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The mean-variance (EV) portfolio selection rule has recently been challenged by a new procedure referred to as the Stochastic Dominance Rule (SD), which is touted as being theoretically and empirically superior. However, the SD procedure suffers from at least one technical deficiency not associated with the EV model--the lack of a search algorithm that builds efficient combinations of assets. The purpose of this paper is to evaluate the significance of this problem and to consider procedures for its alleviation. [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 the application of a modified mixed-integer programming algorithm to plan menus in which the portion size of the menu items can vary over a specified positive range. Previous mathematical programming formulations of menu planning problems have either required the variables representing menu items to be bivalent, or have formulated the problem with food groups as decision variables and no integer requirements at all. The former gives rise to a zero-one programming problem and the latter to a "feed-mix" problem. In many instances, a more realistic formulation would require that if a menu item is offered, its portion size must be between a specified upper and lower bound. Although this paper addresses itself chiefly to menu planning, it is readily seen that problems in capital budgeting may be tractable with a similar formulation. It is shown how a branch-and-bound algorithm for mixed-integer programming of the type proposed by Beale and Tomlin can be modified to solve the quasi-integer programming problem resulting from a variable portion size formulation of menu planning problems. [ABSTRACT FROM AUTHOR]

In this paper we discuss the relevancy of the geometric mean as a portfolio selection criteria. A procedure for finding that portfolio with the highest geometric mean when returns on portfolios are lognormally distributed is presented. The development of this algorithm involves a proof that the portfolio with maximum geometric mean lies on the efficient frontier in arithmetic mean variance space. This finding has major implications for the relevancy of much of portfolio and general equilibrium theory. These implications are explored. [ABSTRACT FROM AUTHOR]

This paper proposes a production model for quality surveillance, which is based on a cusum chart using the decision integral criterion. An algorithm for determining the economically optimum control parameters is presented. Some criticisms of the conventional ad hoc design of a cusum chart are made, and it is suggested that the average run lengths (ARL) at the rejectable quality level should be less than 2 when this model is applicable. A simplified version of the algorithm is also devised which 8gives control plans which are close to optimum. This scheme is suitable for application at the factory level. Also included is a table of ARL for some neglected, but useful, values of the decision interval and the process deviate. [ABSTRACT FROM AUTHOR]

Planning horizons are developed for the dynamic economic lot size model with backlogging when the marginal production cost is either constant or variable. The inventory holding and backlogging cost functions are assumed to be concave. An efficient forward algorithm generalizes the Eppen-Gould-Pashigian procedure and enables us to place bounds on the optimal production plan should a horizon not be found. [ABSTRACT FROM AUTHOR]

Decision-making processes usually involve time-consuming and costly operations of observation and communication of the state of the environment and generation and implementation of appropriate actions. Collectively these activities may be called computational and the procedure required to carry them out may be called an algorithm. If the environment is changing stochastically the fixed computational delay involved in operating the algorithm yields obsolete actions resulting in reduced expected return. The loss as a function of delay is a measure of efficiency of the algorithm which depends upon the stochastic properties of the environment. If it is possible to reduce the loss by employing a faster algorithm at a higher cost, the algorithm may be optimally designed and selected from a given family. [ABSTRACT FROM AUTHOR]

Motivated by a planning horizon result for continuous time Markov decision chains, we study decision rules, called preferred, which may be used in the initially stationary part of nearly optimal policies. We characterize these rules and then, under conditions involving state recurrence and accessibility, consider finding such rules. We also discuss the connection between preferred rules and certain discounted process decision rules, and the role of preferred rules in optimal policies. [ABSTRACT FROM AUTHOR]

This note considers a multiple-facility, multiple-product, production-scheduling problem with backordering over a finite planning horizon that consists of discrete production periods during each of which at most one product can be assigned to each facility. Product demands in each period are assumed to be known but not necessarily the same in all periods. The problem objective is to determine an assignment of products to facilities that meets all product demands on a first-come, first-served basis and minimizes the sum of production, inventory, and backordering charges over the horizon. This problem is formulated as a linear, mixed integer program and then transformed into an all-integer program that can be solved using any of the very efficient algorithms for finding minimal-cost network flows. [ABSTRACT FROM AUTHOR]

