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Efficient Methods For Unconstrained Minimization, Leon S. Lasdon Aug 1969

Efficient Methods For Unconstrained Minimization, Leon S. Lasdon

Research Reports from the Department of Operations

It is now well known that the most efficient methods for unconstrained minimization which do not require second derivatives are those which, when applied to a quadratic, generate conjugate directions [1-4]. This insures that a quadratic in n variables is minimized in n steps or less. Since a general twice differentiable function behaves like a positive semidefinite quadratic in the neighborhood of its minimum, methods which will minimize it efficiently must work well on a quadratic. Conjugate direction methods meet this requirement, do not require second derivatives, and can be constructed so that the function is reduced at each step. …


On Determining Significant Factors For Use In Evaluating R & D Projects, Chandrasekhar Das Jul 1969

On Determining Significant Factors For Use In Evaluating R & D Projects, Chandrasekhar Das

Research Reports from the Department of Operations

This report is concerned with selection of factors for the purpose of evaluating Research and Development projects. The approach is statistical. Projects are selected from different Divisions of the Army Materiel Command and ranked according to each of a number of proposed factors. The relative importance of the projects selected from the same Division are known a priori. Correlation coefficients between the a priori and each observed rank-order series are obtained. It is supposed that between two factors, the one having a larger number of significant correlation coefficients is more relevant than the other as a basis for project selection.


A Matrix Approach To R&D Budget Allocation Problems, Samuel Jackson Mathis, Peter Herne, Burton V. Dean Jul 1969

A Matrix Approach To R&D Budget Allocation Problems, Samuel Jackson Mathis, Peter Herne, Burton V. Dean

Research Reports from the Department of Operations

This paper involves an examination of an approach towards the problem of funds allocation in a research environment. The approach uses matrices of projects-sciences and sciences-objectives for which entries are subjectively estimated and compared with weighted objectives. Two examples, using hand calculations and generated data, are given. Conclusions drawn from these examples and possibilities of further applications are discussed.


Probabilistic Programming 1950-1963: An Annotated Bibliography, Robert E. Fricks Jul 1969

Probabilistic Programming 1950-1963: An Annotated Bibliography, Robert E. Fricks

Research Reports from the Department of Operations

This document has been prepared as a part of the author's Doctoral research program in Operations Research at Case Western Reserve University. The motivation for the effort has been purely selfish. Since a comprehensive literature survey in the proposed area of study is a desirable prerequisite to the formulation of a meaningful thesis problem the readings would have been appropriate in any event. Given the volume of writings in the field of interest it is logical that some sort of systematic index be prepared to aid in the retention of the techniques presented by the accumulated literature. This bibliography with …


Applications Of Binary Programming To R&D Project Selection Problems, Arza K. Rao Jun 1969

Applications Of Binary Programming To R&D Project Selection Problems, Arza K. Rao

Research Reports from the Department of Operations

This paper utilizes binary programming formulations of certain R&D project selection problems. This formulation leads to significant computational advantages over the previous formulations. The first problem considered is that of allocating a specified budget among a set of technical approaches, so that the probability of at least one approach being successfully completed is maximized. Secondly, the problem of multi-period allocation is considered, where the objective function is the same as above. Thirdly, a shared project model is also considered, where each project can be allocated different amounts. An algorithm to solve binary programming problems has been developed by Professor Egon …


Computer Time-Saving Applications In Economic Analysis: An Integrated Approach, Martin I. Taft, Arnold Reisman Jun 1969

Computer Time-Saving Applications In Economic Analysis: An Integrated Approach, Martin I. Taft, Arnold Reisman

Research Reports from the Department of Operations

A generalized evaluation program known as EVAL, and a general "present worth" program known as CEBS have been developed in the FORTRAN IV Computer language and are currently operational on a time-sharing or batch basis. The programs lead an individual or a group of people through a systematic step-by-step procedure for evaluating the relative value (utility including present worth) of each of a given set of alternatives with respect to explicitly stated goals and objectives. Applications in such areas as equipment design, selection, optimization and replacement; personnel administration; and allocation of resources are presented.


