Simulating PERT-Path Networks for Resource Allocation

Giovanni Mummolo,
Department of industrial engineering
Politecnico di Bari - Italy
Bari, Italy
E-mail mummolo@poliba.it

Salvatore Digiesi,
Department of industrial engineering
Politecnico di Bari - Italy
Bari, Italy
E-mail s.digiesi@poliba.it

Luigi Ranieri,
Department of industrial engineering
Politecnico di Bari - Italy
Bari, Italy
E-mail l.ranieri@poliba.it

Abstract
Project network techniques provide to help managers
in reducing the risk of schedule overrun. Moreover
traditional Pert type network are often ineffective as far
as planning and control processes are concerned.
The PERT-Path Network Technique (PPNT) was
suggested in (Mummolo, 1994) as an improvement of
the classical PERT-type network technique in project
planning and control processes. PPNT is based on the
same items required by PERT, i.e. PERT network
topology and probability density functions (pdfs) of
activity durations, which represent initial planner
estimates.
Owing to PPNT the description of project evolution
can be defined as a stochastic process. Each state of the
process is defined as a PERT-Path state and represents
a partial or total sequence of completed activities.
Project evolutions differ from each other since they
represent different ways of possible project completion.
Project managers tend to drive a project in
consideration of the supposed excellent financial or
technical performances.
A proper resource allocation could be consistent with a
project evolution, which is considered the most
appropriate one to pursue given technical and/or
economic goals.
In this paper, the authors propose a model to solve a
resource allocation problem, aiming at finding
optimum expected activity durations and,
consequently, at increasing the occurrence probability
that the project will follow the assigned path. The
computational complexity is the most difficult aspect
affecting the resource allocation. An algorithm able to
support planners in finding good solution of the
problem is provided thanks to its ability of identifying
the activities that mainly affect the path occurrence.
The identification is based on a criticality factor, in its
turn depending on activity completion order as well as
on transition probabilities, which are estimated by
numerical simulation of PPNT in case of bounded pdfs
of activity durations. A numerical example is
developed to show limits and capabilities of the
proposed approach.