Linear search with bounded resources

A point is placed at random on the real line according to some known distribution F, and a search is made for this point, beginning at some starting points s on the line, and moving along the line according to some function x(t). The objective of this article is to maximize the probability of finding the point while traveling at most d units. Characterizations of simple optimal searches are found for arbitrary distributions, for continuous distributions with continuous density everywhere (e.g., normal, Cauchy, triangular), and for continuous distributions with density which is continuous on its support (e.g., exponential, uniform). These optimal searches are also shown to be optimal for maximization of the expected number of points found if the points are placed on the line independently from a known distribution F.     

A periodic maintenance model with used equipment and random minimal repair

The maintenance strategy considered in this article is in the class of block replacement policies. The working unit is replaced by new ones at instants T,2T,3T,… independently of the age and state of the unit. If a failure occurs between these instants, the random repair cost is evaluated. If it is smaller than a predetermined control limit then a minimal repair is carried out. Otherwise the unit is replaced by a used unit. The performance of this maintenance strategy is evaluated in terms of average total cost per time unit over an infinite time span. The mathematical model is defined and several analytical results are obtained. A computer program has been written, which solves the mathematical problem, and some examples are given for the cases where the underlying life distribution is gamma, Weibull or truncated normal.     

Transient analysis of multiple-unit reliability systems

A general Markovian model representing several multiple-unit redundant repairable systems is proposed and its transient behavior is studied. Specifically, for multiple-unit reliability system the reliability and availability functions are derived in an explicit form for the transient case. The stationary availability and mean time to system failure are deduced from the main results as special cases.     

Service levels in distribution systems with random customer order size

An approximate method for measuring the service levels of the warehouse-retailer system operating under (s, S) policy is presented. All the retailers are identical and the demand process at each retailer follows a stationary stuttering Poisson process. This type of demand process allows customer orders to be for a random number of units, which gives rise to the undershoot quantity at both the warehouse and retailer levels. Exact analyses of the distribution of the undershoot quantity and the number of orders place by a retailer during the warehouse reordering lead time are derived. By using this distribution together with probability approximation and other heuristic approaches, we model the behavior of the warehouse level. Based on the results of the warehouse level and on an existing framework from previous work, the service level at the retailer level is estimated. Results of the approximate method are then compared with those of simulation. © 1995 John Wiley & Sons, Inc.     

A bayesian approach to environmental stress screening

The article presents a Bayesian analysis for the environmental stress screening problem. The decision problem of deriving optimal stress screen durations is solved. Given a screen duration, the optimal stress level can also be determined. Indicators of the quality of a screen of any duration are derived. A statistical model is presented which allows a posterior density for the rate of early failures of the production process to be calculated. This enables the user to update his opinion about the quality of the process. © 1994 John Wiley & Sons, Inc.     

Characterizing the barlow-wu structure functions

Various mathematical models for multistate systems have been proposed in the literature. Among them the model introduced by Barlow and Wu is the one most intimately related to that of binary systems; hence the Barlow-Wu class possesses many nice properties inherited from the binary systems. In this article we obtain several characterization results for multistate systems, which closely relate the Barlow-Wu class to other classes of multistate systems. The characterizations we obtained originate from the invariance properties of the Barlow-Wu functions, and are easy to apply in verifying whether a particular model is of the Barlow-Wu type. © 1994 John Wiley & Sons, Inc.     

The parallel machine min-max weighted absolute lateness scheduling problem

Given a set of jobs, a processing time and a weight for each job, several parallel and identical machines, and a common due date that is not too early to constrain the scheduling decision, we want to find an optimal job schedule so as to minimize the maximum weighted absolute lateness. We show that this problem is NP-complete even for the single-machine case, and is strongly NP-complete for the general case. We present a polynomial time heuristic for this problem and analyze its worst-case performance. Empirical testing of the heuristic is reported, and the results suggest that the performance is asymptotically optimal as the number of jobs tends to infinity. © 1994 John Wiley & Sons, Inc.     

Equipment replacement under technological change

For infinite-horizon replacement economy problems it is common practice to truncate the problem at some finite horizon. We develop bounds on the error due to such a truncation. These bounds differ from previous results in that they include both revenues and costs. Bounds are illustrated through a numerical example from a real case in vehicle replacement. © 1994 John Wiley & Sons, Inc.     

A face search heuristic algorithm for optimizing over the efficient set

The problem of optimizing a linear function over the efficient set of a multiple objective linear program is an important but difficult problem in multiple criteria decision making. In this article we present a flexible face search heuristic algorithm for the problem. Preliminary computational experiments indicate that the algorithm gives very good estimates of the global optimum with relatively little computational effort. © 1993 John Wiley & Sons, Inc.     

A two-machine repair model with variable repair rate

A two-unit cold standby production system with one repairman is considered. After inspection of a failed unit the repairman chooses either a slow or a fast repair rate to carry out the corresponding amount of work. At system breakdown the repairman has an additional opportunity to switch to the fast rate. If there are no fixed costs associated with system breakdowns, then the policy which minimizes longrun average costs is shown to be a two-dimensional control limit rule. If fixed costs are incurred every time the system breaks down, then the optimal policy is not necessarily of control limit type. This is illustrated by a counterexample. Furthermore, we present several performance measures for this maintenance system controlled by a two-dimensional control limit rule. © 1993 John Wiley & Sons, Inc.