Analysis Of Usage Of The University Circle Development Foundation Bus System, William J. Brown, James K. Hartman Jun 1969

Analysis Of Usage Of The University Circle Development Foundation Bus System, William J. Brown, James K. Hartman

Research Reports from the Department of Operations

An equitable method of allocating the costs of operating the UCDF shuttle bus system across member institutions is one according to which member institutions would be assessed a fraction of the system's costs equal to the ratio of its riders to total ridership. In order to develop such a method, that is to obtain the individual institution ratios, a passenger survey was conducted by non-UCDF personnel. From this survey, institution ratios were computed for ten institutions judged to be the heaviest users of the system. These ratios, separately calculated for each bus route and weekday, weekend, and whole week service, …


Some Flow Shop Scheduling Problems Involving Sequence Dependent Setup Times, Burton D. Corwin May 1969

Some Flow Shop Scheduling Problems Involving Sequence Dependent Setup Times, Burton D. Corwin

Research Reports from the Department of Operations

This research considers two and three machine static flow shop scheduling problems in which exactly one of the machines is characterized by sequence dependent setup times. Based on both the number of machines involved and the position of this particular machine in the shop, five different problems can be identified. The optimality of permutation schedules for each of these problems is investigated. Then, a dynamic programming algorithm for obtaining an optimal permutation schedule is developed for each problem. The computational requirements of each of these algorithms are discussed. Finally, a branch and bound algorithm for obtaining an optimal permutation schedule …


Towards The Design Of An Industrial R & D Management Information System, Peter Herne May 1969

Towards The Design Of An Industrial R & D Management Information System, Peter Herne

Research Reports from the Department of Operations

This report provides a foundation for designing a management information system (MIS) for industrial research and development (R&D) operations. The study, based on published research and interviews with personnel at various management levels in an R&D center, examines the objectives of corporate R&D activities and associated functions. It identifies the information requirements for each management level and analyzes the flow of information between system elements. The report explores general principles and operational challenges of MIS implementation and evaluates specific issues regarding project progress and value. Recommendations are presented to guide the design and optimization of management information systems for industrial …


Cost-Effectiveness In R And D Organizational Resource Allocation, Burton V. Dean, Lewis A. Roepcke May 1969

Cost-Effectiveness In R And D Organizational Resource Allocation, Burton V. Dean, Lewis A. Roepcke

Research Reports from the Department of Operations

A method for use in allocating resources to a multi-laboratory, multi-task research and exploratory development program is described. The basic elements of the underlying model are the (1) tasks, projects, and laboratories, (2) contributing sciences and technologies (S & T's), (3) criticality of such fields to achieving organizational objectives, (4) relative values of objectives, and (5) costs of performing tasks. Structural models are developed for interrelating tasks, S & T fields, and objectives. A cost-effectiveness model is developed for use in allocating resources to tasks. Research and exploratory development effectiveness is measured in terms of the value of task contribution …


Generalized Geometric Distributions In The Theory Of Queues, Richard V. Evans Apr 1969

Generalized Geometric Distributions In The Theory Of Queues, Richard V. Evans

Research Reports from the Department of Operations

The geometric character of the limiting distribution of the joint distribution of the number of customers in the system and a finite valued supplementary- variable are extended to the case of a continuous valued supplementary variable, As an example the results are used to derive the limiting distribution for M|G|1.


Inventory Control Of Substitute Products, Arvindlal A. Shah Mar 1969

Inventory Control Of Substitute Products, Arvindlal A. Shah

Research Reports from the Department of Operations

Multiproduct periodic review dynamic inventory models with stochastic demands are studied. The case of two products in which one is a substitute for the other is considered in detail. For a given substitution policy, optimal restocking policies are obtained which minimize relevant costs over the envisaged planning horizon. When the planning horizon consists of more than one restocking periods the optimal restocking policies are given for both cases when excess demands are backlogged and when they are lost. Simple conditions on unit costs are obtained which guarantee that the optimal restocking policies are simple. Next a model is considered in …


Defining The Role And Estimation Of The Discount Factor In A Security Valuation Model, Yoshiro Kuratani, Joseph E. Bechtold, Samuel J. Mantel Jr. Mar 1969

Defining The Role And Estimation Of The Discount Factor In A Security Valuation Model, Yoshiro Kuratani, Joseph E. Bechtold, Samuel J. Mantel Jr.

