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Full-Text Articles in Business Administration, Management, and Operations
A Numerical Method For Constructing Tables For The Behavior Of Some Infinite Queueing Systems, U. Narayan Bhat, Stuart H. Mann
A Numerical Method For Constructing Tables For The Behavior Of Some Infinite Queueing Systems, U. Narayan Bhat, Stuart H. Mann
Research Reports from the Department of Operations
The need for the construction of tables of transition probabilities in the study of the behavior of queueing systems is discussed and general procedure of the preparation of such tables for the imbedded Markov chain analysis of the systems M/G/1 and G/M/1 is illustrated with the queue M/D/1. Two new measures of utilization and effectiveness are also proposed in the general context.
A Study Of The Queueing Systems M/G/1 And Gi/M/1, U. Narayan Bhat
A Study Of The Queueing Systems M/G/1 And Gi/M/1, U. Narayan Bhat
Research Reports from the Department of Operations
This report examines single-server queueing systems, focusing on M/G/1 (Poisson arrivals with general service times) and GI/M/1 (general independent arrivals with negative exponential service times). Traditional approaches, often relying on transforms to analyze distributions, have been criticized for obscuring key behavioral details. The report explores more recent advancements and research in queueing systems. The author presents a simplified method for studying queueing systems that minimizes the use of transforms while maintaining analytical rigor, making it well-suited for teaching and practical applications. The report extends its applicability to systems with group arrivals and services, using Kendall’s notation to denote queue configurations.
Mathematical Programming With Monotonic Constraint Functions, William P. Pierskalla
Mathematical Programming With Monotonic Constraint Functions, William P. Pierskalla
Research Reports from the Department of Operations
The mathematical programming problem -- find a non-negative n-vector x which maximizes f(x) subject to the constraints g^i(x) ≥ 0, i = 1,...,m -- is investigated where f(x) is assumed to be concave or strictly quasi-concave and the g^i(x) are monotonic increasing functions. It is shown that under certain conditions on g^i(x), the Kuhn-Tucker-Lagrange conditions are necessary and sufficient for the optimality of x*. It is also shown that the g^i(x) are an interesting class of functions since, among other properties, they are closed under non-negative addition, under the addition of any scalar, and under multiplication of non-negative members of …
The Tri-Substitution Method For Obtaining Near-Optimal Solutions To The Three-Dimensional Assignment Problem, William P. Pierskalla
The Tri-Substitution Method For Obtaining Near-Optimal Solutions To The Three-Dimensional Assignment Problem, William P. Pierskalla
Research Reports from the Department of Operations
In a previous paper we presented an algorithm which will find the optimal solution to the multi-index assignment problem. That algorithm was based on branch and bound techniques and the search was performed over the entire tree of feasible solutions. It is not felt that that algorithm will be particularly efficient for certain large multi-dimensional assignment problems. Thus, we now present a method which will achieve a close-to-optimal (if not the optimal) solution in a reasonable amount of time for moderately large three-index assignment problems.
Optimal Allocation Of Shunt Capacitors On A High-Voltage Transmission System, William A. Mccuskey
Optimal Allocation Of Shunt Capacitors On A High-Voltage Transmission System, William A. Mccuskey
Research Reports from the Department of Operations
The basic allocation procedure and the cycling procedure outlined above are tools which hopefully will be useful to the utility in its system planning. More research is necessary to (1) extend the present method to a full- scale optimization and (2) extend and modify the procedures to consider trade- offs in cost of capacitor allocation over time. The ultimate goal would be to develop a procedure which optimally planned both capacitor and generation capacity increases over a number of years. The procedures presented here are a step toward this goal.
