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.     

Scheduling to minimize the weighted sum of completion times with secondary criteria

A result of Smith previously published in this journal [3], on the use of secondary criteria in scheduling problems, is shown to be incorrect and a counter example is presented. Heck and Roberts [2] suggested that their paper would be extended in the same way Smith's algorithm was. A new algorithm is given that converges to a local optimum for both problems.     

Armor configurations via dynamic programming

The problem of selecting materials, their thicknesses and order for armor designed for the defeat of shaped charge threats, has been formulated as a constrained optimization problem. The mathematical model provides an optimal order and thickness of each layer of material such that the resulting armor configuration will be of minimum mass per unit area subject to constraints on total thickness and shaped charge jet tip exit velocity.     

Confidence bounds and propagation of uncertainties in system availability and reliability computations

This paper develops bounds on the uncertainties in system availabilities or reliabilities which have been computed from structural (series, parallel, etc.) relations among uncertain subsystem availabilities or reliabilities. It is assumed that the highly available (reliable) subsystems have been tested or simulated to determine their unavailabilities (unreliabilities) to within some small percentages of uncertainty. It is shown that series, parallel and r out of n structures which are nominally highly available will have unavailability uncertainties whose percentages errors are of the same order as the subsystem uncertainties. Thus overall system analysis errors, even for large systems, are of the same order of magnitude as the uncertainties in the component probabilities. Both systematic (bias type) uncertainties and independent random uncertainties are considered.     

Systems analysis and planning-programming-budgeting systems (PPBS) for defense decision making

Systems analysis office titles have permeated both government and business organization charts in recent years. Systems analysis as a discipline, however, even though increasingly accepted, has eluded precise definition. For the most part, it has been loosely described as “quantitative common sense” and “the general application of the scientific method.” Emphasis is placed upon the application of eclectic disciplines to a wide variety of problems. Concepts and techniques have been drawn heavily from economics, mathematics, and political science. In the Department of Defense, systems analysis has been used extensively in the evaluation of weapon systems during the last 9 years. During the 1960's, it provided the underlying concepts for the control system PPBS (Planning-Programming-Budgeting System). This article traces the origins of systems analysis within the Department of Defense and describes and analyzes the application of the technique. Although there always exists disagreement, it is generally accepted that the origin of systems analysis coincided with the inception of R. S. McNamara's administration of the Department of Defense. McNamara organized the Systems Analysis office under Mr. Charles Hitch, who had previously developed many basic systems analysis concepts at project RAND. From Hitch's basic concepts, the approach became increasingly sophisticated in evaluating complex weapons systems. Coincidently, the organizational procedures for implementing systems analysis also evolved. Under the current Department of Defense administration, the new organizational procedures emerging are contrasted with the old.     

Optimal replacement of parts having observable correlated stages of deterioration

A single component system is assumed to progress through a finite number of increasingly bad levels of deterioration. The system with level i (0 ≤ i ≤ n) starts in state 0 when new, and is definitely replaced upon reaching the worthless state n. It is assumed that the transition times are directly monitored and the admissible class of strategies allows substitution of a new component only at such transition times. The durations in various deterioration levels are dependent random variables with exponential marginal distributions and a particularly convenient joint distribution. Strategies are chosen to maximize the average rewards per unit time. For some reward functions (with the reward rate depending on the state and the duration in this state) the knowledge of previous state duration provides useful information about the rate of deterioration.     

Optimality conditions for convex semi-infinite programming problems

This paper gives characterization of optimal Solutions for convex semiinfinite programming problems. These characterizations are free of a constraint qualification assumption. Thus they overcome the deficiencies of the semiinfinite versions of the Fritz John and the Kuhn-Tucker theories, which give only necessary or sufficient conditions for optimality, but not both.     

Computational results for a stopping rule problem on averages

Suppose x₁, x₂, … are independently distributed random variables with Pr (x_i = 1) = Pr(x_i = ?1) = 1/2, and let s_n =