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The article presents abstracts of contributed papers submitted for presentation at the Chicago Meeting. The paper "Computer Simulation in a Missile Operational Cycle," by Robert T. Morrison explains a model of a hypothetical weapon system is analyzed by simulation techniques using a digital computer. All the important parameters affecting the model are identified and values selected. Random numbers selected by the computer are used to determine the occurrence of missile and GSE malfunctions according to the failure rates established and also to determine the repair times for the missiles and GSE if malfunctions occur. Another paper "A Measure of Effectiveness for Weapon-System Evaluation," by Robert T. Morrison explains a concept for a measure of effectiveness is developed for evaluating and judging weapon-system design and operation The proposed measure of effectiveness considers the most important factors in any complex system-maximum performance and reliability with minimum cost and time This paper shows how the measure of effectiveness is valuable for system analysis in judging between alternative proposed systems in preliminary design and measuring and evaluating the selected system progress from prototype design through final system operation and maintenance.

Comments on the paper 'A General Method for Nonlinear Programming,' by Anthony V. Fiacco, Nicholas M. Smith and David Blackwell. Application of the principle of entry into a constrained space to Carroll's technique; Computation of the starting point for the original problem.

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.

Presents a letter to the editor about the optimal policy in a maintenance cost problem.

A central question of many previous monetary studies has been the determination of the effects of various forces upon the actual supply of money in the economy. One of a number of competing monetary supply hypotheses (Brunner and Meltzer) has focused on the relationship between bank reserves and deposit creation. This theoretical structure was first suggested in earlier works by Phillips and Crick. Recent studies of similar nature, including those of Mellon and Orr, Morrison, and Brown and Lloyd, have employed the techniques of inventory theory to examine the factors influencing bank credit expansion. Similar inventory treatments of other cash balance and portfolio adjustment models are presented in the works of Baumol, Eppen and Fama, Lloyd, and Chitre. In the present paper, the effects of various forces on the optimal expansion of credit and the holding of reserves are investigated using the techniques of dynamic programming (see, for example, Bellman and Dreyfus). Discussed in the paper are the effects on bank credit expansion of uncertainty about reserve losses, various types of penalty costs, costs of adjustment, uncertain future interest rates, and of various institutional structures under which the bank must operate. This latter topic is important because of the Federal Reserve policy change of September 1968. Prior to that time, required reserves and actual reserves were computed over the same reserve period. Since that time, however, the required reserves in any period are known with certainty at the beginning of the period and depend upon deposit levels two periods earlier. For purposes of mathematical convenience, this latter structure is treated here as a one-period lag. [ABSTRACT FROM AUTHOR]

This article informs about the Operations Research Society of America's "Thirteenth National Meeting" which was held at Boston, Massachusetts from May 15-17, 1958. From a total 521 registrations, there were 301 were members, 186 were non-members, 34 were students. Seventy-one contributed and twelve invited papers were read. For the purpose twelve sessions were held, nine of which were half-day sessions. All-day sessions were held on Dynamic Programming, on Operational Gaming and Simulation and on Techniques of Simulation Using Digital Computers, the latter was the only session on May 17 and was held at the Computation Center of the Massachusetts Institute of Technology. The subjects of some of the individual sessions, and their chairmen, were: George E. Kimball for Dynamic Programming; Philip M. Morse for Forecasting; William Young for Contributed Papers; John M. Magee for Experimentation; Jay W. Forrester for Operations Research in Data Processing and Leon S. Pocinky for Techniques in Simulations Using Digital Computers.

The article presents an analytical model for the derivation and selection of an optimal profit curve for a given firm by utilizing its internal financial data. The underlying model of the Riesz-Kakutani representation theorem is reviewed and used as a basis to select optimal examples from a firm's various possible profit curves.