This paper considers a test score model in which the true score and the measurement error are autocorrelated. After some preliminary remarks on corrections for attenuation, the paper focuses on the three-wave ease (t = 1, 2, 3), demonstrating identifiability, showing an estimation algorithm, and providing a numerical illustration. [ABSTRACT FROM AUTHOR]

This paper describes several algorithms for computing the residual sums of squares for all possible regressions with what appears to be a minimum of arithmetic (less than s x floating-point operations per regression) and shows how two of these algorithms can be combined to form simple leap and bound technique for finding the best subsets without examining all possible subsets. The result is a reduction of several orders of magnitude in the number of operations required to find the best subsets. [ABSTRACT FROM AUTHOR]

This paper extends the current state of public facilities location problems on a road network to cover situations in which the number of users at each node may be a random variable. The basic location model is reformulated as a chance-constrained programming problem with fractile criterion. A computational procedure for solving the non-linear deterministic equivalent problem derived is presented. Finally, a hypothetical numerical example illustrates the possibility of changes in the location decision when the stochastic nature of the problem is taken into account. [ABSTRACT FROM AUTHOR]

Easily manipulated list structures for recording the basis tree for adjacent extreme point (“simplex type”) network algorithms are paramount to the development of computationally efficient network algorithms. This paper presents a new list structure which is shown to be computationally more efficient and to require one-third less computer memory to implement than all alternate list structures. [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]

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]

We consider the problem of portfolio selection for a risk averse investor wishing to allocate his resources among several investment opportunities in order to maximise the expected utility of final wealth. The calculation of the optimal investment proportions generally requires the solution of a stochastic program whose dimension is the number of risky investments. The computations are simplified dramatically when there is a risk free asset and the investment returns are jointly normally distributed, in this ease Tobin has shown that the investment proportions in the risky assets are independent of the utility function and Lintner has shown that these proportions may be obtained from the solution of a fractional program. It is shown under mild hypotheses that the fractional program has a pseudo-concave objective and that the program always has a unique solution. The solution may be sought in several ways, perhaps most efficiently via Lemke's algorithm applied to a linear complementarity problem. The optimal investment proportions in all assets may be found by solving a stochastic program having one random variable and one decision variable via a search technique. Data on the major pooled Canadian equity pension funds were used to provide an empirical test of the suggested solution approach. Five common classes of utility functions were utilized with varying parameter values. For each class there are smooth curves that related the investment in the risk free asset to the parameters of the utility function. The investor is more risk averse when faced with quarterly data. [ABSTRACT FROM AUTHOR]

An original procedure for the determination of the optimum value of tool life criterion of cutting tools tooled with throw-away carbide tips is described in this paper. The procedure has the character of an iterative method, on the basis of which one can reach the optimum value of tool life criterion with respect to attaining the minimum machining cost. The algorithm of the given method is represented in a bar chart, where we can see two calculation cycles, their purpose and other relationships. A practical example closes the paper. [ABSTRACT FROM AUTHOR]

The process of designing the tool layout for a single spindle multi-station automatic chucking lathe has been analysed and formulated as a set of algorithms which enable the process to be performed automatically on a digital computer. A simple, cheap and natural means of communication between the design office and the computer has been designed, and the computer output has been arranged to convey the resulting information clearly by means of layout drawings for each station and of tabulated operating data. The procedures developed should be of great value to machine tool manufacturers, particularly at the quotation stage, and to companies possessing such machines. [ABSTRACT FROM AUTHOR]

The article demonstrates the existence of a well-defined concept for the cost of capital under pure capital rationing. Academic debate concerning the appropriate discount rate to be applied to cost of capital models has flourished since the applicability of mathematical programming to capital budgeting problems was demonstrated by Professor H. Martin Weingartner. The authors present a general proof of a reformulation of the Weingartner model for pure capital rationing. It is argued that the model should be extended to include measures from the external market.

