Nomenclature of Operations

Before stepping in the operational characteristics we briefly explain the nomenclature such is to be like it is more easy and lucid to know after a minute bit of practice. We will suggest to follows this scheme instead of common scheme of writing integer subscripts to indicate the operations even while both of them are technically correct. We employ the following nomenclature for our Petri net models in Flexible Manufacturing Systems:

We indicate:

'i' like job type,

'j' like process,

'k' like machine.

Hence combining these three we acquire complete notation of an operation like:

O_{i, j, k} presents the j^th process of i^th job type being represented on machine k. A job can be carried out by some sequence of operations even while the generic sequence of process keeps the same. These sequences of operations form a significant part to the flexibility of a Flexible Manufacturing Systems. While we talk about flexibility we mean the capability of the system to generate multiple types of products and share the resources.

Hence we have stated different components of the Flexible Manufacturing Systems and have explained the criteria for association of time along with places and transitions. We are here in a position to undertake an illustration in order to highlight the different aspects of the modelling power of a Petri net while applied to the different.

We have talked about sufficient concepts needed for a manufacturing system's modelling employing Petri nets. We take up an illustration to discuss these aspects.

Illustration .1

Take a three machine system M₁, M₂, M₃ along with a robot R and four types of jobs as J₁, J₂, J₃, J₄ to be carried out. Table no.1 presents the necessity for each job to be carried out.

                                                                Table no.1: Processes and Jobs Requirement

We seem the Job J₁ first. The first process is carried out along with either J₁ with R or J₂ along with R in conjunction. Likewise the second process can be carried out along with merely machine M₃ without employing the robot R. This should be obvious that the process 2 cannot begin unless process 1 has ended. Hence, the table automatically presents the technological precedence constraints between the processes. Though, no precedence constraints are considered inside the various job types. For illustration, second process of J₂ can be carried out before first process of J₁. We notice also the job J₃ has simply two processes to be finished. We provide the Petri net model of J₁ along with an initial marking as shown in following figure.