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Fig. 16.1
General structure of a logistics network
facilities comprise facilities that are not subject to location decisions. Typically,
such facilities include suppliers as well as existing plants and/or warehouses that
should be maintained. In addition, customer zones are viewed as special members
of this set as they have demand requirements for multiple commodities. As shown in
Fig. 16.1 , no restrictions are imposed on the availability of transportation channels
for the flow of materials through the network. In particular, direct commodity flows
from upstream sources to customer zones (or to facilities not immediately below in
the hierarchy) are possible as well as flows between facilities in the same echelon.
In this rather general network typology, procurement, production, distribution, and
customer service decisions are to be made along with facility location and sizing
decisions. The mathematical model in Sect. 16.2.2 captures the aforementioned
features. The required notation is first introduced in Sect. 16.2.1 . Several special
cases and extensions are discussed in Sect. 16.2.3 .
16.2.1
Notation and Definition of Decision Variables
Tab le 16.1 introduces the index sets that are used in the base model. In addition to the
various types of network entities, also multiple commodities are considered, ranging
from raw materials and intermediate products to finished goods. Moreover, different
kinds of resources may be available for manufacturing and handling commodities.
Tab le 16.2 describes input parameters related to logistics operations. Multi-stage
production processes can be taken into account through bills-of-materials (BOMs).
In this case, the relationships between components and parent items are defined
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