A GENERALIZED ACTIVITY NETWORK MODEL

In recent years activity networks for projects with both random and de terministic alternative outcomes in key nodes have been considered. Th e developed control algorithm chooses an optimal outcome direction at every deterministic alternative node which is reached in the course of the project's realization. At each routine decision-making node, the algorithm singles out all the subnetworks (the so-called joint variant s) which correspond to all possible outcomes from that node. Decision- making results in determining the optimal joint variant and following the optimal direction up to the next decision-making node. However, su ch models cover a limited class of alternative networks, namely, only fully-divisible networks which can be subdivided into nonintersecting fragments.In this paper, a more generalized activity network is consid ered. The model can be applied to a broader spectrum of R&D projects a nd can be used for all types of alternative networks, for example, for non-divisible networks comprising nodes with simultaneously 'must fol low', random 'exclusive or' and deterministic 'exclusive or' emitters. The branching activities of the third type refer to decision-making o utcomes; choosing the optimal outcome is the sole prerogative of the p roject's management. Such a model is a more universal activity network ; we will call it GAAN-Generalized Alternative Activity Network. The p roblem is to determine the joint variant optimizing the mean value of the objective function subject to restricted mean values of several ot her criteria. We will prove that such a problem is a NP-complete one. Thus, in general, the exact solution of the problem may be obtained on ly by looking through all the joint variants on the basis of their pro per enumeration. To enumerate the joint variants we will use the lexic ographical method in combination with some techniques of discrete opti mization. A numerical example will be presented. Various application a reas are considered.