85 results
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2. Optimizing the Teaching-Learning Process Through a Linear Programming Model--Stage Increment Model.
- Author
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Stanford Univ., CA. School of Education., Catholic Univ. of America, Washington, DC. School of Education., Belgard, Maria R., and Min, Leo Yoon-Gee
- Abstract
An operations research method to optimize the teaching-learning process is introduced in this paper. In particular, a linear programing model is proposed which, unlike dynamic or control theory models, allows the computer to react to the responses of a learner in seconds or less. To satisfy the assumptions of linearity, the seemingly complicated non-linear teaching-learning process is converted into a neat linear form. A theorem is proposed and proven which provides the theoretical basis for treating the teaching-learning process as a piece-wise linear form. By taking probability of success as a negative cost coefficient, a mathematical programing model is proposed for the local optimizations which lead to the global optimization when the theorem is applied. Through this Stage Increment Model, sound and scientific optimization of the teaching-learning process for the individual becomes a reality. (Author/MF)
- Published
- 1971
3. Noneconomic Analysis Considerations for Management and Information System for Occupational Education.
- Author
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Management and Information System for Occupational Education, Winchester, MA. and Creager, John A.
- Abstract
As the first of two papers delineating the design of Massachusetts' Management and Information System for Occupational Education (MISOE), these specific dimensions of MISOE structure and function are considered: (1) the distinction between economic and noneconomic analysis, (2) distinctions among census, sample, and other data, (3) the distinction between descriptive and simulative analysis, and (4) functional levels, management levels, and management scope. Information retrieval and analysis for MISOE necessitates: (1) translation of inquiries into analytic hypotheses, (2) the selection of pertinent MISOE subsystems, data types and levels, analytical operations, and models, (3) performing the analyses and interpreting their results, and (4) reporting the results to the inquiry source. Discussions of general analysis requirements and considerations precede the detailing of specific analytical models and algorithms for MISOE, such as multiple linear regression and factor analysis. Dynamic simulation, linear programing, and nonlinear programing models are discussed, in addition to specific noneconomic analysis factors to consider within and among MISOE's subsystems of static space. Technical reports on MISOE's research methodology are appended. Related documents are available in this issue as VT 018 600, VT 018 602, VT 018 809, and VT 018 810. (AG)
- Published
- 1972
4. 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
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5. 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
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6. DETERMINATION OF OPTIMUM PACKAGING FREQUENCY OF ITEMS JOINTLY REPLENISHED.
- Author
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Goyal, S. K.
- Subjects
MANUFACTURING processes ,PACKAGING research ,OVERHEAD costs ,VARIABLE costs ,INVENTORY management systems ,MATHEMATICAL models ,ALGORITHMS ,ECONOMIC lot size - Abstract
This paper presents a systematic procedure for obtaining the optimum packaging frequencies for a number of items which are manufactured jointly but packaged individually immediately after manufacture. The method described in the paper is equally applicable to those problems where the optimum purchasing policy is to be obtained for a number of items procured from a single supplier. An example involving twenty jointly replenished items is solved to illustrate the procedure given in the paper. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
7. A Note on Linear Programming Algorithm Design: A Combinatorial Problem.
- Author
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Roes, P. B. M.
- Subjects
COMPUTER storage devices ,LINEAR programming ,DISTRIBUTION (Probability theory) ,ALGORITHMS ,MAGNETIC tapes ,MATHEMATICAL models - Abstract
As linear programming models grow bigger and bigger in size, much actual data that must be memorized is often put on magnetic tape or disk, and consequently there is an improportionately fast rise in the consumption of computer time. To cut down this expense, on ever increasing effort Is mode to design more efficient algorithms. This paper is meant to support the effort. If is attempted to find some characteristics of the way pivot column is found. The number of repetitions of a certain transfer of data from tape to core memory is considered. After some simplification, the problem is restated in a general way. The generating function of the probability distribution and the moment generating function of the number of repetitions is found. Asymptotic formulas are given for the moments using result from a paper of S. Narumi [1]. The results may be applied to write very efficient routines that search for an extreme value in a table. Formulas provide a means of calculating the computer timings in this case. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
8. The Optimal Control of Partially Observable Markov Processes over a Finite Horizon.
- Author
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Smallwood, Richard D. and Sondik, Edward J.
- Subjects
MARKOV processes ,STOCHASTIC processes ,MATHEMATICAL models ,DISCRETE-time systems ,SYSTEM analysis ,MATHEMATICAL functions ,ALGORITHMS - Abstract
This paper formulates the optimal control problem for a class of mathematical models in which the system to be controlled is characterized by a finite-state discrete-time Markov process. The states of this internal process are not directly observable by the controller; rather, he has available a set of observable outputs that are only probabilistically related to the internal state of the system. The formulation is illustrated by a simple machine-maintenance example, and other specific application areas are also discussed. The paper demonstrates that, if there are only a finite number of control intervals remaining, then the optimal payoff function is a piecewise-linear, convex function of the current state probabilities of the internal Markov process. In addition, an algorithm for utilizing this property to calculate the optimal control policy and payoff function for any finite horizon is outlined. These results are illustrated by a numerical example for the machine-maintenance problem. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
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9. A DYNAMIC MODEL FOR BOND PORTFOLIO MANAGEMENT.
- Author
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Bradley, Stephen P. and Crane, Dwight B.
- Subjects
BOND funds ,DECISION theory ,DECISION making ,INVESTMENTS ,ECONOMIC indicators ,PORTFOLIO management (Investments) ,ALGORITHMS ,MATHEMATICAL decomposition ,MATHEMATICAL programming ,INVESTMENT analysis ,FINANCIAL management ,MATHEMATICAL models - Abstract
The bond portfolio problem is viewed as a multistage decision problem in which buy, sell, and hold decisions are made at successive (discrete) points in time. Normative models of this decision problem tend to become very large, particularly when its dynamic structure and the uncertainty of future interest rates and cash flows are incorporated in the model. In this paper we present a multiple period bond portfolio model and suggest a new approach for efficiently solving problems which are large enough to make use of as much information as portfolio managers can reasonably provide. The procedure utilizes the decomposition algorithm of mathematical programming and an efficient technique developed for solving subproblems of the overall portfolio model. The key to the procedure is the definition of subproblems which are easily solved via a simple recursive relationship. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
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10. FINDING THE K SHORTEST LOOPLESS PATHS IN A NETWORK.
