Geoscience Reference
In-Depth Information
Table 16.1
Index sets
Symbol
Description
Index symbol
N
Set of potential locations for new facilities
i
E
Set of existing facilities that could be closed
i
I
Set of selectable facilities, I D N [ E
i
j; j 0
J
Set of non-selectable locations (e.g., customer zones)
`; ` 0
L
Set of all entities, L D I [ J
P
Set of products
p; q
M, H
Set of manufacturing, resp. handling, resources
m; h
Table 16.2
Logistics parameters
Symbol
Description
d `p
Demand of location ` 2 L for product p 2 P (typically, d ip D 0 for i 2 I)
Ǜ ` qp
Number of units of product q 2 P required to manufacture one unit of product
p 2 P (q ¤ p) at facility ` 2 L
` mp
Number of units of resource m 2 M required to manufacture one unit of product
p 2 P at facility ` 2 L
` hp ; O ` hp
Number of units of resource h 2 H required to handle one unit of product p 2 P
upon its arrival at, resp. shipment from, facility ` 2 L
KM m ; KH h
Capacity of manufacturing resource m 2 M, resp. handling resource h 2 H
EM m ; EH h
Maximum increase in capacity of manufacturing resource m 2 M, resp. handling
resource h 2 H
by given parameters. Capacities of service facilities are modeled in a general way
through manufacturing and handling resources. Three different relation types are
considered. In a many-to-one relationship, several resources are available at the
same facility. Some resources may be product-specific (e.g., a machine dedicated to
a given item) while others may be shared by multiple commodities (e.g., production
line or order picking system). A one-to-one association corresponds to the classical
way of modeling capacity in facility location models (e.g., storage space in a
warehouse). One-to-many relationships can also be modeled, although these are less
common. This could be the case, for example, of a team of experts responsible for
several production lines in different facilities. Resource availability can be increased
at additional expense, e.g., through overtime work or leasing extra storage space.
Resource consumption is described by specific parameters. In the case of handling
resources, the same type of equipment (e.g., forklift truck) may be required with
different intensity to unload incoming goods at a facility and load goods to be
shipped from the same facility.
Tab le 16.3 summarizes all facility and logistics costs. Facility costs are related
to establishing new facilities and closing existing facilities, and typically reflect
economies of scale. In addition, facility operating costs represent, for example,
business overhead costs such as staff and security costs. Logistics costs are incurred
for purchasing items from external sources (e.g., procurement of raw materials),
 
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