Minimal disconnecting sets in directed multi-commodity networks

The problem of finding minimal disconnecting sets for multi-commodity directed networks may be solved using an arc-path formulation and Gomory's all-integer integer programming algorithm. However, the number of network constraints may be astronomical for even moderately sized networks. This paper develops a finite algorithm similar to Gomory's, but requiring no more than m rows in the tableau, where m is the number of arcs in the network.     

On the reliability,availability and bayes confidence intervals for multicomponent systems

The problem of computing reliability and availability and their associated confidence limits for multi-component systems has appeared often in the literature. This problem arises where some or all of the component reliabilities and availabilities are statistical estimates (random variables) from test and other data. The problem of computing confidence limits has generally been considered difficult and treated only on a case-by-case basis. This paper deals with Bayes confidence limits on reliability and availability for a more general class of systems than previously considered including, as special cases, series-parallel and standby systems applications. The posterior distributions obtained are exact in theory and their numerical evaluation is limited only by computing resources, data representation and round-off in calculations. This paper collects and generalizes previous results of the authors and others. The methods presented in this paper apply both to reliability and availability analysis. The conceptual development requires only that system reliability or availability be probabilities defined in terms acceptable for a particular application. The emphasis is on Bayes Analysis and the determination of the posterior distribution functions. Having these, the calculation of point estimates and confidence limits is routine. This paper includes several examples of estimating system reliability and confidence limits based on observed component test data. Also included is an example of the numerical procedure for computing Bayes confidence limits for the reliability of a system consisting of N failure independent components connected in series. Both an exact and a new approximate numerical procedure for computing point and interval estimates of reliability are presented. A comparison is made of the results obtained from the two procedures. It is shown that the approximation is entirely sufficient for most reliability engineering analysis.     

On a class of nash-solvable bimatrix games and some related nash subsets

This work is concerned with a particular class of bimatrix games, the set of equilibrium points of which games possess many of the properties of solutions to zero-sum games, including susceptibility to solution by linear programming. Results in a more general setting are also included. Some of the results are believed to constitute interesting potential additions to elementary courses in game theory.     

The role of internal storage capacity in fixed cycle production systems

The reliability of a serial production line is optimized with respect to the location of a single buffer. The problem was earlier defined and solved by Soyster and Toof for the special case of an even number of machines all having equal probability of failure. In this paper we generalize the results for any number of machines and remove the restriction of identical machine reliabilities. In addition, an analysis of multibuffer systems is presented with a closed form solution for the reliability when both the number of buffers and their capacity is limited. For the general multibuffer system we present an approach for determining system reliability.     

An application of statistical techniques to estimate engineering man-hours on major aircraft programs

Data on 23 lots of various aircraft programs were gathered. Total engineering man-hours, and information on performance, weight, area, avionics systems, data, and schedule were subjected to least squares analysis. An equation is presented which indicates a relationship between total engineering manhours and a set of seven predictor variables. While the equation derived could only be used with confidence by the manufacturer whose data was analyzed, this article should be looked upon as demonstrating a method of data analysis which others may also find useful, not only for predicting engineering manhours in major aircraft programs, but also in other situations where there is an abundance of possible predictor variables, and the problem is to sort out a meaningful subset of these variables. In order to demonstrate the viability of the formula obtained, comparisons were made with various bid programs.     

Applications of a generalized combinatorial problem of smirnov

In this paper applications of results obtained by these authors for a generalized version of a problem proposed by Smirnov, are considered. The areas of application explored are system interface, queueing, transportation flow, and sequential analysis. The included table should be invaluable to the reader in applying these results. Finally the relationship between the limiting and exact expressions relating to this table is also explored.     

Optimum quantiles for the linear estimation of the parameters of the extreme value distribution in complete and censored samples

The present study is concerned with the determination of a few observations from a sufficiently large complete or censored sample from the extreme value distribution with location and scale parameters μ and σ, respectively, such that the asymptotically best linear unbiased estimators (ABLUE) of the parameters in Ref. [24] yield high efficiencies among other choices of the same number of observations. (All efficiencies considered are relative to the Cramér-Rao lower bounds for regular unbiased estimators.) The study is on the asymptotic theory and under Type II censoring scheme. For the estimation of μ when σ is known, it has been proved that there exists a unique optimum spacing whether the sample is complete, right censored, left censored, or doubly censored. Several tables are prepared to aid in the numerical computation of the estimates as well as to furnish their efficiencies. For the estimation of σ when μ is known, it has been observed that there does not exist a unique optimum spacing. Accordingly we have obtained a spacing based on a complete sample which yields high efficiency. A similar table as above is prepared. When both μ and σ are unknown, we have considered four different spacings based on a complete sample and chosen the one yielding highest efficiency. A table of the efficiencies is also prepared. Finally we apply the above results for the estimation of the scale and/or shape parameters of the Weibull distribution.     

Inventory management with advance capacity information

An important aspect of supply chain management is dealing with demand and supply uncertainty. The uncertainty of future supply can be reduced if a company is able to obtain advance capacity information (ACI) about future supply/production capacity availability from its supplier. We address a periodic‐review inventory system under stochastic demand and stochastic limited supply, for which ACI is available. We show that the optimal ordering policy is a state‐dependent base‐stock policy characterized by a base‐stock level that is a function of ACI. We establish a link with inventory models that use advance demand information (ADI) by developing a capacitated inventory system with ADI, and we show that equivalence can only be set under a very specific and restrictive assumption, implying that ADI insights will not necessarily hold in the ACI environment. Our numerical results reveal several managerial insights. In particular, we show that ACI is most beneficial when there is sufficient flexibility to react to anticipated demand and supply capacity mismatches. Further, most of the benefits can be achieved with only limited future visibility. We also show that the system parameters affecting the value of ACI interact in a complex way and therefore need to be considered in an integrated manner. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011