# Sustainable Facility Location-Routing Problem for Blood Package Delivery by Drones with a Charging Station

Shirin Ghasemi, Reza Tavakkoli-Moghaddam, Mahdi Hamid, Meysam Hosseinzadeh

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Shirin Ghasemi, Reza Tavakkoli-Moghaddam, Mahdi Hamid, Meysam Hosseinzadeh. Sustainable Facility Location-Routing Problem for Blood Package Delivery by Drones with a Charging Station. IFIP International Conference on Advances in Production Management Systems (APMS), Sep 2021, Nantes, France. pp.3-14, 10.1007/978-3-030-85906-0_1 . hal-04022139

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# Sustainable Facility Location-Routing Problem for Blood Package Delivery by Drones with a Charging Station

Shirin Ghasemi[0000-0002-6515-230X], Reza Tavakkoli-Moghaddam[0000-0002-6757-926X] (✉), Mehdi Hamid[0000-0003-1498-7507] and Meysam Hosseinzadeh[0000-0001-6598-9671]

School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
tavakoli@ut.ac.ir

**Abstract.** This paper proposes a multi-objective integrated facility location and drone routing problem in blood package delivery by considering sustainability factors. We seek to locate the predetermined number of capacitated launching facilities and charging stations for the drones' battery. Candidate construction points are ranked by the TOPSIS method in terms of sustainability indicators. The objectives are to maximize the weight of selected points and the amount of demand coverage while minimizing the transferring and constructing facilities cost. Then, we assign drones to open launch facility and demand points to drones and launch facility. It should be noted that we consider the drone's battery consumption, and if the drone battery is not enough to continue its mission, we assign them to an opened charging station. GAMS software is employed to solve small-sized problems. The solution result indicates the performance of our model.

**Keywords:** Sustainable location-routing, Drone delivery system, TOPSIS method, Blood delivery

## 1 Introduction and Literature Review

Unmanned aerial vehicles (UAVs) or drones have attracted significant attention in differential application areas like rescue operations [1], relief distribution [2], healthcare [3], emergency applications like search and rescue [4], civilian sector [5], agriculture [6] and military [7]. However, their role in packages delivery is more common nowadays due to high traffic jams and increased competitiveness for faster service [8, 9]. Several prominent companies (e.g., Google, UPS, Flytrex, and Amazon) have resorted to using drones for package deliveries or commercial service [10]. Drone's rapid deployment ability and mobility have led to their use for transporting perishable materials or hospital packages and drugs too. Most of these materials, particularly blood products, have a short lifespan, so their delivery should be managed accurately. One of the emerging fields of using drones is their utilization as a means of delivering blood packages.

Drones, as aerial vehicles, have a much lower payload carrying capacities and range for carrying cargo than trucks; besides, as the payload increases, their maximum range of coverage decreases. That is why a drone-based delivery system needs more depots or launch sites across the distribution area. Also, unpredictable weather conditions can
dramatically affect energy consumption or the drone range, so it is necessary to con-
struct some charging stations throughout the region. It should be noted that drones are
beneficial to environmental sustainability due to less carbon dioxide (CO2) emissions
in comparison with trucks [11]. Nevertheless, the charging stations release some carbon
dioxide and cause air pollution. Therefore, it is necessary to consider environmental
sustainability indicators for locating and constructing these facilities.

Most of the previous studies on drone delivery applications are conducted on drone
scheduling and routing problems [12, 13]. Recently, researchers have much concen-
trated on facility location problems (FLPs) in drone delivery problems. FLPs play a
crucial role in designing an efficient delivery system to increase accessibility and max-
imize demand coverage. Several articles focused on determining the optimal location
for a relief distribution center in a post-disaster supply chain network by using drones.
They aim to minimize the total cost or travel times [14, 15]. Nevertheless, the crucial
aim in the relief distribution or drug and blood packages delivery is the maximum cov-
erage of demand points, which has been rarely studied. Pulver and Wei [16] attempted
to maximize primary and secondary demand point coverage in medical delivery by us-
ing drones. However, they did not take into account the capacity of each drone launch-
ing site. They also did not consider the drone’s battery consumption as its payload func-
tion. Kim et al. [17] proposed a two-stage pickup and delivery model for medical de-
ivery by using drones. First, they solved a facility location problem to construct depot
facilities, second, the drone’s routing problem has been addressed.

