MODELLING FLEXIBLE MANUFACTURING SYSTEMS - Modelling with Generalised Stochastic Petri Nets - page 175

The pull strategies, on the contrary, are driven by the demand: every time
the in-process inventory is lower than a given threshold, a request for new
products is issued to the machine that feeds the inventory. This strategy
gives good response time only if in-process inventory is large enough.
The Just-In-Time strategy belongs to the class of pull strategies, and has
the additional constraint of keeping the in-process inventory as small as
possible.
In [ 65] and [ 72] these and other aspects of FMSs are described, and several
applications of PN theory in this framework are highlighted. In the following
sections two examples will be developed that show how it is possible to model
and analyse FMSs using GSPNs.

8.2 A Kanban System

The first example system we are going to consider is the so-called Kanban.
The Kanban philosophy originated in Japanese industry; it is based on the
Just-In-Time (JIT) control method. Kanban systems are a special kind of
pull production systems designed to minimize the size as well as the fluctua-
tion of in-process inventory. Kanban is the Japanese word for card: the flow
of cards controls the flow of items in the production line. A Kanban system
is a linear system of production cells; the demand for finished parts from a
cell depends exclusively on the needs of the next cell that are communicated
through cards posted on a bulletin board. As a result, each cell produces
its parts just-in-time to meet the demand of succeeding cells, hence it is the
final product demand that ultimately controls the system behaviour.
In Fig. 8.1 a block diagram model of a sequential Kanban system with a
single type of cards is depicted. Each cell has a fixed number of cards (not
necessarily the same number in each cell) that are initially posted in the
bulletin board. Parts can be stored in the input and output buffers of each
cell; every part has to be associated with a card from the pool of cards of
that cell; hence at any time each cell contains at most as many parts as the
number of cards it owns. If cell i has a finished part in its output buffer
(observe that the part has to have an attached card k i belonging to the pool
of cards of cell i), and a card k i+1 is posted in the bulletin board of cell
i + 1, then the part is transferred to the input buffer of cell i + 1 labelled
with the card k i+1 while card k i is detached from the part and posted in the
bulletin board of cell i. A part in the input buffer of cell i is processed as
soon as the machine is available, and is deposited in the output buffer when
the processing is completed.
A simple GSPN model of cell i is depicted in Fig. 8.2; the same model
was presented in [9, 41] . Tokens in place BB i represent cards posted in the
bulletin board. Places IB i and OB i represent the input and output buffer,
respectively. A token in place idleM i represents the condition “machine M i