Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early-tardy penalties

We examine the problem of scheduling n jobs with a common due date on a single machine. The processing time of each job is a random variable, which follows an arbitrary distribution with a known mean and a known variance. The machine is not reliable; it is subject to stochastic breakdowns. The objective is to minimize the expected sum of squared deviations of job completion times from the due date. Two versions of the problem are addressed. In the first one the due date is a given constant, whereas in the second one the due date is a decision variable. In each case, a general form of the deterministic equivalent of the stochastic scheduling problem is obtained when the counting process related to the machine uptime distribution is a generalized Poisson process. A sufficient condition is derived under which optimal sequences are V-shaped with respect to mean processing times. Other characterizations of optimal solutions are also established. Based on the optimality properties, algorithms with pseudopolynomial time complexity are proposed to solve both versions of the problem. © 1996 John Wiley & Sons, Inc.     

Optimal number of minimal repairs before replacement of a system subject to shocks

A system is subject to shocks that arrive according to a nonhomogeneous Poisson process. As shocks occur a system has two types of failures. Type 1 failure (minor failure) is removed by a minimal repair, whereas type 2 failure (catastrophic failure) is removed by replacement. The probability of a type 2 failure is permitted to depend on the number of shocks since the last replacement. A system is replaced at the times of type 2 failure or at the nth type 1 failure, whichever comes first. The optimal policy is to select n* to minimize the expected cost per unit time for an infinite time span. A numerical example is given to illustrate the method. © 1996 John Wiley & Sons, Inc.     

A Cryptographic Escrow for Treaty Declarations and Step-by-Step Verification

The verification of arms-control and disarmament agreements requires states to provide declarations, including information on sensitive military sites and assets. There are important cases, however, in which negotiations of these agreements are impeded because states are reluctant to provide any such data, because of concerns about prematurely handing over militarily significant information. To address this challenge, we present a cryptographic escrow that allows a state to make a complete declaration of sites and assets at the outset and commit to its content, but only reveal the sensitive information therein sequentially. Combined with an inspection regime, our escrow allows for step-by-step verification of the correctness and completeness of the initial declaration so that the information release and inspections keep pace with parallel diplomatic and political processes. We apply this approach to the possible denuclearization of North Korea. Such approach can be applied, however, to any agreement requiring the sharing of sensitive information.     

Reactor-grade plutonium and nuclear weapons: ending the debate

The claim that reactor-grade plutonium cannot or will not be used to produce nuclear weapons has been used to justify non-nuclear-weapon states’ large stockpiles of plutonium that has been separated from highly radioactive spent fuel. However, by using reduced-mass plutonium cores, it is possible to manufacture reliable nuclear weapons with reactor-grade plutonium. These weapons can have the same design, size, weight, and predetonation probability as weapons using weapon-grade plutonium and would require no special cooling. The increased radiation from reactor-grade plutonium could be easily managed by shielding and operational procedures. Weapons using plutonium routinely produced by pressurized-water reactors could have a lethal area between 40 percent and 75 percent that of weapons using weapon-grade plutonium. In the past, both Sweden and Pakistan considered using reactor-grade plutonium to produce nuclear weapons, and India may be using reactor-grade plutonium in its arsenal today. Despite claims to the contrary, the United States used what was truly reactor-grade plutonium in a successful nuclear test in 1962. The capability of reactor-grade plutonium to produce highly destructive nuclear weapons leads to the conclusion that the separation of plutonium, plutonium stockpiling, and the use of plutonium-based fuels must be phased out and banned.     

Late Medieval Lance Use: Mounted Combat and Martial Arts in Western Europe from the 14th to the 16th Century

Despite the lance’s status and the amount of attention the couched lance has received in historiography, study of its martial art has been neglected. The various lance types and techniques used by western European cavalry have only recently begun to receive scholarly attention. Additionally, Medieval European lance use has too often been studied in isolation, without an adequate understanding of the idiosyncratic and asymmetrical dynamics of mounted combat. Although the charge with the couched lance was a valid tactic, it was only one of many. Light and heavy lances were used in one hand or two to trip, block, unhorse, and wrestle. These techniques were governed by the harsh laws of distance, speed, impact, iron, and asymmetry. By utilizing the surviving Fechtbücher and several Peninsular and Near Eastern sources, a brief foray into the diverse techniques of lance use and their purposes has been attempted here.     

