resource allocation in multi-server dynamic pert networks using multi-objective programming and markov process

in this research, both resource allocation and reactive resource allocation problems in multi-server dynamic pert networks are analytically modeled, where new projects are expected to arrive according to a poisson process, and activity durations are also known as independent random variables with exponential distributions. such system is represented as a queuing network, where multi servers at each service station are allocated, and also each activity of a project is operated at a devoted service station with only one server located at a node of the network based on first come first serve (fcfs) policy. in order to propose a novel approach for modeling of multi-server dynamic pert network, initially the network of queues is transformed into a stochastic network. then, a differential equations system is organized to solve and obtain approximate completion time distribution for any particular project by applying an appropriate finite-state continuous-time markov model. finally, a multi-objective model including four conflicted objectives is presented to optimally control the resources allocated to the service stations in a multi-server dynamic pert network, and the goal attainment method is further employed to solve a discretetime approximation of the primary multi-objective problem.