Alias: Multiple Names for a Set

Sometimes it is necessary to have more than one name for the same set, e.g., in models that deal with the interactions of elements within the same set. In input-output models for example, each commodity may be used in the production of all other commodities and it is necessary to have two names for the set of commodities to specify the problem without ambiguity. Example:

from gamspy import Container, Set, Alias

m = Container()

i = Set(m, name = "i", records=["i" + str(i) for i in range(5)])
ip = Alias(m, name = "ip", alias_with = i)

A second name ip for the set i is established that can be used instead of the original set name i.

Note

The newly introduced set name may be used as an alternative name for the original set; the associated set will always contain the same elements as the original set.

Besides using the Alias() class directly, one can also facilitate the addAlias() method of the Container class (which internally calls Alias()):

h = Set(m, name="h", records=list(range(1, 6)))
hp = Alias(m, name="hp", alias_with=h)

It is possible to create an alias from another alias object. In this case a recursive search will be performed to find the root parent set – this is the set that will ultimately be stored as the alias_with property. We can see this behavior in the following example:

from gamspy import Container, Set, Alias

m = Container()

i = Set(m, name = "i", records=["i" + str(i) for i in range(5)])
ip = Alias(m, name = "ip", alias_with = i)
ipp = Alias(m, "ipp", ip)

In [1]: ip.alias_with.name
Out[1]: 'i'

In [2]: ipp.alias_with.name
Out[2]: 'i'

Warning

If an alias is to be used for the universal set, the gamspy.UniverseAlias() class has to be used. More about this in The Universal Set: * as Set Identifier.

Typical examples for the usage of aliases are problems where transportation costs between members of one set have to be modeled. Example:

from gamspy import Set, Alias, Parameter
import pandas as pd

m = Container()

i = Set(m, name = "i", description = "plant locations", records=[
    "palmasola", "pto-suarez", "potosi", "baranquill", "cartagena"
])

cost = pd.DataFrame(
    [
        ("pto-suarez", "palmasola",  87.22),
        ("potosi",     "palmasola",  31.25),
        ("potosi",     "pto-suarez", 55.97),
        ("baranquill", "palmasola",  89.80),
        ("baranquill", "pto-suarez", 114.56),
        ("baranquill", "potosi",     70.68),
        ("cartagena",  "palmasola",  89.80),
        ("cartagena",  "pto-suarez", 114.56),
        ("cartagena",  "potosi",     70.68),
        ("cartagena",  "baranquill", 5.00),
    ],
    columns=["from", "to", "us$ per ton"],
)

tran = Parameter(m, name="tran",
                       description = "transport cost for interplant shipments (us$ per ton)",
                       domain=[i, i], records=cost)

The parameter tran is two-dimensional and both indices are the set i. The data for the transport cost between the plants is given in this symbol; note that the transport costs are given only for one direction here, i.e. the costs from pto-suarez to palmasola are explicitly specified in the parameter while the costs in the opposite direction are not given at all:

	palmasola	pto-suarez	potosi	baranquill
pto-suarez	87.22	nan	nan	nan
potosi	31.25	55.97	nan	nan
baranquill	89.8	114.56	70.68	nan
cartagena	89.8	114.56	70.68	5

The following alias statement introduces ip as another name for the set i. The parameter mui is also two-dimensional and both indices refer to the set i, but this time the alias ip is used in the second position. The parameter mui is defined to contain the transport costs from one plant location to the other, in both directions.

ip = Alias(m, name = "ip", alias_with = i)

mui = Parameter(m, name = "mui",
                      description = "transport cost: interplant shipments (us$ per ton)",
                      domain = [i, ip])

mui[i,ip] = tran[i,ip] + tran[ip,i]

Resulting in the following data for mui

	palmasola	pto-suarez	potosi	baranquill	cartagena
palmasola	nan	87.22	31.25	89.8	89.8
pto-suarez	87.22	nan	55.97	114.56	114.56
potosi	31.25	55.97	nan	70.68	70.68
baranquill	89.8	114.56	70.68	nan	5
cartagena	89.8	114.56	70.68	5	nan

Note that if mui were defined without the alias, then all its entries would have been zero.