- Author
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Yen, Jin Y.
- Subjects
ALGORITHMS ,NETWORK analysis (Planning) ,OPERATIONS research ,BRANCH & bound algorithms ,MATHEMATICAL optimization ,MATHEMATICAL models ,LINEAR statistical models ,SYSTEMS engineering ,INDUSTRIAL management - Abstract
This paper presents an algorithm for finding the K loopless paths that have the shortest lengths from one node to another node in a network. The significance of the new algorithm is that its computational upper bound increases only linearly with the value of K. Consequently, in general, the new algorithm is extremely efficient as compared with the algorithms proposed by Bock, Kantner, and Haynes [2], Pollack [7], [8], Clarke, Krikorian, and Rausan [3], Sakarovitch [9] and others. This paper first reviews the algorithms presently available for finding the K shortest loopless paths in terms of the computational effort and memory addresses they require. This is followed by the presentation of the new algorithm and its justification. Finally, the efficiency of the new algorithm is examined and compared with that of other algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 1971
- Full Text
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11. AN ALGORITHM FOR THE QUADRATIC ASSIGNMENT PROBLEM.
- Author
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Graves, G. W. and Whinston, A. B.
- Subjects
RESOURCE allocation ,QUADRATIC assignment problem ,ASSIGNMENT problems (Programming) ,ECONOMIC models ,COMBINATORIAL optimization ,COMBINATORICS ,ECONOMIC statistics ,MATHEMATICAL statistics ,MATHEMATICAL models ,ALGORITHMS ,MATHEMATICAL analysis ,PROBLEM solving - Abstract
The paper presents a new approach to solving a class of combinatorial economic allocation problems. One member of this class is known as the quadratic assignment problem. Besides presenting an algorithm to solve this problem, we will discuss in general terms the techniques for treating combinatorial problems. A novel feature of the paper is the development of the statistical properties of the criterion function. These statistical properties are used in conjunction with a general enumerative procedure to form the main parts of the algorithm. Using the idea of confidence level enumeration, an extension of the algorithm is proposed which should allow for the effective treatment of large scale combinatorial problems. Finally we present some computational results in order to illustrate the effectiveness of the general approach. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
12. OPTIMAL PRODUCTION SCHEDULING AND EMPLOYMENT SMOOTHING WITH DETERMINISTIC DEMANDS.
- Author
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Lippman, Steven A., Rolfe, Alan J., Wagner, Harvey M., and Yuan, John S.C.
- Subjects
PRODUCTION scheduling ,MATHEMATICAL variables ,LABOR supply ,LABOR costs ,INVENTORY control ,PRODUCTION control ,STATISTICAL smoothing ,INVENTORY accounting ,ALGORITHMS ,MATHEMATICAL models ,EDUCATION ,MANAGEMENT - Abstract
In this paper we study a model that minimizes the sum of production, employment smoothing, and inventory costs subject to a schedule of known demand requirements over a finite time horizon. The three instrumental variables are work force producing at regular-time, work force producing on overtime, and the total work force. Overtime is limited to be not more than a fixed multiple of regular time. The idle portion of the work force and the levels of inventory are resultant variables. We postulate the following shape characteristics for the cost functions production costs are convexlike, smoothing costs are V-shaped, and holding costs are increasing, both the production and holding cost functions need not be stationary. In this paper, we provide upper and lower bounds on the cumulative regular-time plus overtime work force for any sequence of demand requirements. We also give the form of an optimal policy when demands are monotone (either increasing or decreasing). Finally, we derive the asymptotic behavior of optimal policies when demands are monotone and the planning horizon becomes arbitrarily long. All of these results, which convey information about the numerical values of optimal policies, given specific demands and an initial level of inventory, depend only on the shape characteristics of the cost functions. Algorithmic techniques are discussed elsewhere. [ABSTRACT FROM AUTHOR]
- Published
- 1967
- Full Text
- View/download PDF
13. DECOMPOSITION OF PROJECT NETWORKS.
- Author
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Parikh, Shailendra C. and Jewell, William S.
- Subjects
PRODUCTION scheduling ,OPERATIONS research ,CRITICAL path analysis ,MANAGEMENT software ,PROJECT management ,ALGORITHMS ,COMPUTER storage devices ,MATHEMATICAL models ,COMPUTER networks ,SIMULATION methods & models ,MATHEMATICAL models in business ,MANAGEMENT science - Abstract
This paper considers "critical path" networks which are used for the planning and scheduling of projects that consist of well defined sequences of individual activities. When the number of activities is large, it becomes difficult to prepare a network for the project as one unit, and it may also be difficult to store the network in the high speed memory of a digital computer. Also, in the cases where there are two or more independent projects, which are weakly inter-related by common activities, the problem of efficient scheduling of all the projects becomes quite difficult. This paper presents a method to "tear" or "decompose" a project network into several subnetworks, schedule the subnetworks and then to put the subnetworks back together. A computational algorithm is first given for time-only networks; then two computational formulations are given for cost-time network of project subnetworks. The latter essentially generalize the algorithm due to Fulkerson, in order to handle piecewise linear, convex, cost-time curves for some or all of the activities. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
