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A simple linear model is constructed for production, use and recycling of various paper and related products. This model is used to estimate the maximum feasible recycling rate given the current state of pulp and paper technology. Parametric linear programming is used to investigate the effect of the efficiency of collecting, sorting and transporting waste paper on the fraction recycled. [ABSTRACT FROM AUTHOR]

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.

Many methods have been developed to determine the proper reorder points and order quantities in an inventory system. These methods are based on a wide range of inventory models—from elementary deterministic models to sophisticated probabilistic models with time-varying parameters. This paper deals with two topics related to these calculations which were encountered during the design of an inventory control system for a firm in the heavy goods industry. A mathematical model is developed to describe the average annual variable cost of maintaining the inventory. Based on this model, the paper evaluates the savings obtained by using a simultaneous solution for reorder point and order quantity rather than a simpler separate solution. Then, this model is extended to describe the effect of batch withdrawals as a renewal process. The paper presents an adjustment which can be applied to the original reorder points based on unit withdrawals. Both of these topics are described in the context of a practical application. [ABSTRACT FROM AUTHOR]

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 t0 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]

Joint ordering strategies are of extreme importance in many inventory control situations. This paper considers a situation involving two items having identical characteristics including unit Poisson demand. The joint ordering rule is to order both items up to a level Q each time the level of either of them drops to zero. Expressions for the probability mass function of the remnant stock, the expected value of the remnant stock, the expected time between orders, and the long-run cost per unit time are shown. The joint ordering strategy is compared with the situation where the two items are treated independently. When the cost of placing an order for two items is equal to that for a single item, it turns out that it is never preferable to use the independent strategy. [ABSTRACT FROM AUTHOR]

Gaming and simulation mean different things to different people. Currently there exist separate schools of individuals working on interrelated but basically different areas. Each has its own special goals and terminology. Yet there is a sufficient overlap among them that it is important to clarify the common and different interests and terminology. The general topic of gaming is ripe for an examination to see to what extent there exists a basic methodology and theory of gaming. This paper addresses itself, in part, to this problem. Different types of games and different purposes are discussed. It is stressed that there is not one validation problem but many validation and specification problems which must be addressed if professional standards are to be attained. [ABSTRACT FROM AUTHOR]

This paper explores several important notions relevant to modern utility theory. Restricting the discussion to the consideration of bivariate utility functions, the paper defines and examines the interrelationships between (1) independence in the utility sense, (2) trade-off or indifference curves, and (3) transformation curves (as defined herein). Following the form in which a set of basic axioms of utility are stated, independence is defined in terms of indifference between 50-50 gambles, and it is shown that, if the condition of the definition holds, then φ (x, y), the bivariate utility function, can be written as a function of x plus a function of y. The concepts of trade-off curve (indifference curve) and transformation curve are also defined on the basis of the indifference relation but are not concerned with gambles. After exploring relationships among the three notions it is shown how the utility curves for the two variables under independence can be constructed on the basis of two trade-off curves. [ABSTRACT FROM AUTHOR]

In an earlier paper ("Some Models of Inventory and an Application", Management Science, Vol. 2, No. 4, July, 1956) the author analyzed four inventory systems which were referred to as Models I, II, III, IV. In the present paper the notion of equivalence of inventory systems is introduced and it is shown that Models I and II are equivalent and so are models III and IV. The results are also extended to systems with non-zero leadtime. In all cases considered it is shown that the total expected costs of the systems (with or without leadtime) can be expressed in the form c1 ∫0S (S - r)f(r) dr + c2 ∫ S ∞ (r - S)f(r) dr. [ABSTRACT FROM AUTHOR]

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]

