results
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2. A Note about Kantorovich's Paper, "Mathematical Methods of Organizing and Planning Production"
- Author
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Koopmans, Tjalling C.
- Published
- 1960
3. A Linear Programming Analysis of Paper Recycling
- Author
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Virendra K. Gupta and C. Roger Glassey
- Subjects
Linear programming ,Computer science ,business.industry ,Strategy and Management ,Pulp (paper) ,Waste paper ,Management Science and Operations Research ,engineering.material ,Paper recycling ,Hardware_GENERAL ,engineering ,Simple linear model ,Operations management ,Process engineering ,business - Abstract
A simple linear model is constructed for production, use and recycling of various paper and related products. This model is used to estimate the maximum feasible recycling rate given the current state of pulp and paper technology. Parametric linear programming is used to investigate the effect of the efficiency of collecting, sorting and transporting waste paper on the fraction recycled.
- Published
- 1974
4. ZEITSCHRIFT FÜR DIE GESAMTE STAATSWISSENSCHAFT.
- Author
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König, Heinz, Thoss, Rainer, Hoffman, Lutz, Rott, W., Helmstädter, Ernest, Stegemann, Klaus, Gahlen, Bernhard, and Hesse, Helmut
- Subjects
ECONOMICS ,LINEAR programming ,PAPER industry ,ECONOMIC development - Abstract
This article presents abstracts of several papers about economics published in the July 1965 of the journal Zeitschrift Für Die Gesamte Staatswissenschaft. In the article The Optimal Location of Industry: An Interregional Linear Program for the West German Paper Industry, Heinz König and Rainer Thoss gave a general formulation of an interregional optimization model and discussed the advantages and limitations of this method of regional analysis. While in the article Development Theories of Balanced and Unbalanced Growth: A Confrontation, Lutz Hoffman reviewed the discussion on balanced growth and unbalanced growth.
- Published
- 1965
5. A Heuristic Programming Solution to a Nonlinear Cutting Stock Problem
- Author
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Haessler, Robert W.
- Published
- 1971
6. A Note About Kantorovich's Paper, 'Mathematical Methods of Organizing and Planning Production'
- Author
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Tjalling C. Koopmans
- Subjects
Structure (mathematical logic) ,Matrix (mathematics) ,Operations research ,Linear programming ,Computer science ,Strategy and Management ,Production (computer science) ,Transportation theory ,Management Science and Operations Research ,Commodity (Marxism) ,Mathematical economics - Abstract
Discussion on two early papers of Professor Kantorovich, from 1939 and 1949, that proved to be remarkable documents in the history of management science, of linear programming, and of economic theory in general. The 1949 paper discusses transportation models for a single commodity and for many commodities (including empty vehicles), and a single-commodity model for a capacitated network, with applications to sections of the Russian railroad network. All problems considered in the 1939 paper reprinted in this issue are what would now be called linear programming problems. The coefficient matrices of the problems labeled “A” and “B” exhibit special structures somewhat similar to that of the transportation problem matrix. Problem “C,” while appearing still to have a somewhat special structure, is in fact equivalent to the general linear programming problem.
- Published
- 1960
7. Letter to the Editor—Comments on a Paper by Bowman
- Author
-
William W. White
- Subjects
Letter to the editor ,Operations research ,Linear programming ,Computer science ,Programming language ,Management Science and Operations Research ,computer.software_genre ,computer ,Computer Science Applications - Abstract
In the paper, “Assembly-Line Balancing by Linear Programming,” that appeared in Operations Research 8, 385–389 (1960), E. H. Bowman presented two linear program formulations for the assembly-line balancing problem. These two formulations are referred to as the First Linear Program and the Second Linear Program, respectively. The following are comments about, and a reformulation of, the First Linear Program.
- Published
- 1961
8. Letter to the Editor—Comments on a Paper By Romesh Saigal: 'A Constrained Shortest Route Problem'
- Author
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Marc Rosseel
- Subjects
Dynamic programming ,Combinatorics ,Route problem ,Linear programming ,Node (networking) ,Minor (linear algebra) ,Computer Science::Programming Languages ,Linear programming formulation ,Extension (predicate logic) ,Management Science and Operations Research ,Computer Science Applications ,Mathematics - Abstract
Romesh Saigal presents a zero-one linear program and a dynamic programming algorithm for finding the shortest route containing exactly q arcs from node 1 to node n in a network (N, A) with distances c(i,j). This note shows that the linear programming formulation and his extension based on it are defective, and that the dynamic programming algorithm can lead to suboptimal solutions, but a minor change in the dynamic programming formulation relieves the difficulty.
