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X
0 x i`p
M
y ri ; i 2[ r2R I r ;` 2 L nf i g ;p 2 P
r2R
(16.20)
X
0 x ` ip
M
y ri ; ` 2 L nf i g ;i 2[ r2R I r ;p 2 P
r2R
(16.21)
x jj 0 p 0; j;j 0 2[ r2R J r .j ¤ j 0 /; p 2 P
(16.22)
v r`p 0; r 2 R; ` 2 L; p 2 P
(16.23)
y ri 2f 0;1 g ; r 2 R; i 2 I r :
(16.24)
The proposed model is generic in the sense that it includes multiple types of
products and components at different stages (inspected, repaired, refurbished, etc.).
Moreover, it considers reverse BOMs and transitions between the stages of products
through various recovery options. The problem is modeled with a profit oriented
objective function accounting for the revenues from different recovery options in
addition to costs.
In terms of problem complexity, the above RLND model has similar attributes to
the forward network design problem (P 1 ). Moreover, general purpose optimization
software (e.g., CPLEX or Gurobi) can be used to solve (P 2 ). However, for large-
sized instances there may be a need for customized algorithms and heuristics.
16.3.3
Special Cases and Model Extensions
The generic model (P 2 ) can be easily tailored to different applications. A reverse
logistics network design application for the collection and recovery of waste
electrical and electronic equipment is detailed in Sect. 16.4.4 .
The term closed-loop supply chain refers to a network comprising both forward
and reverse flows. Figure 16.4 depicts the structure of such a network. The cost of
processing a return flow in a supply chain designed by considering only forward
flows can be much higher than processing a flow in the forward direction. Thus,
supply chain networks that include flows in the reverse direction should be designed
by integrating forward and reverse logistics activities. The models introduced in
Sects. 16.2.2 and 16.3.2 are readily extendible to the design of closed-loop supply
chains. The interested reader is referred to Krikke et al. ( 2003 ), Easwaran and Üster
( 2009 ), and Salema et al. ( 2010 ) for exemplary studies determining the locations of
facilities within closed-loop supply chain networks.
As emphasized in Sect. 16.2.3 , the dynamic nature of the (re-)design problem
should not be disregarded. Multi-period models in RLND were proposed, for
example, by Lee and Dong ( 2009 ), Salema et al. ( 2010 ), and Alumur et al. ( 2012 ).
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