Hub Location Routing Problem: The portability effect

Hub Location Routing Problem: The portability

effect

Master Thesis

M.Sc. Supply Chain Management

University of Groningen, Faculty of Economics and Business

January 20, 2020

Author: Georgios Dilopoulos

Student number: 3742423

E-mail:

g.dilopoulos@student.rug.nl

Supervisor: dr. Ilke Bakir

Co-assessor: dr. ir. Paul Buijs

Acknowledgement

Abstract

The standard way of doing business for contemporary logistic service providers, involves a city depot, from which delivery vans start their delivery route. These companies try to minimize their transportation cost through economies of scale. However, previous research has investigated if this is possible to be achieved through the hub location and routing problem. Innovative ideas include mobile depots and dynamic hub location in inner cities, which are proven to be cost efficient but also more sustainable, creating less emissions and road congestion. This paper intends to discover if portable hubs, in combination with cargo bikes, minimize transportation cost, compared to a system with fixed locations throughout multiple periods. Thus, a LP model is proposed, which is an adjusted multi-period HLRP with multiple possible hub locations and the portability feature of the hubs. The objective of this model is to minimize the transportation cost, which is based on the routing distance of the cargo bikes, but includes also the fixed cost, for opening a hub location, and the moving cost, when a hub is re-located from one period to another. The first computational experiment conducted, is comparing the fully portable system with the non-portable one, while the other experiment is a sensitivity analysis for all parameters that influence the systems. The results show that the fully portable system is more efficient, for all tested instances, than the non-portable system, achieving less routing distance and transportation costs.

Contents

1. Introduction………4

2. Theoretical Background………7

2.1. Mobile depots………...7

2.2. Last-mile delivery cargo bikes……….8

2.3. Hub location problem………...9

2.4. Hub location and routing problem………..10

3. Problem description……….12

4. Methodology……….14

5. Computational study………18

5.2. Testing Framework and Expectations……….18

5.3. Results……….…19

1. Introduction

Nowadays, the goal of many companies is to minimize cost and be more efficient. The same holds for logistics service providers, (LSPs), companies, which, among other goals, seek new delivery options to minimize their transportation cost, while being more ecologically friendly. Existing last-mile delivery options for parcels have overwhelmed the inner part of cities, causing CO2 emissions to rise, but, they are also the main cause for congestion. Even though environmentally friendly vehicles have a positive impact causing fewer emissions, they are still responsible for the congestion they create. According to Cagliano, De Marco, Mangano, & Zenezini, (2017), the traveled distance has a great impact on the number of stops a delivery vehicle makes, considering that the greater the distance, the more stops it will make. As can be seen in Figure 1-1, the delivery truck is blocking traffic, causing vehicles to stop and wait until it is safe to pass. In addition, the longer the travel time, congestion worsens, which may have more negative effects than cost savings from delivering to more customers (Figliozzi, 2010). In order to achieve the goal of minimizing costs and solve the problems that delivery vehicles create, this thesis investigates the option of portable hubs, (PHs), in inner cities. Implementing smaller hubs all over a city, instead of only a central hub in the outskirts of it, will minimize the use of delivery trucks, hence eliminating congestion caused by them. The difference from previous studies (Aykin, 1995; de Camargo, de Miranda, & Løkketangen, 2013; Karimi, 2018; Rodríguez-Martín, Salazar-González, & Yaman, 2014; Taghipourian, Mahdavi, Mahdavi-Amiri, & Makui, 2012; Wasner & Zäpfel, 2004), is that these smaller hubs will be portable ones, which will be re-located depending on demand. From that point on, cargo bikes, (CBs), will be responsible for home delivery. This way cargo bikes will be moving in neighborhoods and smaller streets, adding to the decongestion of central roads.

Figure 1-1 Real life example (Groningen, October 2019)

systems. The focus will be on minimizing the cost of the last-mile, mainly by replacing delivery vans with portable hubs and environmentally friendly cargo bikes, which will also provide advantages for congestion and emissions (Koning & Conway, 2016). The subject of multiple portable hubs has not been researched extensively, due to the fact that it is a new concept, but with some papers involving comparable notions and ideas (Arvidsson & Pazirandeh, 2017; Bashiri, Rezanezhad, Tavakkoli-Moghaddam, & Hasanzadeh, 2018; Dell’Amico & Hadjidimitriou, 2012; Güden & Süral, 2014; Halper & Raghavan, 2011; Hörhammer, 2014; Janjevic & Ndiaye, 2014; Lei, Lin, & Miao, 2014; Marujo et al., 2018; Taghipourian et al., 2012; Verlinde, Macharis, Milan, & Kin, 2014). Perboli & Rosano, (2019), suggest as future research linked to their study about the combination of traditional and more ecologically friendly transportation modes, the mobile hub system. To tackle this hub location routing problem, (HLRP), a mathematical model will be introduced that will calculate, based on distance, the optimal locations for the hubs and the delivery route. Through different experiments, the following research question will be answered:

-Are portable hubs cost effective against the current system of hubs with a fixed location?

cost (Choubassi, Seedah, Jiang, & Walton, 2016; Gruber, Kihm, & Lenz, 2014; Rudolph & Gruber, 2017). Additionally, pollution-wise, having fewer delivery trucks results in a steep decrease of the carbon footprint of a company (Schliwa, Armitage, Aziz, Evans, & Rhoades, 2015; Choubassi et al., 2016). Another expectation is that road congestion will be less intense due to less delivery trucks stopping and blocking traffic. Nevertheless, although all of these papers are relevant to this thesis, to my knowledge no other study makes a connection between the mobility of portable hubs, from one period to another, with the routing problem, for the final delivery.

The goal in this thesis is to build a typical HLRP model (Aykin, 1995; de Camargo et al., 2013; Karimi, 2018; Kartal, Hasgul, & Ernst, 2017; Rodríguez-Martín et al., 2014; Wasner & Zäpfel, 2004), with adjustments for the multi-period aspect and the portability effect, in order to apply it in inner cities and find optimal locations for multiple PHs. This will be helpful in many ways, especially from a managerial standpoint. The practical added value is also the main objective of the model, the minimization of costs. Although it is proven that the reduction of costs is possible from using CBs instead of delivery vans (Choubassi et al., 2016; Gruber et al., 2014; Rudolph & Gruber, 2017), the portability of hubs is expected to lower costs even more. On the other hand, the theoretical added value is the portability characteristic of hubs in multi-period scenarios. Multi-period HLPs have been investigated (Bashiri et al., 2018), but do not include the portability option, and studies closely related to portability (Verlinde et al., 2014), such as the mobile depots, do not consider different locations for multiple periods. This thesis is bridging this gap, including in the HLRP multiple periods and portable hubs that can change locations from one period to another. Additionally, apart from the benefits this concept can add to current systems, it could set the base for future research to build upon and also increase the data and literature that exist on this topic.

2. Theoretical Background

Based on previous literature, this section begins with explaining the notion of mobile hubs and why many papers study it. Afterwards the use of cargo bikes in inner cities is justified, showcasing, through numerous papers, the effect they have on transportation cost, the environment and road congestion. Thereafter the HLP will be introduced, presenting all relevant papers and their findings. Lastly, the HLRP is introduced and several similar studies are demonstrated in order to understand what is missing in literature and what this thesis is offering.

2.1 Mobile depots

In recent years, researchers showed an increased interest in achieving a more ecologically friendly option, thus they started investigating the effect of mobile depots in city centers. This is one of the reasons research has oriented against switching hub locations to mobile depots, in order to get closer to the service areas. Being closer to customers, translates to less transportation costs due to the fact that delivery routes are getting shortened. Several papers introduce creative ideas, such as Dell’Amico & Hadjidimitriou, (2012), who proposed a concept that consists of two vehicles, a large truck, that carries multiple containers, and a delivery van, that can carry one container. The rationale behind this is that the large truck transports containers, from the depot to a transshipment area, where the delivery vans will get a container and deliver to the destination points (Dell’Amico & Hadjidimitriou, 2012). The result was less traffic in the city, fewer kilometers travelled and as a result emissions were also lower (Dell’Amico & Hadjidimitriou, 2012). Another one is from Arvidsson & Pazirandeh, (2017), who suggested a similar mobile depot, which will be a freight truck that will drive around the city, seen in Figure 2-1, connect with cargo bikes or small vehicles, which will take the small containers to the final delivery point. In line with the previous study, Anderluh, Hemmelmayr, & Nolz, (2017), created a two echelon system, with first being the van delivery outside the city center and second the inner city CB delivery, but with spaces just outside the borders of the inner city, in order to transfer loads from vans to bikes.

& Kin, (2014), who investigate the real life experiment from TNT, in the city of Brussels, and their mobile depot called TNT Express, as can be seen in Figure 2-1. This is a large trailer that is fully equipped, including an office space, a warehouse compartment and a loading dock, and is moved every day from the depot to a specific space in the city center and delivers packages by cargo bikes in the nearby area (Verlinde et al., 2014). The results of this study showed a large decrease in emissions mainly because of fewer diesel kilometers travelled (Verlinde et al., 2014). Finally, the concept of parked delivery vans playing the role of mobile depots, from where cargo bikes will do the remaining part of the delivery process, is also closely related to the one this thesis proposes and highly efficient for closed city centers or areas with limited space for large vehicles (Marujo et al., 2018).

