The “signature” of a coherent system and its application to comparisons among systems

Various methods and criteria for comparing coherent systems are discussed. Theoretical results are derived for comparing systems of a given order when components are assumed to have independent and identically distributed lifetimes. All comparisons rely on the representation of a system's lifetime distribution as a function of the system's “signature,” that is, as a function of the vector p= (p₁, … , p_n), where p_i is the probability that the system fails upon the occurrence of the ith component failure. Sufficient conditions are provided for the lifetime of one system to be larger than that of another system in three different senses: stochastic ordering, hazard rate ordering, and likelihood ratio ordering. Further, a new preservation theorem for hazard rate ordering is established. In the final section, the notion of system signature is used to examine a recently published conjecture regarding componentwise and systemwise redundancy. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 507–523, 1999     

Capacitated selection problem

Optimizing the selection of resources to accomplish a set of tasks involves evaluating the tradeoffs between the cost of maintaining the resources necessary to accomplish the tasks and the penalty cost associated with unfinished tasks. We consider the case where resources are categorized into types, and limits (capacity) are imposed on the number of each type that can be selected. The objective is to minimize the sum of penalty costs and resource costs. This problem has several practical applications including production planning, new product design, menu selection and inventory management. We develop a branch‐and‐bound algorithm to find exact solutions to the problem. To generate bounds, we utilize a dual ascent procedure which exploits the special structure of the problem. Information from the dual and recovered primal solutions are used to select branching variables. We generate strong valid inequalities and use them to fix other variables at each branching step. Results of tests performed on reasonably sized problems are presented. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 19–37, 1999     

Class scheduling algorithms for Navy training schools

The problem of developing good schedules for Navy C-Schools has been modeled as a combinatorial optimization problem. The only complicating feature of the problem is that classes must be grouped together into sequences known as pipelines. An ideal schedule will have all classes in a pipeline scheduled in consecutive weeks. The objective is to eliminate the nonproductive time spent by sailors at C-Schools who are waiting for the next class in a pipeline. In this investigation an implicit enumeration procedure for this problem was developed. The key component of our algorithm is a specialized greedy algorithm which is used to obtain a good initial incumbent. Often this initial incumbent is either an optimal schedule or a near optimal schedule. In an empirical analysis with the only other competing software system, our greedy heuristic found equivalent or better solutions in substantially less computer time. This greedy heuristic was extended and modified for the A-School scheduling problem and was found to be superior to its only competitor. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 533–551, 1998     

An application of the MTP2 property on bounds on system reliability

This paper is concerned with the joint prior distribution of the dependent reliabilities of the components of a binary system. When this distribution is MTP₂ (Multivariate Totally Positive of Order 2), it is shown in general that this actually makes the machinery of Natvig and Eide [7] available to arrive at the posterior distribution of the system's reliability, based on data both at the component and system level. As an illustration in a common environmental stress case, the joint prior distribution of the reliabilities is shown to have the MTP₂ property. We also show, similarly to Gåsemyr and Natvig [3], for the case of independent components given component reliabilities how this joint prior distribution may be based on the combination of expert opinions. A specific system is finally treated numerically. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 741–755, 1997     

An exact solution approach for the time-dependent traveling-salesman problem

We present an algorithm for solving the time-dependent traveling-salesman problem (TDTSP), a generalization of the classical traveling salesman problem in which the cost of travel between two cities depends on the distance between the cities and the position of the transition in the tour. The algorithm is derived by applying Benders decomposition to a mixed-integer linear programming formulation for the problem. We identify trivial TDTSPs for which a standard implementation of the algorithm requires an exponential number of iterations to converge. This motivates the development of an efficient, network-flow-based method for finding Pareto-optimal dual solutions of a highly degenerate subproblem. Preliminary computational experience demonstrates that the use of these Pareto-optimal solutions has a dramatic impact on the performance of the algorithm. © 1996 John Wiley & Sons, Inc.     

Asymptotically optimal linear time algorithms for two‐stage and three‐stage flexible flow shops

We consider two‐stage and three‐stage flexible flow shops with parallel machines in each stage and the minimum makespan objective. We develop linear time algorithms for these problems with absolute worst‐case bounds either sharper or no worse than the currently available ones and we accomplish this with lower complexity algorithms. We also demonstrate the asymptotic optimality of a class of algorithms for multistage flexible flow shop problems (which includes the proposed algorithms) under certain probabilistic assumptions on the job processing times. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 259–268, 2000     

On the orbit characteristics of the M/G/ 1 retrial queue

In teletraffic applications of retrial queues only the service zone is observable. Another part of a retrial queue, the orbit, which represents the delay before repeated attempts to get service, cannot be observed. Thus, it is very important to get general results about behavior of the orbit. We investigate two characteristics of the orbit, namely, the orbit busy period and the orbit idle period, which seem to be very useful from this point of view. © 1996 John Wiley & Sons, Inc.     

Varieties of defection strategies from multinational military coalitions: Insights from operation Iraqi freedom

How do states defect from multinational military coalitions? The question deserves considerable academic scrutiny, as states increasingly rely on coalitions to prosecute military missions. Yet to the extent that coalition defection has been explored, the extant literature tends to see defection as a binary undertaking – states are either in or out. In practice, however, defection is an act of risk minimization in a manner that forces other coalition partners to fill resulting operational gaps. A coalition can therefore appear stable due to a constant number of flags associated with the mission, but in practice be much less coherent and capable. After defining defection as a non-routine abrogation of operational responsibility at other coalition partners’ expense, significantly prior to mission conclusion, this article explores several states’ participation in Operation Iraqi Freedom and the various manners by which they defected from that coalition. It concludes with implications for future scholarship.