Discretionary Priority Processes, Maximilian Etschmaier
Discretionary Priority Processes, Maximilian Etschmaier
Research Reports from the Department of Operations
Single server queuing systems are considered where two populations with different priority indices emanate from infinite sources and request service. The service times are independent random variables drawn from two different distributions. The actual service time requirement is only known upon completion of the service. The discipline followed is such that a low priority customer is preempted upon arrival of a high priority customer only if the elapsed service time is less than z. If the elapsed service time is more than z, the high priority customer waits until the completion of the service. Optimal values of z are obtained …
Sales And Restocking Policies In A Single Item Inventory System, Richard V. Evans
Sales And Restocking Policies In A Single Item Inventory System, Richard V. Evans
Research Reports from the Department of Operations
A single product inventory system with linear costs is considered when customers are of two different types. Penalty costs for lost sales differ for the two types of customers and, therefore, optimal system control requires different shortage probabilities for the two classes. In one case, high penalty customers independently arrive while at the other extreme it is assumed that there is only one such customer. Single critical number policies are optimal in the simple situations. If the priority type customers become active and register displeasure by changing their demand pattern when their demands are not satisfied, simple convexity or Polya …
Optimizing Models Of After Tax Earnings Incorporating Depletion Allowances, Daniel Teichroew, Kevin Rice, Gordon P. Wright, William G. Lesso
Optimizing Models Of After Tax Earnings Incorporating Depletion Allowances, Daniel Teichroew, Kevin Rice, Gordon P. Wright, William G. Lesso
Research Reports from the Department of Operations
Optimization problems in the extractive industries differ from that in other industries in that these industries are permitted to claim a tax allowance for depletion of natural resources. This depletion allowance must be calculated for each mining property separately, based on a relatively complex formula specified in the Internal Revenue Code. The problem of optimizing after-tax earnings for a firm with more than one mine is formulated under the following conditions: constant unit price, linear cost function, no annual change in inventory level and a fixed tax rate. The pre-tax and after-tax earnings functions under these assumptions are piecewise linear. …
Optimal Issuing Policies In Inventory Management -- Ii, William P. Pierskalla
Optimal Issuing Policies In Inventory Management -- Ii, William P. Pierskalla
Research Reports from the Department of Operations
We are concerned with further generalizations of the inventory depletion model where the inventory deteriorates in time as it remains on the shelf. Once put in use, an item from the inventory of n items has a nonnegative field life, L(s), which is a function of the age, s, of the item upon issuance to the field. The objective is to determine the order of issue that maximizes the total field life of the stockpile. Optimal policies of the form LIFO, last in first out, or FIFO, first in first out, are sought. Earlier writers have considered a static model …
A Computational Algorithm For A Class Of Dynamic Programming Problems, B. Miller, Daniel Teichroew
A Computational Algorithm For A Class Of Dynamic Programming Problems, B. Miller, Daniel Teichroew
Research Reports from the Department of Operations
This paper describes an algorithm for finding the optimum value of a decision variable in the standard dynamic programming recurrence equation, when the state is described by one variable and the return function and state transition function are both linear one-to-one functions of the decision variable. The approach has been successfully programmed for a class of dynamic programming problems and has been found to be computationally much faster than searching over a set of possible decision values, even when the Fibonacci search method (the fastest search method available) is used. [Likely published circa 1966.]
Optimal Issuing Policies In Inventory Management -- I, William P. Pierskalla
Optimal Issuing Policies In Inventory Management -- I, William P. Pierskalla
Research Reports from the Department of Operations
We are concerned with generalizations of the inventory depletion model where the inventory deteriorates in time as it remains on the shelf. Earlier authors writing on this subject have placed many restrictive assumptions on the model. The assumption of one demand source withdrawing items from the stockpile is removed and the case of several demand sources is considered. Next, it is assumed that there is a constant penalty cost, p, each time an item is issued. p can be described as an installation or work stoppage cost. Finally, the assumption that the field life, L(S), is a concave or convex …
Mathematical Programming With Joint Stochastic Constraints, Pierre J. Doulliez
Mathematical Programming With Joint Stochastic Constraints, Pierre J. Doulliez
Research Reports from the Department of Operations
In the present thesis, we want to show that a programming problem with joint stochastic constraints can be treated generally and under relatively simple conditions, as a quasi-concave programming problem. In some cases, the same problem may be equivalent to a concave programming problem after a logarithmic transformation. It has been shown by Charnes and Cooper that a stochastic programming problem where each constraint has to be achieved with a given probability, can be put under the form of a deterministic programming problem which is concave under some assumptions [1]. The "joint chance-constraint" formulation presented here is less restrictive and …
A Dynamic Restorative Emergency Procedure For An Electrical Power Network, Benjamin Avi-Itzhak, Burton V. Dean, Maurice W. Sasieni
A Dynamic Restorative Emergency Procedure For An Electrical Power Network, Benjamin Avi-Itzhak, Burton V. Dean, Maurice W. Sasieni
Research Reports from the Department of Operations
The study described in this working paper is a first attempt of its kind to develop a computerized mathematical procedure for controlling an electric power system in emergency situations. An emergency situation arises when there is reason to believe that the system is unable to supply all the power demanded by customers. The C.E.I. system is supported by interconnection tie lines that help overcome power deficiency in almost all conceivable situations. Nevertheless, in cases of a breakdown involving more than one major component of the network, the interconnections might not be able to withstand the additional flows into the C.E.I. …
Stochastic Scheduling - Part Iii Optimization Procedures, Gifford H. Symonds
Stochastic Scheduling - Part Iii Optimization Procedures, Gifford H. Symonds
Research Reports from the Department of Operations
This study explores optimization procedures for scheduling production under deterministic demand. An objective function minimizes production rates and inventory costs, modeled as convex, differentiable functions. The derived optimal schedule balances production and inventory levels, ensuring proportional adjustments across periods. The findings offer a mathematical framework for efficient production planning and inventory management.