14. THE GENERALIZED STEPPING STONE METHOD FOR THE MACHINE LOADING MODEL.
- Author
-
Eisemann, Kurt
- Subjects
LINEAR programming ,ALGORITHMS ,MATHEMATICAL programming ,SIMPLEXES (Mathematics) ,MATHEMATICAL models ,MATHEMATICAL models in business ,TOPOLOGY ,NUMERICAL analysis ,BUSINESS mathematics ,MANAGEMENT science ,SIMULATION methods & models - Abstract
This paper gives a detailed description of an algorithm for the solution of a specialized Linear Programming model, to be called the Machine Loading model. It is a generalization of the Transportation Problem, in that weighting factors are applied to the individual elements which form the row and column sums. For the Machine Loading model, the simplex method reduces to a specialized algorithm which generalizes the stepping stone method of the Transportation Problem [2], [3]. With the resulting generalized stepping stone method, it becomes practicable to solve many large-scale problems for which the direct application of the simplex method would be impracticable. The present paper is restricted to a discussion of the following topics: (I) the general characteristics of the model and its topological features; (ii) a detailed solution algorithm, including a consideration of degenerate cases and the use of a computer; (iii) a more restrictive capacitated model and the corresponding modifications to the solution algorithm; and (iv) the complete illustrative solution of a numerical example. The purpose is to aid interested readers in gaining familiarity with the algorithm and facility in the solution of numerical problems. No derivations or proofs will be included. [ABSTRACT FROM AUTHOR]
- Published
- 1964
- Full Text
- View/download PDF
15. Ambiguity in Limited Entry Decision Tables.
- Author
-
King, P. J. H.
- Subjects
DECISION logic tables ,SYSTEM analysis ,ALGORITHMS ,SEMANTICS ,MATHEMATICAL models ,DECISION making - Abstract
The use of decision tables as a tool in systems analysis and for program specification is now becoming accepted. Rules on redundancy, contradiction, and completeness for limited entry tables were published in 1963. These ore usually used for checking, preceded if necessary by a conversion from extended to limited entry form. Processors which automatically translate tables to more conventional program usually base their diagnostic facilities on these rules. In this paper it is suggested that these rules ore unsatisfactory and that the important aspect of checking is to eliminate ambiguity from tables. Ambiguity is defined and discussed, and a procedure for producing checked out decision tables is proposed. The theoretical basis of the algorithm used is established. The importance of well-designed diagnostic facilities in decision table processors is emphasized. [ABSTRACT FROM AUTHOR]
- Published
- 1968
- Full Text
- View/download PDF
16. A PARAMETRIC DECOMPOSITION APPROACH FOR THE SOLUTION OF UNCAPACITATED LOCATION PROBLEMS.
- Author
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Swain, Ralph W.
- Subjects
INDUSTRIAL location ,DECOMPOSITION method ,MANAGEMENT education ,STUDY & teaching of operations research ,FACILITY management ,MATHEMATICAL programming ,MATHEMATICAL models ,LOCATION analysis ,ALGORITHMS ,EDUCATION - Abstract
This paper presents a new approach to determining the optimal facility locations for uncapacitated location problems in two stages. First, it is shown that a subset of all solutions to the uncapacitated public facility location problem can be obtained by considering a closely related private location problem. The exact nature of the problem is established using the Generalised Lagrange Multiplier results given by Everett. In the second section of the paper a particularly efficient parametric decomposition algorithm, which is based on the results of the first section, is presented. Computational results are given which summarize the current level of experience with the algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
17. SELF-SCALING VARIABLE METRIC (SSVM) ALGORITHMS. Part 2.
- Author
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Oren, Shmuel S.
- Subjects
SCALING laws (Statistical physics) ,ALGORITHMS ,FOUNDATIONS of arithmetic ,METRIC system ,MANAGEMENT science ,MATHEMATICAL variables ,APPROXIMATION theory ,QUALITATIVE research ,MATHEMATICAL models ,EXPERIMENTS - Abstract
This part of the paper introduces some possible implementations of Self-Scaling Variable Metric algorithms based on the theory presented in Part I. These implementations are analyzed theoretically and discussed qualitatively. A special class of SSVM algorithms is introduced, which has the additional property of being invariant under scaling of the objective function or of the variables. Experimental results are provided for a particular case of this class. This case has been tested in comparison to the DFP algorithm on a variety of functions with up to 50 variables. The results indicate that the new method has substantial advantage for functions with a large number of variables. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
18. A MATHEMATICAL MODEL OF SUPPLY SUPPORT FOR SPACE OPERATIONS.
- Author
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Freeman, Raoul J., Gogerty, David C., Graves, Glenn W., and Brooks, Robin B. S.
- Subjects
EXTRATERRESTRIAL bases ,MATHEMATICAL models ,OPERATIONS research ,LOGISTICS ,PRODUCTION scheduling ,MANAGEMENT ,ALGORITHMS - Abstract
This paper develops a methodology to evaluate various aspects of logistics supply support of space bases. It is assumed that there exists at the space base a schedule of operations that reflects the day-to-day living, build-up, and scientific experimental activities that are to be carried on. These activities, in turn, set a series of demands or requirements for products over a time spectrum. The supply system must deliver products so as to meet the amounts and times of the product requirements. Each product or module has an earliest and latest time by which it must be delivered. A mathematical model is developed that plans a series of trips, the dates at which each is to be sent, and the composition of the cargoes on each trip that satisfy the series of requirements over a time spectrum imposed by the activities at the space base. The series of trips are an expression of an efficient plan that simultaneously considers demands for different products at different future times and observes the various constraints of the system (e.g., cargo capacity of spaceships). The mathematical formulation of this scheduling problem is a simple non- linear discrete programming problem. An algorithm has been developed for its solution, and a description thereof is presented. The model is illustrated by showing how it would supply a long-term lunar base. Various uses of the model are described. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
19. MINIMAL COST CUT EQUIVALENT NETWORKS.
- Author
-
Picard, Jean-Claude and Ratlife, H. Donald
- Subjects
NETWORK analysis (Planning) ,FINANCIAL management ,OPERATIONS research ,PROBLEM solving ,MATHEMATICAL models ,GROUP extensions (Mathematics) ,COST control ,COST ,ALGORITHMS ,EDUCATION - Abstract
This paper is concerned with the following problem in network synthesis. Suppose that we are given a network with real-valued capacities on each arc. There is a cost associated with each arc which is proportional to the magnitude of the arc capacity. We wish to determine new arc capacities such that the capacity of each cut in the new network differs from the capacity of the corresponding cut in the original network by a specified constant and such that the total cost is minimized. This problem is shown to be equivalent to solving a minimum cost flow problem on a related network. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
