Multi-Period Facility Location - Location Science - page 289

planning horizon. Hinojosa et al. ( 2000 ) proposed a Lagrangean relaxation based
procedure in order to compute lower and upper bounds. The problem would be later
extended by Hinojosa et al. ( 2008 ) to include inventory decisions. The new model
proposed extends the reformulation proposed by Van Roy and Erlenkotter ( 1982 )
(i.e., the decision variables represent the changes in the locations—installation of
new facilities and removal of existing ones—in the different periods of the planning
horizon). A Lagrangean relaxation based procedure was also proposed.
Caneletal.( 2001 ) also investigated a system with two echelons: factories and
facilities (e.g., distribution centers). Unlike the problems investigated by Hinojosa
et al. ( 2000 , 2008 ), location decisions are to be made only for the lower echelon.
Furthermore, facilities can be opened and closed more than once during the planning
horizon. Multiple commodities are considered as well as an important feature much
relevant is real logistic systems: the possibility of making direct shipments from the
upper echelon to the customers. The authors proposed an exact approach for the
problem based on branch-and-bound and dynamic programming.
Jena et al. ( 2012 ) investigated a multi-period capacitated facility location prob-
lem that in addition to the decisions about where to locate new facilities, consider
the possibility of relocating existing facilities or expanding the capacity of existing
ones. The authors also consider the possibility of temporarily closing facility parts.
The problem arises within the context of logging companies that wish to plan for
locating accommodation camps for their workers over some finite planning horizon.
The authors proposed several mixed integer linear programming formulations for
the problem that they compared in terms of the bounds provided by linear relaxation
and tested in instances that use data provided by a real company. They also
observed that the problem calls for a very specific cost structure associated with
capacity changes. This motivated a more recent work (Jena et al. 2014 )inwhicha
general cost structure is associated with capacity changes. A mixed integer linear
programming modeling framework was then proposed and shown to generalize
two important special cases: facility closing and reopening and capacity expansion
and reduction. Alternative formulations were also proposed for these special cases
which were compared with the above general modeling framework in terms of the
linear relaxation bounds. A combination of the above mentioned cases can also
be accommodated in the general modeling framework proposed. In that work, the
general model was solved using an off-the-shelf solver. Computational tests were
performed using a large set of generated instances.
Albareda-Sambola et al. ( 2009 ) extended the model proposed by Roodman and
Schwarz ( 1977 ) for handling the so-called multi-period incremental service facility
location problem. In each time period, a minimum number of facilities is to be
established that should be kept operating until the end of the planning horizon. All
the customers must start being served in some period and remain served until the
end of the planning horizon. The problem is motivated by some practical problems
requiring a multi-period plan for progressively extending some service to the popu-
lation in some region. Accordingly, the service level is progressively increased over
time until all customers are being served. A Lagrangean relaxation based procedure
was proposed in that paper for obtaining lower and upper bounds. A particular