一个新的组合恒等式及其证明

本文以定理的形式提出一个新的组合恒等式。它是在恒虚警算法研究和性能分析中经常遇到的恒等式。对此,文中给出详细的证明。在证明过程中,我们还提出了有关该定理在实际中可以直接应用的3个引理和2个推论。     

When is model complexity too much? Illustrating the benefits of simple models with Hughes' salvo equations

The simulations that many defense analysts rely upon in their studies continue to grow in size and complexity. This paper contrasts the guidance that the authors have received—from some of the giants of military operations research—with the current practice. In particular, the analytic utility of Hughes' simple salvo equations is compared with that of the complex Joint Warfighting System (JWARS), with respect to JWARS' key performance parameters. The comparison suggests that a family of analytic tools supports the best analyses. It follows that smaller, more agile, and transparent models, such as Hughes' salvo equations, are underutilized in defense analyses. We believe that these models should receive more attention, use, and funding. To illustrate this point, this paper uses two very simple models (by modern standards) to rapidly generate insights on the value of information relative to force strength. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

A multiechelon inventory model with multiple failures

This article presents a recoverable spares model for performance evaluation in a multiechelon inventory environment. This model explicitly incorporates the phenomenon known as multiple failures, in which more than one part can require replacement or repair when an end-item reaches a maintenance base. The model is shown to be computationally intractable, and an approximation scheme is presented to estimate system performance. © 1993 John Wiley & Sons, Inc.     

On the equivalence of jit and mrp as technologies for reducing wastes in manufacturing

JIT (just-in-time) is widely regarded as an excellent tool for reducing costs and cycle times, and for improving quality in manufacturing operations. JIT follows a multistep procedure. First, it identifies and prioritizes wastes or non-value-adding activities. Second, it forces these wastes to be removed. MRP (materials requirements planning) can identify the same wastes and prioritize them in the same way that JIT does, by using data from the MRP database and master production schedule, and a waste identification model. In this article, a model is developed which describes the process by which the classic JIT system identifies and prioritizes waste. An equivalent MRP waste identification model is then developed for the production environment of the classic JIT system. (The classic JIT system was developed to produce many products having low to medium volumes.) The results developed here can be extended to other production environments where adaptations of the classic JIT system are used. An example, taken from an actual application, is presented to illustrate the models and the equivalence of JIT and MRP as systems for identifying and prioritizing wastes in manufacturing. © 1993 John Wiley & Sons, Inc.     

Order-statistic calculation,costs, and service in an (s,Q) inventory system

A retailer or distributor of finished goods, or the manager of a spare-parts inventory system, must generally forecast the major portion of demand. A specific customer-service level p (fraction of replenishment intervals with no stockout) implies two challenges: achieve the service within a small interval plus or minus, and do so with a minimum-cost investment in inventory. The pth fractile of lead-time demand (LTD) is the reorder point (ROP) for this service measure, and is often approximated by that fractile of a normal distribution. With this procedure, it is easy to set safety stocks for an (s, Q) inventory system. However, Bookbinder and Lordahl [2] and others have identified cases where the normal approximation yields excessive costs and/or lower service than desired. This article employs an order-statistic approach. Using available LTD data, the ROP is simply estimated from one or two of the larger values in the sample. This approach is sufficiently automatic and intuitive for routine implementation in industry, yet is distribution free. The order-statistic method requires only a small amount of LTD data, and makes no assumptions on the form of the underlying LTD distribution, nor even its parameters μ and ρ. We compare the order-statistic approach and the normal approximation, first in terms of customer service and then using a model of expected annual cost. Based upon characteristics of the available LTD data, we suggest a procedure to aid a practitioner in choosine between the normal and order-statistic method. © 1994 John Wiley & Sons, Inc.     

Alternate methods of project scheduling with limited resources

The applicability of critical path scheduling is limited by the inability of the algorithm to cope with conflicting resource demands. This paper is an assessment of the effectiveness of many of the heuristic extensions to the critical path method which resolve the conflicts that develop between the resources demanded by an activity and those available. These heuristic rules are evaluated on their ability to solve a large multiproject scheduling problem.     

Lower confidence limits for the impact probability within a circle in the normal case

Lower confidence limits are derived for the impact probability within a circle of fixed radius. The bivariate normal distribution with zero means, unequal variances, and zero correlation is the probability model for impacts. A new representation of the impact probability function is offered. This presentation is valid also for the dependent case, where the eigenvalues of the covariance matrix replace the variances. When the ratio of variances is known the lower confidence limits are uniformly most accurate (UMA). A few alternative approaches are compared by simulation when the ratio of variances is unknown.