- Published
- 1968
9. Thirteen Papers on Algebra, Topology, Complex Variables, and Linear Programming
- Author
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V. Rohlin, O. Vvedenskiĭ, V. Vladimirov, V. Gavrilov, D. Faddeev, E. Filippovič, V. Boltjanskiĭ, I. Bazilevič, S. P. Novikov, V. Levin, O. Kozlov, Ja. Geronimus, P. Soltan, A. Roĭter, and V. Proizvolov
- Subjects
Algebra ,Linear programming ,Complex variables ,Algebra over a field ,Topology (chemistry) ,Mathematics - Published
- 1968
10. Optimal Design of Flexible Pavement Sections : Technical Paper
- Author
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S R Yoder, Joseph C Oppenlander, and Salim Said Hejal
- Subjects
Optimal design ,Subbase (pavement) ,Engineering ,Pavement engineering ,Systems analysis ,Linear programming ,Mathematical model ,business.industry ,Total cost ,Constraint (computer-aided design) ,Structural engineering ,business ,Reliability engineering - Abstract
Although several methods are available for the design of flexible pavements, no existing technique explicitly considers the optimal combination of flexible pavement components to minimize the total in-place cost of the pavement system. The purpose of this systems analysis was to develop a rational method for the optimal selection of the arrangement of the various pavement components. This cost minimization must be realized within the boundary conditions that are imposed by the practical limitations of the design parameters. The design model consists of an objective function and various constraint equations. The total cost of the pavement system is quantitatively described by this objective function, and a minimum-cost solution is obtained for each combination of material costs and design conditions. The various constraining equations quantify the boundary conditions to which the design of a flexible pavement is subject. These physical limitations complete the realism of the mathematical model in describing the real-world situation of flexible pavement design. The design model was solved by a modified linear programming technique. In developing practical solutions to the design model, optimal flexible pavements are designed for cross-sections without subbase, cross-sections with subbase through shoulders, and cross-sections with subbase and subdrains. The design requirements for the various components are predicated on the design parameters of traffic conditions, soil support values, pavement material characteristics, environmental effects, and pavement performance requirements and on unit costs of pavement components. Substantial cost savings result in the selection of flexible pavement sections by this design procedure.
- Published
- 1969
11. Optimal Selection of Flexible Pavement Components : Technical Paper
- Author
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Joseph C Oppenlander, Thomas R. Buick, and Salim Said Hejal
- Subjects
Pavement engineering ,Engineering ,Mathematical optimization ,Systems analysis ,Linear programming ,business.industry ,Total cost ,Constraint (computer-aided design) ,Range (statistics) ,Boundary value problem ,Structural engineering ,Minification ,business - Abstract
Although several methods are available for the design of flexible pavements, no existing technique explicitly considers the optimal combination of flexible pavement components to minimize the total in-place cost of the pavement system. The purpose of this systems analysis was to develop a rational method for the optimal selection of the thicknesses of the various pavement components. This cost minimization must be realized within the boundary conditions that are imposed by the practical limitations of the design parameters. The design model consists of an objective function and seven constraint equations. The total cost of the pavement system is quantitatively described by this objective function, and a minimum-cost solution is obtained for each combination of material costs and design conditions. The various constraining equations quantify the boundary conditions to which the design of a flexible pavement is subject. These physical limitations complete the realism of the mathematical model in describing the real-world situation of flexible pavement design. The design model was solved by a modified linear programming technique. In developing practical solutions to the design model, 31,680 optimal flexible pavements were designed for highway construction conditions indicative of Indiana. The thickness requirements for the various layers are specified for each combination of structural number, minimum total thickness, and unit costs of pavement materials. Cost savings which range from 2 to 15 percent result in the thickness selection of flexible pavement components by this design procedure.
- Published
- 1968
12. STOCHASTIC LINEAR PROGRAMMING AND ITS APPLICATION TO ECONOMIC PLANNING11'Journal Paper' No. J—of the Iowa Agricultural and Home Economics Experiment Station, Ames, Iowa. Project No. 1200
- Author
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Jati K. Sengupta and Gerhard Tintner
- Subjects
Sequence ,Mathematical optimization ,Linear programming ,First-countable space ,Limit point ,Decision rule ,Topological space ,Stochastic programming ,Mathematics ,Linear-fractional programming - Abstract
This chapter discusses stochastic linear programming and its application to economic planning. An extension of the duality theorem of nonstochastic programming in the area of stochastic linear programming in its two approaches has been considered using the properties of a first countable topological space and the convergence of the sequence of distinct and selected points in the parameter space to a limit point. When the cost of sampling is introduced in the parameter space defined by a stochastic linear program, this line of discussion of the active approach would lead to the sequential probability ratio tests in some modified manner. A third class of decision rules, much more general than the first two classes, may be defined by alternative rules of mapping from the uncertainty space to the certainty space.
- Published
- 1965
13. A Comment on a Paper of Maxwell
- Author
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Jeffrey B. Sidney
- Subjects
Mathematical optimization ,Linear programming ,Strategy and Management ,Minor (linear algebra) ,Management Science and Operations Research ,Notation ,Computer Science::Operating Systems ,Integer programming ,Computer Science::Distributed, Parallel, and Cluster Computing ,Cutting-plane method ,Scheduling (computing) ,Mathematics - Abstract
In his paper “On Sequencing n Jobs on One Machine to Minimize the Number of Late Jobs,” [Maxwell, W. L. 1970. On sequencing n jobs on one machine to minimize the number of late jobs. Management Sci. 16(5, January).], Maxwell presents an integer programming formulation (which we shall call P) of a one-machine job-shop problem, and attempts to prove the validity of Moore's optimal algorithm [Moore, J. M. 1908. An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Sci. 15(1, September).] by applying cutting plane constraints to the program P. Unfortunately, Maxwell's proof is incorrect. In this brief note, we shall locate Maxwell's error, and present an example, which casts doubt on the possibility of minor modifications being sufficient to correct the proof. We shall adopt much of the notation of Maxwell's paper.
