In this paper, the resource allocation problem in multi-class dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)) is studied. The dynamic PERT network is modeled as a queuing network, where new projects from different classes (types) are generated according to independent Poisson processes with different rates over the time horizon. Each activity of a project is performed at a devoted service station with one server located in a node of the network, whereas activity durations for different classes in each service station are independent and exponentially distributed random variables with different service rates. Indeed, the projects from different classes may be different in their precedence networks and also the durations of the activities. For modeling the multi-class dynamic PERT networks with CONPIP, we first consider every class separately and convert the queueing network of every class into a proper stochastic network. Then, by constructing a proper finite-state continuous-time Markov model, a system of differential equations is created to compute the project completion time distribution for any particular project. The problem is formulated as a multi-objective model with three objectives to optimally control the resources allocated to the service stations. Finally, we develop a simulated annealing (SA) algorithm to solve this multi-objective problem, using the goal attainment formulation. We also compare the SA results against the results of a discrete-time approximation of the original optimal control problem, to show the effectiveness of the proposed solution technique. 
Resource allocation in multi-class dynamic PERT networks with finite capacity