- View/download PDF
20. ON THE LOADING PROBLEM--A COMMENT.
- Author
-
Lev, Benjamin
- Subjects
ALGORITHMS ,HEURISTIC programming ,MATHEMATICAL programming ,MATHEMATICAL optimization ,RESOURCE allocation ,RESOURCE management ,MATHEMATICAL models ,MATHEMATICAL analysis ,NUMERICAL analysis ,OPERATIONS research ,PROBLEM solving - Abstract
The author responds to the paper "The Loading Problem," by Eilon and Christofides. He focuses on suggesting a solution to the problem. The recommended solution involves a heuristic algorithm that allegedly requires fewer computations than the one proposed by Eilon and Christofides. It is suggested that the simpler algorithm offered by the author reaches mathematical optimization as often as the aforementioned algorithm. It is further proposed that the algorithm presented by Eilon and Christofides cannot be used to solve multi-dimensional programming problems. The author goes on to discuss a numerical analysis that can be used for the allocation of industrial resources. Related mathematical models are discussed in detail. A table comparing the results of the two algorithms is also presented.
- Published
- 1972
- Full Text
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21. EFFICIENT DISTRIBUTION OF RESOURCES THROUGH THREE LEVELS OF GOVERNMENT.
- Author
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Cassidy, R. G., Kirby, M. J. L., and Raike, W. M.
- Subjects
RESOURCE allocation ,ASSET allocation ,OPERATIONS research ,GOVERNMENT policy ,ALGORITHMS ,DECISION making ,MATHEMATICAL models ,FEDERAL budgets ,PLANNING - Abstract
This paper presents a model for determining how a central government can most efficiently allocate resources among other levels of government. The model explicitly includes the fact that lower levels of government can make independent decisions once they have been given resources by the central government. A key feature of the model is the mathematical formulation of the central government's objective of distributing resources efficiently, while at the same time being as fair as possible to all those receiving allocations. An algorithm for solving the model is presented along with a numerical example. [ABSTRACT FROM AUTHOR]
- Published
- 1971
- Full Text
- View/download PDF
22. A SIMPLEX METHOD FOR A CLASS OF NONCONVEX SEPARABLE PROBLEMS.
- Author
-
Alloin, Guy
- Subjects
PROBLEM solving ,MATHEMATICAL statistics ,MATHEMATICAL programming ,CONVEX functions ,SEPARABLE algebras ,REAL variables ,NONLINEAR programming ,ALGORITHMS ,MATHEMATICAL models - Abstract
In this paper we present an extension of the simplex procedure to deal with separable programming problems where the objective is composed of functions which are either convex or concave and where the feasible solution set is convex. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
23. ELEMENTS OF LARGE-SCALE MATHEMATICAL PROGRAMMING PART I: CONCEPTS.
- Author
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Geoffrion, Arthur M.
- Subjects
MATHEMATICAL programming ,MANAGEMENT science ,ALGORITHMS ,COMPUTER programming ,MATHEMATICAL optimization ,OPERATIONS research ,LINEAR programming ,LARGE scale systems ,BUSINESS mathematics ,MATHEMATICAL analysis ,MATHEMATICAL models - Abstract
A framework of concepts is developed which helps to unify a substantial portion of the literature on large-scale mathematical programming. These concepts fall into two categories. The first category consists of problem manipulations that can be used to derive what are often referred to as "master" problems; the principal manipulations discussed are Projection, Inner Linearization, and Outer Linearization. The second category consists of solution strategies that can be used to solve the master problems, often with the result that "subproblems" arise which can then be solved by specialized algorithms. The Piecewise, Restriction, and Relaxation strategies are the principal ones discussed. Numerous algorithms found in the literature are classified according to the manipulation/strategy pattern they can be viewed as using, and the usefulness of the framework is demonstrated by using it (see Part II of this paper) to rederive a representative selection of algorithms. The material presented is listed in the following order: The first section is introductory in nature, and discusses types of large-scale problems, the scope of discussion and the literature, and the notation used. The second section, entitled "Problem Manipulation: Source of 'Master' Problems" covers the subjects of projection, inner linearization and outer linearization. The third section, "Solution Strategies: Source of 'Subproblems'," discusses piecewise strategy, restriction and relaxation. The fourth section is entitled "Synthesizing Known Algorithms from Manipulations and Strategies," and is followed by a concluding section and an extensive bibliography. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
24. ADDENDUM TO STANKARD AND GUPTA'S NOTE ON LOT SIZE SCHEDULING.
- Author
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Hodgson, Thom J.
- Subjects
ECONOMIC lot size ,INVENTORY control ,PRODUCTION scheduling ,DYNAMIC programming ,MATHEMATICAL programming ,INVENTORIES ,COST allocation ,INDUSTRIAL costs ,SYSTEMS engineering ,MATHEMATICAL models ,ALGORITHMS ,PROBLEM solving - Abstract
This paper presents a grouping procedure which yields improved solutions to Bomberger's Lot Size Scheduling Problem [1]. The group definition is a generalization of the group definition proposed by Stankard and Gupta [3]. Moreover, the generalization leads to a pseudo dynamic programming procedure which is readily programmable. Computational experience has shown the procedure to be extremely efficient. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
25. A CLASS OF INSIDE-OUT ALGORITHMS FOR GENERAL PROGRAMS.
- Author
-
Gould, F. J.
- Subjects
ALGORITHMS ,STOCHASTIC convergence ,NONLINEAR programming ,MATHEMATICAL programming ,MATHEMATICAL optimization ,GEOMETRICAL constructions ,MANAGEMENT science ,MATHEMATICAL models ,MATHEMATICAL analysis ,OPERATIONS research ,MATHEMATICAL functions ,PROBLEM solving - Abstract
In this paper the Fiacco-McCormick SUMT technique is embedded in a class of inside-out algorithms. Convergence is demonstrated for the nonlinear programming problem under fairly general conditions and the algorithms are interpreted in a geometric structure. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
26. A BACKLOGGING MODEL AND MULTI-ECHELON MODEL OF A DYNAMIC ECONOMIC LOT SIZE PRODUCTION SYSTEM--A NETWORK APPROACH.
- Author
-
Zangwill, Willard I.