- Published
- 1972
14. A NOTE ON EXTREME-POINT SOLUTIONS AND A PAPER BY LEMKE, SALKIN, AND SPIELBERG.
- Author
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Glover, Fred
- Subjects
LINEAR programming ,MATRICES (Mathematics) - Abstract
This paper gives a framework for unifying and slightly generalizing certain properties of extreme-point solutions exploited by an approach of LEMKE, SALKIN, and SPIELBERG for solving set-covering problems. [ABSTRACT FROM AUTHOR]
- Published
- 1971
- Full Text
- View/download PDF
15. Letter to the Editor—Comment on Dantzig's Paper on Discrete Variable Extremum Problems
- Author
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Richard Bellman
- Subjects
Dynamic programming ,Mathematical optimization ,Revised simplex method ,Linear programming ,GEORGE (programming language) ,Knapsack problem ,Functional equation ,Management Science and Operations Research ,Discrete variable ,Linear complementarity problem ,Computer Science Applications ,Mathematics - Abstract
In his interesting paper on discrete-variable extremum problems, George Dantzig (Dantzig, G. 1957. Discrete-variable extremum problems. Opns Res. 5 266–277.) discusses the “knapsack” problem. He presents two approximate methods based upon linear programming techniques, and an exact solution based upon the functional equation method of dynamic programming (Bellman, R. 1957. Dynamic Programming. Princeton University Press.).
- Published
- 1957
16. Optimality and Degeneracy in Linear Programming
- Author
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Charnes, A.
- Published
- 1952
- Full Text
- View/download PDF
17. The Allocation of Aircraft to Routes-An Example of Linear Programming under Uncertain Demand
- Author
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Ferguson, Allen R. and Dantzig, George B.
- Published
- 1956
18. Elements of Large Scale Mathematical Programming: Part II: Synthesis of Algorithms and Bibliography
- Author
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Geoffrion, Arthur M.
- Published
- 1970
19. Operational Research Methods: What Are They?
- Author
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Jessop, W. N.
- Published
- 1956
- Full Text
- View/download PDF
20. A. Cobham, R. Fridshal, and J. H. North. An application of linear programming to the minimization of Boolean functions. Switching circuit theory and logical design, Proceedings of the Second Annual Symposium, Detroit, Mich., October 17-20, 1961, and Papers from the First Annual Symposium, Chicago, Ill., October 9-14, 1960, American Institute of Electrical Engineers, New York1961, pp. 3–9
- Author
-
Thomas H. Mott
- Subjects
Algebra ,Philosophy ,Operations research ,Linear programming ,Logic ,Computer science ,Switching circuit theory ,Minification ,Boolean function - Published
- 1965
21. Comments on a paper by Wax [Corresp.]
- Author
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L. Grey
- Subjects
Wax ,Linear programming ,Library and Information Sciences ,Information theory ,Linear code ,Upper and lower bounds ,Computer Science Applications ,Algebra ,visual_art ,visual_art.visual_art_medium ,Low-density parity-check code ,Algorithm ,Information Systems ,Mathematics - Published
- 1961
22. COMMENTS ON A PAPER BY BOWMAN.
- Author
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White, William W.
- Subjects
LETTERS to the editor ,LINEAR programming - Abstract
A letter to the editor is presented in response to the article "Assembly-Line Balancing by Linear Programming," by E. H. Bowman in a 1960 issue of "Operations Research 8."
- Published
- 1961
- Full Text
- View/download PDF
23. A COMMENT ON A PAPER OF MAXWELL.
- Author
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Sidney, Jeffrey B.
- Subjects
JOB shops management ,INTEGER programming ,MATHEMATICAL programming ,PRODUCTION management (Manufacturing) ,ALGORITHMS ,LINEAR programming ,MATHEMATICAL optimization ,MATHEMATICAL models ,MANAGEMENT science research ,OPERATIONS research - Abstract
The article presents comments on the management science paper "On Sequencing n Jobs on One Machine to Minimize the Number of Late Jobs," by William L. Maxwell. The paper focused on an integer programming formulation of a one-machine job shop problem. The author contends that Maxwell made in error in proving the validity of an optimal algorithm by applying cutting plane constraints to the problem. The author explains that the problem cannot be solved through traditional cutting plane procedures. The author provides a mathematical model in an attempt to correct the proof.
- Published
- 1972
- Full Text
- View/download PDF
24. OPERATIONAL RESEARCH IN BUSINESS
- Author
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MOORE, P. G.
