The markovian multi-criteria multi-project resource-constrained project scheduling problem

Abstract

This chapter develops a Markovian multi-objective mathematical programming model for the resource allocation problem in dynamic PERT networks with a finite capacity of concurrent projects. It is assumed that new projects are generated according to a Poisson process and activity durations are independent random variables with exponential distributions. This system is represented as a queueing network with finite concurrent projects, where each activity of a project is operated at a dedicated service station with one server located in a node of the network. In this investigation, not only activity durations, but also operating costs of service stations per period are all considered as independent random variables. This problem is formulated as a multi-objective model using continuous-time Markov processes with three conflicting objectives to optimally control the resources allocated to service stations. It is impossible to solve this problem optimally in a reasonable time, and consequently we apply a particle swarm optimization (PSO) method to solve this multi-objective continuous-time problem using a goal attainment technique. Finally, to show the effectiveness of the proposed PSO, we compare the results of a discrete-time approximation of the original optimal control problem with the results obtained by the proposed PSO.