A Preliminary Model For The Aircraft Loading Problem, Burton V. Dean
A Preliminary Model For The Aircraft Loading Problem, Burton V. Dean
Research Reports from the Department of Operations
An international airline has the problem of determining the optimal number of first-class and economy class passengers, as well as the optimal fuel and freight loads to be carried. The airline wishes to find the aircraft loading solution that maximizes total profits. Revenue and cost equations are constructed as functions of the passenger, fuel, and freight variables. A total flight profit function is developed. An aircraft loading model is constructed as a maximization of the profit function subject to seating, fuel, weight, and volume constraints. The optimal value of the loading variables may be determined as the solution to a …
Stochastic Scheduling - Part Ii The Location Of Planning Horizons, Gifford H. Symonds
Stochastic Scheduling - Part Ii The Location Of Planning Horizons, Gifford H. Symonds
Research Reports from the Department of Operations
This paper examines optimal stochastic scheduling, a framework that integrates deterministic activity vectors for the initial period and stochastic vectors for future periods to optimize expected outcomes across a sequence of time periods. Each stochastic schedule adapts to state conditions revealed incrementally, ensuring that revised schedules reflect updated data distributions. Adhering to the Optimality Principle, which disregards past operations, and the Planning Horizon Principle, which restricts considerations beyond a defined horizon, the approach ensures sequential optimization within and across planning periods. Key periods, such as the planning horizon, are critical due to their influence on the objective functional and operational …
Scoring And Profitability Models For Evaluating And Selecting Engineering Projects, Burton V. Dean, Meir J. Nishry
Scoring And Profitability Models For Evaluating And Selecting Engineering Projects, Burton V. Dean, Meir J. Nishry
Research Reports from the Department of Operations
Recent developments in allocation theory may be applied to research management decision problems in the firm. Of major importance to firms employing engineers in new product development activities are problems involving the specification and allocation of resources such as manpower, funds, equipment, and facilities. To solve these problems, quantitative measures of organizational performance must be derived that are consistent with corporate goals and that include the relevant resource variables, noncontrollable variables, parameters, and constraints. Mathematical models are constructed and solved in this paper that yield solutions for allocating manpower resources to projects. A scoring model is constructed and then used …
Stochastic Scheduling - Part I Stochastic Programming For A Single Period, Gifford H. Symonds
Stochastic Scheduling - Part I Stochastic Programming For A Single Period, Gifford H. Symonds
Research Reports from the Department of Operations
This study addresses stochastic scheduling, focusing on production and order schedules under uncertain demands. The approach involves periodically revising schedules to incorporate updated demand data, optimizing decision values for the current period and expected values for future periods. A novel method is introduced to transform stochastic scheduling problems into certainty equivalent problems, ensuring that solutions to the latter also optimize the original stochastic problem. The methodology emphasizes determining certainty equivalents of stochastic constraints, identifying critical planning horizons, and developing optimization procedures for inter-horizon schedules. Part I formulates and solves one-period programming problems, selecting stochastic solutions that meet probability constraints, thus …
Scoring And Profitability Models For Evaluation Of Engineering Projects Builder Products Division Emerson Electric Company, Burton V. Dean, Meir J. Nishry
Scoring And Profitability Models For Evaluation Of Engineering Projects Builder Products Division Emerson Electric Company, Burton V. Dean, Meir J. Nishry
Research Reports from the Department of Operations
Recent developments in allocation theory may be applied to research management decision problems in the firm. Of major importance in technical based firms are problems involving the specification and allocation of such technical resources as manpower, funds, equipment, and facilities. Initial steps in the solution of company technical resource allocation problems involve the specification of corporate objectives and their transformation into research objectives and goals. Quantitative research organizational measures of performance must be derived which are consistent with research goals and which include the relevant resource variables, noncontrollable variables, parameters, and constraints. Mathematical models are constructed and solved in this …
Decentralized Management Of Interacting Processes: A Technique Of Nonlinear Programming, Leon S. Lasdon, S. Sankar Sengupta
Decentralized Management Of Interacting Processes: A Technique Of Nonlinear Programming, Leon S. Lasdon, S. Sankar Sengupta
Research Reports from the Department of Operations
The existence and structure of the scheme is considered convergence of the price-adjustment rule used by the central agency is discussed. The result, applicable to intereacting processes, promises on a computational basis, significant advantages. Conceptually, it greatly extends the applicability of some basic economic concepts, and indicates the possibility of a merger of pricing theory and equlilbrium of allocation with modern control theory.