- Published
- 1967
25. COMMENTS ON A PAPER BY ROMESH SAIGAL: "A CONSTRAINED SHORTEST ROUTE PROBLEM".
- Author
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Rosseel, Marc
- Subjects
LINEAR programming ,ALGORITHMS ,VECTOR algebra ,COMPUTER programming ,CONSTRAINTS (Physics) ,DYNAMIC programming ,MATRICES (Mathematics) ,DISTANCES - Abstract
The article presents a zero-one linear program and a dynamic programming algorithm for finding the shortest route containing exactly q arcs from node 1 to node n in a network (N, A) with distances c(i, j). This note shows that the linear programming formulation and his extension based on it are defective, and that the dynamic programming algorithm can lead to suboptimal solutions, but a minor change in the dynamic programming formulation relieves the difficulty. A special feature of this linear program is that there can never be a loop in the basis, because the vectors corresponding to the variables of a loop are linearly dependent. The last comment is related to the dynamic programming algorithm. One is allowed to pass through a node more than once in the shortest route . The proposed method for solving this program consists of converting it into a shortest route problem containing exactly q arcs. But for some arbitrary reason, the dynamic program is formulated in such a way that one can never have starting node 1 more than once in the final solution.
- Published
- 1968
- Full Text
- View/download PDF
26. A PROGRAMMING APPROACH TO CORPORATE FINANCIAL MANAGEMENT.
- Author
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MYERS, STEWART C. and POGUE, GERALD A.
- Subjects
CORPORATE finance ,LINEAR programming ,MATHEMATICAL programming ,CAPITAL budget ,FINANCE ,CAPITAL investments - Abstract
In this paper we present an outline of LONGER, a financial planning model based on mixed integer linear programming. The model is based on recent advances in capital market theory, but at the same time it recognizes certain additional considerations that are manifestly important to the financial manager. Thus, we believe that the model has good potential for practical application, although in this paper we emphasize LONGER's relationship to finance theory. We will skim over a number of issues that are critical in a practical application; a later paper will discuss these issues and present LONGER at a practical level of detail. Still another paper has worked out implications for decentralized capital budgeting rules. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
27. PRODUCTION SCHEDULING BY THE TRANSPORTATION METHOD OF LINEAR PROGRAMMING.
- Author
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Bowman, Edward H.
- Subjects
PRODUCTION scheduling ,SALES ,LINEAR programming ,MANUFACTURED products ,PRODUCT management ,TRANSPORTATION problems (Programming) ,MARKETING management ,SCHEDULING - Abstract
With fluctuating sales, a manufacturer must have fluctuating production, or fluctuating inventory, or both Penalties are associated with either type of fluctuation Several papers place this problem into a conventional linear-programming framework This paper suggests that the same problem may be placed into a transportation-method framework and, further, that many transportation problems may be extended to include multiple time periods where this is meaningful A generalized scheduling problem is placed here into the standard form of the transportation table [ABSTRACT FROM AUTHOR]
- Published
- 1956
- Full Text
- View/download PDF
28. ON NONLINEAR FRACTIONAL PROGRAMMING.
- Author
-
Dinkelbach, Werner
- Subjects
FRACTIONAL integrals ,NONLINEAR programming ,LINEAR programming ,MATHEMATICAL programming ,ALGORITHMS ,PARAMETER estimation ,QUADRATIC programming ,CONCAVE functions ,CONVEX functions ,POLYHEDRAL functions ,NUMERICAL solutions to Lagrange equations - Abstract
The main purpose of this paper is to delineate an algorithm for fractional programming with nonlinear as well as linear terms in the numerator and denominator. The algorithm presented is based on a theorem by Jagannathan [7] concerning the relationship between fractional and parametric programming. This theorem is restated and proved in a somewhat simpler way. Finally, it is shown how the given algorithm can be related to the method of Isbell and Marlow [6] for linear fractional programming and to the quadratic parametric approach by Ritter [10]. The Appendix contains a numerical example. [ABSTRACT FROM AUTHOR]
- Published
- 1967
- Full Text
- View/download PDF
29. ON SOME WORKS OF KANTOROVICH, KOOPMANS AND OTHERS.
- Author
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Charnes, A. and Cooper, W. W.
- Subjects
INDUSTRIAL management ,MANAGEMENT science ,LINEAR programming ,GAME theory ,MANAGEMENT games ,DECISION making ,DECISION theory ,ALGORITHMS ,RANDOM variables - Abstract
Commentary is presented for an article published in the July 1960 issue of "Management Science," written by L. V. Kantorovich with an introductory note by T. C. Koopmans. According to the author, in his introduction Koopmans addresses in particular a linear programming problem and a matrix game presented by Kantorovich. Also presented is an interpretation of the article's treatment of decision variables and mathematical optimization. The author notes that the article presents algorithms that have been improved from their contemporary presentations.
- Published
- 1962
- Full Text
- View/download PDF
30. A NOTE ON LINEAR PROGRAMMING AND CAPITAL BUDGETING.
- Author
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MYERS, STEWART C.
