T main goal of this paper is to describe a new multistage Monte Carlo (MMC) simulation method for solving influence diagrams using local computation. Global methods have been proposed by others that sample from the joint probability distribution of all the variables in the influence diagram. However, for influence diagrams having many variables, the state space of all variables grows exponentia...

In this paper, we are interested in routing vehicles to minimize unmet demand with uncertain demand and travel time parameters. Such a problem arises in situations with large demand or tight deadlines, so that routes that satisfy all demand points are difficult or impossible to obtain. An important application is the distribution of medical supplies to respond to large-scale emergencies, such a...

Data and chance are the two related topics that deal with uncertainty. On the discussions of probability and statistics in both research and instruction, the existing literature depicts an artificial separation, to which other researchers (Shaughnessy, 2003; Steinbring, 1991) have already called attention in recognition of the inseparable nature of data and chance. Hence, this paper addresses h...

The main goal of this paper is to describe a new Monte Carlo method for solving influence diagrams using local computation. We propose a forward Monte Carlo sampling technique that draws independent and identically distributed observations. Methods that have been proposed in this spirit sample from the entire distribution. However, when the number of variables is large, the state space of all v...

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicted. Based on the notion of chance measure, a concept of uncertain random entropy is introduced and used to provide a quantitative measurement of the uncertainty associated with uncertain random variables and its properties are studied in this paper. Relative entropy is a measure of the differ...

This paper considers the minimum spanning tree problem with uncertain random weights in an uncertain random network. The concept of uncertain random minimum spanning tree is initiated for minimum spanning tree problem with uncertain random edge weights. A model is presented to formulate a specific minimum spanning tree problem with uncertain random edge weights involving a distance chance distr...

In this paper, we are interested in routing vehicles to minimize unmet demand under uncertainty. Such a problem arises in situations with large demand or tight deadlines, so that routes that satisfy all demand points are difficult or impossible to obtain. An important application is the distribution of medical supplies to respond to large-scale emergencies, such as natural disasters or terroris...

Using results from parametric optimization, we derive for chance-constrained stochastic programs quantitative stability properties for locally optimal values and sets of local minimizers when the underlying probability distribution is subjected to perturbations in a metric space of probability measures. Emphasis is placed on verifiable sufficient conditions for the constraint-set mapping to ful...

The distribution of reversible programs tends to a limit as their size increases. For problems with a Hamming distance fitness function the limiting distribution is binomial with an exponentially small chance (but non zero) chance of perfect solution. Sufficiently good reversible circuits are more common. Expected RMS error is also calculated. Random unitary matrices may suggest possible extens...