Decentralized Management Of Interacting Processes: A Technique Of Nonlinear Programming (Ii), Leon S. Lasdon, S. Sankar Sengupta
Decentralized Management Of Interacting Processes: A Technique Of Nonlinear Programming (Ii), Leon S. Lasdon, S. Sankar Sengupta
Research Reports from the Department of Operations
In this part certain conditions are established under which an equilibrium point of the algorithm of price-adjustment (P - E) is asymptotically stable in the large. These conditions are phrased as requirements on the functions involved in the original or integrated problem. It is shown that although the usual concavity requirements (for maximization problems) are sufficient to guarantee stability, much less will suffice. Mathematically, this appears as the fact that, for stability, only the sum of certain quadratic forms - one for each sub-problem - must be negative, so that one or more positive terms may be cancelled by others …
The Decomposition Principle In Engineering Problems: Towards A Multi-Level Concept Of Problem Solving, Hamilton A. Chase, S. Sankar Sengupta
The Decomposition Principle In Engineering Problems: Towards A Multi-Level Concept Of Problem Solving, Hamilton A. Chase, S. Sankar Sengupta
Research Reports from the Department of Operations
In a previous report it was shown that a large system of differential equations could be decomposed into smaller groups (called subproblems) such that the solutions of the subproblems converged to the solution of the original system. It was also shown that the decomposition was most effective when the original problem was decomposed along the boundaries of weakest interaction in terms of the Lipschitz constants. This last fact, however, is a desirable but not essential condition. The major purpose of the present report is to develop certain techniques which will facilitate the application of the decomposition principle as stated in …
The Decomposition Principle In Engineering Problems: Towards A Multi-Level Concept Of Problem-Solving, Hamilton A. Chase, S. Sankar Sengupta
The Decomposition Principle In Engineering Problems: Towards A Multi-Level Concept Of Problem-Solving, Hamilton A. Chase, S. Sankar Sengupta
Research Reports from the Department of Operations
The principal result of this report is a demonstration that systems of ordinary differential equations of engineering that are too large for the available computers can be solved by a principle of "decomposition." It is shown that the systems of resulting subproblems are members of a larger class of problems. The properties of this class are investigated and conditions stated under which the solutions of the subproblems converge to those of the original problem. A measure of the interaction between the subproblems is suggested for a subsequent investigation.
Errors, Estimates, Optimality, Shiv K. Gupta, Arthur J. Yaspan, Maurice W. Sasieni, Burton V. Dean
Errors, Estimates, Optimality, Shiv K. Gupta, Arthur J. Yaspan, Maurice W. Sasieni, Burton V. Dean
Research Reports from the Department of Operations
We are frequently faced with having to make decisions in situations where there is uncertainty about the outcome, but where we can exercise some control. In order to do so in a rational manner we must first define a criterion of optimality. Many workers have used the expected outcome when the actual outcome could not be determined in advance; they have then minimized the expected outcome*. Other definitions of optimality are possible and will be discussed here. A typical situation may be represented by a mathematical model E = f(X_i, Y_j) i = 1, 2, ... n, j = 1, …
An Exploratory Study On The Consideration Of Observational Errors In The Design Of Information Collection Procedures, Arthur J. Yaspan, Michael H. Halbert, Russell L. Ackoff
An Exploratory Study On The Consideration Of Observational Errors In The Design Of Information Collection Procedures, Arthur J. Yaspan, Michael H. Halbert, Russell L. Ackoff
Research Reports from the Department of Operations
An information-collection situation is said to arise when a sample is to be taken from some universe, observations are to be made on the elements of the sample, and action is to be undertaken on the basis of these observations with the expectation of return. An information-collection procedure in such a situation is specified by assigning values to the following two quantities: n : the number of elements in the sample, l : the resources expended in making an observation on one element of the sample. An information-collection procedure is considered optimal, in this paper, if the expected return from …