Research Reports from the Department of Operations

There has recently been an increasing amount of interest in security valuation models stemming both from their widening use in portfolio selection methods and from the attempt to integrate investment theory and financial management. In the latter situation, some type of security valuation model is necessary to identify and measure the market response to internal financing and investment decisions. In the literature, many cross-sectional models have shown very poor explanatory capability because the random disturbances have been so large that they have overpowered and obscured whatever systematic forces the model has been attempting to measure. Some authors have endeavored to …


Community Values And Operations Research, Samuel J. Mantel, Jr., Burton V. Dean Mar 1969

Community Values And Operations Research, Samuel J. Mantel, Jr., Burton V. Dean

Research Reports from the Department of Operations

If there is any characteristic that can be singled out as the distinctive phenomenon of our twentieth century it must be the rapid growth in the complexity of organizations and their decision processes. Errors in making decisions can be extremely costly in both human and material resources. Indeed, the long life of many capital investments means that the results of some errors may be, for all intents and purposes, irreversible. Certainly the decision problems involved in urban transportation and land-use planning are among the most difficult and complicated decisions we can make. We face the question, "What will be the …


Prepaid Dental Plan: Final Report, Burton V. Dean, U. Narayan Bhat, Amar J. Singh, Chandrasekhar Das Feb 1969

Prepaid Dental Plan: Final Report, Burton V. Dean, U. Narayan Bhat, Amar J. Singh, Chandrasekhar Das

Research Reports from the Department of Operations

This report presents a methodology for designing a Prepaid Dental Plan. Important factors that characterize the design of a plan are dealt with at length. Quantitative methods have been developed to measure the cost and performance of a plan. A dynamic programming technique to select the optimal plan, which minimizes total unsatisfied needs, for a specified budget level is developed. Numerical examples have been provided to illustrate the use of these methods. Results of a statistical analysis of dental plan data are summarized.


Long-Range Planning & Operations Research, Vaclav Kluson Jan 1969

Long-Range Planning & Operations Research, Vaclav Kluson

Research Reports from the Department of Operations

In the present paper a system of long-range planning devised for planning on the level of an industrial section in Czechoslovakia is described. To facilitate understanding of some special problems solved, a brief survey of the Czechoslovakian economic and managerial reform is presented in Part II. This survey is based on the conditions and thinking during mid 1968, supplemented by some information regarding recent changes. Part III is devoted to the presentation of the planning system concept as shown in the flow chart of Appendix A. This concept can be applied with few modifications to the company or corporation level …


Analysis Of Congestion Problems In Ucdf Operations, James K. Hartman Jan 1969

Analysis Of Congestion Problems In Ucdf Operations, James K. Hartman

Research Reports from the Department of Operations

The study addresses congestion issues within the University Circle Parking System, where the number of users significantly exceeds available parking spaces. This over-assignment has led to user complaints about the inability to find parking during peak hours. The primary goal was to collect and analyze data to reassign parkers from overcrowded lots and develop future over-assignment policies. The research focused on three lot complexes: 29 & 33, 45, 23 & 22, and 20 & 21. Data collection involved identifying who was assigned to park in these lots and who actually parked there during peak hours. This information helped calculate the …


Advanced Materiel Systems Planning Program Translation And Simulation, Burton V. Dean, Andrew J. Leeson Jan 1969

Advanced Materiel Systems Planning Program Translation And Simulation, Burton V. Dean, Andrew J. Leeson