This paper presents a general model to be used in adjusting cash flows which occur over future time intervals to reflect the effects of continuous compounding and/or discounting. The method is illustrated by means of a hypothetical example. The framework of analysis employed here may be extended to other systems having similar characteristics of growth and decay. In the physical and biological sciences, it often happens that the rate of change in the quantity of a substance is proportional to the amount of the substance present at the time. In such cases, the associated system is said to be subject to "exponential growth" or "exponential decay." A classic example of this phenomenon is the continous decomposition of radioactive materials. In this instance, the rate of decomposition at any given time is proportional to the amount of material remaining at that time. Similarly, the reproduction of bacteria is a familiar process which, under certain conditions, involves exponential growth. Exponential models have been used to describe a wide variety of systems in the social sciences and medicine. For example, human populations under certain conditions are subject to exponential growth. Isard [10] cites several studies involving the use of an exponential form to predict changes in city population. This same methodolgy may be extended to analyses involving wildlife and marine population patterns, migration, disease epidemics, and other analogous economic and sociological systems. In this paper, the primary concern is with cash flow systems. It should be noted however, that the model developed here may be extended to other applications. [ABSTRACT FROM AUTHOR]

In this paper a proof of Herbert Scarf's on the optimality of (S,s) policies in inventory theory is extended to cases where differentiability of cost functions may not be available. In addition to an ordering cost composed of a unit cost plus a reorder cost all that is needed in the proof is that the expected holding and shortage cost function be convex. [ABSTRACT FROM AUTHOR]

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]

A simple extension of the Lagrange optimization method is valuable in allocating defense resources among a large number of independent defense locations. This kind of allocation problem is complicated by the fact that the attacker can optimize his attack against whatever defense is chosen. This paper describes an extended or double Lagrange method, which provides strictly optimal allocations for the attacker, but not necessarily for the defender. Nevertheless, by careful use of the method, it is possible to obtain defense allocations that are at least approximately optimum. The major part of the paper provides a technique for verifying results and computing bounds for the error—a technique that is necessary because the uncritical application of the method can occasionally give results that are far from optimum. [ABSTRACT FROM AUTHOR]

A fundamental question m long-range planning for the logistic support of an ocean area is the size and location of bases. The present paper proposes a measure of effectiveness, called the 'logistic effectiveness,' for a given set of bases supporting the region. This is done by a maximizing process. Then the sizes of the bases are varied, subject to a budgetary constraint, and an 'optimal base structure' found. For small numbers of bases, for instance three bases, the calculations may be done by hand. Two numerical examples are presented. The paper is intended as a contribution to theory and not for immediate practical application. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of increasing the efficiency of Monte Carlo calculations. The methods of doing so permit one to reduce the sample size required to produce estimates of a fixed level of accuracy or, alternatively, to increase the accuracy of the estimates for a fixed cost of computation. Few theorems are known with regard to optimal sampling schemes, but several helpful ideas of very general applicability are available for use in designing Monte Carlo sampling schemes. Three of these ideas are discussed and illustrated in simple cases. These ideas are (1) correlation of samples, (2) importance sampling, and (3) statistical estimation. [ABSTRACT FROM AUTHOR]

This paper considers the decision maker whose evaluation and consequent choice of actions is accomplished through the use of the expected utility hypothesis. In cases where the utility function is increasing with upper and lower bounds then the utility function can be characterized by a distribution function, and we can take advantage of the various properties of such functions as well as existing results with respect to such functions. Using these properties and results we can determine the certainty equivalents as a function of the parameters of the distribution function (utility function) and the parameters of the probability distribution on the uncertain payoff. The following cases are considered: (1) Gaussian distribution function and Gaussian probability distribution, (2) Exponential distribution function and exponential distribution and (3) Exponential distribution function and Gaussian probability distribution. [ABSTRACT FROM AUTHOR]

The optimum coupon schedule for serial bonds issued by municipalities has been solved as a knapsack problem, and is widely implemented in bank and nonbank underwriting firms. A large subset of issues carries the additional requirement that limits the number of distinct coupons which the underwriters may assign to the issue. The paper formulates this problem as a dynamic programming model and discusses the computational aspects relating to this formulation by comparing it with a direct 0/1 integer programming model. Some computational experience is also provided. [ABSTRACT FROM AUTHOR]