Chauhan et al. [18] developed a single-stage model for capacitated launch facilities and allocating demand points to drones. They proposed a function of drone energy consumption by considering drones’ payload and demand point distance. They did not include charging stations in their model and assumed that the drones would be charged the night before the flight and they are fully charged in the planning periods. Hong et al. [19] developed a coverage model for a drone’s delivery system that optimizes the location of recharging stations of drones. The study conducted by Shavarani et al. [20] addressed the refuel and launching stations for the drone delivery problem and try to minimize the total cost of the system. However, they assumed that in each mission just one demand point is covered. Several authors have mentioned the collaboration of trucks and drones for package delivery, which, despite the increased service speed, causes problems for the environment due to truck’s CO2 emissions [21, 22]. Kitjacharoenchai et al. [23] developed a synchronized truck-drone routing model. In their proposed model, the drone mission started from the truck and after serving multiple demand points, they returned to the truck. Besides, UAV charging stations emit some CO2 gas that has not been addressed in previous research, which should be considered in locating charging stations. There are also many sustainable factors influencing the construction of launching and charging stations (e.g., availability of resources, climatic conditions of the region, and access to rescue equipment) that should be considered in the model.

In response to the urgent requirement of medical centers for blood products, we pro-
vide a sustainable integrated multi-objective facility location-routing model for blood
packages delivery by drones. First, we determine several sustainable indicators to rank
the potential candidate point of facility location by the TOPSIS method (as one of the
well-known multi-criteria decision-making methods). Then, our FLP model attempt to find the best point for drones' launching and charging station simultaneously, by maximizing the weight of each potential candidate point. Our model also aims to minimize the total delivery and construction cost of facilities while maximizing demand coverage. Then, we assign drones to open launch facilities according to their limited capacity, afterward we assign demand points to open launch facilities and drones. It should be noted that if a drones' battery is not enough to complete its mission, drones should be assigned to an open charging station.

To the best of our knowledge, no study considers sustainability in the combination of drones' launching and charging station location and drones' routing problem together by considering drones' battery consumption in its mission together, so our contribution is novel.

The remainder of this paper is organized as follows. The problem statement and the proposed mathematical formulation are illustrated in Section 2. The numerical results are investigated in Section 3. Finally, the conclusion and the relevant future studies are provided in Section 4.

## 2 Problem Definition

In this section, we present sustainable multi-objective mixed-integer linear programming (MILP) formulations for location and routing problems in blood delivery systems by drones. At the beginning of the planning period, there is a set of potential points to construct drone charging and launching facilities, which must be decided whether to open them according to sustainable indicators, which is shown in Table 1. The weight of these indicators' importance is determined according to related papers and experts' opinions. Then, each of these candidate points is ranked and weighted based on these indicators by employing the TOPSIS method that is generally proposed by Tzeng and Huang [24], which is a multi-criteria decision analysis method. This method attempts to select an alternative that has the least geometric distance from the positive ideal solution (PIS) [25] and the greatest geometric distance from the negative ideal solution (NIS) [25]. The output of the TOPSIS method is an input parameter for the mathematical model, besides our proposed model aims to maximize the total weight of the selected points.

In our model, there is a set of demand locations $k$ with the demand of $v_{kp}$ from blood product $p$; which their demand is met by the Central Blood Bank, and a set of available fully-charged drones $d$. It should be noted that there are two kinds of demand points, critical and non-critical points, in which all demand of critical point should be satisfied. However, for the other points, at least 70 percent of its demands should be met. Launch stations are introduced as temporary warehouses for blood packages, which are delivered to customers by drones, too. The planning period is short-term due to the nature of blood delivery and the different blood product's shelf life is about a few days to several weeks, so, they are not exposed to corruption. We aim to locate $P_s$ launch facilities for maximizing the service rate and demand rate coverage by minimizing the total cost, including the construction cost of facilities, delivery, and drone battery consumption
cost. Then, we allocate drones to opened launch facilities by considering the facility's capacity. Then, each drone makes a one-to-many routing mission to cover the demand point, by considering the drone carrying capacity and battery consumption in its mission. In our model, if the remain drone's battery capacity is not enough for traveling between nodes *i* to *j* (it is less than the consumption battery rate between nodes *i* to *j*), it should go to an open charging station; then, it can continue its mission and visit the next demand point according to its routing. It should be noted that the amount of battery consumption rate is calculated according to the weight of the drone and its battery, the weight of the blood packets carried, and the traveled distance. Fig. 1 indicates the schematic representation of our proposed drone delivery system.