- Subjects
CAPITAL budget ,LINEAR programming ,MATHEMATICAL models of capital ,RATIONING ,MATHEMATICAL models of finance ,MATHEMATICAL programming - Abstract
This paper is the latest chapter in the controversy begun by William H. Bautool and Richard E. Quandt in their criticism of Weingartner's work on capital budgeting under capital rationing. A thorough review and partial resolution of the matter has been offered in recent articles by Willard T. Carleton and Edwin J. Elton. My purpose here is to try to complete the job. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
31. LINEAR PROGRAMMING AND CAPITAL BUDGETING MODELS: A NEW INTERPRETATION.
- Author
-
CARLETON, WILLARD T.
- Subjects
LINEAR programming ,CAPITAL budget ,RATIONING ,CAPITAL investments ,PRODUCTION scheduling ,STRATEGIC planning - Abstract
One of the most impressive achievements in capital budgeting theory during recent years has been by H. Martin Weingartner, who successfully employed the technique of linear (and integer linear) programming to solve the "capital budgeting under capital rationing" problem. A subsequent debate between Weingartner and William J. Baumol and Richard E. Quandt, however, has suggested the possibility that programming approaches create more questions than solutions, it is the thesis of this paper that some of the major issues between Weingartner and Baumol-Quandt can be resolved easily through appeal to the larger corporate financial model of which project selection is but one part. In particular, it is possible to suggest what is the appropriate objective function to be employed in selecting a set of projects; what is the best intellectual construction and operating significance of the term "capital rationing"; and what is the relationship under capital rationing of the discounting rate to the size of the capital budget. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
32. COMMENTS ON A PAPER BY M. L. WOLFSON: 'SELECTING THE BEST LENGTHS TO STOCK'
- Author
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Cohen, Gerald D.
- Subjects
STOCK prices ,STOCKS (Finance) ,DYNAMIC programming ,NONLINEAR programming ,INTEGER programming ,LINEAR programming ,ALGORITHMS - Abstract
This article presents comments on a paper by M.L. Wolfson related to selecting the best lengths to stock. The problem considered in the paper by Wolfson is a classic specimen of the type ideally structured for direct and practical solution by dynamic programming. The author's algorithm, given in the paper, is in the spirit of this method, but its understanding could be greatly simplified if put into the recursive formalism of dynamic programming.
- Published
- 1966
- Full Text
- View/download PDF
33. A LINEAR PROGRAMMING MODEL OF RESOURCE ALLOCATION IN A UNIVERSITY.
- Author
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Koch, James V.
- Subjects
LINEAR programming ,MATHEMATICAL models ,RESOURCE allocation ,SCHOOL administrators ,STATE universities & colleges ,VECTOR analysis ,PRODUCTION scheduling - Abstract
This paper describes the application of a linear programming model to the process of resource allocation at Illinois State University. The model developed is a general model designed to assist academic administrators in allocating the scarce resources at their disposal. The model, and the assumptions upon which it is based, may be altered to suit the particular decision criteria of any particular academic institution. The linear programming model developed here maximizes an objective function which reflects the total net social profit realized by the university on its outputs to society. This objective function was maximized subject to a myriad of constraints which reflected the limitations of budget, space, and other scarce inputs. Further, the constraints reflect the joint interdependency of many parts of the university and the particular educational delivery system employed by a given department. The outputs of the model include the optimal mixture of academic outputs by the university, the optimal distribution and usage of inputs inside the university, and the shadow price of each input. While the linear programming model developed here is general and may be applied to any university, it was applied to Illinois State University in this paper. In the case of Illinois State University, the model recommended a substantial reduction in emphasis upon teacher education. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
- View/download PDF
34. Asymptotic Linear Programming.
- Author
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Jeroslow, Robert G.
- Subjects
LINEAR programming ,ALGORITHMS ,MATHEMATICAL functions ,PRODUCTION scheduling ,MATHEMATICAL programming ,MATHEMATICAL models - Abstract
This paper studies the linear programming problem in which all coefficients (even those of the stipulations matrix) are rational functions of a single parameter t called ‘time,’ and provides an algorithm that can serve problems of the following two types: (1) Steady-state behavior [the algorithm can be used to determine the functional form x(t) of the optimal solution as a function of t, this form being valid for all ‘sufficiently large’ values of t], and (2) sensitivity analysis [if a value t
0 of ‘time’ is given, the algorithm can be used to determine the two possible functional forms of the optimal solution for all values of t ‘sufficiently dose’ to t0 (the first functional form valid for t«t0 , the second for t»t0 )]. In addition, the paper gives certain qualitative information regarding steady-state behavior, including the following result: If for some one of the properties of consistency, boundedness, or bounded constraint set, there exists a sequence tn ↗+∞ such that the linear program at tn has this property for all n, then the program has this property for all ‘sufficiently large’ values of t. [ABSTRACT FROM AUTHOR]- Published
- 1973
- Full Text
- View/download PDF
35. On the Set-Covering Problem.
- Author
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Balas, Egon and Padberg, Manfred W.
