Tests for transient means in simulated time series

We present a family of tests to detect the presence of a transient mean in a simulation process. These tests compare variance estimators from different parts of a simulation run, and are based on the methods of batch means and standardized time series. Our tests can be viewed as natural generalizations of some previously published work. We also include a power analysis of the new tests, as well as some illustrative examples. © 1994 John Wiley & Sons, Inc.     

A generalized model for the economic design of x̄control charts for production systems with increasing failure rate and early replacement

This article generalizes the model for the economic design of x̄-control charts of Duncan [4], starting from the more recent papers of Lorenzen and Vance [8] and Banerjee and Rahim [3]. The classical model of Duncan [4] and its several extensions including the unified model of Lorenzen and Vance [8] assumed exponentially distributed in-control periods and provided uniform sampling schemes. Banerjee and Rahim [3], however, assumed a Weibull-distributed in-control period having an increasing failure rate and used variable sampling intervals. The present article is an extension of the work of Banerjee and Rahim [3], where a general distribution of in-control periods having an increasing failure rate is assumed and the possibility of age-dependent repair before failure is considered. Several different truncated and nontruncated probability models are chosen. It is proposed that economic benefits can be achieved by adopting a nonuniform inspection scheme and by truncating a production cycle when it attains a certain age. Numerical examples are presented to support this proposition. Finally, the effect of model specification in the choice of failure mechanism is investigated. © 1993 John Wiley & Sons, Inc.     

Algorithms for the constrained maximum-weight connected graph problem

Given a positive integer R and a weight for each vertex in a graph, the maximum-weight connected graph (MCG) problem is to find a connected subgraph with R vertices that maximizes the sum of the weights. The MCG problem is strongly NP-complete, and we study a special case of it: the constrained MCG (CMCG) problem, which is the MCG problem with a constraint of having a predetermined vertex included in the solution. We first show that the Steiner tree problem is a special case of the CMCG problem. Then we present three optimization algorithms for the CMCG problem. The first two algorithms deal with special graphs (tree and layered graphs) and employ different dynamic programming techniques, solving the CMCG problem in polynomial times. The third one deals with a general graph and uses a variant of the Balas additive method with an imbedded connectivity test and a pruning method. We also present a heuristic algorithm for the CMCG problem with a general graph and its bound analysis. We combine the two algorithms, heuristic and optimization, and present a practical solution method to the CMCG problem. Computational results are reported and future research issues are discussed. © 1996 John Wiley & Sons, Inc.     

Some comments on the optimal assembly problem

It is shown that two recent results of Baxter and Harche [1] on monotone and balanced optimal assemblies hold only under conditions that are more restrictive than those originally proposed by the authors. We describe such additional conditions, illustrate why they are needed, and establish their sufficiency. We also consider a recent result by Malon [11] and demonstrate that, while the result itself is correct, its two proofs were incomplete. A complete proof of an extension of the result is then suggested. © 1995 John Wiley & Sons, Inc.     

A replacement model with overhauls and repairs

This article generalizes the classical periodical replacement model with minimal repair by considering the effect of the overhaul, which is assumed to be able to rejuvenate the system. The generalization is based on the notion of the virtual age of a system introduced by Kijima, Morimura, and Suzuki [“Periodical Replacement Problem without Assuming Minimal Repair,” European Journal of Operational Research, 37 , 194–203 (1988)]. © 1995 John Wiley & Sons, Inc.     

Optimal force mix in heterogeneous combat

This article presents models for determining the optimum number of Red weapons required to win a heterogeneous combat in which m(m> 1) types of Red weapons face a single type of Blue weapon under a newly defined termination policy. Red aims at either minimizing the total cost or maximizing the aggregated remaining force strength. Kuhn-Tucker and simulated annealing techniques are used for obtaining the optimal solution. The methodology is illustrated by analysing heterogeneous combat to determine (i) the feasibility of introducing new types of weapons and (ii) the number of weapons required to win if a specific type of weapon, say infantry, dominates. © 1995 John Wiley & Sons, Inc.     

Single-machine scheduling of stochastic jobs subject to deterioration or delay

N jobs are available for processing by a single machine. Jobs make (stochastic) progress while being processed but deteriorate while awaiting processing. The pioneering work of Browne and Yechiali, who developed scheduling policies for such models, is extended (i) to incorporate a precedence relation on the job set, delimiting the class of admissible policies, and (ii) to preemptive scheduling models. For the latter, we demonstrate that under appropriate conditions there is an optimal policy which is nonpreemptive. This is also achieved for a class of preemptive models in which processing generates delays for waiting jobs. A single class of algorithms is shown to generate optimal policies for many of the problems considered. © 1992 John Wiley & Sons, Inc.     

An algorithm for the discrete bilevel programming problem

The bilevel programming problem (BLPP) is an example of a two-stage, noncooperative game in which the first player can influence but not control the actions of the second. This article addresses the linear formulation and presents a new algorithm for solving the zero-one case. We begin by converting the leader's objective function into a parameterized constraint, and then attempt to solve the resultant problem. This produces a candidate solution that is used to find a point in the BLPP feasible reagion. Incremental improvements are sought, which ultimately lead to a global optimum. An example is presented to highlight the computations and to demonstrate some basic characteristics of the solution. Computational experience indicates that the algorithm is capable of solving problems with up to 50 variables in a reasonable amount of time.     

On the bivariate negative binomial distribution of mitchell and paulson

The bivariate negative binomial distribution of Mitchell and Paulson [17] for the case b = c = 0 is shown to be equivalent to the accident proneness model of Edwards and Gurland [4] and Subrahmaniam [19,20]. The diagonal series expansion of its joint probability function is then derived. Two other formulations of this distribution are also considered: (i) as a mixture model, which showed how it arises as the discrete analogue to the Wicksell-Kibble bivariate gamma distribution, and (ii) as a consequence of the linear birth-and-death process with immigration.