Bounds on the availability function

This paper gives bounds on the availability function for an alternating renewal process with exponential failure and general repair times. A bound on the error is also given. Several of the bounds with greatest practical consequence are worked out and illustrated. Repair distributions for which a lower bound on availability is easily computed are gamma (integer shape parameter), log normal, and Weibull. Finally, some simulation results for log normal repair versus gamma repair are given.     

Min/max bounds for dynamic network flows

This paper presents an algorithm for determining the upper and lower bounds for arc flows in a maximal dynamic flow solution. The procedure is basically an extended application of the Ford-Fulkerson dynamic flow algorithm which also solves the minimal cost flow problem. A simple example is included. The presence of bounded optimal are flows entertains the notion that one can pick a particular solution which is preferable by secondary criteria.     

Allocation of resources to offensive strategic weapon systems

In this paper a very versatile game model is developed for use in the long range planning of our strategic force posture. This highly aggregate model yields optimal force mixes for the triad (land- and sea-based missile systems and bombers) under a variety of constraints. The model described here is a survivability model; however, it is shown how the model can still be used as a measure of overall system effectiveness. Constraints imposed on the problem include both SALT and budget limitations.     

The bilinear programming problem

The paper deals with bilinear programming problems and develops a finite algorithm using the “piecewise strategy” for large-scale systems. It consists of systematically generating a sequence of expanding polytopes with the global optimum within each polytope being known. The procedure then stops when the final polytope contains the feasible region.     

Stationary (s,s) policies for a finite horizon

In the finite-horizon stochastic (s, S) inventory model with periodic review the parameters of the optimal policy generally vary with the length of the horizon. A stationary policy, however, is easier to implement and may be easier to calculate. This paper studies optimal stationary policies for a finite horizon and relates them to optimal policies through their relation to optimal stationary policies for an infinite horizon.     

Equivalent knapsack-type formulations of bounded integer linear programs: An alternative approach

In this paper we show that every bounded integer linear program can be transformed into an integer program involving one single linear constraint and upper and lower bounds on the variables, such that the solution space of the original problem coincides with that one of the equivalent knapsack-type problem.     

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 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.     

An alternative proof of the IFRA property of some shock models

Let , where A (t)/t is nondecreasing in t, {P(k)^1/k} is nonincreasing. It is known that H(t) = 1 — H (t) is an increasing failure rate on the average (IFRA) distribution. A proof based on the IFRA closure theorem is given. H(t) is the distribution of life for systems undergoing shocks occurring according to a Poisson process where P (k) is the probability that the system survives k shocks. The proof given herein shows there is an underlying connection between such models and monotone systems of independent components that explains the IFRA life distribution occurring in both models.     

On a class of nash-solvable bimatrix games and some related nash subsets

This work is concerned with a particular class of bimatrix games, the set of equilibrium points of which games possess many of the properties of solutions to zero-sum games, including susceptibility to solution by linear programming. Results in a more general setting are also included. Some of the results are believed to constitute interesting potential additions to elementary courses in game theory.