Economic Sustainability in Last-Mile Drone Delivery Problem with

Fulﬁllment Centers: A Mathematical Formulation

Maria Elena Bruni

1 a

, Sara Khodaparasti

2 b

and Guido Perboli

2 c

Department of Mechanical, Energy and Management Engineering, University of Calabria, Cosenza, Italy

Department of Management and Production Engineering, Polytechnic University of Turin, Turin, Italy

Keywords:

Last-Mile Delivery, Energy Consumption, Fulﬁllment Center, Mixed Integer Program.

Abstract:

This study is motivated by the increasing growth in the competitive e-commerce market where on-line

business-to-customer retailers, seeking for cost-efﬁcient and timely delivery services, are persuaded to adopt

a drone-based delivery system against the traditional terrestrial one. Recently, the drone-aided delivery ser-

vices have signiﬁcantly been eased, thanks to the development of fulﬁlment centers, as aerial base stations

monitoring and arranging back-and-forth drone trips between the fulﬁlment centers and customers’ sites that

also provide the retailers with services such as package handling, restocking, and drone recharge. Obviously,

adopting a drone-based delivery system incurs various expenses: besides drone recharge, maintenance, and

energy consumption costs, the usage cost for fulﬁllment centers, namely tariff, should be paid by the retailers

to the FC manager. This study aims to address the economic sustainability of a drone-aided delivery system

with fulﬁllment centers and to provide the retailer with an optimal delivery plan maximizing his proﬁt. This

could eventually provide a stable platform for new and small-sized business-to-customer retailers trying to

survive in such a competitive market and to promote the use of drone fulﬁllment centers.

1 INTRODUCTION

The boom in e-commerce and the tremendous growth

in on-line retail have created intense competition

among new and small-sized Business-to-Customer

(B2C) companies striving to meet customer expec-

tations in terms of cost-efﬁcient and timely delivery.

This has provided potentials for the development of e-

logistics services suggesting drone-based delivery so-

lutions (Pani et al., 2020). The increasing interest to-

wards drone-based delivery services, coming from the

evident environmental impact, cost-inefﬁciency and

long delivery time of terrestrial vehicles, has chal-

lenged logistics stakeholders to resort to more in-

novative and sustainable delivery solutions as Un-

manned Aerial Vehicles (UAVs) or drones. The Ama-

zon Prime Air project, Google Wing projects, Deutch

Post DHL, and JingDong (Liu et al., 2021) are only

a few examples of this successful and ambitious idea

of introducing drone-aided delivery into the logistic

sector.

https://orcid.org/0000-0002-3152-5294

https://orcid.org/0000-0003-3858-2571

https://orcid.org/0000-0001-6900-9917

Recently, Amazon announced that by the end of

2024, the Amazon Prime Air will be expanded to

Italy, UK, and other cities in the United States (Ama-

zon, 2023), integrating in such a way, drone deliveries

into Amazon’s existing fulﬁllment center network.

Fulﬁllment Centers (FC) are specialized distribu-

tion centers that facilitate the drone integration into

delivery systems. These drone base stations offer

landing, takeoff, drone recharge, and package han-

dling services to on-line retailers. Obviously, small

B2C retailers cannot afford possessing such costly in-

frastructures. FC managers provide the service at a

cost (also referred to as tariff ) per drone, that might

also be time-varying. Each delivery has an associated

revenue, and a set of preferred time intervals. The

variation in tariffs and revenues is related to the dy-

namic nature of the problem: tariffs reﬂect changes

in workforce prices, whilst revenues vary depending

on the type of shipping (standard, express) and by

the customer’s preferences. This suggests the use

of a multi-period framework (instead of a static one)

where the decisions can be adapted over time in order

to capture such variations (Bakker and Nickel, 2024;

Khodaparasti et al., 2018). In addition, the FC tar-

iffs affect the economic sustainability of the drone-

382

Bruni, M., Khodaparasti, S. and Perboli, G.

Economic Sustainability in Last-Mile Drone Delivery Problem with Fulﬁllment Centers: A Mathematical Formulation.

DOI: 10.5220/0012464100003639

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 13th International Conference on Operations Research and Enterprise Systems (ICORES 2024), pages 382-389

ISBN: 978-989-758-681-1; ISSN: 2184-4372

delivery system and the proﬁtability of the retailer

business. Recent researches showed the potentials

for the establishment of new multi-level FCs to facili-

tate last-mile drone delivery services across European

cities (Aurambout et al., 2022).