This paper examines properties and interrelations of several concepts of generalized concavity. It shows that the class of functions that are both ‘generalized concave’ and ‘generalized convex’ is closely related to the class of monotone functions of a single variable. After excluding a certain small class of exceptions, the paper shows that, for arbitrary (perhaps not differentiable) functions, concave implies pseudoconcave, pseudoconcave implies strictly quasiconcave, and strictly quasiconcave implies quasiconcave. Several results characterizing the extreme values of generalized concave functions are given. [ABSTRACT FROM AUTHOR]

This paper considers the case of a product consisting of several components, each of which is batch manufactured. It assumes that the product demands occur singly, and that the components are manufactured in equal-batch quantities in a reorder level-batch quantity system. The paper is concerned with the optimal phasing of the components in order to minimize the variance of holding cost for the product. It shows that the optimal policy is independent of the order of sequencing of the components and is given when the phase lag between consecutive components in the cycle is equal to [(Ai+Aj)/∑all i Ai. (q/2), where Ai, Aj are the unit values of the components, and q is the batch quantity. A specific example is included to illustrate the three-component case and the discrete practical solution for any number of components is indicated. [ABSTRACT FROM AUTHOR]

The past decade has given rise to a considerable amount of research in the fields of inventory control and production planning. One of the most useful mathematical models originated with the paper of K. D. ARROW, T. E. HARRIS, AND J. MARSCHAK, "Optimal Inventory Policy," Econometrica 19, 250-272 (1951). This model was further improved in RICRARD BELLMAN'S book, Dynamic Programming, pp. 152-182, Princeton University Press, Princeton, New Jersey, 1957. In the present paper, another formulation of the same problem is exhibited. The attentive reader will observe many similarities to the dynamic programming formulation. [ABSTRACT FROM AUTHOR]

Although the earliest discussions of linear programming date back to the 1930's, to the work of German and Austrian mathematicians and economists, the mathematics has been extensively developed only in the past six or eight years. Because of the relative newness of the subject, the literature is widely scattered and it is rather difficult for one just starting to learn about linear programming to know where to begin. Because of human limitations, the bibliography is necessarily incomplete. All papers and books that could be acquired that seemed to deal with the subject were perused and, if applicable, included. No extensive effort was made, however, to include papers dealing more or less exclusively with closely related topics, for example, the problem of determination of value and optimal strategies in a zero-sum, two-person game, the pure inequalities problem with no optimization, the subjects of convex functions and convex polyhedra, unless they also relate these topics directly to linear programming.

This paper introduces an efficient branch and bound algorithm for a special class of mixed integer programming problems called the warehouse location problem. A set of branching decision rules is proposed for selecting warehouses to be constrained open and closed from any node of the branch and bound tree. These rules are tested for their efficiency in reducing computation times and storage requirements to reach optimal solutions. An improved method of solving the linear programming problems at the nodes which substantially reduces the computations is also introduced in this paper. [ABSTRACT FROM AUTHOR]

Many manufacturing firms produce component parts both for assembly into new products and to meet orders for spare parts. An inventory model for this situation would involve two types of demands: probabilistic demand as spares and deterministic (or scheduled) withdrawals as components for assembly. Relevant costs would include a setup cost for replenishment orders, inventory carrying costs, and backorder costs. An analytical model approximating these characteristics is formulated. An optimal dynamic program for the periodic review case is briefly discussed; this policy is extremely costly to implement, however. Two feasible operating policies are considered in the paper: a continuous review (Q, r)-type policy and a simple periodic review scheduling heuristic. The paper concludes with sample economic comparisons of the cost of the (Q, r)-type policy and the heuristic policy for a set of numerical examples. [ABSTRACT FROM AUTHOR]

In an earlier paper [5], we generalized and extended Beckmann's results [1] for a production and inventory problem with proportional smoothing costs and demands being random variables. Our previous results concerned the finite horizon nonstationary case. Here we consider the infinite horizon stationary case. Two curves in the plane determine an optimal policy. They are shown to have slopes between minus one and zero, to be differentiable, and to be bounded by two straight lines with a slope Of minus one. These results are used (a) to accelerate each iteration of a successive approximations algorithm and (b) to formulate a linear programming problem from whose solution an optimal policy can be determined. [ABSTRACT FROM AUTHOR]

The paper presents a method for solving the linear programming problems, which is itself a step towards the generalization of the classical Simlex Method. It replaces two basic variables by two non-basic variables at each iteration. Naturally this will reduce the total number of steps to reach the final solution. The paper also includes the solution of one example to illustrate the applicability of the method. [ABSTRACT FROM AUTHOR]

