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American Journal of Applied Sciences 5 (12): 1742-1749, 2008 ISSN 1546-9239 © 2008 Science Publications

Modeling and Simulation of Projects with Petri Nets
S. Kumanan and K. Raja Department of Production Engineering, National Institute of Technology, Tiruchirappalli, India
Abstract: Traditional project management tools and other revised tools are limited in representation of the problem andin dealing situation dynamically. This paper details the use of Petri nets as a graphical and mathematical modeling and simulation tool in project management. In this context, the benefits of Petri nets are indicated. A Petri net aided software, a PETRI-PM is developed to model, simulate and analyze the project. Extensions to make Petri nets suitable for project management applications areproposed. The use of a PPC-matrix for token movements is proposed. The paper also discusses the implications of the model and the analysis it supports. The usefulness of the software is exemplified with a case study. Key words: Project management, petri nets, simulation, reachability, invariant analysis INTRODUCTION Project management is a complex task. Its functions like planning, scheduling and controlare 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 ProgramEvaluation 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 ReviewTechnique (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: nonautomatic rescheduling of activities, non-suitability to resolve conflicts arising fromresource 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 ANDSIMULATION 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, itis 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, communicationprotocols, legal systems and Decision making models[1]. A variety of Petri nets are reported in literature: timed[3], coloured[4], stochastic[5], untimed[2], [6] [7] predicate , priority , 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

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