Search techniques for a nonlinear multiprocessor scheduling problem

The problem of assigning computer program modules to functionally similar processors in a distributed computer network is investigated. The modules of a program must be assigned among processors in such a way as to minimize interprocessor communication while taking advantage of affinities of certain modules to particular processors. This problem is formulated as a zero-one quadratic programming problem, but is more conveniently modeled as a directed acyclic search graph. The model is developed and a backward shortest path labeling algorithm is given that produces an assignment of program modules to processors. A non-backtracking branch-and-bound algorithm is described that uses a local neighborhood search at each stage of the search graph.     

A sampling procedure and public policy

This paper describes the background of the Office of Management Budget Circular A-21, “Principles for Determining Costs Applicable to Grants, Contracts, and Other Agreements with Educational Institutions,” that describes the requirement for effort reporting. A sampling procedure is proposed as an alternative to 100% reporting.     

Periodic replacement when minimal repair costs vary with time

A policy of periodic replacement with minimal repair at failure is considered for a complex system. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed at any intervening system failures. The cost of a minimal repair to the system is assumed to be a nonde-creasing function of its age. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the system. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited in the case where the system life distribution is strictly increasing failure rate (IFR).     

A class of continuous nonlinear programming problems with time-delayed constraints

A general class of continuous time nonlinear problems is considered. Necessary and sufficient conditions for the existence of solutions are established and optimal solutions are characterized in terms of a duality theorem. The theory is illustrated by means of an example.     

On the reliability,availability and bayes confidence intervals for multicomponent systems

The problem of computing reliability and availability and their associated confidence limits for multi-component systems has appeared often in the literature. This problem arises where some or all of the component reliabilities and availabilities are statistical estimates (random variables) from test and other data. The problem of computing confidence limits has generally been considered difficult and treated only on a case-by-case basis. This paper deals with Bayes confidence limits on reliability and availability for a more general class of systems than previously considered including, as special cases, series-parallel and standby systems applications. The posterior distributions obtained are exact in theory and their numerical evaluation is limited only by computing resources, data representation and round-off in calculations. This paper collects and generalizes previous results of the authors and others. The methods presented in this paper apply both to reliability and availability analysis. The conceptual development requires only that system reliability or availability be probabilities defined in terms acceptable for a particular application. The emphasis is on Bayes Analysis and the determination of the posterior distribution functions. Having these, the calculation of point estimates and confidence limits is routine. This paper includes several examples of estimating system reliability and confidence limits based on observed component test data. Also included is an example of the numerical procedure for computing Bayes confidence limits for the reliability of a system consisting of N failure independent components connected in series. Both an exact and a new approximate numerical procedure for computing point and interval estimates of reliability are presented. A comparison is made of the results obtained from the two procedures. It is shown that the approximation is entirely sufficient for most reliability engineering analysis.     

The use of dynamic programming methodology for the solution of a class of nonlinear programming problems

This paper presents an application of a method for finding the global solution to a problem in integers with a separable objective function of a very general form. This report shows that there is a relationship between an integer problem with a separable nonlinear objective function and many constraints and a series of nonlinear problems with only a single constraint, each of which can be solved sequentially using dynamic programming. The first solution to any of the individual smaller problems that satisfies the original constraints in addition, will be the optimal solution to the multiply-constrained problem.     

On the equivalence between the Node-ARC and ARC-Chain formulations for the multi-commodity maximal flow problem

The purpose of this article is to formulate the multi-commodity maximal flow problem into a node-arc form and to show that when decomposition is applied to this form the resulting master and subproblems become precisely those described by Ford & Fulkerson [3] using the arc-chain formulation. A generalization to the problem is then considered which can potentially speed its convergence.