The appealing features of drone-based delivery

solutions in terms of low environmental implications

(CO

footprint and noise pollution) have somehow

shifted the focus of practitioners and operational re-

searchers to its green sustainability, ignoring or even

downplaying the importance of addressing economic

viability measures in delivery systems.

The present study aims to address the economic

sustainability of drone-based delivery services with

FCs through the design of an efﬁcient delivery sys-

tem operating on a daily basis, where drone-speciﬁc

features, as energy consumption and recharge time,

along with customers’ preferences in terms of deliv-

ery time are properly incorporated. To design such

a holistic delivery service, we adopt a multi-period

framework that enables us to capture the inherent dy-

namicity of problem in terms of time-variant tariffs

and delivery revenue.

We should highlight that the economic sustain-

ability of system is highly affected by the retailer de-

cisions on how (questioning the transport mode) and

when the delivery plans are scheduled. With the aim

of maximizing the retailer total proﬁt over a short-

term planning horizon of one working day, we present

the optimal delivery plan specifying i) the transport

mode and the delivery schedule for each customer; ii)

the deployment schedule for each drone; iii) the set

of FCs used to host the deployed drones. We also in-

vestigate the impact of different tariff setting policies

on the system economic viability providing the logis-

tics companies/the FC manager with managerial in-

sights on how the appropriate share of FCs resources

among different retailers could help to establish a sta-

ble platform for e-logistics businesses. In this way,

we address the economic viability and sustainability

of drone-deliveries with FCs in B2C logistics, inves-

tigating the effect of tariffs on both the retailer’s rev-

enue and the sustainability of delivery system.

The rest of the paper is organized as follows. Sec-

tion 2 presents a review on pure-drone delivery prob-

lem in the literature pointing up the gaps. Section

3 describes the problem and presents the mathemat-

ical formulation. Section 4 is devoted to the compu-

tational experiments conducted on a real case study

for the Portland city adapted from (Chauhan et al.,

2019) and the discussion on managerial insights. Fi-

nally, Section 5 provides the concluding remarks and

potential directions for future research.

2 LITERATURE REVIEW

Large part of the literature on UAV-based logistics

systems is devoted to contributions on multi-modal

delivery models where a ﬂeet of drones and au-

tonomous trucks cooperate to serve customers (Bruni

et al., 2022; Dell’Amico et al., 2022; Moshref-Javadi

and Winkenbach, 2021). However, the present con-

tribution falls in the class of pure-play drone-based

models where deliveries are handled just by drones.

The literature on pure drone delivery problem

is categorized in two main streams depending on

whether drones perform multi-visit or single visit

tours. The multi-visit case involves routing deci-

sions where drones can visit multiple customers per

trip (Torabbeigi et al., 2020).This, of course, limits

the applicability of proposed models to cases wherein

the drone payload capacity and battery charge al-

low multiple deliveries per trip and requires to ac-

count for load-dependent energy consumption rates in

drone battery. Following this stream, (Dorling et al.,

2016) and (Cheng et al., 2020) presented multi-visit

drone delivery models where the energy consumption

in drone battery is explicitly modeled. (Bruni et al.,

2023b) studied a routing problem for last-mile drone

delivery with shared FCs and homogeneous parcel

weight where the objective is to minimize the total

travel cost (Bruni et al., 2023b). The authors model

the energy consumption rates considering internal and

external factors that affect energy consumption, in-

cluding drone-speciﬁc features (such as the number

of rotors, the drone frame and battery mass), the envi-

ronmental factors (air density and gravitational force),

and the mass of order(s) carried by drone. There are

also other contributions on multi-visit drone delivery

problem that account for energy consumption rates

under the travel time uncertainty that is not the fo-

cus of present paper, and therefore, we refer the inter-

ested reader to (Bruni and Khodaparasti, 2022a; Bruni

et al., 2023a; Bruni and Khodaparasti, 2022b).

As mentioned earlier, the limited drone ﬂight

endurance, payload and battery capacity makes the

adoption of routing plans in many drone delivery ap-

plications impractical. On the other hand, the sin-

gle visit drone delivery case where each drone per-

forms multiple trips delivering the order of one sin-

gle customer per trip is more realistic and practical,

as supported by many contributions in the literature

(Chauhan et al., 2019; Figliozzi, 2020; Pani et al.,

2020; Dukkanci et al., 2021).