This paper considers non-linear programming models in which randomized solutions are allowed. That is, we consider the minimization of the expected value of a non-linear function subject to constraints on the expectation of nonlinear functions, where the expectations are taken with respect to randomized decision strategies. Saddle-point and related optimality conditions similar to those given in [10] and [11] for convex functions are obtained with only very mild restrictions on the shape of the optimizing and constraint functions. We also consider when the optimal solution need not be randomized and how the notions of Lagrange multipliers and game theory are related to our results. We offer an economic interpretation of our solution. A few simple examples are given to illustrate the implications of randomized strategies. It is also pointed out how the results of this paper are related to the decomposition methods widely used to solve mathematical programming problems. [ABSTRACT FROM AUTHOR]

This article provides a framework for clarifying and testing a version of the "income-smoothing" hypothesis. In general, each version of the hypothesis is concerned with the extent to which managers may attempt to affect the volatility of a series of reported accounting numbers via selections and applications of accounting procedures. Two classes of stochastic processes will be considered with respect to rates of return. These classes are martingales and mean-reverting processes. A characterization of optimal smoothing action for an N-period horizon was derived via dynamic programming tools. This characterization provided access to several propositions regarding optimal smoothing actions under each kind of stochastic process and at various stages within the N-period horizon. These propositions indicate what one should expect if optimal smoothing is pursued by firms' managements. Moreover, they indicate that nonzero smoothing is no: always optimal. The paper only dealt with the effects of optimal smoothing actions on reported accounting numbers.

Presents a letter to the editor about the optimal design of optimization experiments.

A mathematical program with a maximin objective function is defined as an optimization problem of the following type: Maxz=min[sub i] c[sub i]x[sub i], subject to AX = b, X * (This character cannot be converted in ASCII text) O. Although the c[sub i] can be in the interval (-- ∞, ∞), the paper discusses the more common practical case where all c[sub t] * (This character cannot be converted in ASCII text) 0. It shows that problems of this type arise in a variety of applications where it is required to maximize a production function of the 'fixed proportion' type subject to a set of linear constraints. Although it is well known that the solution to this type of problem can be found by linear programming, this paper shows that, if the existence of a certain condition can be demonstrated, then a simplified method can be used to determine the optimum solution. Many problems of practical interest can be solved by this simplified method; an example involving the readiness of a ship is presented. [ABSTRACT FROM AUTHOR]

The model described in this paper was developed to provide guidance for price and promotion decisions in a consumer-goods division doing business in the United States marketplace. Demand is a dynamic function of price and promotion; the total market is divided into M interacting market segments that often have different needs and wants for the product and that can be sent different promotional messages; the segments usually have different price and promotion elasticities. For a given planning horizon, the model determines the optimal price to be charged in the M segments, the optimal promotional budget, and its allocation over the M segments. A convex programming formulation is utilized. The paper discusses the reality of the environment to be modeled, develops the model in relation to this reality, and then provides an empirical illustration of the model. [ABSTRACT FROM AUTHOR]

This paper examines a production system with variable repair-service rates. Considering costs dependent on the service rates and costs due to lost production, it seeks to minimize the long-run expected average cost of the system. The model is a continuous-time Markovian decision problem. The paper states sufficient conditions for eliminating from consideration certain service rates and for the existence of an optimal stationary policy from a 'simple' class. It also gives an example of a nonsimple optimal policy. [ABSTRACT FROM AUTHOR]

This paper deals with systems (such as electronic devices and corporations) that are designed to accomplish multiple goals and whose internal structures are characterized by networks of interacting component parts. Each component of such a system is typically associated with a probability of failure, while each system goal is associated with a reward value. Failure of any network component may ultimately result in the inability to achieve one or more goals and force the forfeiture of the associated rewards. A basic problem in component-system design is to determine how the expectation of total reward may be maximized through the cost-limited acquisition of redundant (backup) components. This paper provides a formal statement of this redundancy-optimization problem and argues that the problem may not be solved easily by standard linear or integer programming techniques. It introduces an algorithm to solve this problem, proves its convergence, and presents computational results taken from a battery of test problems and an algorithm-efficiency study based on these tests. [ABSTRACT FROM AUTHOR]