Research Reports from the Department of Operations

Previous studies have indicated the need to develop computer programs for use in simulating R&D systems planning problems. This study is concerned with developing a UNIVAC 1108 program which simulates alternative budgeting and project selection decisions in planning Army Materiel Command R&D programs. Simulations are conducted to test the effects of errors in estimating parameter values on solutions. Risks, costs, and values are required input data for the computer programs. Case Western Reserve University's UNIVAC 1108 was used in this study. This report was prepared as part of the activities of the Department of Operations Research, School of Management, Case …


Allocation For Exploratory Development: Modifications In The Torque Model, Allan L. Service Jan 1969

Allocation For Exploratory Development: Modifications In The Torque Model, Allan L. Service

Research Reports from the Department of Operations

The Project TORQUE (Technology or Research Quantitative Utility Evaluation) methodology is examined in detail. A multi-level mathematical program model of the TORQUE procedure is developed. Two kinds of limitations are identified: one arising from procedural uncertainties and the other from process uncertainties. Various modifications in the formulation of the objective function are proposed to deal with these limitations. Directions for future work are indicated.


On The Least Positive Root Of The Equation Z = K(Z) In Queueing Theory, Izzet Sahin Jan 1969

On The Least Positive Root Of The Equation Z = K(Z) In Queueing Theory, Izzet Sahin

Research Reports from the Department of Operations

In the study of the queue GI/M/1 (with general independent inter-arrivals, exponential service times and a single server) some results of interest are expressed in terms of the least positive root ξ of a functional equation of the form z = K(z). A computational procedure to obtain ξ numerically with any preassigned degree of accuracy for the queues Ek/M/1 (with Erlangian interarrivals) and D/M/1 (with constant interarrivals) is given. Some upper bounds for the root ξ are also obtained.


On The Design Of A Ucdf Management Information System, Fred Preston Jan 1969

On The Design Of A Ucdf Management Information System, Fred Preston

Research Reports from the Department of Operations

This report presents the characteristics and computer programs developed for use by the University Circle Development Foundation (UCDF) in the management of the UCDF parking system. The current system is briefly described and the characteristics of the design of the management information system are specified. Included in the system design are (1) list requirements, (2) permit application forms, (3) information processing characteristics, and (4) file design and construction. Computer programs are described and presented in the Appendix. Operating characteristics including application form processing and tape handling are specified. This management information system has been placed in use by UCDF and …


Transportation Systems For Maternity And Infant Care Project Patients, Amar J. Singh Dec 1968

Transportation Systems For Maternity And Infant Care Project Patients, Amar J. Singh

Research Reports from the Department of Operations

This study examines the operations of the Maternity and Infant Care Project based at Cleveland Metropolitan General Hospital, which experienced lower-than-expected patient utilization during its first two years. Using Operations Research techniques, the study identifies four key areas for improvement: staff size and skills, location of centers and clinics, patient incentives, and patient transportation. A specific focus is placed on transportation, directly tied to addressing patient needs. Three transportation systems were evaluated, including the Mobile Medical Clinic (trailer type), which demonstrated lower operating costs compared to the existing system and an alternative door-to-door service. The Mobile Medical Unit is recommended …


Towards A Research And Development Management Game, Alfred R. Michenzi Dec 1968

Towards A Research And Development Management Game, Alfred R. Michenzi

Research Reports from the Department of Operations

The major emphasis of this report is to outline some general attributes for an R & D management game. The attributes stress realism and interaction of decisions as a good way of making a successful educational experience out of playing the game. Examples of two organizations actively working in R & D management training are included.


On A Computer-Aided Systems Approach To Personnel Administration, Arnold Reisman, Martin I. Taft Dec 1968

On A Computer-Aided Systems Approach To Personnel Administration, Arnold Reisman, Martin I. Taft

Research Reports from the Department of Operations

A systematic evaluation methodology has been developed which integrates some major concepts from value, utility, decision, subjective probability theories and the Delphi method for obtaining a consensus of opinions. These theories are applied to the process of evaluation of personnel for recruitment, promotions, merit raises, transfer, salary administration, training and development. The model requires and utilizes as inputs explicitly stated sets of long-range goals, short-range objectives, resource needs, evaluative criteria, weighting and utility functions, as well as the subjective judgments of appropriate evaluators. The processing of this information may be implemented by manual calculations, batch processing on an IBM 1620 …


