service. A mathematical model and a heuristic are
defined to solve the problem. The objective is to min-
imize total costs, considering the routes and the cost
of opening the lockers. Computational tests were per-
formed with two sets of instances: random and based
on real data. The branch-and-bound method was ap-
plied to the proposed mathematical model, obtaining
results for instances with 100 patients and 50 poten-
tial lockers with a time limit of 7200 seconds. The
proposed heuristic achieves solutions that surpass the
optimization software, CPLEX, with only a fraction
of the time (4.18% better for the set of random in-
stances and 3.64% better for the instances based on
real data). The heuristic proved to be consistent in
obtaining the same results considering 10 executions
for each instance.
Wang et al. (2017) discussed relevant questions
about the use of lockers. The paper uses Singapore’s
case as an example, where the lockers from POPSta-
tion, a leader in this market, are positioned at 2500m
from each other. From 2015 to 2017 it was observed
that several lockers were closed permanently. Ac-
cording to the authors, the location of the lockers is
crucial for its popularization, so they must be posi-
tioned in an attractive way for the customer. The com-
petition between various companies and their lock-
ers should also be considered. The article also con-
tributed to the literature because it was the first work
related to lockers and your positions, which is based
on real and public data. Real distances between loca-
tions were also used instead of the Euclidean distance,
commonly used in the literature.
Huang et al. (2019) present the problem of vehicle
routing using electric cars and stations. The stations
can be of three types, the first one, only to recharge
cars used on delivery of goods, the second one, only
to store goods of customers, such as locker, the third
one, a hybrid station, which can be used for both pur-
poses. In the work, two integer programming models
are proposed: in the first one, the routes for supply-
ing the lockers and the routes for customer deliveries
are separated; in the second one, a hybrid route is al-
lowed. A hybrid heuristic is proposed which, com-
pared to CPLEX, presents good results efficiently and
effectively. The results obtained show that the use
of lockers combined with door-to-door deliveries can
help to reduce the cost of deliveries.
Relevant reasons are presented for calculating the
routes separately. Firstly, it is not possible to measure
the time that would be spent on each customer. There-
fore, on a hybrid route, if a delivery to a customer is
delayed, one is forced to delay the delivery to a locker,
which will affect multiple users. Second, the hours of
interest for deliveries are different: lockers may be lo-
cated at points with congestion during business hours,
so it is interesting to deliver at less busy times, while
for door-to-door delivery, deliveries are usually dur-
ing business hours. Third, the required skills of the
driver are different depending on the type of delivery
he/she will make: for door-to-door deliveries, the de-
livery person must have interpersonal skills while for
the supply to lockers the driver must have availability
in times less conventional.
In this paper, a variation is also proposed that al-
lows for more work shifts. The same vehicle can be
used during the day for door-to-door deliveries and,
at night, for supplying lockers. In this variation, the
vehicle may have more than one route associated with
it and the fixed cost of the vehicle is considered only
once. In all of the proposed models, the objective is to
minimize the total costs including expenses with the
construction of the stations and the fixed costs of the
vehicles, considered heterogeneous. We do not con-
sider the construction costs, as lockers are built only
once and used for years. Considering these costs on
a daily delivery would highly overestimate the cost.
The instances used to test the methods were created
by the authors by combining several instances of the
literature. They consider electrical vehicles but char-
acteristics about charging electric cars at stations are
not considered, such as charging waiting time, the
possibility of changing batteries or charging queue.
As part of The Federated Lockers and Collection
Points program, the government of Singapore has pro-
posed the creation of the Locker Alliance (LA) which
consists of a network of lockers to complement exist-
ing lockers and to improve the performance of deliv-
eries to consumers. Lyu and Teo (2019) aim to deter-
mine the best design of the locker network in order to
increase its coverage and use. With the increasing in
coverage, it is expected that the concentration of ex-
isting deliveries in the central business district (CBD)
would be reduced by 7.5% due to the possibility of
collecting items in locations away from the CBD.
Unlike the current work, the solutions obtained by
them are evaluated on the perspective of the attrac-
tiveness of the use of lockers, that is, the objective
is to optimize the location of the lockers so that the
volume of users who choose this type of delivery is
maximized. The data collected in the study are from
a time when LA did not exist, and therefore, the work
takes into account that after the implementation of the
network, certain changes will occur in the choice of
users. Using real data, a model was developed and
calibrated to calculate whether the user would be sub-
ject to using the locker, thus, it was possible to mea-
sure the effectiveness of the network design concern-
ing the popularity of locker. The supply and delivery
ICEIS 2020 - 22nd International Conference on Enterprise Information Systems
462