Figure 2-1 Left: The mobile depot TNT Express. Source: www.transportjournal.com, Right: Suggested mobile depot from

Arvidsson & Pazirandeh,( 2017)

2.2 Last-mile delivery cargo bikes

McCormack, (2019), who found that regulations for trucks in city centers and flexibility of cargo bikes, that can move in bike lanes, on sidewalks and roads, make CBs even more efficient. The option of implementing micro-hubs in the delivery area, where CBs can pick up and deliver packages, was suggested by Fikar et al., (2018), and demonstrated that with consolidation, total delay steeply fell and total traveled distance rose as the average order per person was growing.

Although these studies show an overall positive outcome for CBs, this thesis has a more specific objective. That is to utilize cargo bikes that start from inside the service area, where a portable hub will be located, and not from the central depot in cities with traffic limitations. While Schliwa, Armitage, Aziz, Evans, & Rhoades, (2015) found similar results for cargo bikes and pointed out that it is an economically feasible solution, as seen in Table

2-1, most goals can be achieved, mainly for cities with traffic regulations or with narrow streets.

On that result, the paper of Choubassi, Seedah, Jiang, & Walton, (2016), for the U.S. Postal Service, dealt with the change of vehicles with cargo bikes, considering different settings but with the existing depots. The results showed that the electric tricycle had the lowest net present value, in congested areas, and was even more competitive against similar modes of transport, when the depot is located in the delivery area, as in this thesis, and higher population density (Choubassi et al., 2016). Concluding, for an extensive literature review that includes more information on the topic of sustainable vehicles for the last mile delivery in cities, the paper of de Oliveira, De Mello Bandeira, Goes, Gonçalves, & De Almeida D’Agosto, (2017) can be studied.

Table 2-1Impact of different modes of transport. From Schliwa et al.,( 2015)

Economic goals Social goals Environmental goals Sustainability impact Modes of transport Traffic congestion Delivery time Infrastructur e costs Reduction of accidents Reduction of vehicles Livability Reduction of pollutants Reduction of CO2 emissions Reduction of noise Diesel vans - - - -

Modal shift to electric vans (low-carbon)

0 0 0 0 0 + + + +

Modal shift to cargo bikes (sustainable)

+ + + + + + + + +

2.3 Hub location problem

location to another smoother, taking into consideration several factors that can change over time, such as suppliers, customers, transportation, company structure and political regulations. From a strategic perspective, Melo, Nickel, & Saldanha Da Gama, (2006), developed a mathematical model to calculate when and how fast the relocation should happen, but with several constraints related to capacity and the relocation budget for opening a new facility. Hörhammer, (2014), on the other hand, developed a model based upon the fact that in any period a hub can be closed and opened at a non-hub location but also that the capacity can fluctuate at any hub. This is in line with the paper from Taghipourian, Mahdavi, Mahdavi-Amiri, & Makui, (2012), who created a model that considers abrupt changes, such as weather conditions for airplanes, and named the temporary hubs where airplanes land, virtual hubs, that open and close for a short amount of time. Additionally, Correia, Nickel, & Saldanha-da-Gama, (2018), attempted to solve a multi-period HLP, but with several different possible locations.

As a result of these concepts, mobile facilities where investigated in different scenarios. In the railway setting, Güden & Süral, (2014), tried to solve the question of how many mobile facilities are needed and where to allocate them in order to minimize the cost. Accordingly, Halper & Raghavan, (2011), concluded that these mobile facilities can be stationed at distinct places and can be relocated, at any point in time, in order to cover the demand. The mobile HLP can be interpreted in many ways, so Lei, Lin, & Miao, (2014), consider the current situation, the delivery trucks, as mobile facilities that cover demand by moving around and serving people when parked and static. The most recent paper is the one from Bashiri, Rezanezhad, Tavakkoli-Moghaddam, & Hasanzadeh, (2018), who through analytical testing came to the conclusion that mobile hub structures are more efficient than any current network of stationary hubs, in fast changing settings. This is also where this thesis contributes to literature. Although several ideas are closely related to the portable hubs concept, the link with routing has not been done to the best of my knowledge. Finally, for a detailed review of the literature on facility location problems and hub location problems, the papers of Alumur & Kara, (2008), Arabani & Farahani, (2012) and Farahani, Hekmatfar, Arabani, & Nikbakhsh, (2013) can be studied.

