An adaptive dynamic programming algorithm for a stochastic multiproduct batch dispatch problem

We address the problem of dispatching a vehicle with different product classes. There is a common dispatch cost, but holding costs that vary by product class. The problem exhibits multidimensional state, outcome and action spaces, and as a result is computationally intractable using either discrete dynamic programming methods, or even as a deterministic integer program. We prove a key structural property for the decision function, and exploit this property in the development of continuous value function approximations that form the basis of an approximate dispatch rule. Comparisons on single product‐class problems, where optimal solutions are available, demonstrate solutions that are within a few percent of optimal. The algorithm is then applied to a problem with 100 product classes, and comparisons against a carefully tuned myopic heuristic demonstrate significant improvements. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 742–769, 2003.     

Looking ahead in India

India and China contain more than 40% of the world's population, yet in India it is painfully clear that the political commitment necessary to tackle India's greatest problem is not there in full measure. India's present per capita income is less than $300, and nearly 65% of the people live below the poverty line. The average Indian woman produces 5 children; even if the Indian government's efforts to reduce family size to 2 children is successful by the year 2040, India will have a population of 2.5 billion. The possibility that India will succeed in reducing average family size to 2 children appears remote. 30 years ago, India became the 1st developing country to formally make family planning a matter of national policy. In the early years of the national family planning programs, practitioners had access mostly to sterilization and condoms. Over the years, theIndian government persuaded the US and other western donors to give $2 billion to population control programs. Still, the population continues to grow annually at the rate of 2.1%. Government statistics reflect the ups and downs of national population control policies; thenumber of new family planning users increased from 4.3 million in 1974-1975 to 12.5 million in 1976-1977, due largely to a dramatic increase in vasectomies. Tge number of new contraceptive users fell to 4.5 million after the "emergency" was lifted in 1977. The present Indian generation is far more receptive culturally as well as sociologically to the concept of population control than most other developing countries. What is needed now is renewed political committment by the Gandhi adminiostration. India cannot afford to replicate the Chinese way of tackling overpopulation without inflicting human abuses and without undermining its painstakingly cultivated democratic system.     

Algorithms for the minimax transportation problem

In this paper, we consider a variant of the classical transportation problem as well as of the bottleneck transportation problem, which we call the minimax transportation problem. The problem considered is to determine a feasible flow x_ij from a set of origins I to a set of destinations J for which max_(i,j)εIxJ{c_ijx_ij} is minimum. In this paper, we develop a parametric algorithm and a primal-dual algorithm to solve this problem. The parametric algorithm solves a transportation problem with parametric upper bounds and the primal-dual algorithm solves a sequence of related maximum flow problems. The primal-dual algorithm is shown to be polynomially bounded. Numerical investigations with both the algorithms are described in detail. The primal-dual algorithm is found to be computationally superior to the parametric algorithm and it can solve problems up to 1000 origins, 1000 destinations and 10,000 arcs in less than 1 minute on a DEC 10 computer system. The optimum solution of the minimax transportation problem may be noninteger. We also suggest a polynomial algorithm to convert this solution into an integer optimum solution.     

The interactive fixed charge linear programming problem

In many decision-making situations, each activity that can be undertaken may have associated with it both a fixed and a variable cost. Recently, we have encountered serveral practical problems in which the fixed cost of undertaking an activity depends upon which other activities are also undertaken. To our knowledge, no existing optimization model can accomodate such a fixed cost structure. To do so, we have therefore developed a new model called the interactive fixed charge linear programming problem (IFCLP). In this paper we present and motivate problem (IFCLP), study some of its characteristics, and present a finite branch and bound algorithm for solving it. We also discuss the main properties of this algorithm.     

求取鱼雷转角射击转角的实用算法

较为详细地推导了鱼雷转角射击公式,根据分鱼雷转向的不同总结出两类求解公式（各种态好都能用两类公式之一来解算）．最后还讨论了所导出的非线性方程的数值解算方法,该算法具有工程应用价值。     

超精密铣削的三维微加工工艺

本研究旨在对用于获取有雕刻表面金属工件的超精密微加工工艺进行探讨。研究中使用的是车床型的超精密铣床,由分辨率为1nm的X和Z向运动工作台及分辨率为0.0001度的可定位的C轴组成。作为一种铣削工具,一种改进型的由一颗水晶钻构成的“仿球尖铣刀”被放置在X轴的高速气浮轴承之上。这样一来,X轴和C轴的协调运动就可产生三维铣削的效果。为提高表面粗糙度,通过模拟我们研究的刀具边沿和工件表面的接触情况,结果发现,刀具低速进给时切削比较有效。作为三维微加工工艺的一个例子,运用数字仪提供的扫描数据在一个直径为3mm的铜表面上制作一个传统的NOH面罩。经证明,超精密铣床有潜力加工出表面粗糙度为69nm(P—V值)的工件。