Following the single visit drone delivery context,

we may recognize that some contributions model the

energy consumption rates in drone battery as a lin-

ear function in terms of drone payload and travel time

Economic Sustainability in Last-Mile Drone Delivery Problem with Fulﬁllment Centers: A Mathematical Formulation

383

(Chauhan et al., 2019; Chowdhury et al., 2017; Zhu

et al., 2022), while some other studies do not account

for energy consumption (Golabi et al., 2017; Pulver

and Wei, 2018).

To the best of our knowledge, only (Dukkanci

et al., 2021) introduced an explicit calculation of the

energy consumption as a nonlinear function of the

drone speed in a single visit drone delivery prob-

lem where drones are ﬁrst transported by trucks to

the proximity of customers and then perform multi-

ple back-and-forth trips between the trucks and cus-

tomers’ locations to deliver orders.

Another important issue, mostly ignored in the

drone-delivery context, is the battery recharge. In

fact, most contributions do not account for it and for

the charging time spent. For example in (Chauhan

et al., 2019), the battery recharge is not taken into ac-

count and it is assumed that the drone batteries are

recharged overnight or in-between planning periods.

In the present study, we bridge the gap in the liter-

ature by designing a multi-period drone-based deliv-

ery system with FCs, focusing on the economic sus-

tainability and viability of the delivery system. We

provide the retailer with optimal delivery schedules

for a short-term planning horizon where the realis-

tic assumptions on energy consumption in drone bat-

tery, the heterogeneity of ﬂeet, the time required to

recharge batteries after each depletion, the customer

preferences in terms of delivery time, and the time-

dependency of parameters are directly incorporated.

3 PROBLEM DESCRIPTION AND

MATHEMATICAL

FORMULATION

The last-mile drone delivery problem with FCs is de-

scribed as follows. The FCs’ owner manages a set

of existing FCs as the distribution centers special-

ized for drone usage where drones are loaded with

customer packages, launched and dispatched to the

customers’ locations, where the package is left at the

doorstep, and are then retrieved back for the next de-

livery. The FCs offer different services such as re-

stocking and package handling to the retail companies

and are capacitated. The retail companies, consider-

ing the FCs’ usage costs decide on how (by drone or

traditional transport vehicles) and when to plan the

customer deliveries. The retail company can consider

an external delivery service as an alternative option to

deliver some orders. The external service is usually

performed by a terrestrial vehicle that is highly expen-

sive, compared to the drone-delivery option, imposing

a penalty cost to the retailer that loses the potential

proﬁt of that delivery request.

We should note that each customer has prefer-

ences in terms of delivery time, and thus, can be vis-

ited only during one of his preferred time periods.

The retail company’s main goal is to maximize the

total proﬁt (expressed in terms of total revenue mi-

nus total costs) gained from delivering orders within

the preferred delivery times, specifying the transport

mode for each single order (by drone or the terres-

trial service) and the delivery schedules at each time

slot. The total cost includes the FC’s usage cost, the

delivery cost, and the penalty cost for customers not

being served by drones. The usage cost associated to

a FC depends on both the time period at which the

FC is used and its location, raising the issue of opti-

mally select the FCs. The delivery cost includes the

drone usage and maintenance costs plus the routing

expenses monetized in terms of energy consumption

in drone battery. The retail company owns a set of

heterogeneous drones (denoted by U and indexed by

u) and should deliver the orders of a set customers in

I where the location of customer i and its parcel mass

(in kg) are already known. Each customer has pre-

ferred time interval(s) to receive the delivery. The set

of preferred delivery time for customer i is denoted

by E(i) ⊂ H where H denotes the set of time slots

(periods).

In fact, we consider a short-term planning horizon

of one working day discretized into different time pe-

riods, with the same length (usually one hour), to cap-

ture the dynamicity of the problem in terms of time-

varying FC tariffs, customer preferences for deliv-

ery time, and time-dependent delivery revenues. We

should highlight that the hourly granularity is consis-

tent with the average time required to recharge a typ-

ical drone battery (Leslie, 2024).

The representative retail company seeks maximiz-

ing the total proﬁt expressed in terms of revenue mi-

nus the delivery costs. The retail company decides

upon the selection of FCs over different time peri-

ods, the allocation of drones to used FCs, the delivery

schedule for each drone meeting the customers prefer-

ences in terms of delivery time, and ﬁnally the choice

of customers to be served by the alternative vehicle.

