Location and Logistics - Location Science - page 413

Table 16.6 New parameters

Symbol Description

g `p Amount of product p 2 P generated at location ` 2 L

LJ rqp Number of units of product p 2 P obtained by processing one unit of product q 2 P

(q ¤ p) using recovery option r 2 R

KR r` Capacity of recovery option r 2 R at location ` 2 L

ER ri Maximum increase in capacity for recovery option r 2 R at location i 2 I r

RT rp Recovery target for product p 2 P with recovery option r 2 R

RE r`p Revenue from recovering one unit of product p 2 P with recovery option r 2 R at

location ` 2 L (e.g., revenue from recycling or from the secondary market)

RC r`p Cost of recovering one unit of product p 2 P with recovery option r 2 R at location

` 2 L

FC ri Fixed setup cost of establishing recovery option r 2 R at location i 2 N r

SC ri Fixed cost of closing recovery option r 2 R at existing facility i 2 E r

OC r` Fixed cost of operating recovery option r 2 R at location ` 2 L

EC ri Unit cost of expanding capacity of recovery option r 2 R at location i 2 I r

Table 16.7 New decision variables

Symbol Description

y ri 1 if recovery option r 2 R is operated at the selectable facility i 2 I r , 0 otherwise

v r`p Amount of product p 2 P recovered with recovery option r 2 R at location ` 2 L

w ri Number of extra capacity units established for recovery option r 2 R at location

i 2 I r

secondary market or to external (re)manufacturing facilities. Some recovery options
may also incur costs as in the case of product disposal.
Finally, Table 16.7 describes the decision variables. The RNLD model also uses
the flow variables x introduced in Table 16.4 .

16.3.2 A Mixed-Integer Linear Programming Model

With the notation introduced in the previous section, the reverse logistics network
(re-)design problem can be formulated as an MILP as follows. The objective
function ( 16.14 ) maximizes the total profit. It sums the revenues obtained from
various recovery options (e.g., by sending products to recycling facilities, by selling
products to the secondary market) and subtracts the total cost of establishing and
operating the network. The latter comprises the cost of recovering products at
facilities, setting up new recovery options at facilities, closing existing recovery
options, operating new and existing recovery options at facilities, transporting
products, and expanding the capacities of recovery options. Observe that a fixed