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A class of models called interactive Markov chains is studied in both discrete and continuous rime. These models were introduced by Conlisk and serve as a rich class for sociological modeling, because they allow for interactions among individuals. In discrete time, it is proved that the Markovian processes converge to a deterministic process almost surely as the population size becomes infinite. More importantly, the normalized process is shown to be asymptotically normal with specified mean vector and covariance matrix. In continuous time, the chain is shown to converge weakly to a diffusion process with specified drift and scale terms. The distributional results will allow for the construction of a likelihood function from interactive Markov chain data, so these results will be important for questions of statistical inference. An example from manpower planning is given which indicates the use of this theory in constructing and evaluating control policies for certain social systems. [ABSTRACT FROM AUTHOR]

We examine the selection of jurors' names from multiple source lists, using statistical and optimization methodology. Five plans for sampling at random from overlapping lists of names are analyzed for their probabilistic and cost properties. In each plan the probability of a name being selected is independent of which and how many lists it appears on. We consider the optimal ordering of the frames to minimize cost and develop a heuristic for solving this problem. Although the methods are discussed in terms of juror selection, the results apply to sampling from overlapping frames in any context. For instance, if lists of equipment are kept according to possible uses, with versatile equipment listed many times, the methods of this paper can be used to draw a random sample of equipment to check for readiness. [ABSTRACT FROM AUTHOR]

This paper presents an asymptotic analysis of a hierarchical manufacturing system with machines subject to breakdown and repair. The rate of change in machine states is much larger than the rate of fluctuation in demand and the rate of discounting of costs, and this gives rise to a limiting problem in which the stochastic machine availability is replaced by the equilibrium mean availability. The value function for the original problem converges to the value function of the limiting problem. Moreover, the control for the original problem can be constructed from the optimal controls of the limiting problem in a way which guarantees asymptotic optimality of the value function. The limiting problem is computationally more tractable and sometimes has a closed form solution. [ABSTRACT FROM AUTHOR]

In this paper we consider an assembly problem where two critical components are required for assembly of the final product, the demand for which is stochastic. The components can be ordered separately from individual suppliers or in a set (a set refers to the components in the required ratio) from a joint supplier. We consider the case where the assembly stage is free, i.e., the firm procures and stores the components and sells complete sets. The supplier delivery process may be random owing to uncertainty in the production process (e.g., semiconductor industries). We assume that a supplier, with probability β (say), supplies 100% of the order quantity in the current period, and with probability (1 - β) supplies nothing. If there is no delivery during this period, the order is delivered in the next period. The added complexity of coordinating shipments of different components requires careful planning in placing the orders. In the single-period problem, if no order is placed with the joint supplier, the order quantities from the individual suppliers follows an order-up-to policy structure with identical order levels. However, it is optimal to diversify (i.e., order from the joint supplier as well) when the inventory level is below a certain threshold (determined in this paper). With lower initial inventory levels, the firm cannot risk the cost of stockouts if the individual supplier(s) fail to deliver in the current period. With certain conditions on the cost and delivery parameters of the suppliers, we show that the policy structure for the multi-period problem is similar to that of the single-period problem, except that the order up-to-levels are not the same. Intuitively, it might be optimal to order extra components for use in the future. This is a direct consequence of the uncertainty in the delivery timing of the suppliers. Finally we conduct a computational study of the two-period problem and determine the effect of supplier costs and the probability of delivery on the optimal order policy. The policies are intuitive and offer a better understanding of the effect of supply and demand uncertainty on the assembly problem. [ABSTRACT FROM AUTHOR]