Generally speaking, in a discrete location problem the decision maker chooses a set of facilities
among a finite set of possibilities and decides to which facility each customer will be allocated
in order to minimize the allocation cost. However, it is natural to consider the more realistic
situation in which customers have their own criterion to choose one of the open facilities, based
for instance on delivery time or service quality. Giving freedom to the customers results in costs
for the decision maker which are greater than those coming from the forced allocation of customers
to facilities.
Here we consider several facility location problems on a directed network with two kinds of costs. The
so-called customer cost is the one that each customer takes into account to select the
facility that provides him with the service (like delivery time or a measure of loss of quality).
Therefore, once the facilities are located, a customer will choose that of minimum customer cost
for him. The so-called company cost includes any cost that derives from the allocation of
the customers (demand points) to the facilities they have chosen. The aim is to minimize the
company cost taking into account the decisions of the customers once the company opens its facilities.
Additionally, the company can reduce its costs by upgrading the network. To this end, a limited
amount of money (budget) can be used to reduce (upgrade) the company costs associated to the
arcs of the network. Then, the aim is to simultaneously find the location of facilities and
the distribution of the budget (or part of it) among the arcs of the graph in order to
minimize the total cost, obtained adding up the upgraded company costs and the upgrading of the network.
Different problems arise depending on the criterion used to locate the facilities
and the distribution scheme. In this article we will address the upgrading of the
$p$-median location problem, a two-stage facility
location problem, a single allocation hub location problem and a tree of hubs location problem.
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