In summary, the problem’s main assumptions are

listed as follows:

• A set of capacitated FCs are available to host the

drones

• A set of heterogeneous fully charged drones is

available

• The planning horizon is divided into a set of dis-

crete time slots

ICORES 2024 - 13th International Conference on Operations Research and Enterprise Systems

384

• Each drone can use only one FC throughout the

entire planning horizon

• Each customer has preferences in terms of deliv-

ery time, limiting its visit to speciﬁc time periods

• At the beginning of a typical time period, each

drone, if deployed, is loaded with a single cus-

tomer’s order and is launched from its host FC,

delivers the order to the customer’s location and

is retrieved at the FC

• Drones are allowed to perform multiple single-

visit trips within the same time period to serve

multiple customers, as long as the drone battery

is not depleted

• Battery recharge is allowed only at FCs and if the

battery needs to be recharged, the drone spends

the subsequent time period in the FC and therefore

cannot be deployed

Figure 1 illustrates the delivery scheme for a typical

drone-based delivery problem with FCs.

Figure 1: Scheme of the delivery system: A delivery exam-

ple with 3 FCs, 4 drones, and 10 customers.

The problem notation is presented in Table 1.

Table 1: Notation for the mathematical model.

Sets and Indices

I set of customers indexed by i

D set of FCs indexed by j

H set of time slots indexed by h

U set of drones indexed by u

E(i) ⊆ H set of preferred delivery time slot for customer i

Parameters

usage cost (tariff) for FC j at time slot h

λ penalty cost for using external delivery service

revenue for the order delivery of customer i at time slot h by a drone

energy consumption of drone u across the path between FC j and customer i

i j

energy consumption of drone u across the path between customer i and FC j

battery capacity of drone u

capacity of FC j (in terms of total number of deliveries) at time slot h

i j

delivery cost of drone u to deliver order of customer i from FC j

Decision variables

u j

binary variable takes 1 if drone u is deployed from FC j at

time slot h; and 0 otherwise

i j

binary variable takes 1 if order of customer i is delivered at time h by

drone u from FC j; and 0 otherwise

binary variable takes 1 if customer i is served by express delivery

service; and 0 otherwise

u j

binary variable takes 1 if drone u assigned to FC j is deployed at least in

one time slot

The mathematical formulation is cast as follows:

max :

∑

i∈I

∑

j∈D

∑

u∈U

∑

h∈H

i j

−



∑

j∈D

∑

u∈U

∑

h∈H

u j

∑

i∈I

∑

j∈D

∑

u∈U

∑

h∈H

i j

∑

i∈I

λw



(1)

∑

i∈I

∑

u∈U

i j

≤ K

j ∈ D, h ∈ H (2)

u j

≤ α

u j

u ∈ U, j ∈ D, h ∈ H (3)

∑

j∈D

u j

≤ 1 u ∈ U (4)

∑

i∈I

+ e

i j

≤ E

u j

u ∈ U, j ∈ D, h ∈ H (5)

u j

+ y

(h+1)

u j

≤ 1 u ∈ U, j ∈ D, h ∈ H, h ̸= |H| (6)

∑

j∈D

∑

u∈U

∑

h∈H

i j

+ w

= 1 i ∈ I (7)

∑

j∈D

∑

u∈U

i j

= 0 i ∈ I, h ∈ H \ E(i) (8)

i j

∈ {0,1} i ∈ I, u ∈ U, j ∈ D, h ∈ H (9)

u j

∈ {0,1} u ∈ U, j ∈ D, h ∈ H (10)

∈ {0,1} i ∈ I (11)

The objective function (1) represents the total proﬁt of

the retail company expressed in terms of the revenue

minus tariffs, delivery and penalty costs. Constraints

(2) set an upper bound on the total number of deliv-

eries performed from each FC during each time slot.

Constraints (3) show the relation between variables α

and y. Constraints (4) ensure that if a drone is de-

ployed at least once from a FC, it should stay at that

speciﬁc FC for the whole planning horizon, and thus,

avoiding the unnecessary reallocation of drones be-

tween different FCs. Constraints (5) model the drone

energy consumption over multiple trips, ensuring that,

the total energy consumption over the back-and-forth

trips of each time period is below the battery capac-

ity. As said earlier, each drone could perform multi-

ple back-and-forth trips between its host FC and dif-

ferent customers’ sites within the same time period,

if the battery is not depleted. Constraints (6) imply

that each drone can be deployed only once during any

two subsequent time slots, imposing one-time slot gap

between consecutive drone deployments, as the time

required for battery recharge.

