Minimax and maximin facility location problems on a sphere

The problem dealt with in this article is as follows. There are n “demand points” on a sphere. Each demand point has a weight which is a positive constant. A facility must be located so that the maximum of the weighted distances (distances are the shortest arcs on the surface of the sphere) is minimized; this is called the minimax problem. Alternatively, in the maximin problem, the minimum weighted distance is maximized. A setup cost associated with each demand point may be added for generality. It is shown that any maximin problem can be reparametrized into a minimax problem. A method for finding local minimax points is described and conditions under which these are global are derived. Finally, an efficient algorithm for finding the global minimax point is constructed.     

A performance comparison of empirical Bayes and Bayes estimators of the Weibull and gamma scale parameters

A mean-squared error comparison of smooth empirical Bayes and Bayes estimators for the Weibull and gamma scale parameters is studied based on a computer simulation. The smooth empirical Bayes estimators are determined as functions of up to 15 past estimates of the parameter of interest. Results indicate that at best the mean-squared errors of the empirical Bayes estimators are about 20–40% larger than those of the corresponding squared-error optimal Bayes estimators.     

Scheduling with earliest start and due date constraints on multiple machines

We consider the scheduling of n jobs on m identical machines when the jobs become available for processing at ready times a_i, a_i, ? 0, require d_i time units for processing and must be completed by times b_i for i = 1, 2, … n. The objective chosen is that of minimizing the total elapsed time to complete all jobs subject to the ready time and due date constraints, preemption is not allowed. We present a multi-stage solution algorithm for this problem that is based on an implicit enumeration procedure and also uses the labelling type algorithm which solves the problem when preemption is allowed.     

On sequencing with earliest starts and due dates with application to computing bounds for the (n/m/G/Fmax) problem

Recent efforts to improve lower bounds in implicit enumeration algorithms for the general (n/m/G/F_max) sequencing problem have been directed to the solution of an auxiliary single machine problem that results from the relaxation of some of the interference constraints. We develop an algorithm that obtains optimal and near optimal solutions for this relaxed problem with relatively little computational effort. We report on computational results achieved when this method is used to obtain lower bounds for the general problem. Finally, we show the equivalence of this problem to a single machine sequencing problem with earliest start and due date constraints where the objective is to minimize the maximum lateness.     

Estimation of a hidden service distribution of an M/G/∞ system

The maximum likelihood estimator of the service distribution function of an M/G/∞ service system is obtained based on output time observations. This estimator is useful when observation of the service time of each customer could introduce bias or may be impossible. The maximum likelihood estimator is compared to the estimator proposed by Mark Brown, [2]. Relative to each other, Brown's estimator is useful in light traffic while the maximum likelihood estimator is applicble in heavy trafic. Both estimators are compared to the empirical distribution function based on a sample of service times and are found to have drawbacks although each estimator may have applications in special circumstances.     

Johnson's approximate method for the 3 × n job shop problem

The effectiveness of Johnson's Approximate Method (JAM) for the 3 × n job shop scheduling problems was examined on 1,500 test cases with n ranging from 6 to 50 and with the processing times A_i, B_i, C_i (for item i on machines A, B, C) being uniformly and normally distributed. JAM proved to be quite effective for the case B_i ? max (A_i, C_i) and optimal for B_i, ? min (A_i, C_i).     

Landmarks in defense literature

The Brain of an Army: a Popular Account of the German General Staff. By Spenser Wilkinson. Archibald Constable, London (1st edition 1890, 2nd edition 1895)