Supporting Demand Supply Network Optimization with Petri Nets - Distributed Artificial Intelligence, Agent Technology, and Collaborative Applications - page 374

Definition 1
DSNnet_skeleton = { NodeTypes  { AND_node, OR_node }, ArcTypes,
ParameterPool, ParameterMap }, where
NodeTypes = types of nodes in analysis (e.g. customer, manufacturing, buffer)
ArcTypes = types of arcs in analysis (e.g. transportation arcs)
ParameterPool = collection of all cost parameters used in the analysis
ParameterMap ⊆ NodeTypes × 2 ParameterPool  ArcTypes × 2 ParameterPool
A company is responsible for defining its own DSNnet_skeleton. NodeTypes and ArcTypes are stan-
dard—customer node, manufacturing node, buffer node, and transport arc typically suffice. Parameter-
Pool may differ greatly from company to company. For example, the percentage used to estimate stock
obsolescence is different in ICT business as compared to construction business - value of bricks does
not diminish as quickly in stock as that of unsold mobile phones or PCs. The companies in fast price
erosion environments (e.g. Dell) have a stronger incentive to make their demand supply networks agile
than construction material suppliers. ParameterPool may change during a company's lifetime. Finally,
ParameterMap associates each NodeType and ArcType to the specific cost parameters associated with
it. To illustrate, I show the DSNnet_skeleton in use inside Nokia Corporation.
Illustration 1 - Nokia's DSNnet_skeleton
{ NodeTypes = { Customer, Manufacturing, Buffer }  { AND_node, OR_node},
ArcTypes = { DSNarc },
ParameterPool = { bill of materials cost, buffer inventory carrying cost,
transport inventory carrying cost, freight cost, production cost,
investment cost, duty cost, tax cost, manufacturing line verification cost,
sales volume },
ParameterMap = { Customer node  { sales volume },
Manufacturing node  { bill of materials cost, production cost,
investment cost, line verification cost },
Buffer node  { buffer inventory carrying cost },
DSNarc  { transport inventory carrying cost, freight cost, duty cost,
tax cost }
}
}
Definition 2 - DSNnet
DSNnet = { Nodes, Arcs, F, DSNnet_skeleton, Typing, Valuation}, where
Nodes = set of Nodes (Petri Net places, color = Real)
Arcs = set of Arcs (Petri Net transitions, transition guards are TRUE)
F ⊆ Nodes × Arcs  Arcs × Nodes, each arc's inscription is X, a Real number variable
DSNnet_skeleton = as defined above
Typing ⊆ Nodes × DSNnet_skeleton.NodeTypes  Arcs × DSNnet_skeleton.ArcTypes