A note on first passage times in birth and death and nonnegative diffusion processes

Consider a birth and death process starting in state 0. Keilson has shown by analytical arguments that the time of first passage into state n has an increasing failure rate (IFR) distribution. We present a probabilistic proof for this. In addition, our proof shows that for a nonnegative diffusion process, the first passage time from state 0 to any state x is IFR.     

Parameter estimation for the EOQ lot-size model: Minimax and expected value choices

This article provides formulas for estimating the parameters to be used in the basic EOQ lot-size model. The analysis assumes that the true values of these parameters are unknown over known ranges and perhaps nonstationary over time. Two measures of estimator “goodness” are derived from EOQ sensitivity analysis. Formulas are given for computing the minimax choice and the minimum expected value choice for the parameter estimates using both measures of estimator “goodness”. A numerical example is included.     

Multivariate age-dependent imperfect repair

In this article we consider models of systems whose components have dependent life lengths with specific multivariate distributions. Upon failure, components are repaired. Two types of repair are distinguished. After perfect repair, a unit has the same life distribution as a new item. After imperfect repair, a unit has the life distribution of an item which is of the same age but has never failed. We study a model in which the mechanism for determining the nature of the repair is age dependent.     

Production planning for multi-resource network systems

Production planning for large-scale production systems requiring the allocation of numerous resources is considered. It is demonstrated how the dynamic activity analysis developed by Shephard leads to linear programming solutions of production planning problems. Three types of planning problems are formulated: maximization of output levels for a given time horizon; minimization of production duration for given output histories; and minimization of production costs for given output histories.     

Sequencing n jobs on two machines with setup,processing and removal times separated

The paper extends the machine flow-shop scheduling problem by separating processing time into setup, processing and removal times.     

A note on the influence of missing operations on scheduling problems

This paper attempts to resolve the existing confusion concerning missing operations. Scheduling problems are classified in two groups: (i) null-continuous (NC)—comprising the problems where an optimal schedule remains optimal on replacement of arbitrarily small processing times (existing operations) with zeros (missing operations); (ii) null-discontinuous (NDC)—comprising those problems which are not null-continuous.