- Subjects
PRODUCTION (Economic theory) ,ALGORITHMS ,DYNAMIC programming ,PRODUCTION management (Manufacturing) ,MATHEMATICAL optimization ,MATHEMATICAL models in business ,INVENTORY control ,MATHEMATICAL programming ,PRODUCT management ,INDUSTRIAL costs ,MATHEMATICAL models ,SYSTEMS engineering - Abstract
Two dynamic economic lot size production systems are analyzed in this paper, the first being a single product model with backlogging and the second a multi-echelon model. In each model the objective is to find a production schedule that minimizes the total production and inventory costs. A key conceptual difficulty is that the mathematically perplexing problem of minimizing a concave function is being considered, it is shown that both models are naturally represented via single source networks. The network formulations reveal the underlying structure of the models, and facilitate development of efficient dynamic programming algorithms for calculating the optimal production schedules. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
27. ALGORITHMIC EQUIVALENCE IN LINEAR FRACTIONAL PROGRAMMING.
- Author
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Wagner, Harvey M. and Yuan, John S.C.
- Subjects
ALGORITHMS ,LINEAR programming ,MATHEMATICAL variables ,HYPOTHESIS ,EQUIVALENCE relations (Set theory) ,MATHEMATICAL programming ,PROBLEM solving research ,MATHEMATICAL models ,EDUCATION - Abstract
This paper demonstrates the equivalence of several published algorithms for solving the so-called linear fractional programming problem. [ABSTRACT FROM AUTHOR]
- Published
- 1968
- Full Text
- View/download PDF
28. TOPOLOGY AND COMPUTATION OF THE GENERALIZED TRANSPORTATION PROBLEM.
- Author
-
Lourie, Janice R.
- Subjects
TRANSPORTATION ,TOPOLOGY ,ITERATIVE methods (Mathematics) ,ALGORITHMS ,MATHEMATICAL models of industrial management ,MATHEMATICAL models in business ,NUMERICAL analysis ,MANAGEMENT science ,COMPUTER software ,MATHEMATICAL models ,BUSINESS mathematics ,MANAGEMENT - Abstract
The topology of the Generalized Transportation Problem, at the end of each iteration of the stepping-stone method, is characterized by a variable number of loops to which are attached multiple branched side chains or trees. An efficient computer representation of this structure and methods for updating it are described in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 1964
- Full Text
- View/download PDF
29. A NON-LINEAR EXTENSION OF THE SIMPLEX METHOD.
- Author
-
Wegner, Peter
- Subjects
NONLINEAR statistical models ,MATHEMATICAL programming ,ALGORITHMS ,NONLINEAR theories ,SIMPLEXES (Mathematics) ,SET theory ,ALGEBRA ,MATHEMATICS ,NONLINEAR functional analysis ,NONLINEAR integral equations ,NONNEGATIVE matrices ,DECISION making ,MATHEMATICAL models - Abstract
This paper describes an algorithm for the solution of mathematical programming problems having a linear objective function and non-linear constraints. The algorithm is basically an adaptation of the simplex method to the case of non-linear constraints. Certain complications are, however, introduced through non-linearity in the constraints, and it is shown how these can be overcome. [ABSTRACT FROM AUTHOR]
- Published
- 1960
- Full Text
- View/download PDF
30. An Efficient Equipment-Layout Algorithm.
- Author
-
Neghabat, Farrokh
- Subjects
BUILDINGS ,HEURISTIC ,LOCATION problems (Programming) ,ALGORITHMS ,MATHEMATICAL optimization ,LINEAR statistical models ,MATHEMATICAL models ,OPERATIONS research - Abstract
This paper treats the problem of locating a given number of interrelated physical facilities in a single- or multi-story building as an optimization model such that the weighted sum of the distances along orthogonal directions is minimized, and describes a constructive heuristic algorithm for the one-dimensional model. This linear placement algorithm is then extended to higher dimensions for placing uniform-size equipment modules at homogeneous fixed locations. The algorithm accommodates lower-bound constraints for the linear case efficiently and produces near-optimal solutions. Its significance, as demonstrated by comparison with some existing heuristic procedures, is that it has the capability of handling efficiently problems with large numbers of equal-size facilities whose solutions are computationally intractable using the present optimum-producing methods. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
31. NESTED DECOMPOSITION AND MULTI-STAGE LINEAR PROGRAMS.
- Author
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Glassey, C. Roger
- Subjects
LINEAR programming ,MATHEMATICAL decomposition ,MATHEMATICAL programming ,MANAGEMENT science ,MATHEMATICAL optimization ,MATHEMATICAL models ,ALGORITHMS ,PRODUCTION scheduling ,MATHEMATICAL variables - Abstract
A multi-stage linear program is defined with linking variables that connect consecutive stages. Optimality conditions for the composite problem are partitioned into local and linking conditions. When the Dantzig-Wolfe decomposition scheme is applied with the first stage as the master, the subproblem is also a MLP with one less stage. The same decomposition is then applied to the subproblem, giving rise to a nested decomposition scheme, in which each stage acts as a master for the following stage and a subproblem for the preceding. Optimizing a single stage problem results in satisfying the "local" optimality conditions. A very general rule is given for selecting the next subproblem to optimize, and finite convergence to a solution satisfying all linking conditions is demonstrated. Procedures for extracting the optimal primal solution at the end of the main algorithm and for initialization are given. Particular rules for selecting the next subproblem and for generating additional proposal vectors are discussed. Finally, it is shown how a variety of problems may be restructured as multi-stage linear programs to which this algorithm may be applied, and some computational experience is reported. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
- View/download PDF
32. MAXIMIZATION BY QUADRATIC HILL-CLIMBING.
- Author
-
Goldfield, Stephen M., Quandt, Richard E., and Trotter, Hale F.