- Subjects
TRANSPORTATION ,MATRICES (Mathematics) ,LINEAR programming - Abstract
This paper establishes some useful properties of the equality-constrained set-covering problem P and the associated linear program P'. First, the Dantzig property of transportation matrices is shown to hold for a more general class of matrices arising in connection with adjacent integer solutions to P'. Next, we show that, for every feasible integer basis to P', there are at least as many adjacent feasible integer bases as there are nonbasic columns. Finally, given any two basic feasible integer solutions x¹ and x² to P', x² can be obtained from x¹ by a sequence of p pivots (where p is the number of indices j∈N for which x¹[subj] is nonbasic and x¹[subj]=1), such that each solution in the associated sequence is feasible and integer. Some of our results have been conjectured earlier by ANDREW, HOFFMAN, AND KRABEK in a paper presented to ORSA in 1968. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
36. CHANCE CONSTRAINED PROGRAMMING WITH JOINT CONSTRAINTS.
- Author
-
Miller, Bruce L. and Wagner, Harvey M.
- Subjects
LINEAR programming ,DYNAMIC programming ,MATHEMATICAL programming ,LOGARITHMIC functions ,NONLINEAR programming ,ALGORITHMS ,OPERATIONS research - Abstract
This paper considers the mathematical properties of chance constrained programming problems where the restriction is on the joint probability of a multivariate random event. One model that is considered arises when the right-hand side constants of the linear constraints are random. Another model treated here occurs when the coefficients of the linear programming variables are described by a multinormal distribution. It is shown that under certain restrictions both situations can be viewed as a deterministic nonlinear programming problem. Since most computational methods for solving nonlinear programming models require the constraints be concave, this paper explores whether the resultant problem meets the concavity assumption. For many probability laws of practical importance, the constraint in the first type of model is shown to violate concavity. However, a simple logarithmic transformation does produce a concave restriction for an important class of problems. The paper also surveys the `generalized linear programming' method for solving such problems when the logarithmic transformation is justified. For the second type model, the constraint is demonstrated to be nonconcave. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
37. THE MULTI-INDEX PROBLEM.
- Author
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Haley, K. B.
- Subjects
TRANSPORTATION problems (Programming) ,TRANSPORTATION ,ALGORITHMS ,PROBLEM solving ,LINEAR programming ,MATHEMATICAL inequalities ,SIMPLEXES (Mathematics) ,OPERATIONS research ,EQUATIONS - Abstract
The multi-index transportation problem is defined and a summary of the algorithm described in an earlier paper is given. This paper discusses the theorems justifying the use of the algorithm and gives a necessary condition for the existence of a solution. It also describes the formulation of three special-structure linear-programming problems as examples of multi-index problems. The three problems discussed are the capacitated Hitchcock problem, transportation where there is more than one method of transport available, and the transformation of one type of multi-index problem into another. A final section describes problems that have restrictions in the form of inequalities. [ABSTRACT FROM AUTHOR]
- Published
- 1963
- Full Text
- View/download PDF
38. The San Francisco Meeting.
- Subjects
OPERATIONS research ,LINEAR programming ,QUADRATIC forms ,SQUARE root - Abstract
Presents abstracts of invited and contributed papers published in the fall 1961 issue of the journal 'Operations Research.' 'Experiments in Linear Programming,' by Philip Wolfe; 'Programs With Linear and Square Root of Quadratic Forms in the Objective,' by E. Eisenberg; 'Some Results and Problems in Linear Programming Under Uncertainty,' by Albert Madansky.
- Published
- 1961
39. PROGRAM of the Eight Annual (Seventeenth National) Meeting of the Operations Research Society of America.
- Subjects
MEETINGS ,CONFERENCES & conventions ,LINEAR programming ,STRATEGIC planning ,PRODUCTION planning - Abstract
The article presents information on the program of the Eight Annual Meeting of the Operations Research Society of America held in New York City from May 18 to 21, 1960. As part of the meeting, the symposium titled Optimization on Chemical Reactors was held at New York University. John Happel served as chairman of the symposium. There were many papers presented during the meeting. A. V. Butterworth and P.C. Hayes presented their paper which discusses the use of mathematical predictors in a distribution system. Other topics discussed at the meeting include linear programming, strategic planning, and production planning.
- Published
- 1960
40. BIBLIOGRAPHY ON LINEAR PROGRAMMING.
- Author
-
Rohde, F. Virginia
- Subjects
LINEAR programming ,OPERATIONS research ,MATHEMATICAL programming ,BIBLIOGRAPHY ,CONVEX functions ,MATHEMATICAL optimization ,VECTOR analysis - Abstract
Although the earliest discussions of linear programming date back to the 1930's, to the work of German and Austrian mathematicians and economists, the mathematics has been extensively developed only in the past six or eight years. Because of the relative newness of the subject, the literature is widely scattered and it is rather difficult for one just starting to learn about linear programming to know where to begin. Because of human limitations, the bibliography is necessarily incomplete. All papers and books that could be acquired that seemed to deal with the subject were perused and, if applicable, included. No extensive effort was made, however, to include papers dealing more or less exclusively with closely related topics, for example, the problem of determination of value and optimal strategies in a zero-sum, two-person game, the pure inequalities problem with no optimization, the subjects of convex functions and convex polyhedra, unless they also relate these topics directly to linear programming.
