Geoscience Reference
In-Depth Information
Table 16.3
Cost parameters
Symbol
Description
FC i
Fixed setup cost of establishing a new facility in location i 2 N
SC i
Fixed cost of closing existing facility i 2 E
OC `
Fixed cost of operating facility ` 2 L
BC `p
Unit cost of buying product p 2 P at facility ` 2 L from an external source
PC `p
Unit cost of producing product p 2 P at facility ` 2 L
Unit cost of transporting product p 2 P from facility ` 2 L to facility ` 0
TC `` 0 p
2 L
(` ¤ ` 0 )
MC m ; HC h
Unit cost of expanding manufacturing resource m 2 M, resp. handling resource
h 2 H
DC `p
Unit penalty cost for not serving demand of facility ` 2 L for product p 2 P
Table 16.4
Decision variables
Symbol
Description
y i
1 if the selectable facility i 2 I is operated, 0 otherwise
s `p
Quantity of product p 2 P purchased at facility ` 2 L from an external source
z `p
Quantity of product p 2 P manufactured at facility ` 2 L
Quantity of product p 2 P shipped from facility ` 2 L to facility ` 0
2 L (` ¤ ` 0 )
x `` 0 p
w m ; w h
Number of extra capacity units of manufacturing resource m 2 M, resp. handling
resource h 2 H
u `p
Quantity of unsatisfied demand of location ` 2 L for product p 2 P
for manufacturing commodities, and for distributing multiple products through the
network. The latter costs may also include charges for handling goods at the source
facility and at the destination facility (e.g., order picking and warehousing costs).
Furthermore, additional costs are considered for resource expansion. Penalty costs
are also incurred for failing to meet customer demand. These costs represent the
additional expense for outsourcing unfilled demand.
Finally, strategic decisions on facility location and logistics operations are ruled
by the variables in Table 16.4 .
16.2.2
A Mixed-Integer Linear Programming Model
Under the assumption that all inputs are known non-negative quantities, the logistics
network (re-)design problem can be formulated as a mixed-integer linear program
(MILP) as follows.
The objective function ( 16.1 ) describes the aim of the decision-making process,
namely to identify the network configuration with the least total cost. To this end,
fixed costs associated with opening, closing, and operating facilities are considered.
The latter include a fixed cost term for maintaining facilities that are not subject to
 
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