The effects of relocating mobile depots on last-mile delivery

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The effects of relocating mobile depots on last-mile delivery

Master Thesis

MSc. Supply Chain Management

University of Groningen

Faculty of Economics and Business

Supervisor:

Dr. I. Bakir

Co-assessor:

Dr. Ir. P. Buijs

Henk van der Molen

H.p.van.der.molen.1@student.rug.nl

S3493717

26-01-2020

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Abstract

The most inefficient part of a supply chain is the last-mile delivery. This thesis studies the effects of various frequency of relocating Mobile Depots (MDs) on the efficiency of last-mile delivery. A simulation approach is employed which mimics an MD freight distribution system. The model design is based on a sequential heuristic, called cluster-first, route-second. First, the MD locations are determined through k-means++ clustering, after which the VRP is solved through Google Or-tools. Sixteen different scenarios were examined, which deployed various quantities of MDs in combination with four cluster intervals: daily, weekly, monthly and quarterly. It is concluded that a relatively minor effect of frequency of relocation on efficiency of last-mile delivery is established when deploying up to five MDs, whereas when deploying more ten MDs the effect becomes considerably larger in terms of total traveled distance. The results lead to several propositions which provide promising avenues for future research.

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1 INTRODUCTION

Consumers nowadays live in a world of instant gratification. They are accustomed to having access to their online purchases within shorter time frames than ever before and expect it to be free of charge (KPMG, 2019). This societal trend of customer standards changing towards shorter delivery times increases the number of delivery trucks, which in turn causes trucks to drive around with half truckloads or less, because of the higher frequency and smaller order quantities (McKinnon & Ge, 2006). Having these delivery trucks capacitating the infrastructure is inefficient, especially in inner-cities, because of the narrow streets and higher traffic congestion. This inefficiency also makes it more difficult to deliver parcels reliably, affordably and timely (Verlinde, Macharis, Milan, & Kin, 2014). These so-called ‘last mile deliveries’ are the logistics activities that are needed to supply the inhabitants of a city (Lindawati, van Schagen, Goh, & de Souza, 2014). It is seen as a troublesome activity that gained popularity in the literature in the last decade. These last mile deliveries create more traffic congestion, which cause for increased sound levels, but more importantly have a serious negative consequence on air pollution (Crainic, Ricciardi, & Storchi, 2004). According to Goodman (2005), last mile delivery is the most polluting, least efficient and most expensive part of the supply chain and is responsible for 28% of the total transportation cost. In order to decrease these negative externalities and at the same time meet the increasing demand of parcels, logistics companies are exploring new alternatives.

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2 The most dynamic type of MD that was identified in the literature is from an ex-ante case study on mobile depots by Arvidsson & Pazirandeh (2017). This study examined a continuously moving vehicle that was connected with two cargo bikes, which simultaneously delivered parcels. The authors concluded that this system has environmental and social advantages in an urban environment, while sustaining financial viability. The opposite of this constantly moving MD is a project in Brussels by TNT. This project was part of an EU project called STRAIGHTSOL and was researched by Verlinde et al. (2014). The MD stayed in one location in the city center, and was replenished in the morning and evening for a period of three months. Similar to Arvidsson & Pazirandeh (2017), the TNT project realized significant decreases in emissions and travel distance.

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3 This research makes use of a simulation approach to identify how this mobility aspect of different types of MDs stack up against each other. More specifically, a Discrete Event Simulation (DES) is created in Python. A simulation approach is very suitable for this research because it allows to objectively study the relationship between multiple input and output parameters.

