Explicit formulas for the order size and reorder point in certain inventory problems

This study concentrates on distributions of leadtime demand that permit explicit solution to the lot-size, reorder point model. The optimal order size for the general case is first expressed as a function of the economic order quantity and a quantity known as the “residual mean life” in reliability theory. The concept of “no aging” is then utilized to identify a broad class of distributions for which the optimal order size can be determined explicitly, independent of the reorder point.     

Performance of N machine centers of K-out-of-M: G type maintained by a single repairman

We consider a system of N (nonsymmetric) machine centers of the K-out-of-M : G type that are maintained by a single repairman. [A machine center functions if and only if at least K of the M machines belonging to the center are good (G).] Such systems are commonly found in various manufacturing and service industries. A stochastic model is developed that accommodates generally distributed repair times and repairman walk times, and most repair scheduling disciplines. K-out-of-M : G type systems also appear as a modeling paradigm in reliability analysis and polling systems performance analysis. Several performance measures are derived for machine-repair systems having K-out-of-M-type centers. A simple example system is developed in detail that exposes the computations involved in modeling applications. © 1992 John Wiley & Sons, Inc.     

Effect of switch-over devices on reliability of a standby complex system

The behaviour of a standby redundant complex system under imperfect switch-over devices with general waiting and repair time distributions for both types of components has been studied. The Laplace transform of various state probabilities have been derived. A particular case has also been discussed.     

On the solution of some approximate continuous review inventory models

This article compares two types of approximating strategies for solving some continuous review inventory models noniteratively. One of these strategies is to approximate the normalized loss integral by an exponential function whereas the other strategy is to estimate the loss integral as a quadratic function of the right-tail probability. It is found that the latter method is significantly more accurate and versatile than the former method. Theoretical arguments are given to emphasize that both the right-tail probability and the loss integral are key functions involved in those models. Therefore, a good strategy should be not only to estimate these two functions, but also to retain the interrelationships between them. The quadratic method is better than the exponential method primarily because of the latter property.     

On the use of a structural equation for determining inventory order quantities

This article considers a structural equation useful for characterizing the order quantity of several inventory models. A correct interpretation of this equation is provided and it is stressed that the equation should be used in conjunction with another equation for the reorder point. Failure to do so may give rise to improper interpretations and invalid conclusions. A specific case like this is cited for the sake of illustration.     

Sensitivity of the (Q,R) inventory model to penalty cost parameter

This paper treats an approximate continuous review inventory model with backlogging of excess demand and stochastic leadtime. The major result derived is that the behavior of the optimal order size with respect to the shortage cost parameter is determined solely by the “conditional mean residual life” function corresponding to the leadtime demand distribution. Some minor results and illustrative examples are also included.