<table><caption>**Table 1.** Evaluation criteria for location selection of launch site and charging station</caption><thead><tr><th></th><th>Indicators</th><th>No.</th><th>Criterion type</th><th>Launch site's location</th><th>Charging station's location</th></tr></thead><tbody><tr><td rowspan="6">Economy</td><td>Tax policy</td><td>A1</td><td>maximize</td><td>✓</td><td>✓</td></tr><tr><td>Being in line with the economic planning of the region</td><td>A2</td><td>maximize</td><td>✓</td><td>✓</td></tr><tr><td>Possibility of development</td><td>A3</td><td>maximize</td><td>✓</td><td></td></tr><tr><td>Availability of resource</td><td>A4</td><td>maximize</td><td>✓</td><td></td></tr><tr><td>Policies and rules of government</td><td>A5</td><td>maximize</td><td>✓</td><td>✓</td></tr><tr><td>Annual cost (operation and maintenance)</td><td>A6</td><td>minimize</td><td>✓</td><td>✓</td></tr><tr><td rowspan="6">Environment</td><td>Effect on the ecological perspective</td><td>B1</td><td>minimize</td><td>✓</td><td>✓</td></tr><tr><td>Level of environmental protection</td><td>B2</td><td>maximize</td><td>✓</td><td>✓</td></tr><tr><td>Climatic conditions of the region</td><td>B4</td><td>maximize</td><td>✓</td><td></td></tr><tr><td>Amount and speed of the wind</td><td>B5</td><td>minimize</td><td>✓</td><td></td></tr><tr><td>CO2 emissions</td><td>B6</td><td>minimize</td><td></td><td>✓</td></tr><tr><td>destruction level of vegetation and water</td><td>B8</td><td>minimize</td><td>✓</td><td>✓</td></tr><tr><td rowspan="5">Social</td><td>Effect on traffic agglomeration</td><td>C1</td><td>minimize</td><td></td><td>✓</td></tr><tr><td>Effect on nearby inhabitant</td><td>C2</td><td>minimize</td><td>✓</td><td>✓</td></tr><tr><td>Proximity to a skilled workforce</td><td>C3</td><td>maximize</td><td>✓</td><td></td></tr><tr><td>Infrastructure status of operators' workplaces</td><td>C5</td><td>maximize</td><td>✓</td><td>✓</td></tr><tr><td>Operator security</td><td>C6</td><td>maximize</td><td>✓</td><td>✓</td></tr></tbody></table>

The notation and the proposed multi-objective mathematical model are given below, by considering the following assumption:

1. The amount of demand in each planning horizon is proportional to the drone's payload capacity.

2. We did not consider the effect of weather conditions on the drone's battery capacity.

3. The weight and volume of different blood packages are the same.
<figure><img src="image_4.png" /><figcaption>Fig. 1. Overview of the drone air delivery system</figcaption></figure>