Capacitated warehouse location model with risk pooling

In this article, we introduce the capacitated warehouse location model with risk pooling (CLMRP), which captures the interdependence between capacity issues and the inventory management at the warehouses. The CLMRP models a logistics system in which a single plant ships one type of product to a set of retailers, each with an uncertain demand. Warehouses serve as the direct intermediary between the plant and the retailers for the shipment of the product and also retain safety stock to provide appropriate service levels to the retailers. The CLMRP minimizes the sum of the fixed facility location, transportation, and inventory carrying costs. The model simultaneously determines warehouse locations, shipment sizes from the plant to the warehouses, the working inventory, and safety stock levels at the warehouses and the assignment of retailers to the warehouses. The costs at each warehouse exhibit initially economies of scale and then an exponential increase due to the capacity limitations. We show that this problem can be formulated as a nonlinear integer program in which the objective function is neither concave nor convex. A Lagrangian relaxation solution algorithm is proposed. The Lagrangian subproblem is also a nonlinear integer program. An efficient algorithm is developed for the linear relaxation of this subproblem. The Lagrangian relaxation algorithm provides near‐optimal solutions with reasonable computational requirements for large problem instances. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

What you should know about location modeling

Facility location models have been applied to problems in the public and private sectors for years. In this article, the author first presents a taxonomy of location problems based on the underlying space in which the problem is embedded. The article illustrates problems from each part of the taxonomy with an emphasis on discrete location problems. Selected recent research in the area is also discussed. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Network reliability assessment in a random environment

In this paper we consider networks that consist of components operating under a randomly changing common environment. Our work is motivated by power system networks that are subject to fluctuating weather conditions over time that affect the performance of the network. We develop a general setup for any network that is subject to such environment and present results for network reliability assessment under two repair scenarios. We also present Bayesian analysis of network failure data and illustrate how reliability predictions can be obtained for the network. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 574–591, 2003     

Estimating the probability that a simulated system will be the best

Consider a stochastic simulation experiment consisting of v independent vector replications consisting of an observation from each of k independent systems. Typical system comparisons are based on mean (long‐run) performance. However, the probability that a system will actually be the best is sometimes more relevant, and can provide a very different perspective than the systems' means. Empirically, we select one system as the best performer (i.e., it wins) on each replication. Each system has an unknown constant probability of winning on any replication and the numbers of wins for the individual systems follow a multinomial distribution. Procedures exist for selecting the system with the largest probability of being the best. This paper addresses the companion problem of estimating the probability that each system will be the best. The maximum likelihood estimators (MLEs) of the multinomial cell probabilities for a set of v vector replications across k systems are well known. We use these same v vector replications to form v^k unique vectors (termed pseudo‐replications) that contain one observation from each system and develop estimators based on AVC (All Vector Comparisons). In other words, we compare every observation from each system with every combination of observations from the remaining systems and note the best performer in each pseudo‐replication. AVC provides lower variance estimators of the probability that each system will be the best than the MLEs. We also derive confidence intervals for the AVC point estimators, present a portion of an extensive empirical evaluation and provide a realistic example. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 341–358, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10019     

Optimal service rates of a service facility with perishable inventory items

In this paper we optimally control service rates for an inventory system of service facilities with perishable products. We consider a finite capacity system where arrivals are Poisson‐distributed, lifetime of items have exponential distribution, and replenishment is instantaneous. We determine the service rates to be employed at each instant of time so that the long‐run expected cost rate is minimized for fixed maximum inventory level and capacity. The problem is modelled as a semi‐Markov decision problem. We establish the existence of a stationary optimal policy and we solve it by employing linear programming. Several numerical examples which provide insight to the behavior of the system are presented. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 464–482, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10021