2.4 Hub location and routing problem

the service area, having as his main goal to minimize the transportation costs. From that point on, a lot of papers have chosen different approaches or including different adjustments for the HLRPs. One approach was from Çetiner, Sepil, & Süral, (2010) who proposed a heuristic which continuously iterates from hub location to routing and the other way around, in order to adjust one to another. Other approaches include the one from Kartal, Hasgul, & Ernst, (2017), who used a multi-star annealing (MSA) heuristic and the ant colony optimization (ACO) algorithm, to solve the HLRP with simultaneous pick-up and delivery, and derived to the conclusion that costs will be considerably reduced. Additionally, an adjustment like the many-to-many HLRP is a more specific setting, including many origins and many destinations, with the objective to minimize the routing costs between these points, which de Camargo, de Miranda, & Løkketangen, (2013) solved with a branch-and-cut algorithm. A different adjustment is the capacitated HLRP, but with prefixed travel times, hub and vehicle capacities and concurrent deliveries and pickups, a polynomial-size MIP formulation with a set of valid inequalities has been used to solve it (Karimi, 2018).

3. Problem Description

In this section, the problem will be analyzed more specifically. First, an illustrative example will be presented in order to visualize the difference between the current situation and the proposed network from this study. Afterwards, the problem will be defined in detail.

The graphical representation includes 2 figures, with the first one being the current situation and the second one the proposed solution of this thesis. In both examples, the customers are placed at the same spots, although the last mile delivery is being made with different modes of transport. In the first example, delivery trucks start from the depot and follow a route, which covers a big area with many customers, that eventually leads back to the depot. In the proposed solution, there are two trucks that transport the portable hubs to the optimal locations and return immediately to the depot. From the portable hubs, cargo bikes take over and follow a route to deliver to customers and again return to the portable hub location.

Figure 3-1 Left: Current delivery model, Right: Proposed delivery model

4. Methodology

In this section, the optimization model will be presented. First, the assumptions made are given and then the notation will be explained in a table, followed by the formulation of the mathematical model.

4.1 Model Assumptions

The optimization model is based on the following assumption:

 The depot is at a fixed location, serving the whole area.

 The portable hubs are transferred from the depot.

 The movement of portable hubs is done by truck.

 The fixed cost includes costs related to the initial transportation of the portable hub to a location and the cost for reserving that location.

 The moving cost includes costs for moving a hub from one location to another.

 The delivery cost includes costs related to the final delivery of the vehicles.

 Portable hubs have a limited capacity.

 Vehicles are heterogeneous in capacity and range.

4.2 Notation

The notation table below explains all the different characters used in the model and what they represent.

Table 4-1 Sets, Indices, Parameters and Decision variables of the PHLRP

Sets

A Set of all arcs

C Set of all customers

N Set of all nodes, including all customers and all candidate hub B Set of all cargo bikes

H Set of all candidate hubs T Set of all time periods

Parameters

𝑓ℎ Fixed cost for opening hub h, ℎ ∈ 𝐻 𝑚ℎ Moving cost for moving hub h, ℎ ∈ 𝐻

r Delivery cost

𝑒𝑖𝑗𝑡 Distance from node i to node j at time t, 𝑖, 𝑗 ∈ 𝑁, 𝑡 ∈ 𝑇 𝑑𝑖 Demand at node i, 𝑖 ∈ 𝑁 ℎ𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 Capacity of a hub 𝑏𝑛𝑢𝑚𝑏𝑒𝑟 Number of bikes 𝑏𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 Capacity of a bike 𝑏𝑟𝑎𝑛𝑔𝑒 Range of a bike n Number of nodes Decision variables

𝑥𝑖𝑗𝑏𝑡 1, if node j is visited immediately after node i by bike b at time t, 0 otherwise 𝑦ℎ𝑡 1, if hub h is moved at time t, 0 otherwise

𝑧ℎ𝑡 1, if hub h is opened at time t, 0 otherwise 𝑢𝑖𝑏𝑡 MTZ sub-tour elimination variable

