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.     

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.     

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.     

The role of internal storage capacity in fixed cycle production systems

The reliability of a serial production line is optimized with respect to the location of a single buffer. The problem was earlier defined and solved by Soyster and Toof for the special case of an even number of machines all having equal probability of failure. In this paper we generalize the results for any number of machines and remove the restriction of identical machine reliabilities. In addition, an analysis of multibuffer systems is presented with a closed form solution for the reliability when both the number of buffers and their capacity is limited. For the general multibuffer system we present an approach for determining system reliability.     

Analyzing availability using transfer function models and cross spectral analysis

If we look at the literature of reliability and life testing we do not see much on the use of the powerful methods of time series analysis. In this paper we show how the methods of multivariate time series analysis can be used in a novel way to investigate the interrelationships between a series of operating (running) times and a series of maintenance (down) times of a complex system. Specifically, we apply the techniques of cross spectral analysis to help us obtain a Box-Jenkins type transfer function model for the running times and the down times of a nuclear reactor. A knowledge of the interrelationships between the running times and the down times is useful for an evaluation of maintenance policies, for replacement policy decisions, and for evaluating the availability and the readiness of complex systems.     

Optimal admission pricing policies for M/Ek/1 queues

This paper extends the Low-Lippman M/M/1 model to the case of Gamma service times. Specifically, we have a queue in which arrivals are Poisson, service time is Gamma-distributed, and the arrival rate to the system is subject to setting an admission fee p. The arrival rate λ(p) is non-increasing in p. We prove that the optimal admission fee p^* is a non-decreasing function of the customer work load on the server. The proof is for an infinite capacity queue and holds for the infinite horizon continuous time Markov decision process. In the special case of exponential service time, we extend the Low-Lippman model to include a state-dependent service rate and service cost structure (for finite or infinite time horizon and queue capacity). Relatively recent dynamic programming techniques are employed throughout the paper. Due to the large class of functions represented by the Gamma family, the extension is of interest and utility.     

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.     

Statistical analysis of the output data from terminating simulations

In this paper we precisely define the two types of simulations (terminating and steady-state) with regard to analysis of simulation output and discuss some common measures of performance for each type. In addition, we conclude, on the basis of discussions with many simulation practitioners, that both types of simulations are important in practice. This is contrary to the impression one gets from reading the simulation literature, where the steady-state case is almost exclusively considered. Although analyses of terminating simulations are considerably easier than are those of steady-state simulations, they have not received a careful treatment in the literature. We discuss and give empirical results for fixed sample size, relative width, and absolute width procedures that can be used for constructing confidence intervals for measures of performance in the terminating case.     

A note on integer linear fractional programming

This note consists of developing a method for enforcing additional constraints to linear fractional programs and showing its usefulness in solving integer linear fractional programs.     

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.