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Full-Text Articles in Business Administration, Management, and Operations
A User's Guide For A Fortran Subprogram Containing A Dual Backtrack Algorithm For Finding The Lowest Order Of Intermodulation, Susumu Morito, Harvey M. Salkin
A User's Guide For A Fortran Subprogram Containing A Dual Backtrack Algorithm For Finding The Lowest Order Of Intermodulation, Susumu Morito, Harvey M. Salkin
Research Reports from the Department of Operations
This manual outlines a search enumeration (or backtrack) algorithm contained in the radio frequency intermodulation (RFI) backtrack code, SEARCH, and presents user operating instructions and sample computer printouts. Program RFIBCK, written as a FORTRAN subprogram, can be used to find the lowest order of an intermodulation product for a fixed set of frequencies, given such parameters as the guard band, the maximum number of concurrent threats, and the lowest permissible order of intermodulation. A listing of the program, and several randomly generated sample problems, together with their optimal solutions, are also included.
Computational Experience With A Dual Backtrack Algorithm For Identifying Frequencies Likely To Create Intermodulation Problems, Susumu Morito, Harvey M. Salkin, Kamlesh Mathur
Computational Experience With A Dual Backtrack Algorithm For Identifying Frequencies Likely To Create Intermodulation Problems, Susumu Morito, Harvey M. Salkin, Kamlesh Mathur
Research Reports from the Department of Operations
This paper describes the results of a computational study using a particular enumeration procedure, called a backtrack algorithm, to find the lowest order of radio frequency intermodulation. The average lowest order and its standard deviation, the average computer time and its standard deviation, along with other relevant statistics are obtained for a series of randomly generated problems with sets of 5 to 75 threat or source frequencies. Other parameters, such as the guard band, the maximum number of concurrent threats, and the size of the frequency band on the lowest order of intermodulation are varied during the computations. Statistics for …
Two Backtrack Algorithms For The Radio Frequency Intermodulation Problem, Susumu Morito, Harvey M. Salkin, David E. Williams
Two Backtrack Algorithms For The Radio Frequency Intermodulation Problem, Susumu Morito, Harvey M. Salkin, David E. Williams
Research Reports from the Department of Operations
Two or more radio signals, transmitted from a small platform (e.g., a ship, satellite, or airplane, etc.), tend to produce an intermodulation product which could distort a receive signal. The intensity of intermodulation interference due to a given intermodulation frequency is known to be closely related to the lowest order, or simply the order, of the intermodulation product which can be found by solving a single constraint integer program with variables unrestricted in sign, where coefficients of the constraint equation correspond to frequencies. Two variations of backtrack, or search enumeration algorithms, called the primal and dual backtrack algorithms, are developed …
An Efficient Cutting Plane Algorithm For Unconstrained Convex Minimization, Daniel Solow
An Efficient Cutting Plane Algorithm For Unconstrained Convex Minimization, Daniel Solow
Research Reports from the Department of Operations
A cutting-plane algorithm is proposed for minimizing a continuously differentiable convex function of n variables. One notable feature of this algorithm is that each cut is actually a supporting hyperplane, which does not require an iterative procedure. To initiate the whole process, a phase I method based on the complementary pivoting algorithms will be used. Of particular interest is the one-dimensional version of the cutting-plane algorithm, which reduces to a new form of line search.
Solving Differentiable Equations Via Constrained Optimization, Daniel Solow
Solving Differentiable Equations Via Constrained Optimization, Daniel Solow
Research Reports from the Department of Operations
The problem of finding a zero of a continuously differentiable system of m equations in n unknowns (m ≤ n) is transformed into a nonlinearly constrained optimization problem for which a Kuhn-Tucker point is shown to be either a solution of the original system or a point at which the derivative matrix is rank deficient. An algorithm is developed for the special case when m equals 1 and the function is convex. It may sometimes be used for finding a minimum of a continuously differentiable convex function, with the advantage of requiring possibly fewer line searches than an ordinary minimization …
Hoeomorphisms Of Triangulations With Applications To Computing Fixed Points, Daniel Solow
Hoeomorphisms Of Triangulations With Applications To Computing Fixed Points, Daniel Solow
Research Reports from the Department of Operations
In the past decade various complementary pivoting algorithms have been developed to search for fixed points of certain functions and point to set maps. All these methods generate a sequence of simplexes which are "shrinking" to a point. This paper proposes a new method for shrinking the simplexes. It is shown that under certain conditions, the function whose fixed point is sought may be used to control this shrinking process. A computational method for implementing these ideas is also suggested and several examples are solved using this approach.