- Published
- 1957
- Full Text
- View/download PDF
41. AN EFFICIENT BRANCH AND BOUND ALGORITHM FOR THE WAREHOUSE LOCATION PROBLEM.
- Author
-
Khumawala, Basheer M.
- Subjects
WAREHOUSES -- Location ,BRANCH & bound algorithms ,INDUSTRIAL location ,INTEGER programming ,INDUSTRIAL capacity ,LINEAR programming ,PHYSICAL distribution of goods ,MATHEMATICAL optimization ,MATHEMATICAL models of decision making ,ECONOMICS - Abstract
This paper introduces an efficient branch and bound algorithm for a special class of mixed integer programming problems called the warehouse location problem. A set of branching decision rules is proposed for selecting warehouses to be constrained open and closed from any node of the branch and bound tree. These rules are tested for their efficiency in reducing computation times and storage requirements to reach optimal solutions. An improved method of solving the linear programming problems at the nodes which substantially reduces the computations is also introduced in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
42. AN OPTIMIZATION APPROACH TO FREIGHT CAR ALLOCATION UNDER TIME-MILEAGE PER DIEM RENTAL RATES.
- Author
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Allman, William P.
- Subjects
LINEAR programming ,FREIGHT cars ,FREIGHT & freightage ,MATERIALS handling ,SHIPMENT of goods ,RESOURCE allocation ,GOVERNMENT ownership of railroads ,INTERSTATE commerce ,COST control ,RESOURCE management ,ECONOMICS - Abstract
The paper proposes the use of linear programming to "solve" a specific freight car allocation situation wherein a choice of freight cars is available for shipper shipments, and the railroad's car allocation objective is to maximize the expression (freight car rental receivables-freight car rental payables). The freight car rental payment structure which is applicable is that of "time-mileage per diem" rates proposed in the United States by the Interstate Commerce Commission. The paper first describes the problem and its background, and then a model and various extensions are formulated. An example illustrates how costly to a railroad the difference between good and bad car allocation may be. Although the proposed linear programming approach may be manually tractable for small volume car allocation situations, the paper concludes that in most car allocation situations, the approach requires a computerized data base with a "real-time" information and communications system which includes order entry, car rental, routing-distance, and train travel time and yard delay time information. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
43. PRODUCTION SMOOTHING WITH STOCHASTIC DEMAND II: INFINITE HORIZON CASE.
- Author
-
Sobel, Matthew J.
- Subjects
PRODUCTION management (Manufacturing) ,STOCHASTIC processes ,SMOOTHING (Numerical analysis) ,RANDOM variables ,MATHEMATICAL statistics ,MULTIVARIATE analysis ,INVENTORY control ,MATHEMATICAL programming ,LINEAR programming ,MATHEMATICAL optimization - Abstract
In an earlier paper [5], we generalized and extended Beckmann's results [1] for a production and inventory problem with proportional smoothing costs and demands being random variables. Our previous results concerned the finite horizon nonstationary case. Here we consider the infinite horizon stationary case. Two curves in the plane determine an optimal policy. They are shown to have slopes between minus one and zero, to be differentiable, and to be bounded by two straight lines with a slope Of minus one. These results are used (a) to accelerate each iteration of a successive approximations algorithm and (b) to formulate a linear programming problem from whose solution an optimal policy can be determined. [ABSTRACT FROM AUTHOR]
- Published
- 1971
- Full Text
- View/download PDF
44. A SIMULATION MODEL OF CAPITAL BUDGETING UNDER UNCERTAINTY.
- Author
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Salazar, Rodolfo C. and Sen, Subrata K.
- Subjects
CAPITAL budget ,SIMULATION methods & models ,UNCERTAINTY ,RISK management in business ,CAPITAL market ,CAPITAL investments ,ASSET management ,ANALYSIS of variance ,CASH management ,LINEAR programming ,ECONOMICS ,MANAGEMENT - Abstract
This paper describes a simulation model of capital budgeting under uncertainty. It analyzes the effects of two types of uncertainty which influence the cash flows of the potential investment projects. Techniques of simulation and stochastic linear programming (using Weingartner's Basic Horizon model of capital budgeting) are employed to compute the expected return (with an associated measure of the risk involved) of different portfolios of projects. The manager can then select the portfolio which is closest to his personal risk-return preference. The model provides a practical guide to management in the entire process of project search, portfolio generation, and portfolio evaluation which characterizes the capital budgeting decision. [ABSTRACT FROM AUTHOR]
- Published
- 1968
- Full Text
- View/download PDF
45. THE SIMPLEX METHOD: TWO BASIC VARIABLES REPLACEMENT.
- Author
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Paranjape, S. R.
