Assessment of hazardous-inspection policies

Inspection procedures may at times pose a hazard to the system being monitored. In this article, a simple hazardous-inspection model is considered. The character of the optimal ongoing inspection policy (for inspections subsequent to the first) is reviewed, and the possible forms of the optimal initiation policy are established. Efficient computational procedures are developed for calculating optimal policies. Some discussion is included of the counterintuitive nature of some of the results.     

A markov chain version of the secretary problem

This paper deals with the Secretary Problem where n secretaries are interviewed sequentially and the best k must be hired. The values of the secretaries are observed as they are interviewed, but beforehand only the distributions of these values are known. Furthermore, the distributions of two successive secretaries' values are governed by a Markov chain. Optimal hiring policies for finite n and limiting optimal policies as k and n approach infinity are obtained.     

An evaluation of scheduling heuristics for dynamic single-processor scheduling with early/tardy costs

In an endeavor to broaden the application of scheduling models to decisions involving the use of a manager's time we use simulation to investigate the performance of a number of simple algorithms (including eight priority rules and a construction heuristic) in a dynamic setting with tasks arriving (randomly) and scheduling decisions being made, over time. We compare these simple methods relative to a bound that uses an adjacent pairwise interchange algorithm. We model uncertainty in task durations, and costs being incurred for early and tardy task completion (representative of JIT settings). In addition to evaluating the efficacy of the scheduling rules and various preemption strategies (using ANOVA), we highlight the managerial implications of the effects of eight environmental parameters. © 1996 John Wiley & Sons, Inc.     

Consistency of several variants of the standardized time series area variance estimator

In statistical analysis of stationary time series or in steady-state simulation output analysis, it is desired to find consistent estimates of the process variance parameter. Here, we consider variants of the area estimator of standardized time series, namely, the weighted area and the Cramér-von Mises area estimators, and provide their consistency, in the strong sense and mean-square sense. A sharp bound for the (asymptotic) variance of these estimators is obtained. We also present a central limit theorem for the weighted area estimator: this gives a rate of convergence of this estimator, as well as a confidence interval for the variance parameter. © 1995 John Wiley & Sons, Inc.     

An exact aggregation/disaggregation algorithm for large scale markov chains

Many Markov chain models have very large state spaces, making the computation of stationary probabilities very difficult. Often the structure and numerical properties of the Markov chain allows for more efficient computation through state aggregation and disaggregation. In this article we develop an efficient exact single pass aggregation/disaggregation algorithm which exploits structural properties of large finite irreducible mandatory set decomposable Markov chains. The required property of being of mandatory set decomposable structure is a generalization of several other Markov chain structures for which exact aggregation/disaggregation algorithms exist. © 1995 John Wiley & Sons, Inc.     

Steady-state approximation of a multiechelon multi-indentured repairable-item inventory system with a single repair facility

We model a two-echelon multi-indentured repairable-item inventory system where each “base” has a maximum number of identical online machines, and each machine consists of several module types. Machine failures are due to module failures and occur according to an exponential distribution. When a machine fails, the failed module is replaced by an identical spare module if one is available. Otherwise, the module is backordered. All failed modules go to a single “depot” repair facility which consists of a finite number of identical repairmen who are able to repair any module type in an exponentially distributed time, although the repair rates for different module types may differ. The principal contribution of this article is an approximation algorithm for calculating the steady-state characteristics of the system. In comparison with simulation results, the algorithm is quite accurate and computationally efficient. © 1993 John Wiley & Sons, Inc.     

Queueing-location problems on the plane

In this article we present a queueing-location problem where a location of a service station has to be determined. The two main results of this article are a convexity proof for general distances and a theorem that limits the area in the plane where the solution can lie. We also propose some solution procedures.     

New worst-case results for the bin-packing problem

In this note we consider the familiar bin-packing problem and provide new worst-case results for a number of classical heuristics. We show that the first-fit and best-fit heuristics have an absolute performance ratio of no more than 1.75, and first-fit decreasing and best-fit decreasing heuristics have an absolute performance ratio of 1.5. The latter is the best possible absolute performance ratio for the bin-packing problem, unless P = NP. © 1994 John Wiley & Sons, Inc.