Some two-on-two homogeneous stochastic combats

In this article we consider two versions of two-on-two homogeneous stochastic combat and develop expressions, in each case, for the state probabilities. The models are natural generalizations of the exponential Lanchester square law model. In the first version, a marksman whose target is killed resumes afresh the killing process on a surviving target; in the second version, the marksman whose target is killed merely uses up his remaining time to a kill on a surviving target. Using the state probabilities we then compute such important combat measures as (1) the mean and variance of the number of survivors as they vary with time for each of the sides, (2) the win probabilities for each of the sides, and (3) the mean and variance of the battle duration time. As an application, computations were made for the specific case of a gamma (2) interfiring time random variable for each side and the above combat measures were compared with the appropriate exponential and deterministic Lanchester square law approximations. The latter two are shown to be very poor approximations in this case.     

Two heuristics for the economic lot scheduling problem: An experimental study

In this article we present and test two heuristics for the economic lot scheduling problem. The first heuristic was developed by one of us (P.C. Geng) during Ph.D. research, while the other is a convergent implementation of an algorithm due to Doll and Whybark. We study the performance of these heuristics on a large set of test problems constructed using a new form of problem generation that yields random problems within an experimental design.     

Multiperiod allocation of limited resources: A minimax approach

We consider a multiperiod model in which limited resources are allocated among competing activities in each period. The objective is to minimize the maximum weighted deviation of the cumulative activity levels from the cumulative demands among all activities at all periods. All resources are assumed to be storable; that is, surpluses at one period can be used later on. This model is useful, for example, in multiperiod production planning for high-technology industries that assemble a large variety of circuit boards using numerous electronic components. The model is formulated with a minimax objective. We develop an efficient algorithm that can solve large-scale problems very quickly. At each iteration, the algorithm makes use of the solution to a relaxed problem to identify activities that should be permanently set to zero, as well as groups of activities that should have the same value.     

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     

Analysis of a machine repair problem with an unreliable server and phase type repairs and services

In this paper we study a machine repair problem in which a single unreliable server maintains N identical machines. The breakdown times of the machines are assumed to follow an exponential distribution. The server is subject to failure and the failure times are exponentially distributed. The repair times of the machine and the service times of the repairman are assumed to be of phase type. Using matrix‐analytic methods, we perform steady state analysis of this model. The time spent by a failed machine in service and the total time in the repair facility are shown to be of phase type. Several performance measures are evaluated. An optimization problem to determine the number of machines to be assigned to the server that will maximize the expected total profit per unit time is discussed. An illustrative numerical example is presented. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 462–480, 2003     

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     

四轴超精密车床的改进坐标驱动装置

带微进给方式步进电机的PC控制轴系驱动装置可生产光学质量的表面。超精密车床可生产诸如球体和非球体之类的集合体,其表面粗糙度≤5nmRa,可用于光学装置的反光镜或空气轴承转轴的超精密零件。     

Learning and costs in airframe production: A multiple-output production function approach

This article examines the influence of both production rate and learning on airframe program costs. A dynamic multiple-output production model is developed and is used to observe the cost impact of changes in production rate and learning. Several simulations are performed to demonstrate the sensitivity of the optimal time path of cost to changes in the model parameters. The model is applied by estimating parameters from the F102 airframe program.