<table><thead><tr><th colspan="2">Sets:</th><th colspan="2">Parameters:</th></tr></thead><tbody><tr><td>V</td><td>Set of all node</td><td>w<sub>i</sub></td><td>Weight of each candidate points (i ∈ M)</td></tr><tr><td>F</td><td>Set of all Charging stations</td><td>f<sub>i</sub></td><td>Construction cost of node i ∈ M</td></tr><tr><td>S</td><td>Set of all potential launch facility</td><td>c<sub>ijd</sub></td><td>Cost per mile of sending packages from node i to node j by drones d</td></tr><tr><td>I</td><td>Set of all candidate nodes</td><td>r<sub>d</sub></td><td>Battery consumption rate by the drones d per weight and unit of transported</td></tr><tr><td>K</td><td>Set of all demand points</td><td>v<sub>ip</sub></td><td>Amount of each demand point i of blood product p (i ∈ k)</td></tr><tr><td>k<sub>1</sub></td><td>Critical demand points that all demands must be met</td><td>CV<sub>d</sub></td><td>Capacity of drone d</td></tr><tr><td>k<sub>2</sub></td><td>Other demand points</td><td>m<sub>d</sub></td><td>Weight of the drone and its battery</td></tr><tr><td>P</td><td>Set of all blood product p ∈ P</td><td></td><td></td></tr><tr><th colspan="2">Parameters:</th><th colspan="2">Variables:</th></tr><tr><td>BC<sub>d</sub></td><td>Drone's d battery capacity</td><td>L<sub>i</sub></td><td>1 if the launch facility is located at i; 0, otherwise</td></tr><tr><td>Ps</td><td>Maximum number of launch facility</td><td>R<sub>i</sub></td><td>1 if the charging station is located at i; 0, otherwise</td></tr><tr><td>pf</td><td>Maximum number of charging stations</td><td>Q<sub>id</sub></td><td>1 if the d-th drone d is assigned to location i; 0, otherwise</td></tr><tr><td>U<sub>i</sub></td><td>Capacity of each candidate launch facility</td><td>μ<sub>ijd</sub></td><td>1 if the arc (i, j) is traversed by drone d; 0 otherwise</td></tr><tr><td>d<sub>ij</sub></td><td>Travel distance between nodes i and j</td><td>Z<sub>ij</sub></td><td>1 if demand point i is assigned to launch facility j; 0, otherwise</td></tr><tr><td>CD<sub>ip</sub></td><td>Capacity of each launch facility i for blood product p ∈ P</td><td>ρ<sub>ijdp</sub></td><td>remaining delivery demands after leaving node i if drones d travels from node i to node j (for every i, j ∈ N)</td></tr><tr><td>λ<sub>d</sub></td><td>Drone d battery consumption cost</td><td>BL<sub>jd</sub></td><td>Battery level of each drone d when arriving in vertex j</td></tr><tr><td></td><td></td><td>α<sub>k</sub></td><td>Service rate to each demand point</td></tr></tbody></table>

$$ \text{Max} \sum_{i \in S} \sum_{j \in K} \sum_{d \in D} \sum_{p \in P} \alpha_j v_{jp} \mu_{ijd} + \sum_{i \in f} \sum_{j \in K} \sum_{d \in D} \sum_{p \in P} \alpha_j v_{jp} \mu_{ijd} \quad (1) $$

$$ \text{Max} \sum_{i \in f} w_i \times R_i + \sum_{i \in s} w_i \times L_i \quad (2) $$
$$ \text{Min} \left( \sum_{i \in S} \sum_{j \in K} \sum_{d \in D} d_{ij} c_{ijd} \mu_{ijd} \right) + \left[ \left( \sum_{i \in S} \sum_{j \in F} \sum_{d \in D} d_{ij} c_{ijd} \mu_{ijd} \right) + \left( \sum_{i \in F} \sum_{j \in K} \sum_{d \in D} d_{ij} c_{ijd} \mu_{ijd} \right) \right] + \sum_{i \in V} \sum_{j \in I \cup K} \sum_{d \in D} \sum_{p \in P} (p_{ijdp+m_d}) r_d d_{ij} \mu_{ijd} \lambda_d + \left( \sum_{i \in S} f_i L_i \right) + \left( \sum_{i \in F} f_i R_i \right) \quad (3) $$

s.t.