A User's Guide For A Computer System Containing A Search Enumeration Algorithm For The Radio Frequency Intermodulation (Rfi) Problem, Susumu Morito, Harvey M. Salkin, David E. Williams
A User's Guide For A Computer System Containing A Search Enumeration Algorithm For The Radio Frequency Intermodulation (Rfi) Problem, Susumu Morito, Harvey M. Salkin, David E. Williams
Research Reports from the Department of Operations
This manual outlines two search enumeration (or backtrack) algorithms contained in the radio frequency intermodulation (RFI) backtrack code, RFIBCK, and presents user operating instructions and sample computer printouts. Program RFIBCK, written in FORTRAN, can be used to find the lowest order of a given intermodulation product for a fixed set of frequencies. Several randomly generated sample problems, together with their optimal solutions, are also included.
A Constrained Optimization Algorithm For Solving Certain Convex Systems Of Equations, Daniel Solow
A Constrained Optimization Algorithm For Solving Certain Convex Systems Of Equations, Daniel Solow
Research Reports from the Department of Operations
The purpose of this research is to establish a computationally efficient algorithm for solving certain systems of convex equations. In the past, two basic approaches have been developed. The first approach is based on variations of Newton's method and requires rather stringent conditions on the system of equations whereas the second approach is based on the homotopic or continuation method which requires milder conditions for convergence. The approach in this work will be from an optimization standpoint and convergence will be established under reasonable conditions. In addition, a global algorithm for finding the zero of a convex real valued function …
Paying Unemployment Compensation Taxes And Solving The Complete Set Partitioning Problem, Chien-Hua Lin, Harvey M. Salkin
Paying Unemployment Compensation Taxes And Solving The Complete Set Partitioning Problem, Chien-Hua Lin, Harvey M. Salkin
Research Reports from the Department of Operations
It is shown that under certain regulations specified by state law, there is an optimal way for a corporation to pay unemployment compensation taxes. The particular scenario is given along with the natural model which turns out to be a set partitioning problem having all possible nonzero binary columns in the constraint matrix. A highly specialized enumerative algorithm, which never requires the explicit maintenance of the model, is also presented. Computational results and their impact, reflecting recent data from several Ohio based corporations, are listed.
Finding The General Solution Of A Linear Diophantine Equation, Susumu Morito, Harvey M. Salkin
Finding The General Solution Of A Linear Diophantine Equation, Susumu Morito, Harvey M. Salkin
Research Reports from the Department of Operations
A new procedure for finding the general solution of a linear diophantine equation is given. As a byproduct, the algorithm finds the greatest common divisor (gcd) of a set of integers. Related results and discussion concerning existing procedures, are also given.
Using The Blankenship Algorithm To Find The General Solution Of A Linear Diophantine Equation, Susumu Morito, Harvey M. Salkin
Using The Blankenship Algorithm To Find The General Solution Of A Linear Diophantine Equation, Susumu Morito, Harvey M. Salkin
Research Reports from the Department of Operations
This paper shows that the Blankenship algorithm, originally proposed to find the greatest common divisor of several integers and a solution of the associated linear diophantine equation, can be used to find the general solution of the equation. This yields a more efficient method to find the general solution than the one proposed by Bond. The modification of Blankenship's algorithm to avoid generating vectors with huge component values is also proposed.