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]

In this paper, the problem of completing a contract between a buyer and a seller of insurance is presented as a two-person, zero-sum game, and previous results concerning optimal insurance contracts are reviewed from the viewpoint of game theory. While this point of view seems unrealistic, it is seen to lead to theorems which involve contracts actually encountered in the real world. It is shown that an insurance agreement which splits each loss proportionately between the insurer and the insured is optimal from the viewpoint of a risk averting insurance company that seeks to maximize its expected utility when the net insurance premium is fixed. [ABSTRACT FROM AUTHOR]

A cursory survey of the theory of games is presented. The basic models for games in extensive form, normal form, and characteristic function form are discussed, and some generalizations and extensions of these models are mentioned briefly. Some general remarks about the applicability of the theory are made in §2, and a few specific applications are referred to in sections subsequent to the description of the particular models. Mention is made throughout this paper to the other game theoretic articles in this issue in an attempt to place them somewhat within this outline of the subject. [ABSTRACT FROM AUTHOR]

This paper will present a model of equipment replacement in a stochastic environment utilizing a number of the component characteristics of an operations research orientation while being designed to emphasize the role of a stochastic representation of technological change and/or maintenance costs and the implications these have for the decision about replacement of equipment. The "replacement" referred to here is replacement of a machine in its entirety rather than the usual periodic-review-replacement-of-individual-pieces analysis to which the term "replacement" frequently refers in operations research literature. The paper outlines the approaches to equipment replacement in the literature of economics and the well-known Terborgh model and then introduces a stochastic model for studying certain aspects of equipment replacement together with the form of its analytic solution. A comparison of the cost implications of the Terborgh and stochastic model is presented for a specific example utilizing motor vehicle data. In addition, a general analytic comparison of the two replacement rules is provided. [ABSTRACT FROM AUTHOR]

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]

Shuttle cars form a part of the standard equipment employed by the mining industry in the transportation of coal when using the room-and-piller method for extracting coal from underground seams. These cars are subject to frequent failure, so the problem of assigning shuttle cars to sections of the mine is considered in this paper, with the objective of maximizing expected output. A particularly simple solution is found that could be used readily by any mine foreman. [ABSTRACT FROM AUTHOR]

This paper is concerned with characterizing decision rules for the sequential E-model of chance-constrained programming. A key feature of our characterization will be a detailed discussion of various interpretations of the probability operator in the chance constraints. Specifically we define two new classes of decision rules by exhibiting those sets of constraints which locally support the corresponding probability requirements. The question of how the probabilistic constraints for future periods are affected by previous decisions and realizations of the random variables is considered in detail. Since we are primarily concerned with the feasibility of decision rules, we deal mainly with the constraints of the model. The procedure for selecting the optimum rule from among a particular class of feasible rules depends on the objective function and is briefly discussed in the final section along with some implications concerning the form of the optimum rule. The application of our proposed rules to a two-period example previously appearing in the literature concludes the paper. [ABSTRACT FROM AUTHOR]

The paper focuses on multi-stage production systems. If such a system is of the more general type than a production line and many products have to be manufactured according to different technological sequence restrictions then two problems arise: (1) scheduling and (2) sequencing. The formulation of that problem requires the simultaneous consideration of the scheduling and sequencing aspect. The paper integrates these two functions into one single model using zero-one programming. [ABSTRACT FROM AUTHOR]

