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 arc 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 discrete-time approximation of the primary multi-objective problem.