Optimal Labeling On Trees, Raghavendra N. Rao
Optimal Labeling On Trees, Raghavendra N. Rao
Research Reports from the Department of Operations
Consider the problem of labeling the nodes of a given tree on n nodes with labels 1,2,...,n. Let d(i,i+1) be the number of edges in the path from node labeled i to node labeled i+1, i=1,2,...,n. d(n,n+1) is considered as d(n,1). The sum of d(i,i+1) over i=1,2,.. .,n is the quantity, call it SL' of interest. The minimum of SL is 2(n-1) for any tree on n nodes. This result is established and an efficient algorithm is given to achieve this value. This result is extended to trees having non-negative edge lengths. Since this problem can also be considered as …
The Solution Of Nonlinear Programs Using The Generalized Reduced Gradient Method, Arvind Jain
The Solution Of Nonlinear Programs Using The Generalized Reduced Gradient Method, Arvind Jain
Research Reports from the Department of Operations
The Generalized Reduced Gradient Method for nonlinear programming is discussed with emphasis on a fast, reliable computer implementation of the algorithm. The problems studied relate to basis selection, degeneracy, the acceleration of the solution of nonlinear equations, and the design of a mathematical programming system for sparse large-scale nonlinear programs.
Integer Programming By Group Theory, Susumu Morito
Integer Programming By Group Theory, Susumu Morito
Research Reports from the Department of Operations
This report discusses various aspects of group theoretic algorithms in integer programming. A group theoretic algorithm transforms the original integer program to an optimization problem over an abelian group by relaxing nonnegativity, but not integrality, constraints on the variables corresponding to a linear programming basis. More specifically, columns of constraint coefficients, and the right hand sides in the group problem are elements of an abelian group with D elements, where D is the absolute value of the determinant of the linear programming basis. Several groups may be used to derive the optimization problem and the particular group selected indicates the …
A Difficult Small Integer Program, Harvey M. Salkin, Susumu Morito
A Difficult Small Integer Program, Harvey M. Salkin, Susumu Morito
Research Reports from the Department of Operations
An apparently difficult, yet small, integer program has been tested on what we believe to be is a most efficient computer system containing a group theoretic algorithm. Although a good solution was produced, the code did not converge in at most thirty seconds of UNIVAC 1108 time, and thus the integer program can serve as a principal test problem. The model represents a real world chemical blending situation and was received from E. I. DuPont DeNemours & Co., Inc.
Grg System Documentation, Leon S. Lasdon, Allan D. Waren, Margery W. Ratner, Arvind Jain
Grg System Documentation, Leon S. Lasdon, Allan D. Waren, Margery W. Ratner, Arvind Jain
Research Reports from the Department of Operations
This report was prepared as part of the joint activities of the Computer and Information Science Department, Cleveland State University and the Department of Operations Research, Case Western Reserve University, partially supported under Contract 00014-75-C-0240 with the Office of Naval Research and under National Science Foundation Grant SOC74-23808. Reproduction in whole or in part is permitted for any purpose by the United States Government.
Grg User's Guide, Leon S. Lasdon, Allan D. Waren, Margery W. Ratner, Arvind Jain
Grg User's Guide, Leon S. Lasdon, Allan D. Waren, Margery W. Ratner, Arvind Jain
Research Reports from the Department of Operations
This report was prepared as part of the joint activities of the Computer and Information Science Department, Cleveland State University and the Department of Operations Research, Case Western Reserve University, partially supported under Contract 00014-75-C-0240 with the Office of Naval Research and under National Science Foundation Grant SOC74-23808. Reproduction in whole or in part is permitted for any purpose by the United States Government.