In conventional reorder policies for inventory control, stocks are allowed to fluctuate between two prescribed limits: a lower limit corresponding to a safety stock to guard against runouts, and an upper limit to which the stock is replenished from time to time. Methods have been suggested for computing optimal upper and lower limits for the ease of stationary demand patterns. The adoption of two rigid limits for controlling inventories for nonstationary demand patterns, which include trends and seasonal fluctuations, is clearly not satisfactory. Published papers in inventory control rarely devote enough attention to the need for a link between forecasting and a reorder policy. A method is suggested in this paper for computing adaptive control limits based on a forecasting procedure that takes account of seasonal fluctuations and trends. The method has been simulated for inventory models with varying parameters. Invariably it has yielded results which were equal to and usually better than those obtained by the optimal "fixed-limits" method. For example, in the case of a normal demand distribution, and a given level of satisfying demand, the reduction in costs resulting from the adaptive control procedure was found to be well over 30%. [ABSTRACT FROM AUTHOR]

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]

This paper develops a linear periodic review inventory model in which the reorder rule is an extension of the "order up to S" or (S, T) policy where S varies as a general linear function of demand and net inventory. Stationary and non-stationary demand processes are considered. Lead time is assumed to be an integral multiple of the review period and, at most, an independent and identically distributed random variable. Analysis of the model includes stability, transient response, steady-state response, and the effects of common nonlinearities. [ABSTRACT FROM AUTHOR]

This paper establishes sufficient conditions for decision rules to be optimal for two n-period P-models of chance-constrained programming. The models considered are the triangular model with total probability constraints and the block triangular model with conditional probability constraints. It is shown that, for both these models, a sufficient condition for optimality is that the decision rule be the optimal piecewise linear rule. Proofs of theorems are based on results contained in earlier papers by the authors, on n-period E-models of chance-constrained programming. [ABSTRACT FROM AUTHOR]

In a previous paper the concept of a multiple (s, S) policy, generalizing the well-known (s, S) policy, was introduced, and it was shown that for a broad class of situations some multiple (s, S) policy would minimize costs when a single decision was to be made whether or not to order goods to add to inventory. In the present paper it is shown that when n such decisions must be made, some multiple (s, S) policy will minimize total (discounted) costs, though under slightly more restrictive conditions. [ABSTRACT FROM AUTHOR]

The paper develops a new theory for the analyses of games with incomplete information where the players are uncertain about some important parameters of the game situation, such as the payoff functions, the strategies available to various players, the information other players have about the game, etc. However, each player has a subjective probability distribution over the alternative possibilities. In most of the paper it is assumed that these probability distributions entertained by the different players are mutually "consistent", in the sense that they can be regarded as conditional probability distributions derived from a certain "basic probability distribution" over the parameters unknown to the various players But later the theory is extended also to cases where the different players' subjective probability distributions fail to satisfy this consistency assumption In cases where the consistency assumption holds, the original game can be replaced by a game where nature first conducts a lottery in accordance with the basic probability distribution, and the outcome of this lottery will decide which particular subgame will be played, i.e., what the actual values of the relevant parameters will be in the game. Yet, each player will receive only partial information about the outcome of the lottery, and about the values of these parameters. However, every player will know the "basic probability distribution" governing the lottery. Thus, technically, the resulting game will be a game with complete information. It is called the Bayes-equivalent of the original game Part I of the paper describes the basic model and discusses various intuitive interpretations for the latter. Part II shows that the Nash equilibrium points of the Bayes-equivalent game yield "Bayesian equilibrium points" for the original game. Finally, Part III considers the main properties of the "basic probability distribution." [ABSTRACT FROM AUTHOR]

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]

An inter-temporal quadratic programming model for selecting portfolios of risky assets is formulated. The model's application to capital budgeting is discussed in considerable detail. This is followed by briefer discussions of its application in other areas. The paper develops a new and more efficient way of using simulation to calculate the variance-covariance elements required as input to Markowitz-type models; this new procedure makes no further demands on the decision maker than do other simulation models that have been suggested. The paper also shows how such models can be made inter-temporal. Finally, the paper analyses the potentials for extending such models to include other theoretical considerations that have been proposed in the literature. [ABSTRACT FROM AUTHOR]

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]

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]

