Modeling and simulation of projects with Petri nets

American Journal of Applied Sciences, Dec, 2008 by S. Kumanan, K. Raja

INTRODUCTION

Project management is a complex task. Its functions like planning, scheduling and control are difficult since constraints like resource, time and cost to be managed difficult to deal with. To manage these constraints in practice, the modes of operating project are changed often to meet the time and cost tradeoffs. Therefore, the effective management of the project is critical. The most popular methods for project planning and management are based on a network diagram such as Program Evaluation and Review Technique (PERT) and the Critical Path Method (CPM). Although these have been successful in off-line planning and scheduling, it is difficult to dynamically monitor and control the progress of the project and to model resource constraints because information is loosely coupled. The availability of improved tools such as decision CPM (DCPM), Graphical Evaluation and Review Technique (GERT) and Venture Evaluation and Review Technique (VERT) have not satisfied the requirements.

The major hurdle with these tools is the assumption that there are infinite numbers of resources available for each activity of a project (15). Inadequacies of conventional management tools (12) include: non-automatic rescheduling of activities, non-suitability to resolve conflicts arising from resource priorities, incapability of representing resource interdependencies, no provision of information to analyse reasons for the tardy progress of activities and no help in the studies of partial allocation, mutual exclusivity and substitution of resources. Hence, the need for powerful graphical and analytical tools such as Petri net arises in project management.

PETRI NETS IN MODELLING AND SIMULATION

A Petri net (PN) is a graphical and mathematical modeling tool (1) applicable to many systems. They are a promising tool for describing and studying the information processing systems that are characterized as being concurrent, asynchronous, distributed, parallel, non-deterministic and/or stochastic. As a graphical tool, they can be used as visual communication aids. As a mathematical tool, it is possible to set up state equations, algebraic equations and other mathematical models governing the behaviour of the system. The primary difference between Petri nets and modeling tools is the presence of tokens which are used to simulate dynamic, concurrent and asynchronous activities in a system.

Petri nets have been applied successfully in the areas of Performance evaluation, communication protocols, legal systems and Decision making models (1). A variety of Petri nets are reported in literature: untimed (2), timed (3), coloured (4), stochastic (5), predicate (6), priority (7), etc. Analysis methods of High level Petri net i.e. Petri net extended with colour, time and hierarchy can be used for the modelling and analysis of many complex systems encountered in industry (15). These Petri nets are also used for Prototyping of software, (re) design of logistic systems and (re) design of administrative organizations. Stochastic coloured Petri net for modeling flexible manufacturing systems, material handling systems and machines can be used (8). Many extensions to Petri nets are suggested to consider issues specific to the problems on hand. Hierarchical timed extended Petri nets (H-EPNs), a form of extended Petri net, allow the development of structured MIMO subnets to model complex system functionalities (9). A class of modelling tools called augmented timed Petri nets (ATPNs) has been introduced for the modelling and analysis of robotic assembly systems with breakdown (10). Project management has also been identified by some researchers (2) as a prospective area, where the modelling power of Petri net could be explored. Petri nets offer many advantages to project managers (12). Project management approach is drawing increased attention in manufacturing management in recent years and it forms an essential decision making aid as it suits the current trend and characteristics of manufacturing (26). The mathematical theory of Petri nets is very well developed and the theory of invariants, in particular, is very useful in the analysis and verification of a system modeled by nets (20), (21), (22).

Scope of the present paper: The present paper describes the application of Petri nets to project management and its usefulness in modeling, simulation and analysis of Project networks with a case study.

SOFTWARE DEVELOPMENT AND EXTENSIONS TO PETRI NETS

Petri net-aided software, PETRI-PM is developed to deal with project management with stochastic activity times. It has been completely designed using Visual Basic, so as to make use of its graphical and customized application development tools. The package is developed as menu driven with user-friendly message displays. The software has main menu with Project planning module as sub menu Fig. 1. The planning phase is usually identified with construction of the model graphically, during which specific decisions are made on the method of performing jobs as well as their technological ordering and simultaneously, stochastic times can be assigned.