The single period procurement problem where dedicated supplier capacity can be reserved

In this article we consider the single period procurement strategy for an item with uncertainty in its demand and uncertainty in the capacity of the supplier. Dedicated capacity can be ensured by paying a premium charge to the supplier. The other decision variable is the replenishment quantity to request. It turns out to be very easy to select the best value of this latter quantity. On the other hand, we are only able to characterize the general behavior of the expected profit as a function of the level of dedicated capacity. In general, there can be multiple local maxima as a function of the dedicated capacity. However, for the special, but important, case of normally distributed demand, normally distributed capacity and a linear cost for reserving capacity, an algorithm is developed for finding the best level of dedicated capacity. Some preliminary insights regarding the extension to multiple periods are presented. © 1995 John Wiley & Sons, Inc.     

A linear relaxation heuristic for the generalized assignment problem

We examine the basis structure of the linear relaxation of the generalized assignment problem. The basis gives a surprising amount of information. This leads to a very simple heuristic that uses only generalized network optimization codes. Lower bounds can be generated by cut generation, where the violated inequalities are found directly from the relaxation basis. An improvement heuristic with the same flavor is also presented.     

Optimal inventory policies for substitutable commodities with stochastic demand

In this article we consider a stochastic model for two products which have a single-period inventory structure and which can be used as substitutes for each other should the need arise. Substitution will occur with probability one, but at perhaps a different revenue level. We prove that the expected profit function is concave, allowing us to find optimal stocking levels for the two products. We compare optimum inventory levels for the case of single substitution with that where there is no substitution. It is demonstrated for the case of single substitution that total optimum order quantities can actually increase or decrease with the substitution revenue.     

Some experiences using MIL-STD-105 in the united states air force

The historical and, to some extent, the current role of attribute inspection sampling in the United States Air Force is described. Some insight into consideration culminating in revisions made to the original MIL-STD-105 sampling plans is provided. These revisions were motivated from a practitioner's perspective rather than that of a statistical expert. Some significant administrative applications within the Air Force are described, and a practical method, based on the total amount of inspection, is given for distinguishing between sampling plans that have a fixed risk level (i.e., common value on the OC curves).     

On the bivariate negative binomial distribution of mitchell and paulson

The bivariate negative binomial distribution of Mitchell and Paulson [17] for the case b = c = 0 is shown to be equivalent to the accident proneness model of Edwards and Gurland [4] and Subrahmaniam [19,20]. The diagonal series expansion of its joint probability function is then derived. Two other formulations of this distribution are also considered: (i) as a mixture model, which showed how it arises as the discrete analogue to the Wicksell-Kibble bivariate gamma distribution, and (ii) as a consequence of the linear birth-and-death process with immigration.     

A reliability model with states of partial operation

This article generalizes the classical dichotomic reliability model to include states of partial operation. The generalized model can be considered as a special case of a general jump process. Both continuous and discrete state spaces are included. The relationship to cumulative damage shock models is discussed. Properties of the model are investigated and these are illustrated via examples. The equivalence of three forms of component independence is proved, but this equivalence does not generalize to the property of zero covariance. Alternative forms of series and parallel connections and the effect of component replacement are discussed.     

Recurrence relations between moments of order statistics

A general result for obtaining recurrence relations between single moments of order statistics is obtained and has been used to establish the recurrence relations between moments of some doubly truncated distributions. The examples considered are Weibull, exponential, Pareto, power function, Cauchy, and logistic. Recurrence relations are also obtained for nontruncated gamma and beta distributions.     

The effect of stochastic time delays on the reliability of isolated impulse systems

This article concerns the effect of stochastic time delays in the operation of components upon system reliability for isolated impulse systems, for which component delays have hitherto been treated as deterministic. These are systems, such as automatic protective devices, which remain idle for most of their lives but which are required to respond with the utmost speed to input signals arising at arbitrary isolated time instants. System failure can arise from components failing to operate, or from being too slow to operate so that the systems operation is too slow to meet requirements. During operation components are usually subjected to greater stresses than during idling, so that it is assumed that components are subjected to increased failure tendencies during the time it takes them to perform their functions. The effect of stochastic time delays on the evaluation of systems reliability is considered, and a hierarchy of complexity associated with the physical nature of the delays in series and redundant configurations is exposed. Some simple exponential illustrations are presented.