A stock redistribution model

Multi-depot supply systems are subject to stock distribution imbalances; i. e., the fraction of total system stock located at a depot may be too small to support the fraction of system demand expected to be placed on it. In the supply system of concern, a cutomer is always satisfied if there is stock anywhere in the system. Stock redistributions to correct imbalances may reduce both transportation costs and customer waiting times. A model for determining optimum redistribution quantities is formulated, and a practical method of solution for the two depot case is described. Selected numerical illustrations are given.     

Hyperbolic integer programming

The hyperbolic integer program is treated as a special case of a hyperbolic program with a finite number of feasible points. The continuous hyperbolic program also belongs to this class since its solution can be obtained by considering only the extreme points of the feasible set. A general algorithm for solving the hyperbolic integer program which reduces to solving a sequence of linear integer problems is proposed. When the integer restriction is removed, this algorithm is similar to the Isbell-Marlow procedure. The geometrical aspects of the hyperbolic problem are also discussed and several cutting plane algorithms are given.     

Stochastic duels involving reliability

The reliability of weapons in combat has been treated by Bhashyam in the context of a stochastic duel characterized by fixed ammunition supplies. negative exponentially distributed firing times and weapon lifetimes, and a fixed number of spare weapons for each duelist. The present paper takes a different approach by starting with the fundamental duel of Ancker and Williams, characterized by unlimited ammunition and by ordinary renewal firing times, and adding to it weapon lifetimes which can be functions of time or of round position in the firing sequence. Probabilities of winning and tieing are derived and it is shown that under certain conditions the weapon lifetimes are equivalent to random time and ammunition limits.     

Optimal control of an M/G/1 queue with impatient priority customers

An optimal operating policy is characterized for the infinite‐horizon average‐cost case of a single server queueing control problem. The server may be turned on at arrival epochs or off at departure epochs. Two classes of customers, each of them arriving according to an independent Poisson processes, are considered. An arriving 1‐customer enters the system if the server is turned on upon his arrival, or if the server is on and idle. In the former case, the 1‐customer is selected for service ahead of those customers waiting in the system; otherwise he leaves the system immediately. 2‐Customers remain in the system until they complete their service requirements. Under a linear cost structure, this paper shows that a stationary optimal policy exists such that either (1) leaves the server on at all times, or (2) turns the server off when the system is empty. In the latter case, we show that the stationary optimal policy is a threshold strategy, this feature being commonplace in most of priority queueing systems and inventory models. However, the optimal policy in our model is determined by two thresholds instead of one. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 201–209, 2001     

A continuous-review inventory system with lost sales and variable lead time

Using a system-point (SP) method of level crossings, we derive the stationary distribution of the inventory level (stock on hand) in a continuous-review inventory system with compound Poisson demand, Erlang as well as hyperexponentially distributed lead times, and lost sales. This distribution is then used to formulate long-run average cost functions with/without a service level constraint. Some numerical results are also presented, and compared with the Hadley and Whitin heuristic. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 259–278, 1998     

Scheduling to minimize the total compression and late costs

We consider a single-machine scheduling model in which the job processing times are controllable variables with linear costs. The objective is to minimize the sum of the cost incurred in compressing job processing times and the cost associated with the number of late jobs. The problem is shown to be NP-hard even when the due dates of all jobs are identical. We present a dynamic programming solution algorithm and a fully polynomial approximation scheme for the problem. Several efficient heuristics are proposed for solving the problem. Computational experiments demonstrate that the heuristics are capable of producing near-optimal solutions quickly. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 67–82, 1998     

System comparison procedures for automatic target recognition systems

Estimating the performance of an automatic target recognition (ATR) system in terms of its probability of successfully identifying a target involves extensive image collection and processing, which can be very time‐consuming and expensive. Therefore, we investigate the Wald sequential test for the difference in two proportions as a sample size‐reducing alternative to ranking and selection procedures and confidence intervals. An analysis of the test parameters leads to a practical methodology for implementing the Wald test for fairly comparing two systems, based on specific experimental goals. The test is also extended with the modified, sequentially rejective Bonferroni procedure for the multiple pairwise comparison of more than two systems. Two sampling schemes for different experimental goals are also discussed. The test methodology is applied to actual data to compare different configurations of a specific ATR system, with the results demonstrating that the modified Wald sequential procedure is a useful alternative to comparing proportions with confidence intervals, particularly when data are expensive. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 357–371, 1999     

信息技术与初中数学课程整合的实践

当前我国基础教育领域正在进行一场意义深远的课程改革,促进信息技术与课程整合成为其中的重要内容之一。信息技术与中小学数学学科的整合,使得中小学数学教学中学习内容和学习形式、教学观念和教学方式都产生了一系列的变化,本文通过在初中数学教学中进行的信息技术与课程整合实践尝试,总结了将信息技术有效地与中学数学课程整合,可以培养学生学习数学兴趣和实践能力。