The article proposes to reformulate portfolio theory under the assumption that investment relatives are lognormally distributed. Portfolio theory is shown to be correct under assumptions that returns are normally distributed and the investor's utility function is quadratic. Several reasons for questioning and challenging these assumptions are discussed, such as the unrealistic implications of the utility function. The authors present an algorithm for determining portfolios in an efficient set theorem and discuss the implications for the marginal utility of investors.

The purpose of this paper is to furnish a computational scheme for a class of programming problems with nonlinear constraints. The algorithm is sequential in nature, producing a sequence of feasible solutions whose limit points are optimal solutions of the original problem. Further, with a view to accelerating convergence we suggest two variants of the solution procedure. [ABSTRACT FROM AUTHOR]

This paper considers fluid analogues for the standard linear programming problem and for a separable nonlinear programming problem. In the former case the usual duality results are demonstrated using the principle of minimum potential energy. In addition by examining the dynamics of the system a new method, referred to as the R-method, is derived for solving linear programmes, although it is not demonstrated that this has any computational advantages over the standard simplex method, except that degeneracy causes no problems. In the nonlinear case the weak Lagrangian principle is derived. The purpose of the paper is to demonstrate that analogue methods, while being impracticable as a physical method of solving optimisation problems, may give some insight into computational algorithms via dual energy concepts and/or dynamic behaviour. [ABSTRACT FROM AUTHOR]

The problem of determining continuous flows of minimum cost in a network with convex cost functions is considered. The approach used is that of finding, for any given feasible flow, circuit flows of negative incremental costs. In the main theoretical result of this paper, it is proved that if at each stage, given a feasible nonoptimal flow X, the circuit flow with most negative incremental cost is added to X, linear convergence to the optimal solution will be obtained. In addition, this most negative incremental cost determines an upper bound on the difference in cost between the given feasible solution and the optimal. Based on these concepts, an algorithm, which preserves linear convergence, is presented to determine minimum cost flows in networks with convex costs in the arcs. Results of computer runs made for this algorithm are given. The special case of networks with linear costs is also considered. [ABSTRACT FROM AUTHOR]

The paper presents a response to a comment on the article "Economically Optimum Design of CUSUM charts." The author feels that they are making two specific points; they question his use of the word "optimum" and attempt to point out that other search methods may be more appropriate in certain situations. He feels that while they are correct that some search methods work better in certain circumstances, he thinks his use of the word "optimum" is correct and explained thoroughly. Optimum, in this case, refers to the values of the parameter that yield the minimum cost, which he believes he explains in the abstract.

This paper presents a pseudo-boolean formulation of location problems based on a concept of a ‘dummy’ supply source activated outside a given distribution. First, it formulates a simple location problem as a pseudo-boolean function that can be optimized with existing boolean optimization algorithms. Later the formulation is extended to multidimensional location problems. Two such problems are analyzed: the first involves a distribution system with plants for production of different commodities; the second involves a distribution system with consumer demand and its pattern varying with time. [ABSTRACT FROM AUTHOR]

This note presents a numerical investigation of various techniques reported in the branch-and-bound literature applied to the specific problem of optimal redundancy allocation. It compares two common backtracking strategies, deep and broad search, along with a zero-one versus direct problem formulation. Also reported are some highly successful modifications exploiting the specific problem structure. [ABSTRACT FROM AUTHOR]

The purpose of this note is to propose a simpler feasibility criterion for the disjunctive-graph model proposed by BALAS and implemented by GORENSTEIN in an algorithm for resource-constrained project scheduling. [ABSTRACT FROM AUTHOR]

The theory of equivalent integer programs is generalized so that a set of minimal canonical problems always exists within each equivalence class. An example is used to demonstrate how highly computation time depends on the particular canonical problem chosen to be solved by implicit enumeration algorithms. [ABSTRACT FROM AUTHOR]

A simple algorithm is developed for the problem of assigning days off to full-time staff given a cyclic seven-day demand pattern. The formulation assumes that employees are entitled to two consecutive days off each week and that the objective is to find a minimum staff size capable of meeting the requirements. The algorithm involves only hand calculations, and its computing effort is predictable. [ABSTRACT FROM AUTHOR]