- Subjects
APPROXIMATION theory ,QUADRATIC equations ,MATHEMATICAL functions ,ALGORITHMS ,FUNCTIONAL analysis ,MATHEMATICS ,ECONOMETRICS ,ECONOMICS ,ECONOMIC models ,MATHEMATICAL economics ,MATHEMATICAL models ,ECONOMETRIC models - Abstract
The purpose of this paper is to describe a new gradient method for maximizing general functions. After a brief discussion of various known gradient methods the mathematical foundation is laid for the new algorithm which rests on maximizing a quadratic approximation to the function on a suitably chosen spherical region. The method requires no assumptions about the concavity of the function to be maximized and automatically modifies the step size in the light of the success of the quadratic approximation to the function. The paper further discusses some practical problems of implementing the algorithm and presents recent computational experience with it. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
33. MULTIPARTITE OPTIMIZATION.
- Author
-
George, Robley E.
- Subjects
DYNAMIC programming ,TEAMS in the workplace ,MATHEMATICAL optimization ,MATHEMATICAL programming ,ALGORITHMS ,REASONING ,MATHEMATICAL models ,FUNCTION algebras - Abstract
This paper considers the problem of determining the policy to be followed by each member of a team so as to optimize some over-all criterion function characterizing the objective of the team. The reasoning of dynamic programming is employed to formulate the optimization problem, and the discussion is couched in the terms of a classical network problem. The paper first formulates a simple bipartite network optimization and then presents a number of generalizations. Finally, it gives two slightly different computational solutions to an example bipartite optimization problem. [ABSTRACT FROM AUTHOR]
- Published
- 1968
- Full Text
- View/download PDF
34. A Stochastic Multiperiod Multimode Transportation Model.
- Author
-
Midler, Joseph L.
- Subjects
MATHEMATICAL models ,TRANSPORTATION planning ,DYNAMIC programming ,TRANSPORTATION ,STOCHASTIC processes ,QUADRATIC equations ,ALGORITHMS - Abstract
This paper develops a dynamic programming model for selecting an optimal combination of transportation modes over a multiperiod planning horizon. The formulation explicitly incorporates uncertainty regarding future requirements or demands for a number of commodity classes. In addition to determining the optimal modes to employ, the model assigns individual commodity classes to various modes, determines which supply points serve which destinations, and reroutes carriers from destinations to alternative sources where they will be most effective. The model is formulated as an optimal discrete time stochastic control problem where cost is quadratic and dynamic equations linear in the state and control variables. This model may be solved in closed form by an efficient dynamic programming algorithm that permits the treatment of relatively large scale systems. A iso developed is an alternative, generally suboptimal method of solution, based upon wiving a sequence of convex programming problems over time. This technique may be employed for a more general class of problems. In both methods the use of 'shadow prices' that arise is discussed. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
35. THE EQUIVALENCE OF INTEGER PROGRAMS TO CONSTRAINED RECURSIVE SYSTEMS.
- Author
-
Nanda, Patanjali S.
- Subjects
RECURSIVE programming ,INTEGER programming ,LINEAR programming ,MATHEMATICAL programming ,TRAVELING salesman problem ,ALGORITHMS ,MATHEMATICAL models ,OPERATIONS research ,MANAGEMENT education - Abstract
It has been established that integer programs with integral, recursive constraint matrices have integral extreme points for integral, nonnegative requirement vectors. In this paper, it is first shown that the assignment problem can be transformed to such a program, but with upper bounds on some variables. This equivalent program leads to additional results for solving the assignment problem. Algorithms are then delineated to transform matching, covering and travelling salesman problems to equivalent recursive programs of the aforementioned type, but with bounds on some variables. These results are extended to programs with special structure in their constraint matrices. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
- View/download PDF
36. MULTIPARAMETRIC LINEAR PROGRAMMING.
- Author
-
Gal, Tomas and Nedoma, Josef
- Subjects
LINEAR programming ,MATHEMATICAL programming ,MATHEMATICAL optimization ,VECTOR analysis ,MATRICES (Mathematics) ,PRICING ,ALGORITHMS ,PROBLEM solving ,MATHEMATICAL models - Abstract
The multiparametric linear programming (MLP) problem for the right-hand sides (RHS) is to maximize z = c
T x subject to Ax = b (λ), x ≧ 0, where b(λ) can be expressed in the form b(λ) = b* + Fλ, where F is a matrix of constant coefficients, and λ is a vector-parameter. The multiparametric linear programming (MLP) problem for the prices or objective function coefficients (OFC) is to maximize z = cT (v)x subject to Ax = b, where x ≧ 0, where c(v) can be expressed in the form c(v) = c* + Hv, and where H is a matrix of constant coefficients, and v a vector-parameter. Let Bi be an optimal basis to the MLP-RHS problem and Ri be a region assigned to Bi such that for all λ Ri the basis, Bi is optimal. Let K denote a region such that K = ui Ri , provided that the Ri for various i do not overlap. The purpose of this paper is to present an effective method for finding all regions Ri that cover K and do not overlap. This method uses an algorithm that finds all nodes of a finite connected graph. An analogous method is presented for the MLP-OFC problem. [ABSTRACT FROM AUTHOR]- Published
- 1972
- Full Text
- View/download PDF
37. A GENERALIZED LAGRANGE MULTIPLIER ALGORITHM FOR OPTIMUM OR NEAR OPTIMUM PRODUCTION SCHEDULING.
- Author
-
Evans, J. P. and Gould, F. J.
- Subjects
LAGRANGE equations ,PRODUCTION scheduling ,PRODUCTION (Economic theory) ,ALGORITHMS ,OVERTIME pay ,OVERTIME ,WORKING hours ,OPERATING revenue ,INDUSTRIAL costs ,MATHEMATICAL optimization ,MATHEMATICAL models ,ECONOMICS - Abstract
In this paper we apply the concept of generalized Lagrange multipliers, introduced by Everett [4], to the development of an algorithm for a one-period multiproduct production model, where the objective is to maximize profit subject to constraints on aggregate regular time and overtime production. We assume no difference between the cost of idle time and regular time labor, so that the regular time cost is fixed. Overtime cost is variable. The price for each product is constant (independent of quantity sold), and everything produced can be sold. The optimum production schedule (maximum profit) will depend upon revenues, overtime costs, setup times, and productivities. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
38. THE EFFICIENCY OF COMPUTER ALGORITHMS FOR PLANT LAYOUT.
- Author
-
Ritzman, Larry P.