4.3 Optimization Model

∑ 𝑥_{𝑖𝑗𝑏𝑡} 𝑗∈𝑁 = ∑ 𝑥𝑗𝑖𝑏𝑡 𝑗∈𝑁 ∀𝑖 ∈ 𝐶, ∀𝑏 ∈ 𝐵, ∀𝑡 ∈ 𝑇, (5) ∑ ∑ 𝑥𝑖𝑗𝑏𝑡 𝑏∈𝐵 𝑗∈𝑁 = 1 ∀𝑖 ∈ 𝐶, ∀𝑡 ∈ 𝑇, (6) ∑ ∑ 𝑥𝑗𝑖𝑏𝑡 𝑏∈𝐵 𝑗∈𝑁 = 1 ∀𝑖 ∈ 𝐶, ∀𝑡 ∈ 𝑇, (7) ∑ ∑ ∑ 𝑥𝑖𝑗𝑏𝑡𝑑𝑖 𝑏∈𝐵 𝑗∈𝑁 𝑖∈𝐶 ≤ ℎ𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 ∀𝑡 ∈ 𝑇, (8) ∑ ∑ 𝑥𝑖𝑗𝑏𝑡𝑑𝑖 𝑗∈𝑁 𝑖∈𝐶 ≤ 𝑏𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 ∀𝑏 ∈ 𝐵, ∀𝑡 ∈ 𝑇, (9) ∑ ∑ 𝑥𝑖𝑗𝑏𝑡 𝑗∈𝑁 𝑖∈𝑁 𝑒𝑖𝑗𝑡≤ 𝑏𝑟𝑎𝑛𝑔𝑒 ∀𝑏 ∈ 𝐵, ∀𝑡 ∈ 𝑇, (10) 𝑢𝑗𝑏𝑡 ≥ 𝑢𝑖𝑏𝑡+ 𝑛𝑥𝑖𝑗𝑏𝑡− 𝑛 + 1 ∀𝑖 ∈ 𝐶, ∀𝑗 ∈ 𝐶, ∀𝑏 ∈ 𝐵, ∀𝑡 ∈ 𝑇, (11) 𝑦ℎ𝑡≥ 𝑧ℎ𝑡− 𝑧ℎ𝑡−1 ∀ℎ ∈ 𝐻, ∀𝑡 ∈ 𝑇, (12) 𝑥𝑖𝑗𝑏𝑡 ∈ {0,1} ∀(𝑖, 𝑗) ∈ 𝐴, ∀𝑏 ∈ 𝐵, (13) 𝑦ℎ𝑡∈ {0,1} ∀ℎ ∈ 𝐻, ∀𝑡 ∈ 𝑇, (14) 𝑧ℎ𝑡∈ {0,1} ∀ℎ ∈ 𝐻, ∀𝑡 ∈ 𝑇, (15) 𝑢𝑖𝑏𝑡 ≥ 0 ∀𝑖 ∈ 𝐶, ∀𝑏 ∈ 𝐵, ∀𝑡 ∈ 𝑇, (16)

5. Computational Study

In this section, the conducted experiments are discussed alongside the results that were generated. The model is applied in Python 3.7, used on the Spyder platform, and Gurobi 8.1.1 optimization package. The model ran on a personal computer with Intel® Core™ i5-8250U @ 1.60GHz, 64-bit processor, 8GB of RAM and Microsoft Windows 10. The first experiment was made to test the effect of hub portability on the total cost, but also the effect of individual costs on hub portability. The second experiment is a sensitivity analysis of different parameters that could influence the hub portability. Below, an overview of the data generation will be made, followed by the expectations of the experiments. Finally, the results will be presented and explained.

5.1 Data Generation

As far as the generation of data is concerned, the distribution of customer locations and candidate hub locations is random, while the number of customers is fixed and set to 5, due to feasibility issues with larger numbers. The distance between locations, is calculated by the Euclidean formulation.

For investigating the hub portability effect, the following constraints are added.

𝑧ℎ𝑡 = 𝑧ℎ𝑡+1 ∀ℎ ∈ 𝐻, ∀𝑡 ∈ {2,3,4,5,6,7}, (17)

𝑧ℎ1 = 𝑧ℎ2 ∀ℎ ∈ 𝐻, (18)

𝑧ℎ3 = 𝑧ℎ4 ∀ℎ ∈ 𝐻, (19)

𝑧ℎ5 = 𝑧ℎ6 ∀ℎ ∈ 𝐻, (20)

The constraints above are used for different portability cases. The model, as presented before, is fully flexible to adapt at any customer layout at any point in time. With the addition of constraint (17), the hub is forced to remain at the same location for all time periods. Finally, constraints (18), (19) and (20) lead to a semi-portable hub, where the hub must stay two consecutive days at one location. For all 3 cases, an experiment is made to test the effect different fixed cost, moving cost and delivery cost, have on the total distance and total cost.

For the second experiment, a sensitivity analysis is conducted for different parameters, such as the number of candidate hub locations, the bike capacity, the bike range and the number of bikes used. These are investigated for extreme numbers in order to see what the effect is when the system is stressed to the limit.

5.2 Testing Framework and Expectations

comparison, the flexible hub location will produce the best results with the minimum distance needed for delivering to customers. However, the partial flexibility every two days is also expected to be performing better than the fixed hub location, although with a small improvement. Overall, the effect of different fixed, moving and delivery costs, on distance and total cost, will be tested and the results in all cases are anticipated to be better for the fully portable system.

