Study on the location routing problem of the multistage logistics network


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INTRODUCTION
Over the past few decades, the concept of integrated logistics
system has emerged as a new management philosophy which
aims to increase distribution efficiency. Such a concept
recognizes the interdependence among the location of facilities,
the allocation of suppliers and customers to the facilities, and the
vehicle route. In optimizing logistics system, location allocation
and vehicle routing are crucial choices. Most of time, these two
decisions are tackled separately but, unfortunately, it has been
shown that this strategy often leads to suboptimal solutions [1].
Thus, we should integrate these two problems. The location
routing problem (LRP) avoids suboptimal problem because
considering LAP or VRP separately.



RELATED LITERATURE

Early works that address an integrated location routing
problem (LRP) only concentrate on the location of a single
facility, and use the moment transport cost function to describe
the routing cost incorrectly. By comparing the solutions of an
approach that uses a moment transport cost function, and one
that computes the actual multiple stop route costs for each
potential location, Webb(1968)[2] concludes that the moment
transport cost does not exactly represent the routing cost.


PROBLEM DEFINITION AND MATHEMATICAL MODEL

The location routing problem (LRP) can be defined as
follows: One company delivers the goods for the customer from
one or more facilities. The amount, location and demand of
customer are given. Facilities include factory, depot and delivery
center and so on. Each customer is to be assigned to a facility
which will supply its demand. The shipments of customer
demand are carried out by vehicles which are dispatched from
the facilities, and operate on routes that include multiple
customers. There is a fixed cost associated with opening a
facility at each potential site, and a distribution cost associated
with any routing of vehicles used in the routing, and the cost of
delivery operations. The cost of delivery operations is linear in
the total distance traveled by the vehicles.



CONLUTIONS
The logistics network of traditional LRP model is single-stage.
In practice, logistics network maybe include two-stage, threestage
or multi-stage network. This paper proposes a new LRP
model on the basis of multi-stage logistics network. We have
developed an effective and efficient heuristic method for the
multi-stage location routing problem. Through calculating, we
can confirm the location of logistics facilities, the allocation of
factory, delivery center and customer, and the customer's tour
transport route. But this paper also has some limitation, we only
consider the single-product location routing problem and
deterministic model. In fact, the number, demand, and location
of customers as well as travel times of vehicles may not be
known and consequently should be treated as random variables.