The problem we investigate deals with the optimal assignment of resources to the activities of a stochastic project network. We seek to minimize the expected cost of the project include sum of resource utilization costs and lateness costs. We assume that the work content required by the activities follows an exponential distribution. The decision variables of the model are the allocated resource quantities. We construct a continuous time Markov chain model for the activity network and use the PhaseType distribution to evaluate the project completion time. Then we use Fibonacci search over the interval of permissible allocations to the activity to seek the minimum expected
cost
