The search for an intelligent evader: Strategies for searcher and evader in the two-region problem

This paper considers the search for an evader concealed in one of two regions, each of which is characterized by its detection probability. The single-sided problem, in which the searcher is told the probability of the evader being located in a particular region, has been examined previously. We shall be concerned with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move: his optimal strategy consists of that probability distribution which maximizes the expected time to detection, while the searcher's optimal strategy is the sequence of searches which limits the evader to this expected time. It transpires for this problem that optimal strategies for both searcher and evader may generally be obtained to a surprisingly good degree of approximation by using the optimal strategies for the closely related (but far more easily solved) problem in which the evader is completely free to move between searches.     

A streamlined simplex approach to the singly constrained transportation problem

A primal simplex procedure is developed to solve transportation problems with an arbitrary additional linear constraint. The approach is a specialization of the Double Reverse Method of Charnes and Cooper. Efficient procedures for pricing-out the basis, determining representations, and implementing the change of basis are presented. These procedures exploit the pure transportation substructure in such a manner that full advantage may be taken of the computational schemes and list structures used to store and update the basis in codifying the MODI method. Furthermore, the pricing-out and change-of-basis procedures are organized in a manner that permits the calculations for one to be utilized in the other. Computational results are presented which indicate that this method is at least 50 times faster than the state-of-the-art LP code, APEX-III. Methods for obtaining basic primal “feasible” starts and “good” feasible integer solutions are also presented.     

On single-machine sequencing with order constraints

A collection of jobs is to be processed by a single machine. Each job has a cost function associated with it which may be either linear or exponential, costs accruing when a job is completed. The machine may be allocated to the jobs according to a precedence relation. The problem is to find a strategy for allocating the machine which minimizes the total cost and which is consistent with the precedence relation. The paper extends and simplifies some previous work done by Sidney.     

A decomposable transshipment algorithm for a multiperiod transportation problem

A dynamic version of the transportation (Hitchcock) problem occurs when there are demands at each of n sinks for T periods which can be fulfilled by shipments from m sources. A requirement in period t₂ can be satisfied by a shipment in the same period (a linear shipping cost is incurred) or by a shipment in period t₁ < t₂ (in addition to the linear shipping cost a linear inventory cost is incurred for every period in which the commodity is stored). A well known method for solving this problem is to transform it into an equivalent single period transportation problem with mT sources and nT sinks. Our approach treats the model as a transshipment problem consisting of T, m source — n sink transportation problems linked together by inventory variables. Storage requirements are proportional to T² for the single period equivalent transportation algorithm, proportional to T, for our algorithm without decomposition, and independent of T for our algorithm with decomposition. This storage saving feature enables much larger problems to be solved than were previously possible. Futhermore, we can easily incorporate upper bounds on inventories. This is not possible in the single period transportation equivalent.     

An inventory problem with obsolescence

A stochastic single product convex cost inventory problem is considered in which there is a probability, π_j, that the product will become obsolete in the future period j. In an interesting paper, Barankin and Denny essentially formulate the model, but do not describe some of its interesting and relevant ramifications. This paper is written not only to bring out some of these ramifications, but also to describe some computational results using this model. The computational results show that if obsolescence is a distinct possibility in the near future, it is quite important that the probabilities of obsolescence be incorporated into the model before computing the optimal policies.     

Operational definitions of inventory record accuracy

An inventory stock record is in error when the information on the stock record is not in agreement with the actual physical situation. We address the questions of what is meant by inventory record accuracy as reported in the literature and what should be meant by this term, in the context of the inventory record accuracy problem defined by the Naval Supply Systems Command. The need for, and suggestions of, operational definitions of error measures are demonstrated in terms of the reporting of accuracy statistics, the formulation of inventory record accuracy goals, and the determination of corrective measures.     

Normal and weibull distributions

Numerous applications of the Weibull distribution in diverse fields of human endeavor are well known today. Nevertheless, it is not uncommon to find applications of the normal distribution in such fields of studies as agriculture, biology, chemistry, engineering, physics, sociology and others. At the present time we have at our disposal many more refined statistical techniques for analyzing the normal rather than the Weibull data. Consequently, it is important for applied statisticians to know if some of their data which can be described by the Weibull distribution can also be described by the normal distribution. The present investigation of the author reveals that the normal distri,bution can be considered to be a good approximation to the Weibull distribution as long as its shape parameter is in the open interval (3.25, 3.61). This fact enables them to perform a refined statistical analysis of their data. Conversely, they can now easily compute the desired normal cumulative probabilities from the Weibull distribution function, which would be especially helpful for those standard normal deviates whose cumulative probabilities cannot be read from the available tables of normal cumulative probability. In a similar situation they can also use the Weibull distribution to obtain an approximation to any desired normal deviate for a given normal probability which may be better than those obtained by the linear interpolation method.     

旋转稳定塑料弹体工程设计计算研究

本文以实验结果为依据,首先分析了塑料弹体影响弹丸膛内运动的物理性能,然后结合旋转弹丸的膛内运动特征,经过模拟试验,采用数学拟合法,初步建立旋转稳定弹塑料弹体工程设计计算的数学模型(包括结构尺寸设计计算、强度计算和内弹道计算)。