$$ \sum_{i} L_i \leq Ps \qquad \forall i \in S \qquad (4) $$

$$ \sum_{i} R_i \leq Pf \qquad \forall i \in F \qquad (5) $$

$$ U_i \cdot L_i \leq \sum_{d} Q_{i,d} \qquad \forall i \in S \qquad (6) $$

$$ \sum_{i \in S} Q_{i,d} \leq 1 \qquad \forall d \qquad (7) $$

$$ \sum_{i \in S} Z_{ji} = 1 \qquad \forall j \in K \qquad (8) $$

$$ \sum_{j \in K} \alpha_j v_{jp} Z_{ji} \leq CD_{ip} L_i \qquad \forall i \in S, p \qquad (9) $$

$$ \mu_{kjd} + Z_{ki} + \sum_{o \in S, o \neq s} Z_{jo} \leq 2 \qquad \forall j, k \in K, i \in S, d, k \neq j \qquad (10) $$

$$ \sum_{j \in I} \mu_{ijd} = 1 \qquad \forall i \in K, d \qquad (11) $$

$$ \sum_{j \in I} \mu_{jia} = \sum_{j \in I} \mu_{ijd} \qquad \forall i \in I, d \qquad (12) $$

$$ \sum_{j \in I} \rho_{jidp} - \sum_{j \in I} \rho_{jidp} \geq \alpha_i v_{ip} \qquad \forall i \in K, d, p \qquad (13) $$

$$ \sum_{j \in I} \rho_{jidp} \leq CV_d \mu_{ijd} \qquad \forall i \in I, d, i \neq j \qquad (14) $$

$$ \sum_{j \in K} \rho_{ijdp} \geq \sum_{j \in K} Z_{ji} \alpha_j v_{jp} \qquad \forall i \in S, d, p \qquad (15) $$

$$ \rho_{ijdp} \leq (CV_d - \alpha_i v_{ip}) \mu_{ijd} \qquad \forall j \in I, i \in K, p, d \qquad (16) $$

$$ \rho_{jidp} \geq \alpha_i v_{ip} \mu_{jid} \qquad \forall j \in I, i \in K, p, d \qquad (17) $$

$$ BL_{jd} \leq BC_d \qquad \forall j \in I, d \qquad (18) $$

$$ BL_{jd} \leq BL_{id} - (p_{ijdp+m_d}) r_d d_{ij} \mu_{ijd} + BC_d (1 - \mu_{ijd}) \qquad \forall i, j \in I, d, i \neq j \qquad (19) $$

$$ BL_{jd} \leq BC_d - (p_{ijdp+m_d}) r_d d_{ij} \mu_{ijd} \qquad \forall j \in F, i \in I, d \qquad (20) $$

$$ \alpha_j = 1 \qquad \forall j \in k_1 \qquad (21) $$

$$ 0.7 \leq \alpha_j \leq 1 \qquad \forall j \in k_2 \qquad (22) $$

$$ L_i, R_i, Q_{id}, \mu_{ijd}, Z_{ij} \in \{0,1\}, \rho_{ijdp}, BL_{jd} \geq 0 \qquad (23) $$
The objective (1) attempt to maximize the demand coverage according to service rate of each demand point. Objective (2) maximizes the weight of the selected points for the construction of the facility. Objective (3) tries to minimize the total cost, including the construction cost of facilities, delivery, and drone battery consumption cost. Constraints (4) and (5) ensure that the number of construction facilities (launch facility and charging station) should be less than the allowed number. Constraint (6) states drones should be assigned to launch facilities according to their limited capacity. Constraint (7) ensures each drone should be allocated to at most one open facility. Constraints (8) ensure each demand point is assigned to a launch facility exactly once. Constraint (9) is about the limited launch facility's capacity for delivering packages by considering the service rate of each demand point. Constraint (10) makes sure that two consecutive demand points on a route are assigned to the same launch facility.

Constraint (11) illustrates that each demand location should be placed on exactly one drone route. Constraint (12) is the flow constraint. Constraint (13) ensures that each customer's requirements must be met according to its service rate. Constraint (14) restricts the total package load of any arc not to exceed the drone's capacity. Constraint (15) ensures that the total demands of all customers assigned to the corresponding launch facility are more than the same facility's total load by considering the service rate of each point. Constraints (16) and (17) are bounding constraints for additional variables according to its service rate. Constraint (18) ensures that the battery consumption between each node is less than the drones' battery capacity. Constraints (19) and (20) guarantee that reduces battery level on entry at node *j* based on the distance route from node *i*, drone and its package weight and the drones' battery consumption rate. Constraints (21) and (22) refer to the service rate of demand points; All demand of a critical point must be met, so $α_k$ takes the value 1 (21); for the other point, $α_k$ will be between 0.7 and 1 (22). Constraint (23) is domain constraint.

