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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]

The generalized network problem and the closely related restricted dyadic problem occur frequently in applications of linear programming. Although they are next in order of computational complexity after pure network or distribution problems, the jump in degree of difficulty is such that, in the most general problem, there exist no algorithms comparable in speed to those for pure networks. In this paper we characterize the properties of a special class of generalized network problems that permit a dual feasible basic solution to be determined in one 'pass' through the network. In particular, this class includes the class of pure network problems for which no such procedure has previously existed. Our algorithm also makes it possible to apply LEMKE'S dual method and the poly-ω technique of CHARNES AND COOPER in an efficient manner to solve capacitated (pure) network problems. [ABSTRACT FROM AUTHOR]

This article presents an information related to a new journal "Mathematical Programming." This information is announced by the North-Holland Publishing Co., Journal Division in Amsterdam, the Netherlands. It will appear bi-monthly and its editor-in-chief is to be professor Michel L. Balinski of the City University of New York. This new English language journal will publish papers on every theoretical, computational, and applicational aspect of mathematical programming, that is, everything of direct or indirect use for questions surrounding the problem of finding the extreme values of functions of many variables. This includes along with the conventional topics in linear, nonlinear and integer programming, computer experimentation, technique for formulating and applying mathematical programming models, computer programming devices of special interest to the subject, unconstrained optimization, and control theory done in the spirit of mathematical programming.

An examination of computational results using the simplified primal integer programming algorithm of GLOVER reveals the existence of long sequences of iterations following a specific pattern. This paper examines the structure of these sequences so that both the termination of a sequence and the tableau at that point can be predicted. It then constructs an algorithm that exploits this structure by performing the iterations of the sequence implicitly and presents computational results. [ABSTRACT FROM AUTHOR]

The traveling-salesman problem has been the target of a substantial number of computational algorithms over the last two decades. Reported computational experience with these algorithms varies widely; authors, however, have generally failed to explain this variation adequately, or to offer predictive theories for their approaches. This paper (a) develops an underlying theory for the problem, (b) predicts pathological performance of some existing techniques, and (c) presents two algorithms, based upon the theory, with predictable polynomial growth in expected computation time and resistance to pathological problems. [ABSTRACT FROM AUTHOR]

In this paper we present an algorithm for solving mathematical programming problems of the form: Find x = (x[sub 1], ..., x[sub n]) to minimize Σφ[sub i] (x[sub i]) subject to x ε G and I ≤ x ≤ L. Each φ[sub i] is assumed to be lower semicontinuous, possibly nonconvex, and G is assumed to be closed. The algorithm is of the branch and bound type and solves a sequence of problems in each of which the objective function is convex. These problems correspond to successive partitions of the feasible set. Two different rules for refining the partitions are considered; these load to convergence of the algorithm under different requirements on the problem functions. Examples are given, and computational considerations are discussed. [ABSTRACT FROM AUTHOR]

The optimal coupon schedule for municipal bonds with limits on the number of distinct coupons is formulated in terms of two different dynamic programming models which, in contrast to the companion paper, do guarantee an optimal solution, although at the cost of additional computational difficulty. [ABSTRACT FROM AUTHOR]

The article describes digital computing machines and their role in the society. It notes that digital computing machines store their own instructions, processing from one to the next in order, and performing the necessary manipulations on numbers. The parts of an individual computing machine include input systems, output systems, control/logic system, and memory systems. Each of these parts is described in detail in the article. Information on how these machines should be operated by human beings is provided. Instruct

There is given a finite set I and a family of subsets of I. We consider the problem of determining a minimum cardinality subfamily that is a partition of I. A branch-and-bound algorithm is presented. The bounds are obtained by determining chain decompositions of directed acyclic graphs. The computation time required to determine a bound is bounded by a polynomial in the cardinality of I. Some computational experience is reported and relationships with other methods are discussed. [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]

It is the purpose of the present discussion to point out the different methods of computing the various profits of good-will. The importance of this topic lies chiefly in the fact that in their confusion of good-will concepts both jurists and accountants fail to distinguish the returns of efficiency from those of exploitation. In fact, the legal interpretation of consumers' good-will includes in its scope practically all forms of profit, and is, therefore, in many aspects unsound. This confusion of earned and unearned returns in the profits of good-will may more readily be seen if, for purposes of analysis, the incomes of good-will are classified into two separate groups, depending on whether they appear as present or future gains. Reference to such present profits is frequently made by jurists, but seldom do accountants refer to them except in determining the present cost of good-will or in arriving at a proper basis for estimating its future value. Nevertheless, so long as the legal computation of such present good-will profits fails to separate the gains of hard-earned efficiency from unearned increments of good-will exploitation, it presents to the economist a subject of great interest.

This note is concerned with two target assignment models An optimum assignment is one which maximizes the expected value of targets destroyed The first model, which admits an explicit solution, associates values only with the number of targets destroyed An algorithm which enjoys a computational nicety is established when the values of the individual targets are assumed known This latter model is a special case of Flood's target- assignment model [ABSTRACT FROM AUTHOR]

We consider the problem of selecting an optimal traffic network in its simplest form, where there are no congestion costs. The superadditive effect of deleted links on the objective function is pointed out and used to develop some implicit enumeration procedures for this problem. Some efforts are devoted to evaluate these algorithms, and to show how to stop the computations with an "acceptable" approximate solution when computations are taking too much time. [ABSTRACT FROM AUTHOR]

The loading problem is defined as the allocation of given items with known magnitude to boxes with constrained capacity, so as to minimize the number of boxes required. Two methods of solution are considered: The first is by a zero-one programming model, for which the solution procedure is described; the second is by a heuristic algorithm. Fifty problems were solved by the two methods and in all but two the second method yielded the optimal solution with significantly less computing time than that needed by the first method. [ABSTRACT FROM AUTHOR]

The article discusses the emerging technology of computers in the context of management science. The author differentiates between computers and data processors. Magnetic tapes, such as those used by the IBM Electronic Data Processing Machines, are discussed, as are punch cards. The mathematical formulation of problems through the use of linear equations is discussed, as is the application of computing equipment to solve them. In case where a unique solution is not possible, the article describes the application of maximization. Linear programming and the simplex method are discussed. Simulation is used in cases where neither a unique nor an optimum solution can be obtained directly. This may include train scheduling, bus scheduling, airplane scheduling, and other applications.