A probability model for initial crack size and fatigue life of gun barrels

With constant firing, metal fatigue produces cracks in a gun barrel. The useful life of the barrel comes to an end when a crack develops to a critical size. The theory of Fracture Mechanics suggests a formula for crack size growth rate. This formula can be used to determine the life of a barrel, depending on the initial and critical crack sizes and other factors. The initial crack size turns out to be a dominant factor. Unfortunately, accurate measurements are not generally available on the initial crack size. In this paper, we propose a simple probability model for the initial crack size and this, in turn, leads to a probability distribution of the life of the barrel. This last distribution is the well-known exponential distribution with a location shift. The simplicity of this final result is one of the factors that make the model appealing.     

Some constraints on shipping in linear programming models

This note describes some constraints that may be applied to shipping models structured as linear programming problems. These constraints defining port-throughput capability have proven useful in applications of linear programming by the author and provide additional realism in problems of vessel allocation and ship design selection. Increase in model size through the use of the constraints is in general mode rate.     

The probability of survival of a subterranean target under mtensive attack

This paper deals with the analysis of a model for studying the probability of survival of a subterranean target under an intensive attack. Most of the analysis is based on the assumption that the explosions are circularly distributed about the target and that the number of explosions is known. In the last two sections it is shown what effect a relaxation of these assumptions has on the probability of survival of the target.     

Linear programming and the reliability of multicomponent systems

Several problems in the assignment of parallel redundant components to systems composed of elements subject to failure are considered. In each case the problem is to make an assignment which maximizes the system reliability subject to system constraints. Three distinct problems; are treated. The first is the classical problem of maximizing system reliability under total cost or weight constraints when components are subject to a single type of failure. The second problem deals with components which are subject to two types of failure and minimizes the probability of one mode of system failure subject to a constraint on the probability of the other mode of system failure. The third problem deals with components which may either fail to operate or may operate prematurely. System reliability is maximized subject to a constraint ori system safety. In each case the problem is formulated as an integer linear program. This has an advantage over alternative dynamic programming formulations in that standard algorithms may be employed to obtain numerical results.     

Polynomial‐time approximation schemes for two‐machine open shop scheduling with nonavailability constraints

This paper addresses a two‐machine open shop scheduling problem, in which the machines are not continuously available for processing. The processing of an operation affected by a non‐availability interval can be interrupted and resumed later. The objective is to minimize the makespan. We present two polynomial‐time approximation schemes, one of which handles the problem with one non‐availability interval on each machine and the other for the problem with several non‐availability intervals on one of the machines. Problems with a more general structure of the non‐availability intervals are not approximable in polynomial time within a constant factor, unless . © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Skewness correction X̄ and R charts for skewed distributions

This paper proposes a skewness correction (SC) method for constructing the and R control charts for skewed process distributions. Their asymmetric control limits (about the central line) are based on the degree of skewness estimated from the subgroups, and no parameter assumptions are made on the form of process distribution. These charts are simply adjustments of the conventional Shewhart control charts. Moreover, the chart is almost the same as the Shewhart chart if the process distribution is known to be symmetrical. The new charts are compared with the Shewhart charts and weighted variance (WV) control charts. When the process distribution is in some neighborhood of Weibull, lognormal, Burr or binomial family, simulation shows that the SC control charts have Type I risk (i.e., probability of a false alarm) closer to 0.27% of the normal case. Even in the case where the process distribution is exponential with known mean, not only the control limits and Type I risk, but also the Type II risk of the SC charts are closer to those of the exact and R charts than those of the WV and Shewhart charts. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 555–573, 2003     

A robust sensor covering and communication problem

We consider the problem of placing sensors across some area of interest. The sensors must be placed so that they cover a fixed set of targets in the region, and should be deployed in a manner that allows sensors to communicate with one another. In particular, there exists a measure of communication effectiveness for each sensor pair, which is determined by a concave function of distance between the sensors. Complicating the sensor location problem are uncertainties related to sensor placement, for example, as caused by drifting due to air or water currents to which the sensors may be subjected. Our problem thus seeks to maximize a metric regarding intrasensor communication effectiveness, subject to the condition that all targets must be covered by some sensor, where sensor drift occurs according to a robust (worst‐case) mechanism. We formulate an approximation approach and develop a cutting‐plane algorithm to solve this problem, comparing the effectiveness of two different classes of inequalities. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 582–594, 2015     

Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes

In this article, we study generalizations of some of the inventory models with nonlinear costs considered by Rosling in (Oper. Res. 50 (2002) 797–809). In particular, we extend the study of both the periodic review and the compound renewal demand processes from a constant lead time to a random lead time. We find that the quasiconvexity properties of the cost function (and therefore the existence of optimal (s, S) policies), holds true when the lead time has suitable log‐concavity properties. The results are derived by structural properties of renewal delayed processes stopped at an independent random time and by the study of log‐concavity properties of compound distributions. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 345–356, 2015     

The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options

This article generalizes the dynamic and stochastic knapsack problem by allowing the decision‐maker to postpone the accept/reject decision for an item and maintain a queue of waiting items to be considered later. Postponed decisions are penalized with delay costs, while idle capacity incurs a holding cost. This generalization addresses applications where requests of scarce resources can be delayed, for example, dispatching in logistics and allocation of funding to investments. We model the problem as a Markov decision process and analyze it through dynamic programming. We show that the optimal policy with homogeneous‐sized items possesses a bithreshold structure, despite the high dimensionality of the decision space. Finally, the value (or price) of postponement is illustrated through numerical examples. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 267–292, 2015     

Horizontal Inequalities and Sons of the Soil Conflict in China

Why are large population movements conflict-prone in some regions while they remain peacefully integrated elsewhere? I argue that clashes between ethnically distinct indigenous populations and migrants – i.e. ‘Sons of the Soil (SoS) conflict’ – erupt when there are large socio-economic and political horizontal inequalities between ‘dominant migrants’ and locals. A comparative case study of two Chinese minority regions based on ethnographic fieldwork and population data provides a vivid illustration of the mechanisms linking migration to SoS conflict. With fewer HIs between migrants and locals, Inner Mongolia avoided many of the violent clashes that were commonplace in Qinghai, a province fraught with disparities.