This paper is concerned with formulating, exploring and interpreting the uses and constructs which may be derived from a mathematical model of programming type which expresses more realistically than past efforts the actual conditions of current operations. It is an attempt to provide a means of attaining thereby an objective understanding of the implications of actual Federal Reserve liquidity policy on the actions and opportunities of banking institutions. The model presented corresponds to the problem of determining an optimal portfolio for an individual bank over several time periods in accordance with requirements laid down by bank examiners which are interpreted as defining limits within which the level of risk associated with the return on the portfolio is an acceptable one. The problem is transformed into an equivalent one offering advantages of analysis and of computation. Some methods of effective computation are explored. [ABSTRACT FROM AUTHOR]

This paper reports the results of six experiments and analyses performed to explore the applicability of the non-constant-sum case of the theories of von Neumann-Morgenstern, and others, to the actual behavior of people playing games or involved in bargaining situations. The paper suggests directions in which the theory of games might be modified and extended to improve its applicability and usefulness. A "split-the-difference principle" is suggested to augment the usual theory, so as to specify the exact amount of payments to be made in an ordinary two-person bargaining situation such as the sale of a used car. The application of this principle seems satisfactory in the experiments. One experiment suggests that, in a sequence of trials in the same game situation, people tend to start near an equilibrium point and then try to find a better equilibrium, if there is one. The experiments show examples of non-optimal behavior of the bargainers when the judgment necessary to estimate the relevant payoff is obscure. A fair division of five parcels of objects among five players when each player attaches different values to the parcels is outlined and computed, and the effect of coalitions is discussed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of selecting securities for managing an investment portfolio. The field of investment has a long history of detailed analysis by economists and investment analysts. This has resulted in theories of economic behavior (in terms of the securities markets as integral components in economy-wide analyses) and the evolution of a variety of rules of thumb (guided by more or less well founded prognostications) which are designed to steer the investor through complex considerations of yield and risk. Relatively little has been done, however, in devising adequate techniques, of a general kind, which can be used to determine optimum selections for a portfolio after the data have been analyzed, and after the predictions as well as the risk and yield criteria of the investor have been specified. The purpose of this paper is to analyze and explain, by reference to empirical data, some of the recent work done in this area by Dr. Harry Markowitz under the sponsorship of the Cowles Commission. 2 This article is divided into four parts. Part I contains a heuristic introduction to the basic problem together with a mathematical statement of Markowitz's theory of portfolio selection and its basic assumptions. Part II contains a discussion of some of the problems involved in formulating probability beliefs for available investment opportunities. En Part III, the selection technique is demonstrated by application to a very simplified case, and many of the problems involved in more complex cases are brought out. The final section contains a summarization and critique of the theory, its limitations, and its possibilities as a guide to practical decision-making. [ABSTRACT FROM AUTHOR]

This article presents information related to a paper on Bell Telephone Laboratories. The paper focuses on similar business operations carried out at different locations, such as everyday contact with customers which is carried out in approximately twenty-one hundred different business offices within the Bell System. Formal measurement schemes developed to compare the efficiency of the various business units in an objective way. Several problems arising from the influence of the measurement schemes are discussed, and a model is described which is constructed in such a way that such difficulties are minimized.

The article features the author's comments on the research paper "A New Product Analysis and Decision Model." The author acknowledges the important applications of the paper for sequential decision theory in the field of management science, but expresses concern as to generalizations made in the text. It is suggested that the demand function component of the mathematical analysis discussed in the paper. The author proposes that the functional analysis overlooks some main difficulties associated with the featured decision making variables. The industrial product development process is discussed. A heuristic programming approach is also examined.

