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It is shown how Lawler's procedure for the one-machine case can be combined with Johnson's rule to produce a branch-and-bound algorithm for the two-machine version. [ABSTRACT FROM AUTHOR]

Reliability studies give rise to families of distribution functions F[sup (n)] defined recursively by the repeated convolution of a distribution function F with itself according to the scheme F[sup (1)](t) = F(t), F[sup (n+1)](t) = ∫[sup t, sub 0]F[sup (n)](1-x)F'(x)dx, n>1, where F' is the derivative of F, and is usually given by a p.d,f, ∫. In particular, many systems characteristics are defined in terms of integrals of the form ∫[sup 1, sub 0]P[sup (s)](t- x)Q[sup (r)]'(x)dx where P[sup (s)] and Q[sup (r)] are the sth and rth members of families generated from distribution functions P and Q, not necessarily distinct. It is seldom possible or convenient to express the F[sup (n)] in analytical form. An algorithm based on cubic spline interpolation is given here for recursively generating continuous numerical approximations to the F[sup (n)] in a form which allows them to be convoluted together to provide useful approximation to the second of the above integrals. [ABSTRACT FROM AUTHOR]

Experiments conducted on a database testbed at Princeton indicate excessive page-table I/O is the major performance drawback of shadow recovery. In light of this, we propose a method for parametrizing shadow recovery that minimizes page-table I/O without sacrificing too much disk utilization. Using a simple model, we analyze and evaluate our mechanism, comparing it to two conventional ones. [ABSTRACT FROM AUTHOR]

Series function expansion algorithms of the time-domain analysis of boundary value problems are discussed. Electromagnetic fields inside a structure under investigation are expanded into series of basis functions and the expansion coefficients are found by means of the Galerkin method. The numerical cost of algorithms is discussed and a cost efficient approach is proposed for formulations using sine and cosine expansion functions. Compared with conventional time-domain methods the algorithms described show the time evolution of the expansion coefficients rather than the samples of a physical continuum at discrete nodes. [ABSTRACT FROM AUTHOR]

A novel procedure for the numerical modelling of current transport in semiconductor devices is presented. The method is based on high-order trigonometric expansions (Fourier series) of the solution. The expansion coefficients are calculated in a Galerkin-type algorithm. The method offers infinite-order accuracy regardless of the number of spatial dimensions of the model. Well-conditioning and diagonal dominance of the discrete equations render the numerical procedure stable and effective. Significant advantages are expected, particularly for the solution of strongly non-linear multidimensional device models. Properties of the algorithm are demonstrated on standard semiconductor devices. [ABSTRACT FROM AUTHOR]

One of the methods of solving the minimal cost flow problem is to find cycles of negative length in a marginal cost network. These negative cycles indicate a change in the flows around the cycle, which will result in a reduction in the total cost. The proposed method finds negative cycles by attempting to find the shortest chains from a fixed node to all other nodes. Results of computational experiments comparing this algorithm with the out-of-kilter algorithm are presented. These results indicate that the proposed method of repetitively detecting negative cycles yields an efficient minimal cost flow algorithm. [ABSTRACT FROM AUTHOR]

The usefulness of group theoretic methods in solving integer programming (IP) problems is extended by procedures for controlling the size of the groups. The main procedure given shows how an optimal linear programming basis can be altered to reduce the magnitude of its determinant thereby reducing the size of the group induced by the basis. An adaption of Benders' mixed IP algorithm is given which uses these methods. Some limited computational experience is given. [ABSTRACT FROM AUTHOR]

A method is developed for obtaining a solution to the quadratic programming problem with an indefinite quadratic objective function. A search procedure using gradient projection is the core of the method. However at each step an alternate direction to gradient projection is proposed and two methods are given to continue after the revised gradient projection procedure terminates. Although convergence to the solution is not guaranteed, good results were obtained for fifty-seven problems used to test the method. [ABSTRACT FROM AUTHOR]

An algorithm, computationally feasible for large problems, has been formulated for sequencing n jobs through a single facility to minimize the number of late jobs. This algorithm is then extended to solve the problem in which each job is associated with a continuous, monotone non-decreasing deferral cost function. The object is to produce a schedule where the maximum deferral cost incurred is minimal. [ABSTRACT FROM AUTHOR]

The article focuses on the problem concerning the accuracy and dynamics of the adaptation algorithm class for the adaptive systems with a reference model (ASRM). It mentions that the algorithm examines the beneficial properties and possibilities of the systems with variable structure (SVS) and ASRM construction principles. It examines the control system which is identified through a particular vector in the equation for the algorithm. Moreover, it highlights the possible solution for the adaptation algorithm which employed notations, mathematical expression and block matrices.

An efficient algorithm for solving linear goal programming problems using partitioning and elimination procedures is presented. The algorithm takes advantage of the definition of ordinal preemptive factors in the objective function inherent in most goal programming formulations. Preliminary results indicate that the partitioning algorithm is superior to the existing methods for solving goal programming problems. [ABSTRACT FROM AUTHOR]

The article presents the authors' reply to a response to their paper "The Loading Problem," by B. Lev. Lev's response focused on suggesting adjustments to the authors' method of solving a multi-dimensional programming problem, which relates to the economic theory of production. Lev's recommended solution involves a heuristic algorithm that allegedly requires fewer computations than the algorithm proposed by Eilon and Christofides. The authors suggest that the algorithm offered by Lev neglects to take into consideration relevant elements that are related to a problem of industrial capacity and time management. Mathematical models depicting the allocation of industrial resources, such as boxes used for the shipment of goods, are also presented. The authors further discuss the modifications recommended by Lev.

The article comments on an article on "A Note on 'The Formulation of the M-salesman Traveling Salesman Problem.'" The author admits that note correctly points out an error in the formulation, but points out that the error is of no consequence with regard to the results of the paper. According to the author, the incorrect equation was only used to illustrate that the number of implicitly imposed constraints in the multiple salesman problem is proportionally less than the number of implicitly imposed constraints in a one salesman problem of the same dimension. It is noted that the branch and bound algorithm explicitly solves sequences of pure assignment problems.

The article reports on the development of an algorithm for the 0-1 knapsack problem. The authors comment on a study, conducted by Robert M. Nauss, that focuses on an efficient reduction algorithm that can be implemented to solve the knapsack problem. Two heuristic methods are proposed for the resolution of the problem. The authors also examine a branch and bound algorithm and a relaxation algorithm in relation to problem. They request the computation times for each of the mathematical models that are discussed in the study.

This article presents information about a study which is focused on an algorithm for the maximization of Lagrangians through the column generating approach to concave programming. The author suggests the implementation of a dual cutting-plane nonlinear programming algorithm that requires approximate rather than finite maximization. A modified generating approach that can be used to solve concave programming problems is presented. The mathematical model is discussed in detail. The inner product is denoted by juxtaposition. The conditions necessary to prove the nonlinear duality theory are also examined. It is suggested that the nonlinear duality theory can be proved under alternative conditions. The author lists and discusses the aforementioned conditions and provides further information about the theory.

The interacting multiple model (IMM) algorithm has been used in many applications. However, performance analysis of the IMM algorithm is difficult because it uses a set of Kalman filters that are coupled with each other. We present an algorithm to compute the means and cross-covariances of the residuals and state estimation errors of these Kalman filters. Specifically, we derive the cross-covariances, each of which is the covariance of the residuals of two Kalman filters, to account for the mutual interactions. From the means and cross-covariance terms, we then compute the means of the likelihood functions and the mean-squared estimation errors as performance measures of the IMM algorithm. [ABSTRACT FROM PUBLISHER]