This paper treats the optimal location of nuclear-power plants in the Pacific Northwest with respect to capital-construction, operating, and transmission costs. It presents a mathematical formulation of this two-product (peak and energy power) plant-location problem, using the simplex method in conjunction with a branch-and-bound process, and indicates a check procedure using Vogel's approximation method in conjunction with an algorithm for solving the transportation problem and a branch-and-bound process. The paper gives results for demand-growth rates of 4, 5, 6 and 7 percent and alternative designs and their costs. It also discusses the stability of the optimal solution. [ABSTRACT FROM AUTHOR]

This paper develops a new cutting plane for primal integer programming. This cut, when it exists and is used as pivot row, has the property that the minimum of the simplex evaluators of the next tableau is strictly larger (by an integer) than the minimum for the current tableau. The paper gives a sufficient condition in the form of a linear program for the existence of such a cut, and proposes an algorithm for generating such cuts. It also presents two additional sufficient conditions. The process of cut generation is then imbedded into a convergent primal algorithm to be used in an attempt to overcome the proof-of-optimality problem experienced with the primal algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal allocation of the marketing budget within the marketing-mix decision variables so that sales (or profit) is maximized in a planning horizon. Since the influence of marketing mix variables upon sales are, in reality, nonlinear and interactive, a geometric programming algorithm is used that solves this problem. A procedure to estimate a functional of sales on the marketing mix and environmental variables utilizing the experienced judgments of the firm's executives and the raw data is provided. The derived functional is later optimized by the Geometric Programming algorithm under a constraint set consisting of budget and strategy restrictions imposed by a firm's marketing environment, and conditions under which the optimal solution is either local or global are identified. An empirical application for a large midwestern brewery is provided which utilizes and illustrates both the estimation an optimization procedures. [ABSTRACT FROM AUTHOR]

A complementary programming problem is a linear programming problem with the additional restriction that xpxq=0 holds for each specified pair (xp, xq). This paper obtains constraints called C-cuts from the restriction xpxq=0, and uses them to facilitate the computation of the branch-and-bound procedure proposed in an earlier paper [Opns. Res. 19, 1523–1528 (1971)]. Some computational results are also reported. [ABSTRACT FROM AUTHOR]

This paper presents an approach, similar to penalty functions, for solving arbitrary mathematical programs. The surrogate mathematical program is a lesser constrained problem that, in some cases, may be solved with dynamic programming. The paper deals with the theoretical development of this surrogate approach. [ABSTRACT FROM AUTHOR]

This paper introduces a generalization of the frequently discussed problem of finding the optimum redundancy that maximizes the reliability of a network of components. Past work has restricted consideration to arrangements of redundant components called series-parallel networks. This paper allows a much broader class of arrangements called series-parallelseries networks. It is important to consider such arrangements for realistic situations in which components have more than one failure mode, or the combination of parallel paths introduces a failure probability. A dynamic programming algorithm is used to solve the more general problem for the case in which there are no constraints on the optimum solution. The algorithm is extended to handle multiple constraints using dominance and a variety of elimination methods to reduce the storage required in a compurer implementation of the algorithm. Problems with as many as 15 serial components and three constraints have been solved with reasonable digital computer computation times. [ABSTRACT FROM AUTHOR]

This paper sets forth mathematical means for optimizing the simultaneous apportionments of reliability and maintainability by means of two techniques Lagrange multipliers and dynamic programming. Since one of the constraint equations revolves allocating both variables, this simultaneous apportionment problem differs from the usual two-dimensional dynamic programming problems. Two cost problems are treated the first minimizes cost while satisfying availability requirements under the assumption that an unlimited ceiling exists for the cost, and the second maximizes reliability and maintainability given a fixed budget. Although these problems appear closely related, step functions usually preclude considering them together The paper also considers two numerical examples, an interesting cost model for maintainability, and using computers with its models. [ABSTRACT FROM AUTHOR]

This paper finds sufficient conditions for the ergodicity and recurrence of irreducible and aperiodic Markov chains. They extend some of the ones commonly used. The paper also indicates their use in discussing a certain class of queuing problem with state dependent service times. [ABSTRACT FROM AUTHOR]