Set Covering Algorithm And Computer Program Usetco User's Manual, Harvey M. Salkin
Set Covering Algorithm And Computer Program Usetco User's Manual, Harvey M. Salkin
Research Reports from the Department of Operations
These pages discuss the code USETCO which contains an algorithm for the set covering problem. (That is, minimize cx, subject to Ex ≥ e, x≥0, and x integer; where E is an m by n matrix of 1's and 0's, and e is an m vector of 1's.) The special problem structure permits a rather efficient, yet simple, solution procedure which is basically a zero-one search of the single branch type coupled with linear programming and a suboptimization technique. The algorithm has been found to be highly effective for a good number of relatively large problems. Problems from 30 to …
Set Covering Algorithm And Computer Program Usetco Programmer's Manual, Harvey M. Salkin
Set Covering Algorithm And Computer Program Usetco Programmer's Manual, Harvey M. Salkin
Research Reports from the Department of Operations
These pages discuss the code USETCO which contains an algorithm for the set covering problem. (That is, minimize cx, subject to Ex ≥ e, x≥0, and x integer; where E is an m by n matrix of 1's and 0's, and e is an m vector of 1's.) The special problem structure permits a rather efficient, yet simple, solution procedure which is basically a zero-one search of the single branch type coupled with linear programming and a suboptimization technique. The algorithm has been found to be highly effective for a good number of relatively large problems. Problems from 30 to …
Some Problems In Location Theory, Marcos J.A.P. Pacca
Some Problems In Location Theory, Marcos J.A.P. Pacca
Research Reports from the Department of Operations
This dissertation deals with four problems in Location Theory, in which all the distances involved are Euclidean distances. The first problem is the Min-max-one-location problem with arbitrary positive weights. An algorithm to solve the problem of minimizing a ratio of a convex quadratic over a positive linear function subject to a convex set bound by linear constraints is given. It is shown that this ratio problem can be solved by parametrically solving quadratic programming problems. Complementary Pivot Theory is used (Cottle and Dantzig [10]). It is shown that Hearn's Fractional Dual [26], which provides the solution to the Min-max-one-location problem …
Scheduling Intermittently Arriving Jobs To Minimize The Weighted Number Tardy, Keki R. Dadachanji
Scheduling Intermittently Arriving Jobs To Minimize The Weighted Number Tardy, Keki R. Dadachanji
Research Reports from the Department of Operations
The problem of scheduling n jobs on one machine to minimize the weighted number tardy is considered, when job arrival times, processing times, due dates and weights are given constants. It is assumed that jobs may be interrupted at any time, and later resumed without penalty. A taxonomy of special cases for this problem is developed. Polynomial-bounded algorithms are given for some of the special cases and some other special cases are shown to belong to the set of NP-complete problems. A branch-bound solution is presented for the case in which all jobs have the same weight. The algorithm is …
Optimal Design Of Networks With Node Weighted Functions, Shailesh J. Mehta
Optimal Design Of Networks With Node Weighted Functions, Shailesh J. Mehta
Research Reports from the Department of Operations
The design of optimal networks on a set of points is an interesting and important problem. However, the majority of work done so far is in flow problems and on graphs with arc weights. In this dissertation, the problem of constructing optimal networks with node weights is considered. The objective function depends on the weights assigned to the nodes and the degree of the nodes. Special cases of the general design problem of constructing networks or graphs with node weights and arc weights are also treated. The intent of the research was to develop polynomially bounded algorithms. The general design …
Economic Lot Size Determination In Multi-Item, Multi-Level Production-Inventory Systems With Acyclic Network Structures, Phiroz P. Darukhanavala
Economic Lot Size Determination In Multi-Item, Multi-Level Production-Inventory Systems With Acyclic Network Structures, Phiroz P. Darukhanavala
Research Reports from the Department of Operations
The research presented here is oriented toward a company organized as a multi-level, production-inventory system, which can be represented by an acyclic network structure. In our model, we consider dependent stochastic demand and incorporate the concept of service level along with the associated costs of carrying safety stocks at different levels of the manufacturing chain. We develop and test an algorithm that specifically derives the dependent demand distributions and then computes optimal order quantities based on a trade-off between setup, holding, and safety stock costs at all levels. The algorithm, which is iterative in nature, can be easily incorporated into …
Corporate Tax Structures And A Special Class Of Set Partitioning Problems, Chien-Hua Lin
Corporate Tax Structures And A Special Class Of Set Partitioning Problems, Chien-Hua Lin
Research Reports from the Department of Operations
