Bounding methods for facilities location algorithms

Single- and multi-facility location problems are often solved with iterative computational procedures. Although these procedures have proven to converage, in practice it is desirable to be able to compute a lower bound on the objective function at each iteration. This enables the user to stop the iterative process when the objective function is within a prespecified tolerance of the optimum value. In this article we generalize a new bounding method to include multi-facility problems with l_p distances. A proof is given that for Euclidean distance problems the new bounding procedure is superior to two other known methods. Numerical results are given for the three methods.     

Estimating the accuracy of the coverages of outer β-content tolerance intervals,which control both tails of the normal distribution

Tolerance limits which control both tails of the normal distribution so that there is no more than a proportion β₁ in one tail and no more than β₂ in the other tail with probability γ may be computed for any size sample. They are computed from X? - k₁S and X? - k₂S, where X? and S are the usual sample mean and standard deviation and k₁ and k₂ are constants previously tabulated in Odeh and Owen [3]. The question addressed is, “Just how accurate are the coverages of these intervals (– Infin;, X? – k₁S) and (X? + k₂S, ∞) for various size samples?” The question is answered in terms of how widely the coverage of each tail interval differs from the corresponding required content with a given confidence γ′.     

A simulation study of the efficiency of empirical Bayes' estimators of multiple correlated probability vectors

Empirical Bayes' methods had been used by Brier, Zacks, and Marlow [1] for estimating performance characteristic vectors of success probabilities. The problem is that of estimating k-dimensional success probabilities of dependent binomial random variables, which are highly correlated. The present study reinforces the results of the previous one by showing, via simulations, that the relative efficiency of the empirical Bayes estimators, compared to the Stein-type and to the maximum-likelihood ones, is very high. This holds even if the success proportions are based on a small number of trials. We study the case of equicorrelation structure with positive correlations.     

A graphical aid for sensitivity analysis of estimated regression coefficients

A problem often arising in applied linear regression modeling is determining the appropriate weight to attach to each observation. In the extreme, the problem extends to the deletion of observations from a data base. Since the choice of weights, fitting criteria, and estimation procedure depend on the specific objectives of the modeling, universally applicable guidelines are virtually nonexistent. However, the sensitivity of analytic conclusions to weights assigned to “suspect” observations can be conveniently assessed using a graphical display. This report develops such a display based on a modeling of outliers which leads naturally to estimators based on a weighted least-squares criterion, and a data-analytic method for determining how much downweighting to impose on a specific subset of observations. This technique is illustrated with several examples, including one relating air pollution to human mortality.     

Waiting time distributions for transient bulk queues with general vehicle dispatching strategies

A numerical approach is presented for determining the waiting time distribution in a transient bulk-arrival, bulk-service queue. Vehicle departures from the queue are governed by a general dispatch strategy that includes holding with a variable release function and vehicle cancellations. The waiting time distribution of a customer (in a group) arriving at a given point in time is calculated by simulating the process in discrete time and determining at each step the probability the customer has left the system. The dispatch strategies require knowing the total length of the queue as well as the position a customer holds in the queue. An exact approach is compared to an accurate approximation which is 50 to 100 times faster. Comparisons are made with other approaches in the context of steady-state systems.