**1. Introduction**

24 Will-be-set-by-IN-TECH

[1] ANSI/ISA [1995]. *ANSI/ISA-88.01-1995 Batch Control Part 1: Models and Terminology*

[2] Bowden, F. D. J. [2000]. A brief survey and synthesis of the roles of time in Petri nets,

[3] Gradišar, D. & Mušiˇc, G. [2004]. Scheduling production activities using project planning

[4] Gu, T. & Bahri, P. A. [2002]. A survey of Petri net applications in batch processes,

[5] Haupt, R. [1989]. A survey of priority rule-based scheduling, *OR Spectrum* 11(1): 3–16. [6] Hillah, L., Kindler, E., Kordon, F., Petrucci, L. & Treves, N. [2009]. A primer on the Petri

[8] Jain, A. & Meeran, S. [1999]. Deterministic job-shop scheduling: Past, present and future,

[9] Jensen, K. [1997]. *Coloured Petri nets. Basic concepts, analysis methods and practical use*,

[10] Lakos, C. & Petrucci, L. [2007]. Modular state space exploration for timed Petri nets,

[11] Lee, D. & DiCesare, F. [1994]. Scheduling flexible manufacturing systems using Petri nets

[12] Méndez, C., Cerdá, J., Grossmann, I. E., Harjunkoski, I. & Fahl, M. [2006]. State-of-the-art review of optimization methods for short-term scheduling of batch processes, *Computers*

[13] Mušiˇc, G. [2009]. Petri net base scheduling approach combining dispatching rules and local search, *21st European Modeling & Simulation Symposium*, Vol. 2, Puerto de La Cruz,

[14] Nortcliffe, A. L., Thompson, M., Shaw, K. J., Love, J. & Fleming, P. J. [2001]. A framework for modelling in S88 constructs for scheduling purposes, *ISA Transactions* 40(3): 295–305. [15] Piera, M. A. & Mušiˇc, G. [2011]. Coloured Petri net scheduling models: Timed state space

[16] Pinedo, M. L. [2008]. *Scheduling: Theory, Algorithms, and Systems*, 3rd edn, Springer

[17] Potoˇcnik, B., Bemporad, A., Torrisi, F., Mušiˇc, G. & Zupanˇciˇc, B. [2004]. Hybrid modelling and optimal control of a multi product bach plant, *Control Engineering Practice*

[18] Silva, M. & Teruel, E. [1997]. Petri nets for the design and operation of manufacturing

[19] Tuncel, G. & Bayhan, G. [2007]. Applications of petri nets in production scheduling: a review, *The International Journal of Advanced Manufacturing Technology* 34(7-8): 762–773. [20] Wijngaard, J. & Zijlstra, P. [1992]. MRP application the batch process industry, *Production*

[21] Wortmann, H. [1995]. Comparison of information systems for engineer-to-order and

[22] Yu, H., Reyes, A., Cang, S. & Lloyd, S. [2003]. Combined Petri net modelling and AI based heuristic hybrid search for flexible manufacturing systems-part II: Heuristic

[23] Zuberek, W. M. [1991]. Timed petri nets: definitions, properties and applications,

net markup language and ISO/IEC 15909-2, *Petri Net Newsletter* 76: 9–28.

*International Journal on Software Tools for Technology Transfer* 9: 393–411.

and heuristic search, *IEEE Trans. on Robotics and Automation* 10(2): 123–132.

[7] ISA [2008]. *ISA-TR88.95.01 Using ISA-88 and ISA-95 Together*, ISA.

*European Journal of Operational Research* 113(2): 390–434.

exploration shortages, *Math.Comput.Simul.* 82: 428–441.

systems, *European Journal of Control* 3(3): 182–199.

*Microelectronics and Reliability* 31(4): 627–644.

make-to-stock situations, *Computers in Industry* 26(3): 261–271.

hybrid search, *Computers and Industrial Engineering* 44(4): 545–566.

*(Formerly ANSI/ISA-S88.01-1995)*, ANSI/ISA.

tool, *Electrotechnical Review* 71(3): 83–88.

*& Chemical Engineering* 30(6-7): 913–946.

*Computers in Industry* 47(1): 99–111.

Springer-Verlag, Berlin.

Tenerife, Spain, pp. 27–32.

Publishing Company.

*Planning & Control* 3(3): 264–270.

12(9): 1127–1137.

*Mathematical and Computer Modelling* 31(10-12): 55–68.

**7. References**

In Industrial Maintenance Company (IMC) a vast number of entities interact and the global behaviour of this system is made of several emergent phenomena resulting from these interactions. The characteristics of this system have increased both in size and complexity and are expected to be distributed, open and highly dynamic. Multi-Agent Systems (MAS) are well adapted to handle this type of systems. Indeed, the agent abstraction facilitates the conception and analysis of distributed microscopic models [9]. Using any holonic perspective, the designer can model a system with entities of different granularities. It is then possible to recursively model subcomponents of a complex system until the requested tasks are manageable by atomic easy-to-implement entities. In multi-agent systems, the vision of holons is someway closer to the one that MAS researchers have of Recursive or Composed agents. A holon constitutes a way to gather local and global, individual and collective points of view. A holon is a self-similar structure composed of holons as sub-structures. A hierarchical structure composed of holons is called a holarchy. A holon can be seen, depending on the level of observation, either as an autonomous atomic entity or as an organisation of holons (this is often called the Janus effect [12]). Holonic systems have already been used to model a wide range of systems, manufacturing systems [15, 16, 33], health organizations [32], transportation [2], etc. The different organisations which make up an IMC must collaborate in order to find and put in place various strategies to maintain different production sites. In order to honour its contracts, the IMC should handle the whole of its resources (human and material), ensure the follow up in real time the equipment in different production sites and plan actions to be executed. A part of the maintenance could be remotely achieved (tele-maintenance and/or tele-assistance [17], e-maintenance [13], etc.). Several constraints should be integrated in the process of strategy search and decision making before mobilizing operation teams. Concretely, the search for an efficient maintenance strategy should be

