Department of Industrial Engineering, Ardabil Branch, Islamic Azad University, Ardabil, 56157-31567, Iran
Department of Industrial Engineering, Amirkabir University of Technology, Tehran, 15988-46611, Iran
Many real projects complete through the realization of one and only one path of various possible network paths.
Here, these networks are called alternative stochastic networks (ASNs). It is supposed that the nodes of considered
network are probabilistic with exclusive-or receiver and exclusive-or emitter. First, an analytical approach is proposed
to simplify the structure of the network. This approach transforms the network into a simpler equivalent one. This
paper discusses the constrained consumable resource allocation problem in an ASN. Many recent researchers apply
heuristic and simulation methods to solve the constrained resource allocation in these problems. In this paper, we
propose an analytical approach based on multi-objective modeling. The objective functions of this model are the
cumulative distribution function of the completion time of ASN paths. These functions must be maximized within
the desired network completion time. Lexicographic method is used to solve the proposed multi-objective model.
The proposed method is illustrated by an example.