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     

Sequential and systematic sampling plans for the Markov‐dependent production process

Acceptance sampling plans are used to assess the quality of an ongoing production process, in addition to the lot acceptance. In this paper, we consider sampling inspection plans for monitoring the Markov‐dependent production process. We construct sequential plans that satisfy the usual probability requirements at acceptable quality level and rejectable quality level and, in addition, possess the minimum average sample number under semicurtailed inspection. As these plans result in large sample sizes, especially when the serial correlation is high, we suggest new plans called “systematic sampling plans.” The minimum average sample number systematic plans that satisfy the probability requirements are constructed. Our algorithm uses some simple recurrence relations to compute the required acceptance probabilities. The optimal systematic plans require much smaller sample sizes and acceptance numbers, compared to the sequential plans. However, they need larger production runs to make a decision. Tables for choosing appropriate sequential and systematic plans are provided. The problem of selecting the best systematic sampling plan is also addressed. The operating characteristic curves of some of the sequential and the systematic plans are compared, and are observed to be almost identical. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 451–467, 2001     

Response surface analysis of two‐stage stochastic linear programming with recourse

We apply the techniques of response surface methodology (RSM) to approximate the objective function of a two‐stage stochastic linear program with recourse. In particular, the objective function is estimated, in the region of optimality, by a quadratic function of the first‐stage decision variables. The resulting response surface can provide valuable modeling insight, such as directions of minimum and maximum sensitivity to changes in the first‐stage variables. Latin hypercube (LH) sampling is applied to reduce the variance of the recourse function point estimates that are used to construct the response surface. Empirical results show the value of the LH method by comparing it with strategies based on independent random numbers, common random numbers, and the Schruben‐Margolin assignment rule. In addition, variance reduction with LH sampling can be guaranteed for an important class of two‐stage problems which includes the classical capacity expansion model. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 753–776, 1999     

Minimizing weighted mean absolute deviation of flow times in single machine systems

We discuss the problem of scheduling several jobs on a single machine with the objective of minimizing the weighted mean absolute deviation of flow times around the weighted mean flow time. We first show that the optimal schedule is W-shaped. For the unweighted case, we show that all optimal schedules are V-shaped. This characterization enables us to show that the problem is NP-hard. We then provide a pseudopolynomial algorithm for the unweighted problem. Finally, we consider three heuristic algorithms for the unweighted problem and report computational experience with these algorithms. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 297–311, 1998     

Geopolitics over Proliferation: the Origins of US Grand Strategy and Their Implications for the Spread of Nuclear Weapons in South Asia

How much does the United States care about nonproliferation? Recent scholarship suggests that the fear of spreading nuclear weapons was central to the US grand strategy in the Cold War. In one important case, however, this argument does not hold. This article draws on theoretical debates and newly declassified archives to demonstrate the primacy of geopolitics over nonproliferation in Washington’s policy toward India and Pakistan. Despite their rhetoric, Democratic and Republican leaders consistently relegated nonproliferation to the backburner whenever it conflicted with other strategic goals. Moreover, they inadvertently encouraged proliferation in South Asia at three inter-connected levels: technology, security, and identity.     

Terrorism, Crime and Private Armies

The nature of crime and conflict is rapidly evolving. Postmodern war is increasingly influenced by non-traditional and irregular combatants: non-state soldiers. These actors are exploiting technology and networked doctrine to spread their influence across traditional geographic boundaries. This emphasis on non-traditional actors accompanies a shift in political and social organization. This shift may well be a shift in state form: from nation-state to market-state. This transition is fueled by rapid developments in technology and the adoption of network organizational forms. Conflict during this transition blurs the distinctions between and among crime, terrorism and warfare. This essay explores the dynamics of terrorism, crime and private armies during this epochal shift.     

Transient solution of a finite-capacity M/Ga,b/1 queueing system

In this article we consider a single-server, bulk-service queueing system in which the waiting room is of finite capacity. Arrival process is Poisson and all the arrivals taking place when the waiting room is full are lost. The service times are generally distributed independent random variables and the distribution is depending on the batch size being served. Using renewal theory, we derive the time-dependent solution for the system-size probabilities at arbitrary time points. Also we give expressions for the distribution of virtual waiting time in the queue at any time t.