- Subjects
LINEAR programming ,MATHEMATICAL programming ,SYSTEMS engineering ,MATHEMATICAL analysis ,PROBLEM solving ,MANAGEMENT science ,SIMPLEXES (Mathematics) ,MATHEMATICAL variables ,MATHEMATICAL optimization ,OPERATIONS research ,LINEAR systems ,SYSTEM analysis - Abstract
The paper presents a method for solving the linear programming problems, which is itself a step towards the generalization of the classical Simlex Method. It replaces two basic variables by two non-basic variables at each iteration. Naturally this will reduce the total number of steps to reach the final solution. The paper also includes the solution of one example to illustrate the applicability of the method. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
46. CHANCE-CONSTRAINED PROGRAMMING.
- Author
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Charnes, A. and Cooper, W.W.
- Subjects
STOCHASTIC programming ,LINEAR programming ,PROBABILITY measures ,DISTRIBUTION (Probability theory) ,MANUFACTURING processes ,HUMAN error ,DECISION making ,DECISION theory ,OPTIMAL designs (Statistics) ,RANDOM variables ,THEORY of constraints ,PROBABILITY theory - Abstract
A new conceptual and analytical vehicle for problems of temporal planning under uncertainty, involving determination of optimal (sequential) stochastic decision rules is defined and illustrated by means of a typical industrial example. The paper presents a method of attack which splits the problem into two non-linear (or linear) programming parts, (i) determining optimal probability distributions, (ii) approximating the optimal distributions as closely as possible by decision rules of prescribed form. [ABSTRACT FROM AUTHOR]
- Published
- 1959
- Full Text
- View/download PDF
47. WAREHOUSE LOCATION WITH CONCAVE COSTS.
- Author
-
Khumawala, Basheer M. and Kelly, David L.
- Subjects
LOCATION problems (Programming) ,HEURISTIC programming ,MATHEMATICAL programming ,OPERATIONS research ,LINEAR programming ,RESOURCE allocation - Abstract
Copyright of INFOR is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 1974
- Full Text
- View/download PDF
48. Application of Programs with Maximin Objective Functions to Problems of Optimal Resource Allocation.
- Author
-
Kaplan, Seymour
- Subjects
MATHEMATICAL programming ,RESOURCE allocation ,MATHEMATICAL functions ,MATHEMATICAL optimization ,PRODUCTION functions (Economic theory) ,ECONOMIC models ,LINEAR programming - Abstract
A mathematical program with a maximin objective function is defined as an optimization problem of the following type: Maxz=min[sub i] c[sub i]x[sub i], subject to AX = b, X * (This character cannot be converted in ASCII text) O. Although the c[sub i] can be in the interval (-- ∞, ∞), the paper discusses the more common practical case where all c[sub t] * (This character cannot be converted in ASCII text) 0. It shows that problems of this type arise in a variety of applications where it is required to maximize a production function of the 'fixed proportion' type subject to a set of linear constraints. Although it is well known that the solution to this type of problem can be found by linear programming, this paper shows that, if the existence of a certain condition can be demonstrated, then a simplified method can be used to determine the optimum solution. Many problems of practical interest can be solved by this simplified method; an example involving the readiness of a ship is presented. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
49. The Elementary Redundancy-Optimization Problem: A Case Study in Probabilistic Multiple-Goal Programming.
- Author
-
Hendrix, G. G. and Stedry, A. C.
- Subjects
MATHEMATICAL optimization ,MATHEMATICAL programming ,LINEAR programming ,PROBABILITY theory ,ALGORITHMS ,INTEGER programming ,SYSTEM analysis - Abstract
This paper deals with systems (such as electronic devices and corporations) that are designed to accomplish multiple goals and whose internal structures are characterized by networks of interacting component parts. Each component of such a system is typically associated with a probability of failure, while each system goal is associated with a reward value. Failure of any network component may ultimately result in the inability to achieve one or more goals and force the forfeiture of the associated rewards. A basic problem in component-system design is to determine how the expectation of total reward may be maximized through the cost-limited acquisition of redundant (backup) components. This paper provides a formal statement of this redundancy-optimization problem and argues that the problem may not be solved easily by standard linear or integer programming techniques. It introduces an algorithm to solve this problem, proves its convergence, and presents computational results taken from a battery of test problems and an algorithm-efficiency study based on these tests. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
50. Fractional Programming with Homogeneous Functions.
- Author
-
Bradley, Stephen P. and Frey Jr., Sherwood C.
- Subjects
LINEAR programming ,FUNCTION spaces ,MATHEMATICAL functions ,NONLINEAR functional analysis ,PROBLEM solving ,FUNCTIONAL analysis ,METHODOLOGY ,FUNCTIONALS - Abstract
This paper extends the well known results for linear fractional programming to the class of programming problems involving the ratio of nonlinear functionals subject to nonlinear constraints, where the constraints are homogeneous of degree one and the functionals are homogeneous of degree one to within a constant. Two rather general auxiliary problems are developed, and the relations between the solutions of the auxiliary problems and the solutions of the original problem are codified. Applications of the results for specific problems are also presented. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
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