This paper considers the problem of partitioning N entities into M disjoint and nonempty subsets (clusters). Except when both N and N--M are very small, a search for the optimal solution by total enumeration of all clustering alternatives is quite impractical. The paper presents a dynamic programming approach that reduces the amount of redundant transitional calculations implicit in a total enumeration approach. A comparison of the number of calculations required under each approach is presented in Appendix A. Unlike most clustering approaches used in practice, the dynamic programming algorithm will always converge on the best clustering solution. The efficiency of the dynamic programming approach depends upon the rapid-access computer memory available. A numerical example is given in Appendix B. [ABSTRACT FROM AUTHOR]

This paper develops a new algorithm for solving the general nonlinear programming problem that melds the flexible simplex search of NELDER AND MEAD with various additional rules to take care of equality and/or inequality constraints. The set of violated inequalities and equalities is lumped into one inequality constraint loosely satisfied during the early progress of the optimization and more closely satisfied during its final stages. To permit this type of search, the method sets up a special tolerance criterion, a function that does not depend on either the values of the objective function or the values of the constraints. The new algorithm has solved successfully a number of problems that have been proposed in the literature as test problems. Finally, to indicate the algorithm's capabilities, the paper describes an example composed of a linear objective function of twenty-four variables subject to fourteen nonlinear equalities and thirty inequalities. [ABSTRACT FROM AUTHOR]

This is the first of a senes of papers devoted to the computational solution of dynamic programming processes In it we use the functional-equation approach to treat a tactical air-waref are model that A Mengel previously has considered by means of classical variational techniques [ABSTRACT FROM AUTHOR]

In an earlier paper [20] combinatorial programming procedures were presented for solving a class of integer programming problems in which all elements are zero or one. By representing the problem elements in a binary computer as bits in a word and employing logical "and" and "or" operations in the problem-solving process, a number of problems involving several hundred integer variables were solved in a matter of seconds. In the present paper a number of improvements in these earlier algorithms are presented, including a new search strategy, methods for reducing the original problem, and mechanisms for feasibility filtering in multi-word problems. With these improvements problem-solving efficiency has been increased in many instances by an order of magnitude. In addition, the present paper contains computational experience obtained in solving problems for the k-best solutions. [ABSTRACT FROM AUTHOR]

Risk analysts frequently encounter functional relationships concerning costs and revenue which can be expressed as standard algebraic forms. The forms are quadratic, product, or mixed functions of variables which are normally distributed and not necessarily statistically independent. (The ratio functions will hopefully be the subject of a paper that follows this.) Generally, interest focuses on the construction of 2σ or 3σ probability intervals for each form. Since probability distributions of these forms, as far as the risk analyst is concerned, are neither tabled nor easily derived, the desired probability intervals are not easily constructed. This paper shows through analysis, review of previous research, and simulation, that under ordinary conditions the probability distribution of these forms can be approximated by more population distributions (e.g., gamma or normal). The paper suggests rules of thumb that allow one to make probability statements about each form without recourse to costly simulation. An application to a financial planning model for an industrial firm augments the theoretical discussion. [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]

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]

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]

This paper describes a stochastic game in which the play terminates in a finite number of steps with probability 1. The game is called a terminating stochastic game. When the play terminates at any step, the play is regarded to reach to an absorbing state in the Markov chain under consideration. Hence, the terminating stochastic game is a nonstationary Markov chain with rewards in which our concern is the transient behavior before absorption. In particular, when one of the players is a dummy, the stochastic game reduces to a Markovian decision process of special type. This paper discusses such games. We introduce a new concept of rewards and formulate three problems arising in the games by linear programming. Finally, numerical examples are presented. [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]

This paper analyzes the problem of balancing resource capacity utilization against the costs of user delay or inventory investment. Instead of formulating algorithms to solve more classical versions of the problem, this paper describes ways that organizations can drop the cost curve prior to applying an optimizing algorithm. This is done by classifying the techniques and giving examples from organizations which have faced serious smoothing problems. Other organizations can improve their coat performance by adopting some of these techniques. [ABSTRACT FROM AUTHOR]