©2012 Mazigh and Abbas-Turki, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ©2012 Mazigh and Abbas-Turki, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

found while taking into account the following constraints: (a) The urgency level of the maintenance task requested by a given production site, (b) A distance between mobile teams and production sites, (c) The estimated intervention duration, (d) The respect of the legal daily working time of maintenance crew, (e) Verification of the availability of the stored spare parts, (f) The reconstitution of new teams in view of the mentioned constraints.

overcome complex logistical problems thereby the need to develop aiding methods and tools for decision making to efficiently manage this type of organizations. Among the services proposed by an IMC, we can mention: (a) On site intervention, (b) Technical assistance via telephone or distance intervention, (c) The study and improvement of equipment, (d) Organisation and engineering, (e) Formation in industrial maintenance, (f) The search for and the development of new maintenance methods. The focus in this research is to find an efficient maintenance policies taking into account multiples alias. We propose a formal approach, based on the paradigm HMAS, to specify and analyze an efficient and adaptive IMC. As such, a specification approach based on HMAS to be a promising approach to deal with the unpredictable request of maintenance due to their decentralization, autonomy, cooperation features and their hierarchical ability to react to unexpected situation. For this specification, we use ASPECS methodology to identify holonic organization of a steady system and we combine two formal languages: Object-Z and Petri Nets for modeling and

Using Stochastic Petri Net and Object-Z: Application to Industrial Maintenance Organizations

29

Specifying and Verifying Holonic Multi-Agent Systems

The ASPECS process structure is based on the Software Process Engineering Metamodel (SPEM) specification proposed by OMG [25]. This specification is based on the idea that a software development process is collaboration between abstract active entities, called Roles that perform operations, called Activities, on concrete, tangible entities, called Work Products. Such as it was proposed by [4], ASPECS is a step-by-step requirement to code software engineering process based on a metamodel, which defines the main concepts for the proposed HMAS analysis, design and development. The target scope for the proposed approach can be found in complex systems and especially hierarchical complex systems. The main vocation of ASPECS is towards the development of societies of holonic (as well as not-holonic) multi-agent systems. ASPECS has been built by adopting the Model Driven Architecture (MDA) [25]. In [5] they label the three meta-models "domains" thus maintaining the link with the PASSI meta-model. The three definite fields are: (a) The Problem Domain. It provides the organisational description of the problem independently of a specific solution. The concepts introduced in this domain are mainly used during the analysis phase and at the beginning of the design phase, (b) The Agency Domain. It introduces agent-related concepts and provides a description of the holonic, multi-agent solution resulting from a refinement of the Problem Domain elements, (c) The Solution Domain is related to the implementation of the solution on a specific platform. This domain is thus dependent on a particular implementation and

Our contribution will relate to the consolidation of the Problem Domain and the Agency Domain. We propose a formal specification approach for analysis the various organizations

The analysis phase needs to provide a complete description of the problem based on the abstractions defined in the metamodel problem domain CRIO (Capacity, Role, Interaction and Organization). All the activities that make up this first phase and their main products can be identified. Indeed, this phase shows the different steps that can be used for the requirements

and the interactions between them facilitating therefore the *Solution Domain*.

analysis specification of an IMC.

deployment platform.

**3.2. Requirements analysis**

**3. A holonic specification approach of an IMC**

**3.1. A quick overview of ASPECS process**

To satisfy some of these constraints, we propose a formal holonic approach for modelling and analysis all the entities that constitutes an IMC. We use Holonic Multi-Agent Systems (HMAS) in which holons are agents that may be composed of agents for developing complex systems. To this end, we use an Agent-oriented Software Process for Engineering Complex Systems called ASPECS [8]. The process is considered by their authors as an evolution of the PASSI [3] process for modelling HMAS and it also collects experiences about holon design coming from the RIO (Role, Interaction and Organization) approach [11]. It is sufficient to say that the definition of the MAS meta-model adopted by the new process has been the first step and from this element all the others (activities, guidelines and workflow) have been built according to this guideline [4, 30, 31]. This meta-model defines the underlying concepts. A step-by-step guide from requirements to code allows the modelling of a system at different levels of details. Going from each level to the next consists in a refinement of the meta-model concepts. The objective of this work consists in consolidating the ASPECS methodology by using a formal specification and analysis of the various organizations and the interactions between them. This phase will facilitate the code production of organizations, roles and holons. In addition, it will be possible to test each organization, their roles and each holons independently. This type of analysis, will allow checking certain qualitative properties such as invariants and deadlock, as well as a quantitative analysis to measure the indicators of performance (cost of maintenances, average duration of the interventions, average time to reach a site of production, etc). In this chapter, our extended approach will be used to model and analyze an Industrial Maintenance Company (IMC). After a brief presentation of the framework, the maintenance activities in a distributed context are presented. ASPECS process and modelling approach will be introduced in section 3. Analysis and conception phase of this process and their associated activities are then described in order to identify the holonic IMC organisation. In section 4, first we present our specification formalism and second we assign an operational semantics to it. Additionally, we illustrate how to use the operational semantics as a basis for verification purposes. The specification formalism we intend to present combines two formal languages: Stochastic Petri Nets and Object-Z. Finally, Section 5 summarises the results of the chapter and describes some future work directions.
