Consider a directed communications network, where each arc represents the communication link between two geographically distant points. Each communication link between points i and j has a probability of failure of pi j . Then, for any path through the network, the probability of that particular path being operative is the product of the probabilities (1 − pi j)(1 − p jk )(1 − pkl) . . . of the communication links connecting the two points of interest.
a) Formulate a network model to determine the path from s to t having the highest probability of being operative.
b) In what class does the problem formulated in (a) fall?
c) How can this formulation be transformed into a network problem?