Mathematical And Computational Approaches To Some Queueing Processes Arising In Surgery, Augustine O. Esogbue Nov 1968

Mathematical And Computational Approaches To Some Queueing Processes Arising In Surgery, Augustine O. Esogbue

Research Reports from the Department of Operations

Queueing theory has been applied to study congestion problems arising in industrial and economic systems. The method can be profitably used to analyze similar problems in hospital systems. To apply queueing theory to the study and design of allocation processes arising in surgery, we resort to some mathematical artifice. Recursive equations are developed for the generation, via the digital computer, of transition probabilities of a service facility with n service channels. Cases considered include a system with no waiting tolerated (emergencies), a finite waiting line L, and a parallel input stream consisting of both emergencies and scheduled cases. The development …


Use Of Queueing Theory In Studying Research And Development Project Flow, Jon L. Bushnell Oct 1968

Use Of Queueing Theory In Studying Research And Development Project Flow, Jon L. Bushnell

Research Reports from the Department of Operations

This study explores the potential applications of queueing theory to research and development (R&D) operations, drawing parallels between projects in an R&D facility and customers in a traditional queueing system. Projects are accepted, assigned to researchers or queued for future scheduling, and ultimately completed. The research focuses on determining the applicability of established queueing theory techniques rather than developing new methods. To assess feasibility, mathematical models were constructed to represent the system in an idealized manner, requiring identification of key parameters, system characteristics, and performance metrics. The study addresses critical questions, including which queueing models can describe the system, how …


Programming In Markov Processes, Richard V. Evans Oct 1968

Programming In Markov Processes, Richard V. Evans

Research Reports from the Department of Operations

This paper is concerned with optimization problems which arise when one considers the design and control of systems whose basic behavior follows a Markov law. Of crucial importance is the elementary design problem which contrasted with the elementary control problem by examination of their linear programming formulations. Only linear programming formulations seem able to provide significant comparisons at the moment. Unfortunately the linear programming version of the design problem is not appealing from a computational point of view and alternative algorithms are badly needed.


Programming Problems And Changes In The Stable Behavior Of A Class Of Markov Chains, Richard V. Evans Oct 1968

Programming Problems And Changes In The Stable Behavior Of A Class Of Markov Chains, Richard V. Evans

Research Reports from the Department of Operations

This paper develops expressions for the derivatives with respect to a parameter u of the stable probabilities of a class of Markov Chains whose transition matrices are of the form Q + PW. These expressions lead to iterative schemes for calculation which in term suggest gradient algorithms for finding locally optimal chains.


Queueing Systems With First-Order Dependence, U. Narayan Bhat Oct 1968

Queueing Systems With First-Order Dependence, U. Narayan Bhat

Research Reports from the Department of Operations

This paper reviews the historical evolution and current state of queuing theory, tracing its development over six decades. Two periods of peak activity are highlighted: the 1930s, which saw the introduction of foundational analytical methods and queue disciplines for modeling realistic systems, and the 1950s–1960s, marked by the rapid growth of the field and the development of advanced techniques for analyzing finite-time and steady-state systems. Recent years have seen a slowdown in research activity due to the completion of studies on simpler systems and a shift in focus among theoretical and applied scientists. The authors argue that the remaining challenges …


Group Research As An Educational Tool, Burton V. Dean Oct 1968

Group Research As An Educational Tool, Burton V. Dean

Research Reports from the Department of Operations

Educational systems are undergoing rapid changes to meet society's needs for highly educated and creative individuals. College grades, in themselves, are not useful in predicting future success in technical based organizations. Reducing the age of initial contributions of creative individuals would increase total productivity over a lifetime by as much as five percent per year. An analysis of educational and behavioral research studies indicates that group research in educational institutions would reduce competition for grades, on an individual basis, tend to increase the development of creativity, and produce original contributions of a high quality at an early age. A group …