Nomenclature for Transitions and Places

Since for operations we contain a definite nomenclature for transitions and places.

t^b_{i, j , k} presents the beginning of operation O_{i, j , k} .

 t^e_{i, j , k} presents the end of operation O_{i, j , k} .

 pⁱ_{j, k}  presents the k^th initial place of J_j presenting the beginning of the job type J_j, that is the job type J_j is ready.

p _j,k presents the k last place of the J_j that is it presents the end of J_j. In essence this means that the job is ended.

p^f_{i, j, k} presents the operation place presenting O_{i, j , k} .

pⁿ_i,j,k presents the k intermediate place of J_i after j^th process.

 p^r_i presents the resource places for the i^th robot.

p^m_i presents the resource places for the i^th machine.

                                       Figure: A Flexible Manufacturing Systems Model of a Petri Net

 At this time p^r_i is drawn twice just for the clear representation and is in reality a single place.

The number of tokens in the firstly place shows the lot size of the consequent job. A token in the operation place shows the exact operation being performed. A token in the middle place shows that the part is ready for the subsequently process, that is the intermediate place shows the buffer. By utilizing the notation explained above we implicated all places and transitions as shown in Tables no.2 and 3, respectively.

                                                                                       Table no.2: Places

                                                                                  Table no.3: Transitions

This has been previously stated that a job representation can contain more than single initial or final place. For instance, suppose that the operation indicated by p_{1, 2, 3} needs an extra partly completed job as this is an assembly operation. After that the consequent Petri net model of J₁ can be modified as represented in following figure (a). Now additional raw material needed is indicated by place pi_{1, 2}.

                           Figure: (a): representing Additional Place pⁿ_1,1,1 in the Original Model of illustration .1

Likewise we can show one more situation. If the new job type J₅ shares the similar genetic sequence of processes along with J₁ upto the operation shown by p_1,2,3 and does not need any additional processing, the consequent part of the Petri net model can be represented in following figure (b). These situations rather often appear in chemical processes where a process produces a byproduct.

Figure: (b): The Modified Part of the Model along with an additional Place pⁿ_1,1,1 in the Original Model of illustration .1

 We have related time delays along with places. A token in a resource place or an intermediate place is readily available. A token in the operation place is available merely after a delay that consequents to the interval time of the operation. We offer this duration time related with the operations in Table no.4.

                                                           Table no.4: The Operation of J₁ of illustration .1