The traffic assignment problem associated with a given transportation network is the process of distributing zone-to-zone trips on links of the network. A number of methods have been proposed to solve this problem, but none have been found to be entirely satisfactory. This paper is concerned with the nonlinear mathematical model of the problem, where the link-traveling costs are increasing functions of the link flows and no explicit capacity constraint is imposed on individual links. An efficient algorithm is developed, using a node-arc formulation of the problem. It is an adaptation of the convex-simplex method that takes advantage of the very special network structure of the traffic assignment problem formulated in this way. Numerical results obtained with a moderate size street network are presented. [ABSTRACT FROM AUTHOR]

The article comments on the paper "Syminv: An Algorithm for the Inversion of a Positive Definite Matrix by the Cholesky Decomposition," by Terry Seaks, published in volume 40 of "Econometrica." In his article Seaks describes an algorithm for the Cholesky decomposition of a positive symmetric matrix, citing J.H. Wilkinson's work. The author explains that the relevant conclusions in Wilkinson's paper are those for floating point calculation and that the numerical advantage of the Cholesky procedure depends on being able to accumulate inner products accurately.

A direct covariance algorithm is presented for handling problems of component tolerance analysis and random input variations with a particular emphasis for utilization in computer-aided statistical electronic circuit design. It is shown that this result is applicable to a wide range of electronic circuit arrays having non-linear components. Moreover, a systematic procedure is developed for predicting in advance the expected accuracy.
Numerical results comparing the direct covariance algorithm with up to 1000 Monte Carlo ensemble-averaged computer runs are provided. Contrary to popular belief, errors of 10 to 25% are obtained by using 25 to 100 Monte Carlo runs. Improvements in both accuracy and computational speed clearly demonstrate that the direct covariance algorithm is a versatile and effective computer-aided design tool. [ABSTRACT FROM AUTHOR]

The problem of whether to bind, microcopy or discard back issues of journals in a university library branch system is considered and an algorithm is developed to solve the journal disposition problem. A cost-effectiveness approach is pursued, employing an analytical model. This model uses a set of weighted factors to quantify the value of a specific journal to the library. Such factors as relevance, usage, availability elsewhere and capital investment are specified. Budget constraints, which involve the relevant costs of binding and microcopying, are considered, as are upper and lower threshold values on the worth of a journal to guarantee the retention of exceptionally good journals and the disposal of very poor ones. An example based on data from a real university special library situation is presented as an illustration of the model. Thus, this paper extends the work of others in modeling of the library collection development decision process. [ABSTRACT FROM AUTHOR]

A clustering algorithm which is tree-like in structure, and is based on user queries, is presented. It is compared to Bonner's Method, Rocchio's Method, Dattola's Method and the Single Link Method in three different aspects, namely system effectiveness, system efficiency and the time required for clustering. Experimental results using the Cranfield 424 collection indicate that the proposed method is superior to the other methods. [ABSTRACT FROM AUTHOR]

This paper defines a hash coding model for non-unique search keys and derives the expected number of accesses needed to retrieve all desired records from a computer storage device. The assumption that the records are stored on the basis of a non-unique key is often realized in information retrieval environments. The model assumes that the hashing algorithm and, should a collision occur, the skipping algorithm, both distribute the records randomly in memory. The results of this analysis are compared with those from a simulation in which the randomness criterion is not strictly met. [ABSTRACT FROM AUTHOR]

This paper deals with planning production of a single good over a prescribed finite interval of time [0, T]. The costs considered within the problem are production and holding costs; holding costs are incurred for negative inventory (caused by backlogged sales) and positive inventory (caused by production in excess of demand). The demand for the product is treated as a stochastic process. Problem formulation and optimization use tools from continuous-time stochastic variational calculus and control theory. Among its results, the paper proves the uniqueness of the optimal solution and provides an algorithm for the problem. [ABSTRACT FROM AUTHOR]

