Supporting Demand Supply Network Optimization with Petri Nets - Distributed Artificial Intelligence, Agent Technology, and Collaborative Applications - page 372

4. End Product Manufacturer - 100% volume
Supplier 1 for Module B - 60% volume
Supplier 2 for Module B - 40% volume
Supplier 2 for Module C - 100% volume

DSNnet does not resemble a Petri Net since the notion of transitions is missing as in Figure 2. However,
between each pair of nodes a logistics network will incur e.g. freight and duty costs and these elements
are included inside a transition. The transitions are not drawn in the figure for notational convenience,
but Figure 3 shows an equivalent High Level Petri net interpretation of a DSNnet instance. As indicated,
the color of each place is the real number type and each arc contains a variable for a single real number
token. Petri Net interpretations of AND and OR nodes are presented in Figures 4 and 5, respectively.
AND-OR logic for Petri Nets was first introduced in (Baer, 1973; Agerwala & Flynn, 1973).
The above formalism satisfies the modeling requirements for network alternatives but the issue of
data has not yet been addressed. The cost elements pertinent to logistics change from industry to indus-
try, and some cost elements such as obsolescence rate per annum are very different for if one is selling
bricks (low obsolescence rate) or mobile phones (high obsolescence rate). To address this requirement
it is vital to have “metadata” on the types of cost elements as well as their values related to particular
industry or firm. This metadata approach is adopted in the formal definitions below.

f ormal definitions

The definition of DSNnet is divided into three parts. First, I define DSNnet_skeleton (Definition 1),
which gives the metadata for cost elements included in a particular company. Second I define a particu-
lar DSNnet instance (Definition 2). Finally DSNnet system is defined in terms of High Level Petri Net
system with Real number data types (Definition 3).

Figure 3. Showing equivalence between DSNnet and High Level Petri Net

DSNnet Petri Net

Place (color = Real)
- Token values are daily
product demand
- Includes e.g. component and
production costs

Supplier for
Module M.1

Supplier for
Module M.1

x

X = arc variable (type Real)

Freight etc. parameters
Between suppliers

Transition
- includes e.g. freight costs,
duties and taxes

x

Supplier for
Module M.2

Supplier for
Module M.2