Estimating normal tail probabilities

The estimation problem of normal tail probabilities is considered. The form of generalized Bayes estimators is derived and the asymptotic behavior of the mean square errors is studied. This study shows that the best unbiased estimator, a formula for which is given, is superior to the maximum likelihoood estimator or to a class of generalized Bayes procedures for large parametric values, but can be significantly improved for moderate values of the parameter.     

Least-absolute-value estimators for one-way and two-way tables

This paper concerns itself with the problem of estimating the parameters of one-way and two-way classification models by minimization of the sum of the absolute deviations of the regression function from the observed points. The one-way model reduces to obtaining a set of medians from which optimal parameters can be obtained by simple arithmetic manipulations. The two-way model is transformed into a specially structured linear programming problem, and two algorithms are presented to solve this problem. The occurrence of alternative optimal solutions in both models is discussed, and numerical examples are presented.     

Multiproduct lot-size scheduling with proportional product demands

In this paper we consider the multiproduct, multiperiod production-scheduling model of Manne under the assumption that, across products, demands are interrelated over time. When demand requirements are proportional we show that the solution has a specific structure determined by the ratio of setup to production-run time of each product. This structure holds for any length horizon and may permit a substantial (time) savings for column generation solution procedures.     

A single period model for a multiproduct perishable inventory system with economic substitution

This paper develops a single period model for a specific class of multiproduct perishable inventory systems where demands are interdependent. This class of inventory systems has the property that there is economic substitution between products. It is shown that the optimal policy has the economic substitution property, and that the rate of substitution is age dependent. The model serves as a generalization of a theorem discovered by Ignall and Veinott.     

Single machine sequencing with random processing times and random due-dates

A single machine scheduling problem in which both the processing times and due-dates of the jobs awaiting servicing are random variables is analyzed. It is proved that the properties of the shortest processing time rule and the due-date rule which are known for the deterministic situation also hold in the probabilistic environment when they are suitably, and reasonably, refined for this context.