The sensitivity analysis on the other hand, will start with the number of candidate hub locations that can be used. Here the test will be run for 3, 5 and 7 candidate hub locations. The outcome is expected to be better for 7 and gradually worse as we go down. This is because of the increased flexibility and with more options the hubs can be closer to the demand, when shifting from time to time.

For bike capacity, the values for which the model is tested are 3 and 4. This is because two bikes are used in this experiment and five customers with demand of one per customer. The chosen values are expected to give different outputs, because a bike capacity of 3 forces bikes to share customers and distances, while bike capacity equal to 4 offers more space for one bike to serve 4 out of 5 customers.

Similarly with the bike capacity, the effect of changing the range of the bikes will be tested. The experiment will start from the first value that gives a feasible solution, which is a range of 14. It is expected that at range 14, it will be more expensive because of using 2 bikes, instead of a bigger range where one bike could serve all customers.

The final test is the number of bikes that will be used for delivering to customers. This number will range from 1 to 3, with expectations that 1 will produce the worst results and 3 the best. This is because of the larger area that 1 bike has to cover therefore more distance, while 3 bikes can optimize routing and minimize total distance.

5.3 Results

apart from the time and distance they travel. Overall, extreme values are tested for every cost, but when the model is tested with the baseline values, it produces the most reasonable results, for the scale of a problem with 5 customers and a 10x10 service area.

Furthermore, results for the travelled bike distance, when different costs change, are presented in the following graphs. In Graph 5-1, the fixed cost ranges from 5 to 55 with a step of 5, showing a clear advantage of the fully portable and partially portable cases over the non-portable one. It can be seen that the distance for the fully non-portable system is significantly lower from 5 to 50, while for values of 55 and higher the distance reaches a plateau. At this level, the percentage decrease of distance, between the non-portable and the fully portable system is at 4.78%. This happens because from 55 and upwards the fixed cost becomes too big and as a result it is too expensive to use additional hubs. As far as the partially portable system is concerned, it is outperformed by the fully portable one each time it is restricted from moving a hub. Although a fixed cost value of 55 produces the same output as a fixed cost of 100, 55 is not a realistic value and that is the reason the recommended baseline is set to a fixed cost of 100.

Graph 5-1 The effect of fixed cost on bike distance

In Graph 5-2, the moving cost ranges again from 5 to 55 with a step of 5. It can be seen that from a moving cost of 15 the minimum routing distance has been reached, however the recommended baseline is set to 30, which is more realistic. Even though the results show the same decrease in distance, between the non-portable and the fully portable system, of 4.78% for moving cost values over 55, for values under 55 the distance decrease is not changing. This outcome occurs because of the mild effect the moving cost has, thus it does not affect the routing distance as much as the fixed cost. This is due to the fact that the proposed model is too small to be influenced by the moving cost because there are only 2 hubs used and so the moving cost is too small to influence the distance. In a more realistic scenario, when

120,000 130,000 140,000 150,000 160,000 170,000 180,000 5 10 15 20 25 30 35 40 45 50 55 D is ta n ce

Fixed Cost for one location

Bike Distance

more hubs will be used, more re-location of these hubs will occur, which strengthens the effect of the moving cost.

Graph 5-2 The effect of moving cost on bike distance

Finally, in Graph 5-3, the delivery cost ranges from 1 to 11 with a step of 1, producing the same distance decrease, from the fully portable and the non-portable system, of 4.78% for values of 4 and higher, though for values lower than 4, the distance is equal to the distance of the non-portable system. In this case, the extremely low delivery cost is favored over the fixed and moving cost hence the system created is identical to the non-portable one. Thus a delivery cost of 10 is suggested as baseline to avoid losing the portability option and because it is closer to a real life scenario, where adjustments can be made upon whether the re-location of a hub will be used or just the delivery by bike, in order to produce a shorter routing distance.

Graph 5-3 The effect of delivery cost on bike distance 120,000 130,000 140,000 150,000 160,000 170,000 180,000 5 10 15 20 25 30 35 40 45 50 55 D is ta n ce

Moving Cost for one location

Bike Distance

Delivery Cost per distance

Bike Distance

The same experiments are run in order to observe the effect of hub portability on the total cost. Starting with Table 5-1, where the fixed cost ranges from 5 to 55 with a step of 5, it can be seen that the percentage difference between a fully portable system and a non-portable one is shrinking. This happens mainly because after a certain value of fixed cost, the distance reaches its minimum, which means that there is a proportional increase in the total cost as much as in the fixed cost, once the moving cost and delivery cost do not change. Although the difference is getting smaller with increasing the fixed cost, the fully portable system will always be less costly. In this case it happens because the optimal solution includes at least one location change for a hub. Additionally, it can be seen that in case 1, too many hubs are opened because it is cheap and it minimizes the distance. However, as the fixed cost increases, the number of hubs decreases, which supports the decision to set the baseline high in order to avoid opening a hub for each customer. In conclusion, it seems that as long as there is a hub relocation in the optimal solution, the fully portable system will be always more efficient than the non-portable one.