## 3 Numerical Results

In this part, a simple numerical example with 20 candidate point for construction facilities, 8 kinds of drones, 15 demand point (in 3 groups; hospitals, clinics, and medical institutes), and 4 types of blood package include in O, A, B, and AB is presented. We aim to construct launch facilities and charging stations from the candidate point according to the weight of each location and demand point. Table 2 displays the weighted candidate point which gathers from the TOPSIS method. Some critical parameters of the problem are identified in the following tables. For instance, the total capacity of a launch facility from blood packages is in Table 3; the demand for different points from various blood packages is given in Table 4. Also, some physical characteristics of the drone (e.g., battery capacity, consumption rate, and drone capacity to carry blood packages) are prepared in Table 5. These parameters are gathered from the related articles and experts' opinions. It should be noted that the average weight of blood packages is 0.55 kg.
<table><caption>**Table 2.** Weighted of each candidate point that gathers from the TOPSIS method.</caption><thead><tr><th>Candidate point for the launch site</th><th>w<sub>s</sub></th><th>Candidate point for the charging station</th><th>w<sub>f</sub></th></tr></thead><tbody><tr><td>1</td><td>0.12</td><td>11</td><td>0.08</td></tr><tr><td>2</td><td>0.13</td><td>12</td><td>0.1</td></tr><tr><td>3</td><td>0.14</td><td>13</td><td>0.11</td></tr><tr><td>4</td><td>0.11</td><td>14</td><td>0.13</td></tr><tr><td>5</td><td>0.15</td><td>15</td><td>0.16</td></tr><tr><td>6</td><td>0.04</td><td>16</td><td>0.11</td></tr><tr><td>7</td><td>0.05</td><td>17</td><td>0.07</td></tr><tr><td>8</td><td>0.1</td><td>18</td><td>0.08</td></tr><tr><td>9</td><td>0.11</td><td>19</td><td>0.09</td></tr><tr><td>10</td><td>0.05</td><td>20</td><td>0.07</td></tr></tbody></table>

<table><caption>**Table 3.** Total capacity of a launch facility from blood packages.</caption><thead><tr><th>Launch facility</th><th>Total capacity of a launch facility<br>for blood packages</th></tr></thead><tbody><tr><td>11</td><td>105</td></tr><tr><td>12</td><td>80</td></tr><tr><td>13</td><td>70</td></tr><tr><td>14</td><td>90</td></tr><tr><td>15</td><td>100</td></tr></tbody></table>

Since our developed model is multi-objective, we employ the ε-constraint method to achieve a Pareto-optimal solution. The validity of this model is evaluated by GAMS version 25.1.3 software using the CPLEX solver in a personal computer with Intel Core i5 CPU with 2.20 GHz frequency and 8.00 GB RAM. The CPU time of this model is 10.28 seconds. Fig. 2 illustrates Pareto solutions obtained by the ε-constraint method.