Constraint (7) guarantee that each customer’s or-

der is delivered either by a drone or by the exter-

nal service. Constraints (8) are related to the cus-

tomer’s delivery time preferences that prevent deliver-

ies within undesirable time slots. Finally, constraints

(9)-(11) represent the nature of variables.

Following (Dorling et al., 2016), the energy con-

sumption (in Watt-hours, Wh) is expressed as a non-

linear function in terms of drone payload capacity,

frame and battery mass, and the travel time. The en-

Economic Sustainability in Last-Mile Drone Delivery Problem with Fulﬁllment Centers: A Mathematical Formulation

385

ergy consumption for drone u ﬂying from FC j to lo-

cation of customer i with travel time t

(in hour) while

carrying the order of customer i with mass of d

(in

kg) is expressed as:

2ρξ

+ M

+ d

)

3/2

(12)

where g is the gravity constant (in N/kg), ρ represents

the ﬂuid density of air (in kg/m

), ξ

is the area of

spinning blade disc (in m

), s

is the number of ro-

tors of drone u, and W

and M

indicate, respectively,

the drone frame and battery mass (in kg). The energy

consumption of drone u that travels back empty is ex-

pressed as

i j

2ρξ

+ M

)

3/2

i j

(13)

4 COMPUTATIONAL

EXPERIMENTS

In this Section, we test the efﬁciency and the validity

of the proposed model. In particular, we report the

results of a real case study for drone-based last-mile

delivery in Portland city (Chauhan et al., 2019). The

input data and the problem size were slightly mod-

iﬁed to ﬁt the characteristics of drone delivery with

FCs. To be more precise, we ﬁrst solved a maximum

covering model, considering the original case study

with 122 customer locations and 104 potential FCs,

to determine ten potential FCs and the largest set of

customers that can be served by a ﬂeet of ten Alta 8

drones and the following features: battery capacity of

E = 0.355 kWh, the frame and battery mass of, re-

spectively, W = 6.2 kg and M = 2.8 kg, the payload

capacity of 9.1 kg, with s = 8 rotors and ξ = 1.204

. Also, the ﬂuid density of air is set to ρ = 0.1256

kg/m

and g = 9.81 N/kg. This reduced the set of cus-

tomers to 61, for which we set the same order mass

values as reported in the original case study (Chauhan

et al., 2019). We assume a short-term planning hori-

zon of a typical working day from 8 AM to 4 PM, split

into eight time periods, each with one-hour length.

This granularity level is also consistent with the av-

erage recharge time for an Alta 8 drone.

The preferred delivery times of each customer

were generated randomly considering that each cus-

tomer can be served during 3 to 6 different time slots.

We also set the upper bound K

= 5 for the maxi-

mum number of back-and-forth trips operated from

FCs during each period. The delivery revenues (in

dollars) were generated randomly following the uni-

form distribution U(8,20). All the data about the

drone delivery costs and external delivery costs were

taken from (French, 2017). Finally, for the FC tariffs,

we considered a general pricing rule where the forth

and ﬁfth time slots (from 11 AM to 1 PM) have the

highest tariffs, followed by the third, second and ﬁrst

periods. The sixth, seventh and eighth time slots have,

respectively, the same tariffs as the third, second and

ﬁrst ones.Under this general rule, we generated three

different scenarios; in the ﬁrst two scenarios, tariffs

are time-dependent and the third scenario is a time-

invariant case. In Scenarios I and II, the FCs manager

sets, respectively, low and high tariff rates randomly

generated from [0.3, 0.8] and [0.5, 0.9] rounded to one

decimal digit. In Scenario III, the FCs manager set

time-invariant tariffs that are the same for each FC

throughout the planning horizon. Such tariffs for each

FC are calculated as the maximum value over the av-

erage of the tariffs under Scenarios I and II.

Figures 2-4 display the tariffs under each scenario.

Figure 2: Time-dependent tariffs: Scenario I.

Figure 3: Time-dependent tariffs: Scenario II.

ICORES 2024 - 13th International Conference on Operations Research and Enterprise Systems

386

Figure 4: Time-invariant tariffs: Scenario III.

