Location and Logistics - Location Science - page 409

a)

b)

Fig. 16.2 Facility sizing over multiple periods (the crossed symbol indicates a closed facility)

The generic formulation .P 1 / comprises some of the aforementioned features
and it can also be adapted or extended to include further aspects relevant to LND.
For example, it is easy to add single-sourcing requirements to .P 1 / to ensure that
the demand of each customer zone for a particular product is entirely satisfied
from a unique facility. A straightforward extension of .P 1 / is also to embed the
(re-)design of a logistics network in a multi-period planning horizon. Such a
setting is meaningful since the establishment of new facilities is typically a long-
term project involving time-consuming activities and requiring the commitment of
substantial capital resources. In this case, strategic decisions can be constrained by
the budget available in each time period. Logistics decisions will be in turn impacted
by the location choices. Fleischmann et al. ( 2006 ) and more recently Correia et al.
( 2013 ) included this feature in their dynamic network design models.
A multi-period setting is also appropriate for planning the re-design of a logistics
network that is already in place. In this context, existing facilities may have their
capacities expanded, reduced or even moved to new sites over several time periods
as illustrated in Fig. 16.2 (the bars in the figure next to the facilities indicate their
size). In turn, new facilities can be established through successive sizing. A gradual
transfer of production and/or storage capacities from existing locations to new sites
ensures a smooth implementation of relocation plans and avoids logistics operations
from being disrupted. Melo et al. ( 2006 , 2012 , 2014 ) proposed several models and
heuristics for this special form of network re-design.
In the mathematical model .P 1 / all inputs (i.e., logistics and cost parameters)
are taken as known quantities. As noted by Melo et al. ( 2009 ), most of the
research dedicated to LND problems focuses on deterministic formulations. This
is explained by the complexity posed by many of these problems and the serious
computational hurdle that arises when the problem size becomes large. In the last
two decades, increasing attention has been given to the development of new models
that incorporate the uncertainties inherent to decision-making in LND (see Klibi
et al. 2010 ). This is the case, for example, of the multi-echelon LND problem
addressed by Santoso et al. ( 2005 ). Uncertainty is captured with respect to supply
and demand quantities, resource capacities, and processing as well as transportation
costs. Recently, Huang and Goetschalckx ( 2014 ) developed a scenario planning
approach for a similar problem focusing on solution robustness. The goal is to obtain