<table><caption>**Table 4.** Demand for different points from various blood packages.</caption><thead><tr><th>Demand</th><th>p1</th><th>p2</th><th>p3</th><th>p4</th><th>Total</th></tr></thead><tbody><tr><td>1</td><td>2</td><td>3</td><td>5</td><td>4</td><td>14</td></tr><tr><td>2</td><td>4</td><td>4</td><td>4</td><td>4</td><td>16</td></tr><tr><td>3</td><td>3</td><td>4</td><td>5</td><td>7</td><td>19</td></tr><tr><td>4</td><td>5</td><td>2</td><td>4</td><td>5</td><td>16</td></tr><tr><td>5</td><td>2</td><td>5</td><td>6</td><td>6</td><td>19</td></tr><tr><td>6</td><td>4</td><td>5</td><td>5</td><td>6</td><td>20</td></tr><tr><td>7</td><td>6</td><td>6</td><td>5</td><td>6</td><td>23</td></tr><tr><td>8</td><td>3</td><td>4</td><td>3</td><td>4</td><td>14</td></tr><tr><td>9</td><td>3</td><td>5</td><td>3</td><td>5</td><td>16</td></tr><tr><td>10</td><td>3</td><td>3</td><td>3</td><td>5</td><td>14</td></tr><tr><td>11</td><td>3</td><td>4</td><td>3</td><td>4</td><td>14</td></tr><tr><td>12</td><td>5</td><td>4</td><td>4</td><td>4</td><td>17</td></tr><tr><td>13</td><td>6</td><td>5</td><td>4</td><td>3</td><td>18</td></tr><tr><td>14</td><td>6</td><td>5</td><td>6</td><td>3</td><td>20</td></tr><tr><td>15</td><td>4</td><td>3</td><td>6</td><td>2</td><td>15</td></tr></tbody></table>
<table><caption>**Table 5.** Physical characteristics of each drone</caption><thead><tr><th>Drones</th><th>Total blood packages</th><th>Drone's battery capacity (Ah)</th><th>Battery consumption rate (Ah/kg.Km)</th><th>Drone and battery weight (Kg)</th></tr></thead><tbody><tr><td>1</td><td>35</td><td>625</td><td>3</td><td>2.8</td></tr><tr><td>2</td><td>55</td><td>4425</td><td>6</td><td>6</td></tr><tr><td>3</td><td>30</td><td>365</td><td>2.5</td><td>2.3</td></tr><tr><td>4</td><td>45</td><td>2900</td><td>5</td><td>5.6</td></tr><tr><td>5</td><td>32</td><td>530</td><td>2.8</td><td>2.5</td></tr><tr><td>6</td><td>38</td><td>875</td><td>3.4</td><td>3</td></tr><tr><td>7</td><td>36</td><td>675</td><td>3.2</td><td>2.5</td></tr><tr><td>8</td><td>40</td><td>1650</td><td>4.8</td><td>4.2</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Pareto solutions were obtained by the ε-constraint method</figcaption></figure>

## 4 Conclusion

This study presented a novel location-routing problem in blood package delivery with drones by considering sustainability. The problem was supposed to locate a predetermined number of launching site and charging station of drones, considering a trade-off between three objectives, include in minimizing travel and construction cost, maximizing demand coverage, and maximizing the weight of each candidate points, which was obtained by the TOPSIS method by considering various sustainable indicators. The developed model prepares the crucial information on various aspects of the drone's location-routing problem for managers in health care seeking to construct an aerial delivery system for blood package delivery. The proposed model was solved by employing the epsilon method to validate the result. Due to the feature of the problem, developing efficient meta-heuristic or exact methods is suggested to solve large-sized problems. Moreover, the uncertainty in some parameters can be addressed in future studies.

## References

1. Xiang, G., Hardy, A., Rajeh, M., Venuthurupalli, L.: Design of the life-ring drone delivery system for rip current rescue. In: Proceedings of the 2016 IEEE Systems and Information Engineering Design Symposium (SIEDS), Charlottesville, VA, USA, 26-29 April 2016, IEEE, pp. 181-186 (2016).
2. Golabi, M., Shavarani, S. M., Izbirak, G.: An edge-based stochastic facility location problem in UAV-supported humanitarian relief logistics: A case study of Tehran earthquake. Natural Hazards 87(3), 1545-1565 (2017).

3. Scott, J., Scott, C.: Drone delivery models for healthcare. In: Proceedings of the 50th Hawaii International Conference on System Sciences, Hilton Waikoloa Village, Hawaii, USA, 4-7 January 2017 (2017).

4. Karaca, Y., Cicek, M., Tatli, O., Sahin, A., Pasli, S., Beser, M. F., Turedi, S.: The potential use of unmanned aircraft systems (drones) in mountain search and rescue operations. The American Journal of Emergency Medicine 36(4), 583-58 (2018).

5. Thiels, C. A., Aho, J. M., Zietlow, S. P., Jenkins, D. H.: Use of unmanned aerial vehicles for medical product transport. Air Medical Journal 34(2), 104-108 (2015).

6. Albornoz, C., Giraldo, L. F. Trajectory design for efficient crop irrigation with a UAV. In: Proceedings of the 2017 IEEE 3rd Colombian Conference on Automatic Control (CCAC), Cartagena, Colombia, 18-20 October 2017, IEEE, pp. 1-6 (2017).