- Subjects
PLANT layout ,COMPUTER algorithms ,ALGORITHMS ,COMPUTER software ,INDUSTRIAL engineering ,PRODUCTION engineering ,PRODUCTION (Economic theory) ,FACTORY design & construction ,FACILITY management ,LOCATION analysis ,MATHEMATICAL models ,PROBLEM solving - Abstract
This paper presents the results of comparing experimentally the performance of four of the more promising computer algorithms for the plant layout problem. CDC 3600 computer programs are tested with twenty-six test problems. The resulting solutions are evaluated in respect to both computer time requirements and objective function values. The experiment shows how these two performance measures vary with the algorithm used and various test problem characteristics. With the exception of two studies [4], [8], information on comparative performances of layout algorithms is very limited. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
39. AN IMPLICIT ENUMERATION ALGORITHM FOR THE CONCAVE COST NETWORK FLOW PROBLEM.
- Author
-
Florian, M. and Robillard, P.
- Subjects
NETWORK analysis (Planning) ,BRANCH & bound algorithms ,CONCAVE functions ,EXTREMAL problems (Mathematics) ,MATHEMATICAL programming ,COST analysis ,REAL variables ,ALGORITHMS ,OPERATIONS research ,MANAGEMENT science ,MATHEMATICAL models ,TRANSPORTATION problems (Programming) - Abstract
The objective of this paper is the construction of a branch-and-bound algorithm for computing minimum cost flows in capacitated networks when the cost of passing a flow over an arc is concave. The method is based on the equivalence of the general network flow problem to a network flow problem in a bipartite network of a special form. An optimal flow is found by implicit enumeration of the set of extremal flows in that network. [ABSTRACT FROM AUTHOR]
- Published
- 1971
- Full Text
- View/download PDF
40. AN r-DIMENSIONAL QUADRATIC PLACEMENT ALGORITHM.
- Author
-
Hall, Kenneth M.
- Subjects
MATRICES (Mathematics) ,ALGEBRA ,FOUNDATIONS of arithmetic ,QUADRATIC equations ,ABSTRACT algebra ,CLUSTER analysis (Statistics) ,ALGORITHMS ,MATHEMATICAL models ,EIGENVECTORS ,GRAPHIC methods ,EDUCATION - Abstract
In this paper the solution to the problem of placing n connected points (or nodes) in r-dimensional Euclidean space is given. The criterion for optimality is minimizing a weighted sum of squared distances between the points subject to quadratic constraints of the form X'X = 1, for each of the r unknown coordinate vectors. It is proved that the problem reduces to the minimization of a sum or r positive semidefinite quadratic forms which, under the quadratic constraints, reduces to the problem of finding r eigenvectors of a special "disconnection" matrix. It is shown, by example, how this can serve as a basis for cluster identification. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
41. GENERALIZED NETWORKS, GENERALIZED UPPER BOUNDING AND DECOMPOSITION OF THE CONVEX SIMPLEX METHOD.
- Author
-
Rutenberg, David P.
- Subjects
LINEAR programming ,MATHEMATICAL programming ,MATHEMATICAL optimization ,FUNCTIONAL analysis ,CONVEX functions ,MATHEMATICAL decomposition ,NETWORK analysis (Planning) ,SIMPLEXES (Mathematics) ,MATHEMATICAL analysis ,MATHEMATICAL models ,ALGORITHMS ,MATRICES (Mathematics) - Abstract
If the constraint matrix of a linear program has special structure it may be possible to speed computation. Techniques have been developed to take advantages of such special structures as generalized networks, generalized upper bounding, and decomposition. For these matrix structures, it is shown in this paper how to extend the techniques to Zangwill's mathematical programming algorithm, the convex simplex method. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
42. A BRANCH SEARCH ALGORITHM FOR THE KNAPSACK PROBLEM.
- Author
-
Greenberg, Harold and Hegerich, Robert L.
- Subjects
KNAPSACK problems ,INTEGER programming ,MATHEMATICAL programming ,BRANCH & bound algorithms ,ALGORITHMS ,NETWORK analysis (Planning) ,MATHEMATICAL optimization ,COMPUTER programming ,MATHEMATICAL models ,MATHEMATICAL analysis ,OPERATIONS research ,PROBLEM solving - Abstract
This paper presents an algorithm for the solution of the knapsack problem. The method involves searching the nodes of a tree along a single branch at a time. The algorithm eliminates the computational drawbacks inherent in the usual branch and bound schemes. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
43. THE N DAYS OF CHRISTMAS: A MODEL FOR COMPETITIVE ADVERTISING OVER AN INTENSIVE CAMPAIGN.
- Author
-
Bell, Colin E.
- Subjects
ADVERTISING ,ADVERTISING campaigns ,MARKETING management ,COMMERCIAL products ,HOLIDAYS ,COMPETITION ,RESOURCE allocation ,SALES forecasting ,BUDGET ,ALGORITHMS ,MATHEMATICAL models ,MATHEMATICAL analysis - Abstract
During a pre-Christmas campaign in which daily sales are generally increasing, it is important to achieve a proper balance in advertising allocation between the final days of heavy sales and the earlier days of the campaign when sales are lighter but advertising might affect sales farther into the future. This paper presents a model of such a problem for two competing firms, an algorithm for solution of the model, numerical examples, and a proof of the algorithm. An equilibrium solution is found in which each firm applies the same proportioning vector to distribute its total advertising budget over the N days. [ABSTRACT FROM AUTHOR]
- Published
- 1968
- Full Text
- View/download PDF
44. THE CONVEX SIMPLEX METHOD.
- Author
-
Zangwill, Willard I.
