Computing demand properties at the wholesale warehouse level

Computational formulas are given for the mean, variance, and autocorrelation function of the demand process at an upper-echelon facility (warehouse). The demand process at the warehouse is induced by the aggregated inventory replenishment processes of N independently operated lower-echelon facilities (stores) in parallel. Each store, we assume, employs an (s,S) inventory replenishment policy with complete backlogging to satisfy its own random, independently and identically distributed demand. The formulas result from an analysis of the stochastic replenishment process at a single store. Examples of the properties of the demand process at the upper-echelon facility are presented for several lower-echelon environments.     

Nonadjacent extreme point methods for solving linear programs

In this article we present some advanced basis or block-pivoting, relaxation, and feasible direction methods for solving linear programming problems. Preliminary computational results appear to indicate that the former two types of simplex-based procedures may hold promise for solving linear programming problems, unlike the third type of scheme which is shown to be computationally unattractive.     

Adjacent vertices on transportation polytopes

To solve linear fixed charge problems with Murty's vertex ranking algorithm, one uses a simplex algorithm and a procedure to determine the vertices adjacent to a given vertex. In solving fixed charge transportation problems, the simplex algorithm simplifies to the stepping-stone algorithm. To find adjacent vertices on transportation polytopes, we present a procedure which is a simplification of a more general procedure for arbitrary polytopes.     

An operator theory of parametric programming for the generalized transportation problem-III-weight operators

This paper investigates the effect on the optimum solution of a capacitated generalized transportation problem when any coefficient of any row constraint is continuously varied as a linear function of a single parameter. The entire analysis is divided into three parts. Results are derived relative to the cases when the coefficient under consideration is associated, to a cell where the optimal solution in that cell attains its lower bound or its upper bound. The discussion relative to the case when the coefficient under consideration is associated to a cell in the optimal basis is given in two parts. The first part deals with the primal changes of the optimal solution while the second part is concerned with the dual changes. It is shown that the optimal cost varies in a nonlinear fashion when the coefficient changes linearly in certain cases. The discussion in this paper is limited to basis-preserving operators for which the changes in the data are such that the optimum bases are preserved. Relevant algorithms and illustrations are provided throughout the paper.     

Periodic replacement with minimal repair at failure and adjustment costs

We investigate periodic replacement policies with minimal repair at failure, thereby, minimizing the average expected cost per unit time over an infinite time span. The standard cost structure is modified by the introduction of a term which takes adjustment costs into account.     

An operator theory of parametric programming for the generalized transportation problem: II Rim,cost and bound operators

This paper investigates the effect on the optimum solution of a capacitated generalized transportation problem when certain data of the problem are continuously varied as a linear function of a single parameter. First the rim conditions, then the cost coefficients, and finally the cell upper bounds are varied parametrically and the effect on the optimal solution, the associated change in costs and the dual changes are derived. Finally the effect of simultaneous changes in both cost coefficients and rim conditions are investigated. Bound operators that effect changes in upper bounds are shown to be equivalent to rim operators. The discussion in this paper is limited to basis preserving operators for which the changes in the data are such that the optimum bases are preserved.     

An empirical bayes estimator for the scale parameter of the two-parameter weibull distribution

An empirical Bayes estimator is given for the scale parameter in the two-parameter Weibull distribution. The scale parameter is assumed to vary randomly throughout a sequence of experiments according to a common, but unknown, prior distribution. The shape parameter is assumed to be known, however, it may be different in each experiment. The estimator is obtained by means of a continuous approximation to the unknown prior density function. Results from Monte Carlo simulation are reported which show that the estimator has smaller mean-squared errors than the usual maximum-likelihood estimator.     

Optimal allocation of unreliable components for maximizing expected profit over time

In the present paper, we solve the following problem: Determine the optimum redundancy level to maximize the expected profit of a system bringing constant returns over a time period T; i. e., maximize the expression \documentclass{article}\pagestyle{empty}\begin{document}$ P\int_0^T {Rdt - C} $\end{document}, where P is the return of the system per unit of time, R the reliability of this system, C its cost, and T the period for which the system is supposed to work We present theoretical results so as to permit the application of a branch and bound algorithm to solve the problem. We also define the notion of consistency, thereby determining the distinction of two cases and the simplification of the algorithm for one of them.