Page 193 - Sustainability in the Process Industry Integration and Optimization

170 Cha p te r E i g h t

2006), which is mainly due to its ability to increase the efficiency of
business and management systems. The mathematical foundation of
this technology has been developed mainly based on Petri net theory
(Kiepuszewski, ter Hofstede, and van der Aalst, 2003; van der Aalst
and ter Hofstede, 2005). Even though this mathematical methodology
provides a basis for determining the optimal operation of workflows,
it cannot be used to derive an optimal workflow structure.
The structural component of a workflow synthesis problem can
be identified by the sets of products, resources, and (plausible)
activities on materials. The cost of a workflow process that generates
a particular quantity of product is given as the sum of (1) the cost of
the raw materials and (2) the cost related to the activities appearing
in the synthesized workflow process. The cost of an activity is the
sum of its running cost and the investments assigned to the period of
time examined. Both the running cost and investment cost depend
on the “size” of the activity—that is, its output volume. The common
objective for synthesizing workflow processes is to minimize the
total cost under the assumption of unlimited intermediate storage
capacities for any activity.

Example 8.1: Workflow Synthesis (after Tick, Kovács, and Friedler, 2006)
As an example, a set of activities is given by its inputs and outputs in Table 8.1
and represented by P-graph in Figure 8.3.
The P-graph contains the interconnections among the activities. Each feasible
activity network corresponds to a subgraph of the P-graph in Figure 8.3.
A product document represented by A and B can be generated by an appropriate
network of the activities—provided that the problem has at least one feasible
solution. It is important to note that a product can usually be generated by
different types and numbers of activities. When determining the optimal
network for a workflow, all possible networks of each product must be taken
into account.

Activities Input Output
1 C A, F
2 D B
3 E, F C
4 F, G C
5 G, H D
6 H B
7 J F
8 K G
9 K G
10 L H

TABLE 8.1 Plausible Activities for a
Workflow