Queueing Theory has been attacked on two fronts. Some theoreticians say that Queueing Theory is closed. Some practitioners feel that there is very little in it for use. In view of this, it seems that after six decades of development it is time for stock taking. It is hoped that a discussion of the problems, achievements and the shortcomings of Queueing Theory will be helpful for both theorists and practitioners by putting things in proper perspective. This paper reviews some of the major strides taken by Queueing Theory with respect to its three constituent problems: (i) Behavioral, (ii) Statistical, and (iii) Operational. If one looks at the general picture of the developments in these area it is hard not to conclude that, in spite of the practitioners' accusations, the systems studied have become more and more realistic over the years. This review makes an attempt to bring this out. An extensive bibliography which is directive in nature rather than exhaustive should be helpful to an interested researcher or a practitioner in identifying the articles of his interest. A discussion of the future of Queueing Theory concludes the paper. [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]

The non-linear programming problem seeks to maximize a function fix where the n component vector x must satisfy certain constraints ≥(x) = 0, i = 1, ... , m¹ and ≥ (x) 0, i = m¹ + 1, ... , m. The algorithm presented in this paper solves the non-linear programming problem by transforming it into a sequence of unconstrained maximization problems. Essentially, a penalty is imposed whenever x does not satisfy the constraints. Although the algorithm appears most useful in the concave case, the convergence proof holds for non-concave functions as well. The algorithm is especially interesting in the concave case because the programming problem reduces to a single unconstrained maximization problem or, at most, to a finite sequence of unconstrained maximization problems. In addition, the paper presents a new class of dual problems, and the algorithm is shown to be a dual feasible method. Another property of the algorithm is that it appears particularly well suited for large-scale problems with a sizable number of constraints. [ABSTRACT FROM AUTHOR]

The first part of this paper is concerned with the semi-infinite linear programs studied by Charnes, Cooper and Kortanek. A form of the Farkas lemma stated by Haar appears to apply to such programs and leads to a duality theorem. In this paper an example of a semi-infinite program is given which is consistent and which has a finite minimum. However the dual program is found to be inconsistent. With a variation of the example a situation is exhibited in which both the program and its dual are consistent and have finite extrema. In this case, however, the minimum of the former is not equal to the maximum of the latter. The existence of such a ‘duality gap’ indicates that Haar's statement needs qualification. In the second part of the paper a correct form of Haar's theorem is stated and proved. The proof invokes the infinite programming theory of Duffin and Kretschmer. The last part of the paper develops a new duality theory for infinite programs which, as a special case, insures a weak form of duality for programs typified by the examples. This new duality theory is somewhat simpler than previous theories of infinite programming. [ABSTRACT FROM AUTHOR]

When an underwriting syndicate submits a bid for a new issue of municipal bonds, one of the important decisions that it must make involves the scheduling of interest coupons to be placed on the bonds. Given the bid specifications stated by the issuing municipality and some prior decisions of the underwriters, it is shown that the determination of the optimal coupon schedule can be expressed as a linear programming problem. Since this LP problem has a special structure, a simple computational algorithm requiring less computation than the simplex method is derived. This paper goes beyond previous contributions to the literature in three important ways. First, simple formulas for obtaining the dual evaluators are developed; the marginal effect of shifts in the yield curve is also presented. Second, it is shown that in the non-integer year case both the conclusions of previous writers and the conventional heuristics of the market may be erroneous, whereas the general solution techniques developed in this paper remain valid. Finally, a direct analogy between the coupon schedule problem and the microeconomic theory of the firm is used in obtaining the special computational algorithm for this LP problem. [ABSTRACT FROM AUTHOR]

In this paper we consider the dynamic inventory problem in which the demand distribution possesses a density belonging to either the exponential or range family of densities and having an unknown parameter. An a priori density is chosen for the unknown parameter. Using a Bayesian estimation scheme, in- equalities are obtained for the optimal purchase policies as the amount of demand information varies. In addition, asymptotic expansions for the optimal policies are found as the number of observations of the demand becomes large. This paper extends the results of Scarf, [8]. [ABSTRACT FROM AUTHOR]