Location and Logistics - Location Science - page 412

decision variables are first defined in Sect. 16.3.1 . Some special cases and possible
extensions of the proposed model are additionally discussed in Sect. 16.3.3 .

16.3.1 Notation and Definition of Decision Variables

The notation used in the generic RLND model is analogous to the notation
introduced in Sect. 16.2.1 for the forward LND model. Similar to the forward
network design problem, multiple commodities are considered in the configuration
of the reverse logistics network. These are represented by the set P,whichmay
include used, inspected, repaired, or refurbished products, components, or raw
materials. In order to represent a different state (inspected, repaired, refurbished,
etc.) of a certain item, a different product type needs to be defined within the set
P.Table 16.5 describes all index sets that are required for modeling the RLND
problem.
The set of available recovery options may include conventional options, such as
repair, refurbish, and recycle as well as other options such as inspection, disassem-
bly, selling to suppliers, to the secondary market or to external (re)manufacturing
facilities, and disposal. Even though the latter options may not be regarded as
recovery alternatives, in order to provide a generic model incorporating all the
decisions present in real-life reverse logistics networks, they are included in the
set R. Observe that some recovery options may be operated by third-party logistics
providers. These external facilities belong to the set J r . Moreover, it is assumed that
generation points are also included in this set of non-selectable facilities.
Tab le 16.6 introduces the required parameters. Transitions between the stages
of products and reverse BOMs are taken into account by the parameter LJ.For
example, a damaged product can be converted into a repaired product through the
recovery option repair, or a used product can be disassembled into its components
at a disassembly facility. Each recovery option has a given capacity which can be
expanded at selectable facilities. Revenues may be obtained through some recovery
options, e.g., by selling products or components to recycling facilities, to the

Table 16.5 New index sets

Symbol Description Index symbol

R Set of recovery options (e.g., repair, refurbish, recycle) r

N r Set of potential locations for recovery option r 2 R i

E r Set of existing facilities with recovery option r 2 R i

I r Set of selectable facilities with recovery option r 2 R, I r D N r [ E r i

j; j 0

J r Set of non-selectable locations with recovery option r 2 R

(e.g. secondary market, disposal)

Set of all locations, L D[ r2R . I r [ J r / `; ` 0 L