Viability analysis: A formulation aid for all classes of network models

Nonviable network models have edges which are forced to zero flow simply by the pattern of interconnection of the nodes. The original nonviability diagnosis algorithm [4] is extended here to cover all classes of network models, including pure, generalized, pure processing, nonconserving processing, and generalized processing. The extended algorithm relies on the conversion of all network forms to a pure processing form. Efficiency improvements to the original algorithm are also presented.     

A dynamic general linear model for inference from accelerated life tests

We present a new approach for inference from accelerated life tests. Our approach is based on a dynamic general linear model setup which arises naturally from the accelerated life-testing problem and uses linear Bayesian methods for inference. The advantage of the procedure is that it does not require large numbers of items to be tested and that it can deal with both censored and uncensored data. We illustrate the use of our approach with some actual accelerated life-test data. © 1992 John Wiley & Sons, Inc.     

Performance of N machine centers of K-out-of-M: G type maintained by a single repairman

We consider a system of N (nonsymmetric) machine centers of the K-out-of-M : G type that are maintained by a single repairman. [A machine center functions if and only if at least K of the M machines belonging to the center are good (G).] Such systems are commonly found in various manufacturing and service industries. A stochastic model is developed that accommodates generally distributed repair times and repairman walk times, and most repair scheduling disciplines. K-out-of-M : G type systems also appear as a modeling paradigm in reliability analysis and polling systems performance analysis. Several performance measures are derived for machine-repair systems having K-out-of-M-type centers. A simple example system is developed in detail that exposes the computations involved in modeling applications. © 1992 John Wiley & Sons, Inc.     

Simulation of stochastic activity networks using path control variates

This article details several procedures for using path control variates to improve the accuracy of simulation-based point and confidence-interval estimators of the mean completion time of a stochastic activity network (SAN). Because each path control variate is the duration of the corresponding directed path in the network from the source to the sink, the vector of selected path controls has both a known mean and a known covariance matrix. This information is incorporated into estimation procedures for both normal and nonnormal responses. To evaluate the performance of these procedures experimentally, we examine the bias, variance, and mean square error of the controlled point estimators as well as the average half-length and coverage probability of the corresponding confidence-interval estimators for a set of SANs in which the following characteristics are systematically varied: (a) the size of the network (number of nodes and arcs); (b) the topology of the network; (c) the percentage of activities with exponentially distributed durations; and (d) the relative dominance of the critical path. The experimental results show that although large improvements in accuracy can be achieved with some of these procedures, the confidence-interval estimators for normal responses may suffer serious loss of coverage probability in some applications.     

Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs

Jobs with known processing times and due dates have to be processed on a machine which is subject to a single breakdown. The moment of breakdown and the repair time are independent random variables. Two cases are distinguished with reference to the processing time preempted by the breakdown (no other preemptions are allowed): (i) resumption without time losses and (ii) restart from the beginning. Under certain compatible conditions, we find the policies which minimize stochastically the number of tardy jobs.     

Analysis of a bicriteria location model

In this article a bicriteria model, formed by the weighted sum of the minisum and minimax functions for a single-location problem, is investigated. It is shown that all efficient solutions generated by either constrained model are also properly efficient. The bicriteria model and the constrained models are theoretically equivalent, but it is more efficient and simpler to generate nondominated solutions using the constrained criterion approach. When solving the bicriteria model, a critical range is found for which all properly efficient solutions are generated.     

Design and estimation for small sample sensitivity testing

In sensitivity testing for the Department of Defense, the high cost of experimental units necessitates the use of small sample sizes and accentuates the importance of design. This article compares five data collection-estimation procedures. Four of these are modifications of the Robbins-Monro method, and the other is the Langlie. The simulation study is designed as a factorial experiment with response function, sample size, initial design point, gate width, and noise as factors. The estimated V₅₀ and its MSE are the responses compared to assess the small sample behavior of each method. Although there is no single clear-cut winner, the Delayed Robbins-Monro (DRM) with maximum likelihood estimation and the Estimated Quantal Response Curve (Wu [21]) are shown to perform well over a broad variety of conditions.     

Scheduling workers in a constricted area

A generalization of the equi-partitioning problem, termed the 2D-Partition Problem, is formulated. The motivation is an aircraft maintenance scheduling problem with the following characteristics. The complete maintenance overhaul of a single aircraft requires the completion of some 350 tasks. These tasks require a varying number of technicians working at the same time. For large subsets of these 350 tasks, the constraining resource is physical space—tasks must be completed in a physical space of limited size such as the cockpit. Furthermore, there is no precedence relationship among the tasks. For each subset, the problem is to schedule the tasks to minimize makespan. Let m denote the maximum number of technicians that can work at the same time in the physical area under consideration. We present optimization algorithms for m = 2 and 3. © 1996 John Wiley & Sons, Inc.     

General solution to many-on-many heterogeneous stochastic combat

Stochastic combat models are more realistic than either deterministic or exponential models. Stochastic combat models have been solved analytically only for small combat sizes. It is very difficult, if not impossible, to extend previous solution techniques to larger-scale combat. This research provides the solution for many-on-many heterogeneous stochastic combat with any break points. Furthermore, every stage in stochastic combat is clearly defined and associated aiming and killing probabilities are calculated. © 1996 John Wiley & Sons, Inc.     

The advantage of deeper pockets in Silverman's game on intervals

Silverman's game on (1, B) × (1, B) was analyzed by R. J. Evans, who showed that optimal strategies exist (and found them) only on a set of measure zero in the parameter plane. We examine the corresponding game on (1, B) × (1, D) with D > B, and show that optimal strategies exist in about half the parameter plane. Optimal strategies and game value are obtained explicitly. © 1995 John Wiley & Sons, Inc.