Evaluation of base-stock policies in multiechelon inventory systems with state-dependent demands part I: State-independent policies

This article analyzes a model of a multiechelon inventory system. The exogenous demands form Markov-modulated Poisson processes. That is, the demand rates are functions of an underlying Markov chain. Each location follows a base-stock policy which is independent of the state of the underlying Markov chain. We employ the exogenous transit mechanism introduced by Zipkin [7] and Svoronos and Zipkin [6]. The transit times between locations have phase-type distributions. An exact procedure to compute steady-state performance measures is presented. © 1992 John Wiley & Sons, Inc.     

The class of mifra lifetimes and its relation to other classes

In a previous paper, the authors have introduced a class of multivariate lifetimes (MIFRA) which generalize the univariate lifetimes with increasing failure rate average (IFRA). They have also shown that this class satisfies many fundamental properties. In this paper it is shown that other concepts of multivariate IFRA do not satisfy all of these properties. Relationships between MIFRA and these other concepts are given. Finally, positive dependence implications with respect to these classes are also discussed.     

The optimal burn-in testing of repairable equipment

The subject of this paper is the utilization of the “infant mortality” or decreasing failure rate effect to improve the reliability of repairable devices. Decreasing failure rate implies the possibility that devices which exhibit it can be improved by “burn-in testing” of each unit. Such a test serves to accumulate operating time while shielded from the full costs and consequences of failure. A general formulation of the burn-in test decision for repairable devices is presented and some special cases are solved. A class of models, indexed by the degree of partial replacement present in the repair process, is considered and numerical results for the optimal policy are given for several members of that class. A comparison of those results reveals the profitability of testing increases with the complexity of the repairable device.     

One-person games of economic survival

This paper discusses the one-person economic survival game model with a discrete probability distribution for the contribution to surplus variable. The general game model and strategies in these games are examined, and necessary conditions which an undominated, stationary strategy must satisfy are obtained. For a special class of these games a mathematical formulation of the value of the game is given, and examples and theorems which relate to undominated strategies in this class are presented. This paper, in some sense, is a sequel to a portion of a paper by Shubik and Thompson [7] which appeared in this journal.     

A bibliography of search theory and reconnaissance theory literature

This bibliography consists of 75 items on search theory and reconnaissance theory found in periodicals and technical reports. Each entry includes a short summary or a quotation from the pertinent abstract. The items are classified into one or more of the following categories: (1) General Discussion of Problems; (2) Allocation of Effort; (3) Game Theory Formulations; (4) Geometric Search Patterns; (5) Measures of Performance and (6) Miscellaneous.     

Probabilistic models of decreasing failure rate processes

The “infant mortality” effect observed in the statistical treatment of reliability consists of a decreasing with age of the conditional probability of equipment failure (failure rate). One widely applicable explanatory hypothesis is that of population heterogeneity. This is developed here as a basis for several specific models of decreasing failure rate processes. Since, in the case of repairable devices, decreasing failure rate is often observed after the occurrence of failure and repair, consideration is extended to include repair in an explicit way. This union of failure and repair models is a fruitful one in view of the interaction between the two processes and gives a complete picture of the life of the device in terms of a stochastic process, usually with non-independent interfailure times. Four models, of particular significance due to their plausibility, mathematical tractability, and frugality of parameterization, are presented.     

Optimum sequential search with discrete locations and random acceptance errors

Much work has been done in search theory; however, very little effort has occurred where an object's presence at a location can be accepted when no object is present there. The case analyzed is of this type. The number of locations is finite, a single object is stationary at one location, and only one location is observed each step of the search. The object's location has a known prior probability distribution. Also known are the conditional probability of acceptance given the object's absence (small) and the conditional probability of rejection given the object's presence (not too large); these Probabilities remain fixed for all searching and locations. The class of sequential search policies which terminate the search at the first acceptance is assumed. A single two-part optimization criterion is considered. The search sequence is found which (i) minimizes the probability of obtaining n rejections in the first n steps for all n, and (ii) maximizes the probability that the first acceptance occurs within the first n steps and occurs at the object's location for all n. The optimum sequential search policy specifies that the next location observed is one with the largest posterior probability of the object's presence (evaluated after each step from Bayes Rule) and that the object is at the first location where acceptance occurs. Placement at the first acceptance seems appropriate when the conditional probability of acceptance given the object's absence is sufficiently small. Search always terminates (with probability one). Optimum truncated sequential policies are also considered. Methods are given for evaluating some pertinent properties and for investigating the possibility that no object occurs at any location.     

Determining the most vital link in a flow network

The most vital link in a single commodity flow network is that are whose removal results in the greatest reduction in the value of the maximal flow in the network between a source node and a sink node. This paper develops an iterative labeling algorithm to determine the most vital link in the network. A necessary condition for an are to be the most vital link is established and is employed to decrease the number of ares which must be considered.