Table 5-1 Percentage difference the fixed cost creates to the total cost between fully portable and non-portable.

Total Cost

Case

Number of hubs

Cost Portability _{% Difference}

Fully - Non Fixed Moving Delivery Fully Non Partially

indicates that the single hub is moved 2 times in 7 days, which is a more realistic value and frequency. Concluding, the effect the moving cost has on the total cost depends eventually on how many times a hub is moved, so unless no hub re-location is happening, the fully portable system will always produce better results over the non-portable one.

Table 5-2Percentage difference the moving cost creates to the total cost between fully portable and non-portable.

Total Cost Case # hub location changes Cost Portability % Difference Fully - Non Fixed Moving Delivery Fully Non Partially

1 4 100 5 10 2318,79 2413,63 2318,79 -3,93% 2 4 100 10 10 2338,79 2418,63 2338,79 -3,30% 3 2 100 15 10 2357,04 2423,63 2357,04 -2,75% 4 2 100 20 10 2367,04 2428,63 2367,04 -2,54% 5 2 100 25 10 2377,04 2433,63 2377,04 -2,33% 6 2 100 30 10 2387,04 2438,63 2387,04 -2,12% 7 2 100 35 10 2397,04 2443,63 2397,04 -1,91% 8 2 100 40 10 2407,04 2448,63 2407,04 -1,70% 9 2 100 45 10 2417,04 2453,63 2417,04 -1,49% 10 2 100 50 10 2427,04 2458,63 2427,04 -1,28% 11 2 100 55 10 2437,04 2463,63 2437,04 -1,08%

Table 5-3 Percentage difference the delivery cost creates to the total cost between fully portable and non-portable.

Total Cost

Case

Cost Portability % Difference

Fully - Non Fixed Moving Delivery Fully Non Partially

1 100 30 1 900.86 900.86 900.86 0.00% 2 100 30 2 1071.73 1071.73 1071.73 0.00% 3 100 30 3 1242.59 1242.59 1242.59 0.00% 4 100 30 4 1410.82 1413.45 1410.82 -0.19% 5 100 30 5 1573.52 1584.31 1573.52 -0.68% 6 100 30 6 1736.22 1755.18 1736.22 -1.08% 7 100 30 7 1898.93 1926.04 1898.93 -1.41% 8 100 30 8 2061.63 2096.90 2061.63 -1.68% 9 100 30 9 2224.34 2267.77 2224.34 -1.92% 10 100 30 10 2387.04 2438.63 2387.04 -2.12% 11 100 30 11 2549.74 2609.49 2549.74 -2.29%

The results of the sensitivity analysis for the remaining parameters of the model are also important. Starting with the number of candidate hub locations, the test included 3, 5 and 7 possible hub locations. In general, here the baseline used is as in case 1, which has a moving cost of 10, in order to allow the model to re-locate the hubs more times so that a clearer conclusion can be made. More specifically, for every number of hub locations, the test was conducted with extreme values for the fixed, moving and delivery costs, calculating the percentage difference between the fully portable and non-portable system. As can be seen from

Table 5-4 below, although in case 1 total distance is improved almost twice as much from the

balance between moving cost and delivery cost, because that creates the biggest difference from fully portable to non-portable systems.

Table 5-4 The effect of different number of candidate hub locations upon total cost and distance.

Case 1 Case 2 Case 3

Fixed cost 100 100 100 Moving cost 10 14 10 Delivery cost 10 10 7 # hubs 3 5 7 3 5 7 3 5 7 Total cost -0,32% -3,30% -3,50% - -2,82% -2,80% - -2,48% -2,09% Total distance -2,02% -6,43% -12,26% - -5,62% -11,16% - -5,62% -11,16% Next parameter investigated, is the bike capacity and it is tested for the values of 3 and 4. These values are not realistic, but are used in order to test the effect that bike capacity has in our setting of 5 customers. That is the reason for the improvement shown in Table 5-5. The first test involves cases 1 and 2 of the fully portable system, with case 1 having a bike capacity of 3 and case 2 having a bike capacity of 4. The improvement for the extra space is 4.77% in total cost and 8.61% in total distance. These improvements occur because in case 2, the single hub used, was re-located 3 times instead of 1 time in case 1. In a realistic scenario, it is also expected that a bigger bike capacity, which means serving more customers, will increase the effect portability has on cost and routing distance. However, the exact same test for the non-portable system, showed an improvement of 4.47% in total cost and 6.72% in distance. Here the improvements are a result of the better routing when bike capacity is 4. The most important test is comparing cases 2 and 4, so the fully portable system with the non-portable system when bike capacity is 4. Starting with the total cost difference, it can be seen that it is 0.32%, but occurs due to the fact that while distance is smaller in case 2, the single hub is re-located 3 times, so savings from distance, of around 2%, are balanced with additional moving costs. Concluding, when a bike has a larger capacity, it is more flexible in routing distance and can serve more customers, which results in improvements for both fully and non-portable systems. In real life usage, the bigger capacity would give a greater opportunity in improving delivery routing and hub movement.