Both the comments by F. Trenery Dolbear and by Talbot Page and John Ferejohn in June,1974, issue of the "Review," reemphasize an important point concerning the achievement of a Pareto optimum via constant per unit taxes. In the author's original paper he intends to bring out two points: to set down a set of sufficient conditions under which the constant per unit taxes or subsidies envisioned in traditional discussions of Pigouvian schemes would correspond to a Pareto optimal outcome for an economy; and to formally introduce "externality technologies" into a model framework. As with any results developed on sufficient conditions, the assumptions about convexity are stronger than necessary to obtain the theoretical results that that the author stated, but they are not irrelevant if one actually contemplates calculation. All algorithms which might be employed in solving a particular applied problem seek a solution by various myopic gropings which are assured of finding a globally optimal solution only under rather stringent convexity conditions.

Examines the multiplication scheme based on variable bitshift for negative binary numbers. Use of the negative binary adder-subtracter; Description of algorithms for basic arithmetic operations in a general negative base; Illustration of the algorithm for the multiplication of two numbers.

A mean-variance portfolio selection model suitable for the small investor is formulated as a sequence of quadratic integer programming problems. The special structure of these quadratic problems is exploited in a partial enumeration algorithm which uses cutting planes to accelerate convergence. Computational experience is reported on problems ranging in size from fifteen to fifty variables. [ABSTRACT FROM AUTHOR]

This paper presents a dynamic programming algorithm for determining optimal production in a series type multi-echelon inventory system with stochastic final product demand. Setup costs at individual facilities are permitted. For the case where it is physically possible (but not required) for a product unit to pass through all the facilities within a single time period, a second dynamic programming algorithm is presented which can be used in conjunction with the first to substantially decrease computation time. The model can also be readily specialized to the case of deterministic demand and permits a larger class of cost functions than existing deterministic multi-echelon models. [ABSTRACT FROM AUTHOR]

The closed convex polyhedron consisting of all 0-1 normal n-person games with nonempty core is characterized by naming its extreme points. This characterization establishes a geometric setting, in the game space itself, for such solution concepts as the core and the nucleolus. This geometric setting also suggests new solution concepts. A similar geometric setting is also established for the Shapley value, and core and nucleolus solution concepts can be defined in this geometric setting. [ABSTRACT FROM AUTHOR]

The article presents a reply to a response by Erlenkotter to the article, "Dynamic Facility Location" regarding the "incomplete dynamic programming" algorithm. The author believes Erlenkotter was correct in his observation that the "incomplete dynamic programming" algorithm in his paper is equivalent to an algorithm used by H. M. Wagner for equipment replacement. The author contends that it is not always equal, especially in cases with rectangular distance location. He also thinks there are potential problems with the equation in circumstances of very large reductions in the number of static problems.

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 note studies the problem of setting price and production levels simultaneously in a series of N periods, where price is a parameter in the probability distribution of demand. It develops a simple policy characterized by two stock levels and an optimal price line in the price-inventory plane, gives an algorithm to compute such a policy and check conditions for its optimality, and presents a counterexample to the simple policy, using a small set of allowable prices, along with a discussion of both the counterexample and some characteristics of the model. [ABSTRACT FROM AUTHOR]

We consider the problem of maximizing the long-run average expected reward per unit time in a queuing-reward system, which we formulate as a semi-Markov decision process. Control of the system is effected by increasing or decreasing the price charged for the facility's service in order to discourage or encourage the arrival of customers. We assume that the arrival process is Poisson with arrival rate a strictly decreasing function of the currently advertized price, and that the service times are independent exponentially distributed random variables. The reward structure consists of customer payments and holding costs (possibly nonlinear). At each transition (customer arrival or service completion), the manager of the facility must choose one of a finite number of prices to advertize until the next transition. We show that there exist optimal stationary policies and that each possesses the monotonicity property: the optimal price to advertize is a nondecreasing function of the number of customers in the system. An efficient computational algorithm is developed that, in a finite number of steps, produces a stationary policy that is optimal. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for the global maximization of a convex function subject to linear inequality constraints. It is computationally finite and is designed to converge rapidly on problems in which there are few local optima or the global optimum is significantly better than most of the other local optima. [ABSTRACT FROM AUTHOR]