This thesis discusses a special integer program, a complete set partitioning problem in context of a real world situation; namely, that of paying unemployment compensation tax. In the United States, employers are required to pay contribution to a state administered unemployment compensation fund to protect the employees in the event of unemployment. A corporation can often be considered as a composition of subsidiaries, each with their own accounting data. In many states including Ohio, these subsidiaries may be treated individually or in various aggregations, each aggregation becoming a subsidiary, prior to computing the contribution payment. The payment is a function …
Optimal Rearrangement Of Objects, Ashok Kumar Mittal
Optimal Rearrangement Of Objects, Ashok Kumar Mittal
Research Reports from the Department of Operations
This dissertation deals with finding an optimal way of changing a given arrangement to a (specified) new arrangement. Two types of problems are considered. In the first type of problem, there is no extra storage space available for storage of the objects. The rearrangement is done by a sequence of pairwise exchanges. In the second type of problem there is extra storage space available for storage. The rearrangement in this case is done by a vehicle which moves one object at a time. Problems are further classified by type of arrangement as basic cycles, cycles--and general arrangement- and by the …
Critical Path Problem Under Assignment Constraints With The Number Of Men Less Than The Number Of Activities, S. Kumar, D. Wagner, R. Chandrasekaran
Critical Path Problem Under Assignment Constraints With The Number Of Men Less Than The Number Of Activities, S. Kumar, D. Wagner, R. Chandrasekaran
Research Reports from the Department of Operations
The paper concerns the problem of determining the shortest time of project completion under the constraint that the number of men available is less than the number of activities to be performed. Additionally, it is assumed that men differ in skills. In order to solve this problem, two related problems are formulated. The first one does not take into account the constraint that a man cannot perform more than one job at a time. The second one is discrete in time and is used to make a solution of the former problem feasible. An iterative procedure for solving the basic …
Some Algorithms For Solving Extreme Point Mathematical Programming Problems, S. Kumar, D. Wagner
Some Algorithms For Solving Extreme Point Mathematical Programming Problems, S. Kumar, D. Wagner
Research Reports from the Department of Operations
The paper concerns some algorithms for solving extreme point mathematical programming problem formulated in [4]. The algorithms discussed consist in determining lower and upper bounds of the objective function and accomplishing the search for the optimal solution. The direction of search depends upon the choice of the starting point. It can be either lower or upper bound. Algorithms making use of the two possible search direction are discussed in detail. In order to illustrate the application of these algorithms, two numerical examples are solved. Some other algorithms based on different approaches are also briefly discussed.
Design And Testing Of A Generalized Reduced Gradient Code For Nonlinear Optimization, Leon S. Lasdon, Allan D. Waren, Arvind Jain, Margery W. Ratner
Design And Testing Of A Generalized Reduced Gradient Code For Nonlinear Optimization, Leon S. Lasdon, Allan D. Waren, Arvind Jain, Margery W. Ratner
Research Reports from the Department of Operations
Generalized Reduced Gradient (GRG) Methods are algorithms for solving nonlinear programs of general structure. An earlier paper [1] discussed the basic principles of GRG and presented the preliminary design of a GRG computer code. This paper describes a modified version of that initial design, including the experiences that led to the modifications. This paper also is intended to serve as partial system documentation. The code is compared computationally with an interior penalty function code, and anticipated future work on the algorithm is outlined.
Integer Programming By Group Theory: Some Computational Results, Harvey M. Salkin, Susumu Morito
Integer Programming By Group Theory: Some Computational Results, Harvey M. Salkin, Susumu Morito
Research Reports from the Department of Operations
A group theoretic algorithm for the integer program has been computer programmed and tested. It basically consists of a linear programming algorithm, a routine which converts the (relaxed) integer program to a group minimization problem (over the fractional column group or the isomorphic factor group attained via Smith's Normal Form), solving the group problem by dynamic programming or by a shortest path algorithm, and when necessary, uses a branch and bound procedure. Details and computational results are given. Future work regarding other computational strategies available to group theoretic algorithms is also included.
Minimal Spanning Trees With Ratio Criterion, R. Chandrasekaran
Minimal Spanning Trees With Ratio Criterion, R. Chandrasekaran
Research Reports from the Department of Operations
The minimal spanning tree problem is well known, and efficient algorithms exist for solving this problem. One of these algorithms has been called a "greedy" algorithm by Edmonds, who has also described the full potential of such an algorithm. In this paper, we consider a slightly modified objective function. We show that the greedy algorithm does not work for this modified problem, even if it is modified in a suitable way. First we provide a characterization for an optimal tree, which is an extension of a condition found in [2] for the minimal spanning tree problem. This gives us an …