Table 5-5 The effect of bike capacity upon total cost and distance.

Portability Fully Non Fully Non

Case 1 2 3 4 2 4

Bike capacity 3 4 3 4 4 4

Total cost -4.77% -4.47% -0.32%

Total distance -8.61% -6.72% -2.02%

bikes depends on several things, such as the size of the battery, the weight of the cargo or even the traffic. Nevertheless, as seen in Table 5-6, in case 1, the fully portable system is tested against the non-portable for a bike range of 19. The improvement in total cost is 0.32%, while in distance it is 2.02%, and that is because in the fully portable system, a single hub is re-located 3 times, producing smaller routing distance, but the cost savings from the routing distance are equalized with the added moving cost. Although this can result also from the small number of customers in this setting, in a realistic scenario the impact is expected to be greater. On the other hand, in case 2, the fully portable system is tested, to see the difference between a bike range of 14 and 19. These values were chosen because they are proportional to the size of this setting. It can be noticed that the fully portable system is affected by the range of the bike, because the percentage difference here, from 14 to 19, shows a 9.29% improvement in total cost and 8.30% improvement in distance. The difference in cost derives from the fact that when the range is 14, 2 hubs are used and are moved twice, but when the range is 19, 1 hub is used and moved 3 times. On the other hand, the difference in distance was expected, because of the bigger bike range that allowed serving more customers in one trip.

Table 5-6 The effect of bike range upon total cost and distance.

Case 1 2

Bike range 19 14-19

Total cost -0.32% -9.29%

Total distance -2.02% -8.30%

Table 5-7 The effect of the number of bikes used upon total cost and distance.

Portability Fully - Non Fully - Partially

Case 1 2

# bikes 1 2 3 1 2 3

Total cost - -0.32% -0.34% - - -0.34%

6. Conclusion

For the last-mile delivery, logistic service providers have been using for many years the same methods to reach the final customers. Delivery vans are the most common one, although the negative effects these vehicles are causing could have been avoided. First of all, minimizing transportation cost is the LSPs main goal, which in addition to the sustainability rules that are being followed these days, an alternative concept is needed in order to save some costs, while minimizing emissions and road congestion. That is the ambition of this thesis, to investigate the HLRP and the advantages portable hubs could bring, through answering the following question: Are portable hubs cost effective against the current system of hubs with a fixed

location? Thus, to answer this question, a linear programming model has been formulated to

explore if the portability effect can save some last-mile delivery costs and minimize the routing distance. The results from the computational experiments are reassuring that, in all cases, an improvement is made even if it is a small one. More specifically, total delivery costs are lowered, which is mostly an effect of the shorter routing distance from the new system. Finally, this thesis adds to the mobile HLP the routing it was missing and to the HLRP the mobility of hubs that was lacking from literature.

Based on these results, the circumstances that provide the most cost savings in reality would be a high fixed cost combined with low moving and delivery costs. This combination offers more flexibility in choosing to re-locate an existing hub or just deliver by bike, instead of opening another hub location. Additional proposed settings that provide improvements would be to have as many candidate hub locations as possible, cargo bikes with a large capacity and range, but also a big number of bikes, which depends on customer demand. This can be critical in cities with high population density, where bike capacity or range can limit the system and force it to open a hub location near a big concentration of customers. An example where the low moving cost of a hub can show its full potential is during a festive period, when people order more and demand rises.

Python was used for programming this model, which is the reason why the size of the experiments, meaning the number of customers, the demand of each customer and the number of possible hub locations, are intentionally small due to infeasibility issues or large running times. For this reason, a comparison between the proposed model and a heuristic can be made as future work, to discover if this problem can be solved faster, while producing similar results. Finally several constraints can be relaxed, such as the capacity of hubs or bikes, if an evolved model uses an approximation technique, where hub locations will not be predefined, and the model can adjust between locations and routing.

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