Bounds and elimination in generalized markov decisions

In discounted Markov decision processes bounds on the optimal value function can be computed and used to eliminate suboptimal actions. In this paper we extend these procedures to the generalized Markov decision process. In so doing we forfeit the contraction property and must base our analysis on other procedures. Duality theory and the Perron-Frobenius theorem are the main tools.     

Maximal nash subsets for bimatrix games

In this work maximal Nash subsets are studied in order to show that the set of equilibrium points of a bimatrix game is the finite union of all such subsets. In addition, the extreme points of maximal Nash subsets are characterized in terms of square submatrices of the payoff matrices and dimension relations are derived.     

An early-accept modification to the test plans of military standard 781C

This paper is concerned with the statistical test plans contained in Military Standard 781C, “Reliability Design Qualification and Production Acceptance Tests: Exponential Distribution” and the selection and use of these plans. Modifications to the fixed-length test plans of MIL-STD-781C are presented which allow early-accept decisions to be made without sacrificing statistical validity. The proposed plans differ from the probability ratio sequential tests in the Standard in that rejection is permitted only after a fixed number of failures have been observed.     

Efficient multinomial selection in simulation

Consider a simulation experiment consisting of v independent vector replications across k systems, where in any given replication one system is selected as the best performer (i.e., it wins). Each system has an unknown constant probability of winning in any replication and the numbers of wins for the individual systems follow a multinomial distribution. The classical multinomial selection procedure of Bechhofer, Elmaghraby, and Morse (Procedure BEM) prescribes a minimum number of replications, denoted as v*, so that the probability of correctly selecting the true best system (PCS) meets or exceeds a prespecified probability. Assuming that larger is better, Procedure BEM selects as best the system having the largest value of the performance measure in more replications than any other system. We use these same v* replications across k systems to form (v*)^k pseudoreplications that contain one observation from each system, and develop Procedure AVC (All Vector Comparisons) to achieve a higher PCS than with Procedure BEM. For specific small-sample cases and via a large-sample approximation we show that the PCS with Procedure AVC exceeds the PCS with Procedure BEM. We also show that with Procedure AVC we achieve a given PCS with a smaller v than the v* required with Procedure BEM. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 459–482, 1998     

Heuristics for multicomponent joint replacement: Applications to aircraft engine maintenance

This paper considers the maintenance of aircraft engine components where economies exist for joint replacement because (a) the aircraft must be pulled from service for maintenance and (b) repair of some components requires removal and disassembly of the engine. It is well known that the joint replacement problem is difficult to solve exactly, because the optimal solution does not have a simple structured form. Therefore, we formulate three easy-to-implement heuristics and test their performance against a lower bound for various numerical examples. One of our heuristics, the base interval approach, in which replacement cycles for all components are restricted to be multiples of a specified interval, is shown to be robustly accurate. Moreover, this heuristic is consistent with maintenance policies used by commercial airlines in which periodic maintenance checks are made at regular intervals. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 435–458, 1998     

Some properties and computational results for a general repair process

We consider a general repair process where the virtual age V_i after the ith repair is given by V_i = ϕ(V_i−1 + X_i), ϕ(·) is a specified repair functional, and X_i is the time between the (i − 1)th and ith repair. Some monotonicity and dominance properties are derived, and an equilibrium process is considered. A computational method for evaluating the expected number/density of repairs is described together with an approximation method for obtaining some parameters of the equilibrium process. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 391–405, 1998     

Inference for the maximum cell probability under multinomial sampling

This article investigates inference for p_max, the largest cell probability in multinomial trials for the case of a small to moderate number of trials. Emphasis focuses on point and interval estimation. Both frequentist and Bayesian approaches are developed. The results of extensive simulation investigation are included as well as the analysis of a set of crime data for the city of New Orleans taken from the National Crime Survey.     

Distribution of the workload in multiclass queueing systems with server vacations

The steady-state workload at an arbitrary time is considered for several single-server queueing systems with nonpreemptive services for multiple classes of customers (arriving according to Poisson processes) and server vacation (switchover) times. The distribution of the workload at an arbitrary point during the vacation period is obtained for systems with setup times, and for polling systems with exhaustive, gated, or globally gated service disciplines. From the stochastic decomposition property, this workload is added to the workload in the corresponding M/G/1 system without vacations to give the workload at an arbitrary time in vacation systems. Dependence of the workload distribution on the vacation parameters is studied.     

Optimal clustering: A model and method

Classifying items into distinct groupings is fundamental in scientific inquiry. The objective of cluster analysis is to assign n objects to up to K mutually exclusive groups while minimizing some measure of dissimilarity among the items. Few mathematical programming approaches have been applied to these problems. Most clustering methods to date only consider lowering the amount of interaction between each observation and the group mean or median. Clustering used in information systems development to determine groupings of modules requires a model that will account for the total group interaction. We formulate a mixed-integer programming model for optimal clustering based upon scaled distance measures to account for this total group interaction. We discuss an efficient, implicit enumeration algorithm along with some implementation issues, a method for computing tight bounds for each node in the solution tree, and a small example. A computational example problem, taken from the computer-assisted process organization (CAPO) literature, is presented. Detailed computational results indicate that the method is effective for solving this type of cluster analysis problem.     

Parallel machine replacement

We consider the parallel replacement problem in which there are both fixed and variable costs associated with replacing machines. Increasing maintenance costs motivate replacements, and the fixed replacement cost provides incentive for replacing machines of different ages together in “clusters.” We prove two intuitive results for this problem. First, it is never optimal to split a cluster of like-aged machines, and second, it is never optimal to replace newer clusters before older clusters. By incorporating these two results into an algorithmic approach, we vastly reduce the amount of computation required to identify an optimal replacement policy.