Christmas greeting cards are produced in batches, with several designs printed on a sheet simultaneously. The number of cards printed for a design is constrained to be an integer multiple of the number of sheets printed for the set of plates containing the design. The demand for the cards is met by two production runs: a limited number is produced in the first run, primarily as samples for display at the pre-Christmas shows; at the time of initiating the second production run, a more realistic estimate of the demand for each design is available and a significant increase in profits can be obtained by producing the cards economically. This paper presents a simple deterministic model for improving a company's profit in the Christmas-greeting-card trade. [ABSTRACT FROM AUTHOR]

In this paper a periodic review stock system using the so-called (S, s) ordering policy is considered. New and more accurate approximations are found for calculating the optimal values of the reorder point s and the minimum order quantity Δ = S - s. When demands are normally distributed it is shown that the six cost and distribution parameters associated with these approximations can be combined into two effective parameters. This facilitates the derivation of two graphs which can be used with some relatively simple computational procedures to determine approximate optimal values for the reorder point s and minimum order quantity Δ. [ABSTRACT FROM AUTHOR]

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]

The time and cost required for offshore construction operations are often dominated by the influence of weather, particularly wave heights. Historical wave height data can be summarized in a simple probabilistic model that can be used in a Monte Carlo simulation of the construction operations. Such a simulation has been used effectively to evaluate alternative bids on pipeline projects in the Gulf of Mexico. This paper describes the Markovian wave height model we have incorporated in the simulation. [ABSTRACT FROM AUTHOR]

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]

This paper develops regularity conditions for a class of convex programming problems (convex objective functions and linear constraints). The objective functions considered are lower semicontinuous and have bounded level sets. The constraint set may be unbounded. Results pertaining to the solvability, stability and dualizability of such programs are obtained. The results are then applied to a class of nonlinear stochastic programs with recourse. [ABSTRACT FROM AUTHOR]

This paper describes, compares, and contrasts two mathematical models of personnel movement through a hierarchical oration. The first model is a Markov chain, which is described in detail in other literature. The emphasis in this paper is on a cohort model based on people's lifetime behavior in the system. Data from student enrollments is used in comparing the models, and predictions are made and compared with numbers from real situations. [ABSTRACT FROM AUTHOR]

This paper presents a case study on the use of mathematical-computer models in developing operating policies for a university-health-service outpatient clinic. Based on results predicted by the models, actual policy changes were made in the system; the paper compares the subsequent real-world results with those predicted by the models. The comparison demonstrated the validity of the models, and significant improvements were realized in the changed system. An analysis of daily arrival patterns was used to schedule more appointment patients during periods of low walk-in demand in order to smooth the overall daily arrivals. A Monte Carlo simulation model showed the effects of alternative decision rules for scheduling appointment periods during the day to increase patient throughput and physician utilization. [ABSTRACT FROM AUTHOR]

Mathematical models of growing biological populations have existed for many years, but only recently has theoretical and practical research effort been directed to the control and also to the optimal control of these models. Both deterministic and stochastic population models serve as the basis for applying the systems-analysis and control-theory approach of operations research to find optimal, or at least efficient, control strategies for ecological management. Applications of this decision-theory methodology have been made to finding controlling strategies for epidemic and pest populations, harvesting policies for forests, catch and regulation strategies of fisheries and wildlife, treatment strategies of the spread of infection, and even to finding control policies regulating human population. This paper reviews the important contributions to and future challenges in this field and includes a complete bibliography. [ABSTRACT FROM AUTHOR]

This paper presents several fault-testing models. Our system is composed of n components that either work or fail. The systems treated are the k-out-of-n type (k/n). This system works if and only if k or more of its components work, making the series (n/n) and parallel (1/n) systems special cases. Components can be individually tested end tests give perfect information. Each test has a time to complete it and testing procedures are judged by the expected cumulative testing time they require. In the first model, the components are assumed to function or fail independently of each other. A feasible test procedure must determine (as) if the system is working or has failed. This is solved for the series and parallel systems and, under a possibly restrictive hypothesis, for the general k/n system. In another model, the components are assumed to be nominally independent conditioned on the system being failed. Here a feasible test procedure must locate all failed components. This problem is solved for the general k/n system. [ABSTRACT FROM AUTHOR]