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.     

On excess-, current-, and total-life distributions of phase-type renewal processes

Consider a renewal process whose interrenewal-time distribution is phase type with representation (α, T). We show that the (time-dependent) excess-life distribution is phase type with representation (α′, T), where α′ is an appropriately modified initial probability vector. Using this result, we derive the (time-dependent) distributions for the current life and the total life of the phase-type renewal process. They in turn enable us to obtain the equilibrium distributions for the three random variables. These results simplify the computation of the respective distribution functions and consequently enhance the potential use of renewal theory in stochastic modeling—particularly in inventory, queueing, and reliability applications. © 1992 John Wiley & Sons, Inc.     

Bounds and properties of the expected value of sample information for a project-selection problem

In this article we extend the work of Mehrez and Stulman [5] on the expected value of perfect information (EVPI) to the expected value of sample information (EVSI) for a class of economic problems dealing with the decision to reject or accept an investment project. It is shown that shifting the mean of the underlying a priori distribution of X, the project's monetary value from zero in either direction will decrease the associated EVSI of Y, the random sampled information. A theorem is then presented which gives an upper bound on the EVSI over all distributions of Y, as well as the structure of the posterior mean E[X|Y] for which this upper bound is achieved. Finally, the case where E[X|Y] is linear in Y is discussed and its performance compared with that of the optimal case.     

Optimal maintenance policies for constantly monitored systems

A multistate system is assumed to be constantly monitored; i.e., the state of the system is always known with certainty. Damage to the system accumulates via a continuous-time Markov process. A model of the system including restoration costs and state occupation costs is developed. It is shown that under certain conditions the optimal restoration policy for the system is a control limit rule. A control limit rule is a policy which requires restoration of the system whenever the damage exceeds a certain level. Examples are presented to show that there are several situations in which, perhaps surprisingly, control limit rules are not optimal.     

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.     

Optimal job splitting on a multi‐slot machine with applications in the printing industry

In this article, we define a scheduling/packing problem called the Job Splitting Problem, motivated by the practices in the printing industry. There are n types of items to be produced on an m‐slot machine. A particular assignment of the types to the slots is called a “run” configuration and requires a setup cost. Once a run begins, the production continues according to that configuration and the “length” of the run represents the quantity produced in each slot during that run. For each unit of production in excess of demand, there is a waste cost. Our goal is to construct a production plan, i.e., a set of runs, such that the total setup and waste cost is minimized. We show that the problem is strongly NP‐hard and propose two integer programming formulations, several preprocessing steps, and two heuristics. We also provide a worst‐case bound for one of the heuristics. Extensive tests on real‐world and randomly generated instances show that the heuristics are both fast and effective, finding near‐optimal solutions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Dynamic evacuation routes for personnel on a naval ship

We propose a dynamic escape route system for emergency evacuation of a naval ship. The system employs signals that adapt to the causative contingency and the crew's physical distribution about the ship. A mixed‐integer nonlinear programming model, with underlying network structure, optimizes the evacuation process. The network's nodes represent compartments, closures (e.g., doors and hatches) and intersections, while arcs represent various types of passageways. The objective function integrates two potentially conflicting factors: average evacuation time and the watertight and airtight integrity of the ship after evacuation. A heuristic solves the model approximately using a sequence of mixed‐integer linear approximating problems. Using data for a Spanish frigate, with standard static routes specified by the ship's designers, computational tests show that the dynamic system can reduce average evacuation times, nearly 23%, and can improve a combined measure of ship integrity by up to 50%. In addition, plausible design changes to the frigate yield further, substantial improvements. Published 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008     

Moving Beyond Population-Centric vs. Enemy-Centric Counterinsurgency

Historically, insurgency is one of the most prevalent forms of armed conflict and it is likely to remain common in the foreseeable future. Recent experiences with counterinsurgency in Iraq and Afghanistan offer many lessons for future counterinsurgents, but the discourse on the subject continues to be mired in a traditional dichotomy pitting population-centric approaches to counterinsurgency against enemy-centric approaches. Historical analysis suggests that this traditional dichotomy is not a sufficiently nuanced way to understand or plan for such operations. Instead, discussions of counterinsurgency should focus on two dimensions: actions (use of physical force vs. political or moral actions) and targets (active insurgents vs. insurgent support). This perspective divides the space of possible counterinsurgency efforts into four quadrants, suggesting that effective counterinsurgency campaigns find a balance of effort across the four quadrants that is well matched to the specific context.     

Balancing and optimizing a portfolio of R&D projects

A mathematical formulation of an optimization model designed to select projects for inclusion in an R&D portfolio, subject to a wide variety of constraints (e.g., capital, headcount, strategic intent, etc.), is presented. The model is similar to others that have previously appeared in the literature and is in the form of a mixed integer programming (MIP) problem known as the multidimensional knapsack problem. Exact solution of such problems is generally difficult, but can be accomplished in reasonable time using specialized algorithms. The main contribution of this paper is an examination of two important issues related to formulation of project selection models such as the one presented here. If partial funding and implementation of projects is allowed, the resulting formulation is a linear programming (LP) problem which can be solved quite easily. Several plausible assumptions about how partial funding impacts project value are presented. In general, our examples suggest that the problem might best be formulated as a nonlinear programming (NLP) problem, but that there is a need for further research to determine an appropriate expression for the value of a partially funded project. In light of that gap in the current body of knowledge and for practical reasons, the LP relaxation of this model is preferred. The LP relaxation can be implemented in a spreadsheet (even for relatively large problems) and gives reasonable results when applied to a test problem based on GM's R&D project selection process. There has been much discussion in the literature on the topic of assigning a quantitative measure of value to each project. Although many alternatives are suggested, no one way is universally accepted as the preferred way. There does seem to be general agreement that all of the proposed methods are subject to considerable uncertainty. A systematic way to examine the sensitivity of project selection decisions to variations in the measure of value is developed. It is shown that the solution for the illustrative problem is reasonably robust to rather large variations in the measure of value. We cannot, however, conclude that this would be the case in general. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 18–40, 2001