Parametric studies in transportation-type problems

In this paper we present some results in parametric studies on several transportation-type problems. Specifically, a characterization is obtained for the optimal values of the variables in the problem of determining an optimal growth path in a logistics system. We also derive an upper bound beyond which the optimal growth path remains the same. The results are then extended to the goal programming model and the prespecified market growth rate problem.     

Order-preserving allocation of jobs to two machines

In this paper, we consider the problem of minimizing the mean flow time of jobs to be processed on two machines. The jobs have a predetermined order, perhaps reflecting the order of arrival, and each job has a known processing time. We wish to assign the jobs to machines so as to minimize the mean flow time, with the constraint that the original order must be preserved within the subset of jobs assigned to each machine. An efficient algorithm based on dynamic programming is developed.     

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.     

A queue with waiting time dependent service times

Sufficient conditions are developed for the ergodicity of a single server, first-come-first-serve queue with waiting time dependent service times.     

Dynamic programming approach to the optimization of Naval aircraft rework and replacement policies

This paper describes a method for determining optimal repair and replacement policies for aireraft, with specific reference to the F–4. The objective of the analysis is to choose the set of policies from all possible alternatives over a finite planning horizon which minimizes the cost of operations. A dynamic program is presented which seeks an optimal path through a series of decision periods, when each period begins with the choice of keeping an aircraft, reworking it before further operation, or buying a new one. We do not consider changes in technology. Therefore, when a replacement does occur, it is made with a similar aircraft. Multivariate statistical techniques are used to estimate the relevant costs as a function of age, and time since last rework.     

Stochastic leadtimes in continuous-time inventory models

This paper shows that one of the fundamental results of inventory theory is valid under conditions much broader than those treated previously. The result characterizes the distributions of inventory level and inventory position in the standard, continuous-time model with backorders, and leads to the relatively easy calculation of key performance measures. We treat both fixed and random leadtimes, and we examine both stationary and limiting distributions under different assumptions. We consider demand processes described by several general classes of compound-counting processes and a variety of order policies. For the stochastic-leadtime case we provide the first explicit proof of the result, assuming the leadtimes are generated according to a specific, but plausible, scenario.     

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.     

Weibull tolerance intervals associated with moderate to small survival proportions for use in a new formulation of lanchester combat theory

Given herein is an easily implemented method for obtaining, from complete or censored data, approximate tolerance intervals associated with the upper tail of a Weibull distribution. These approximate intervals are based on point estimators that make essentially most efficient use of sample data. They agree extremely well with exact intervals (obtained by Monte Carlo simulation procedures) for sample sizes of about 10 or larger when specified survival proportions are sufficiently small. Ranges over which the error in the approximation is within 2 percent are determined. The motivation for investigation of the methodology for obtaining the approximate tolerance intervals was provided by the new formulation of Lanchester Combat Theory by Grubbs and Shuford [3], which suggests a Weibull assumption for time-to-incapacitation of key targets. With the procedures investigated herein, one can use (censored) data from battle simulations to obtain confidence intervals on battle times associated with given low survivor proportions of key targets belonging to either specified side in a future battle. It is also possible to calculate confidence intervals on a survival proportion of key targets corresponding to a given battle duration time.