All the experiments were run on an Intel Core i7-

10750H, with 2.60 GHz CPU and 16 GB RAM work-

ing under Windows 11. The model was implemented

in the algebraic modeling language AIMMS 4.79.2.5

The solution times for Scenario I and Scenario II, are

10 and 14 minutes, respectively, followed by 15 min-

utes under Scenario III. First, we comment on the re-

sults for Scenario I, considered as the baseline. Fig-

ure 5 displays the optimal delivery plans. All deliv-

eries performed during the same time period are de-

picted by the same color. The selected FCs are dis-

played in red and the non-selected FCs are shown in

black. As we can see, all the orders are delivered by

the drones and no external service is used. We also

observe quite promising results where the retailer ex-

penses, in terms of FC tariffs and total drone related

and delivery costs, represent only 8% of the total rev-

enue. If the drone-based delivery service with FCs is

not available and all the orders are delivered by the

external service, assuming the same delivery cost of

2.5 $ per order as mentioned in (French, 2017), the

retailer business completely fails. This managerial in-

sight shows the importance of adopting an efﬁcient

delivery system to ensure the economic sustainabil-

ity of business. As for the ﬂeet workload, the results

show that each drone is deployed at least within 3

and at most 4 time slots. Reminding the gap imposed

between two consecutive drone deployments, we de-

duce that the workload between drones is appropri-

ately balanced. In total, drones are deployed 35 times

within different slots, performing from 1 to 4 deliver-

ies per time period in order to complete 61 delivery

trips (on average in each drone deployment, 1.7 cus-

tomers are served).

A percentage of 58% of customers preferred to re-

ceive their orders within 11 AM and 1 PM, and there-

fore, many deliveries had to be scheduled within the

forth and the ﬁfth time slots when the tariffs are the

highest. However, the total tariff cost is only 4% of

the total revenue showing that the designed delivery

system not only meets the customers’ expectations

but also is sustainable with respect to economic cri-

teria.

Figure 5: Optimal solution under scenario I.

Figure 6: Optimal solution under scenario II.

We obtained similar results under scenario II where

the FCs manager increases the tariffs on average by

27% (at least 20% and at most 100%). Of course, the

delivery plans are different and the set of used FCs

is different as shown in Figure 6. The increase in the

tariffs increases the total cost for FC usage up to 20%.

However, the results show that it is still beneﬁcial to

use the FC services and to perform all the deliveries

by using drones. This is also an interesting insight for

the FC manager showing that the retail companies can

tolerate on average 30% increase in the tariff rates and

still prefer to handle all deliveries using FC services.

Of course such tolerance exists only in a monopoly

situation where all the FCs belong to the same owner.

Economic Sustainability in Last-Mile Drone Delivery Problem with Fulﬁllment Centers: A Mathematical Formulation

387

Figure 7: Optimal solution under scenario III.

Clearly, in a competitive market, the situation can be

more complicated requiring an in-depth investigation.

The optimal delivery plans under Scenario III are

illustrated in Figure 7. As we can see, even when

the FCs manager imposes time-invariant tariffs, we

can still serve all the customers by drones, showing

the reliability of the designed delivery system. As

expected, under Scenario III, the FC usage costs in-

crease by about 8% and 27%, respectively, compared

to Scenario I and Scenario II. To have an idea on the

computational efﬁciency of the proposed model for

larger instances, we tested the model on a set of cases

with 100, 200, and 500 customers. All the input pa-

rameters for such instances were randomly generated

using the uniform distribution and the minimum and

maximum values reported in the case study. For in-

stance, in the case study the orders’ mass varies from

1.25 to 5 kg, so we set d

∼ U(1.25,5), i ∈ I. The

same general rule was followed to generate other in-

put parameters. Under a time limit of 1500 seconds,

only instance with 500 customers were not solved to

optimality where the gap is below 0.68%.

5 CONCLUSIONS

In this study, we addressed the economic sustainabil-

ity and the efﬁciency of a drone delivery system to

handle the daily last-mile deliveries for small B2C

retailers. The delivery system encompasses a set of

fulﬁllment centers, as specialized drone stations that

facilitate drone deliveries, and a heterogeneous ﬂeet

of drones where each drone performs multiple back-

and-forth single-visit trips between the FCs and cus-

tomers’ locations to deliver the orders. We formu-

lated the problem as a mixed integer program incor-

porating realistic problem features, like energy con-

sumption in drone battery, customer preferences with

respect to delivery time, and the recharging time for

drone batteries. The experiments carried out on a real

case study showed informative insights on the eco-

nomic sustainability of the designed drone-based de-

livery system, under different tariff setting policies.

Future research should focus on the interplay and in-

teraction between the FCs manager and retailer, to

better frame the impact of tariff setting policies on the

delivery service.

ACKNOWLEDGEMENTS

The second author is supported by PNRR project

NEST ”Network 4 Energy Sustainable Transition” -

PE00000021.

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