7. Udeanu, G., Dobrescu, A., & Oltean, M. (2016). Unmanned aerial vehicle in military operations. Scientific research and education in the air force, 18(1), 199-206.

8. Hong, I., Kuby, M., Murray, A. T.: A range-restricted recharging station coverage model for drone delivery service planning. Transportation Research Part C: Emerging Technologies 90, 198-212 (2018).

9. Shavarani, S. M., Nejad, M. G., Rismanchian, F., Izbirak, G.: Application of hierarchical facility location problem for optimization of a drone delivery system: a case study of Amazon prime air in the city of San Francisco. The International Journal of Advanced Manufacturing Technology, 95(9), 3141-3153 (2018).

10. Mack, E.: How delivery drones can help save the world. Forbes, Forbes Magazine (2018).

11. Goodchild, A., Toy, J.: Delivery by drone: An evaluation of unmanned aerial vehicle technology in reducing CO2 emissions in the delivery service industry. Transportation Research Part D: Transport and Environment 61, 58-67 (2018).

12. Peng, K., Du, J., Lu, F., Sun, Q., Dong, Y., Zhou, P., Hu, M.: A hybrid genetic algorithm on routing and scheduling for vehicle-assisted multi-drone parcel delivery. IEEE Access 7, 49191-49200 (2019).

13. Hu, M., Liu, W., Lu, J., Fu, R., Peng, K., Ma, X., Liu, J.: On the joint design of routing and scheduling for vehicle-assisted multi-UAV inspection. Future Generation Computer Systems, 94, 214-223 (2019).

14. Chowdhury, S., Emelogu, A., Marufuzzaman, M., Nurre, S. G., Bian, L.: Drones for disaster response and relief operations: A continuous approximation model. International Journal of Production Economics 188, 167-184 (2017).

15. Golabi, M., Shavarani, S. M., Izbirak, G.: An edge-based stochastic facility location problem in UAV-supported humanitarian relief logistics: a case study of Tehran earthquake. Natural Hazards 87(3), 1545-1565 (2017).

16. Pulver, A., Wei, R.: Optimizing the spatial location of medical drones. Applied Geography 90, 9-16 (2018).

17. Kim, S. J., Lim, G. J., Cho, J., Côté, M. J.: Drone-aided healthcare services for patients with chronic diseases in rural areas. Journal of Intelligent & Robotic Systems 88(1), 163-180 (2017).

18. Chauhan, D., Unnikrishnan, A., Figliozzi, M.: Maximum coverage capacitated facility location problem with range constrained drones. Transportation Research Part C: Emerging Technologies 99, 1-18 (2019).
19. Hong, I., Kuby, M., Murray, A.: A deviation flow refueling location model for continuous space: a commercial drone delivery system for urban areas. In: Advances in Geocomputation, Springer, Cham. pp. 125-132 (2017).

20. Shavarani, S. M., Nejad, M. G., Rismanchian, F., Izbirak, G.: Application of hierarchical facility location problem for optimization of a drone delivery system: a case study of Amazon prime air in the city of San Francisco. The International Journal of Advanced Manufacturing Technology 95(9), 3141-3153 (2018).

21. Wang, D., Hu, P., Du, J., Zhou, P., Deng, T., Hu, M.: Routing and scheduling for hybrid truck-drone collaborative parcel delivery with independent and truck-carried drones. IEEE Internet of Things Journal 6(6), 10483-10495 (2019).

22. Murray, C. C., Chu, A. G.: The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery. Transportation Research Part C: Emerging Technologies 54, 86-109 (2015).

23. Kitjacharoenchai, P., Min, B. C., Lee, S.: Two echelon vehicle routing problem with drones in last mile delivery. International Journal of Production Economics 225, 107598 (2020).

24. Tzeng, G. H., Huang, J. J.: Multiple attribute decision making: methods and applications. CRC Press (2011).

25. Assari, A., Mahesh, T., Assari, E.: Role of public participation in sustainability of historical city: usage of TOPSIS method. Indian Journal of Science and Technology 5(3), 2289-2294 (2012).