- Subjects
CONVEX functions ,LINEAR systems ,SIMPLEXES (Mathematics) ,TRANSPORTATION problems (Programming) ,PROBLEM solving ,MANAGEMENT education ,ALGORITHMS ,MATHEMATICAL models ,STOCHASTIC convergence ,EDUCATION - Abstract
This paper presents a method, called the convex simplex method, for minimizing a convex objective function subject to linear inequality constraints. The method is a true generalization of Dantzig's linear simplex method both in spirit and in the fact that the same tableau and variable selection techniques are used. With a linear objective function the convex simplex method reduces to the linear simplex method. Moreover, the convex simplex method actually behaves like the linear simplex method whenever it encounters a linear portion of a convex objective function. Many of the sophisticated techniques designed to enhance the efficiency of the linear simplex method are applicable to the convex simplex method. In particular, as an example, a network transportation problem with a convex objective function is solved by using the standard transportation tableau and by only slightly modifying the usual procedure for a linear objective function. [ABSTRACT FROM AUTHOR]
- Published
- 1967
- Full Text
- View/download PDF
45. COMMUNICATIONS TO THE EDITOR.
- Author
-
Mansoor, E.M.
- Subjects
ASSEMBLY line balancing ,MANAGEMENT education ,MATHEMATICAL models ,ALGORITHMS ,CRITICAL path analysis ,NETWORK analysis (Planning) ,EDUCATION - Abstract
The article proposes an improvement on A.L. Gutjahr and G.L. Nemhauser's algorithm for the assembly line balancing problem. Gutjahr and Nemhauser have contributed an interesting and useful algorithm for the assembly line balancing problem. The two stages of their method are outlined, including the state generation--where all possible sets or combinations of work elements that are feasible first station assignments without regard to the cycle tune are listed, and the shortest route calculations--where arcs linking appropriate sets are generated. Several examples of the utilization of this method are presented.
- Published
- 1967
- Full Text
- View/download PDF
46. THE EXTENSION OF THE CASCADE ALGORITHM TO LARGE GRAPHS.
- Author
-
Land, A. H. and Stairs, S. W.
- Subjects
FOUNDATIONS of arithmetic ,COMPUTER programming ,BRANCH & bound algorithms ,COMPUTER algorithms ,MATRICES (Mathematics) ,ALGORITHMS ,GRAPHIC methods ,GROUP extensions (Mathematics) ,MATHEMATICAL models ,EDUCATION - Abstract
Large graphs for which the calculation of the shortest distances between all vertices is required often consist of several parts with limited interconnections. This paper shows how this characteristic may be used to reduce computer storage for a matrix type calculation, to reduce calculational labour, and to provide results in a form which is particularly convenient if a subsequent assignment of commodity flow to shortest paths is needed. The technique presented here allows the partition to be arbitrary, save for a single, easily achieved, condition. [ABSTRACT FROM AUTHOR]
- Published
- 1967
- Full Text
- View/download PDF
47. TOWARD BETTER CURRICULA THROUGH COMPUTER SELECTED SEQUENCING OF SUBJECT MATTER.
- Author
-
Taft, Martin Israel and Reisman, Arnold
- Subjects
LEARNING ,OCCUPATIONAL training ,EDUCATION research ,TEACHING methods ,CAREER education ,CURRICULUM ,MATHEMATICAL models ,PROGRESS reports ,HEURISTIC ,MATHEMATICS education ,SCIENCE education ,ALGORITHMS - Abstract
It is generally recognized that reinforcement, over an extended period of time of a given subject matter taught, enhances the student's mastery and subsequent retention of knowledge and/or skills. Recent major studies of curricula have concentrated on the content and method of presentation but have not made any significant strides towards the systematic exploitation of the potential contribution to the learning process of reinforcement through proper sequencing of subject matter presentation. This paper outlines a mathematical model of the established and industrially validated learning and forgetting theories and presents a computer executed heuristic algorithm for the selection of the best schedule for subject presentation. Applications of this methodology can be made at all levels of our educational system; from the elementary grades through graduate school, in highly academic as well as vocational training programs. [ABSTRACT FROM AUTHOR]
- Published
- 1967
- Full Text
- View/download PDF
48. MATRIX ROUNDING PROBLEMS.
- Author
-
Bacharach, Michael
- Subjects
MATRICES (Mathematics) ,ABSTRACT algebra ,CATALECTICANT matrices ,COMPUTER programming ,MATHEMATICAL analysis ,ALGORITHMS ,EXISTENCE theorems ,MATHEMATICAL models ,NETWORK analysis (Planning) ,EDUCATION - Abstract
The problem considered in this paper is that of consistently rounding off the elements of a matrix and its row and column sums. It is shown that a class of rounding problems of this kind is equivalent to a class of problems of determining flows through networks having arbitrary lower as well as upper bounds on edge flows. An existence theorem first proved by Hoffman for flows in such networks is used to show that an important subclass of the matrix rounding problems considered is always soluble. An algorithm for the entire class is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
- View/download PDF
49. Short Communications.
- Author
-
sattley, Kirk and Millstein, Robert
- Subjects
COMPUTER programming ,ALGORITHMS ,COMPUTER operating systems ,INFORMATION retrieval ,MATHEMATICAL models ,ELECTRONIC data processing ,PROGRAMMING languages - Abstract
Comments on articles published in earlier issues of the journal "Communications of the ACM." Discussion on techniques used in automatic segmentation of cyclic program structures;Focus on diverse techniques to assure the integrity of a data base;Information on algorithms to be followed by primitives in order to maximize the amount of parallel activity in a data base.
- Published
- 1970
50. An Algorithm for the Traffic Assignment Problem.
- Author
-
Nguyen, Sang
- Subjects
TRAFFIC assignment ,TRAFFIC estimation ,TRANSPORTATION ,MATHEMATICAL models ,PROBLEM solving ,ALGORITHMS ,ORIGIN & destination traffic surveys - Abstract
The traffic assignment problem associated with a given transportation network is the process of distributing zone-to-zone trips on links of the network. A number of methods have been proposed to solve this problem, but none have been found to be entirely satisfactory. This paper is concerned with the nonlinear mathematical model of the problem, where the link-traveling costs are increasing functions of the link flows and no explicit capacity constraint is imposed on individual links. An efficient algorithm is developed, using a node-arc formulation of the problem. It is an adaptation of the convex-simplex method that takes advantage of the very special network structure of the traffic assignment problem formulated in this way. Numerical results obtained with a moderate size street network are presented. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
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