A review of the existing literature in the field of location and routing was done to identify what algorithms and heuristics were developed and which were suitable for this thesis. This starts off with Location Routing Problem (LRP), which has been around for more than 50 years and was first described by Laporte & Nobert (1987). Many extensions followed throughout the years, but the most relevant is the Mobile Facility Location Routing Problem (MFLRP), which was first introduced by Halper & Raghavan (2011). Only a few papers have been published on the topic after this introduction, and they primarily focused on improving existing mathematical models to solve the problem faster and more accurately. None of the identified papers explored the effects of relocation frequency of these MDs. It should be noted that routing and location problems are NP-Hard problems, and no efficient way of solving them has yet been realised. This thesis does not aim to solve this nor tries to improve any existing algorithms or meta-heuristics. It rather uses a relatively simple meta-heuristic called Guided Local Search (GLS) in combination with k-means clustering to retrieve new insights that can contribute to the field of location theory by identifying what the effects are of relocating MDs. This focus area did not receive much attention lately, according to Perbol & Rosano (2019). Altogether, this leads to the following research question:

“What is the effect of the frequency of relocating mobile depots on achieving efficiency within last mile delivery?”

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2 LITERATURE REVIEW

2.1 MOBILITY OF MOBILE DEPOTS

In literature, various forms of Mobile Depots (MDs) are identified, which are technically very similar in the sense that they are: (i.) replenished with parcels on the outskirts of a city; (ii.) move into the city with the objective to decrease the amount of distance within the inner-city; (iii.) such that a more effective last-mile delivery is established.

The most noticeable difference between Mobile Depots is lies in their degree of mobility. The spectrum varies between staying in one location for three months, to a continuously moving MD. The most immobile MD, that stayed in a single location over the course of three months was utilized by TNT Express in Brussels. The project was evaluated through a Multi Actor Multi Criteria Analysis (MAMCA) by Verlinde et al. (2014), which showed that weekly truck driving distances were decreased with 89% and CO2 emissions fell with 24%. However, they also concluded that operating the MDs was 40% more expensive, and that of the five future scenarios, going back to traditional freight distribution system, gave the optimal outcome regarding the overall operating cost. The research did not consider the effects of mobility of the MD by changing locations. The study states that drop density should be increased for better performance, but does not give any suggestion on how to do so. This research will use the aforementioned project as a scenario that represents the lower boundary of the mobility spectrum. This means that is used as the lowest frequency for relocation determination.

The upper bound of the mobility spectrum was identified in the research of Arvidsson & Pazirandeh (2017). The study described a continuously moving MD, which is supported by two cargo cycles. The MDs location is determined on daily basis by making use of existing bus routes. A sketch of how the MD would look like can be found in figure 1. The research evaluated how the MDs performance stacked up against the current delivery system, both primarily used quantitative methods, but in addition gathered qualitative information on the stakeholder perspective through workshops. The case they described showed that the MD was a more optimal solution, both environmentally and socially considering the urban context, aside from being more financially viable for the transport operators if the utilization rate of the MD is high enough. The mobility of this type of MD is almost limitless in the sense that the MD can go everywhere on the existing road infrastructure.

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5 (figure 1). In terms of mobility, the MDs location is bounded by the banks of the Seine river, and thus some restrictions are in place.

Second, the German company ‘Rytle’ created the MD that fits best to the MD concept studied in this thesis, due to the full flexibility it offers. A truck uses the existing road network and available parking space within a city. The truck lowers a container, which they call a ‘hub’, via a hydraulic system embedded in the container, making it possible for the truck to leave afterwards. The hub, from now on referred to as ‘MD’ can be placed in a nearby location to the final delivery points, from where on the electric cargo bikes, titled ‘MOVR’will take care of getting the parcels to their final destination. These MDs contain nine smaller containers, named a ‘BOX’ that can easily be mounted onto the MOVR minimizing the overload time for the courier.

The above-mentioned difference in mobility and corresponding location determination within these four projects are an important guidance for the scenario development within this thesis. The technical differences of each MD will both have advantages and disadvantages. For instance, there is less traffic congestion on the Seine than on the streets next to it, but the mobility is restricted by the banks of the Seine river. This thesis does not restrict the MDs in their mobility, and allows the MDs to be located purely on the customer locations. By doing this, the focus is purely on the frequency of location determination rather than on technical specifications that allow the MD to move freely. This also allows us to simulate a more generic environment that is more generalizable, such that it can be applied to many cities. From the four projects, the MD concept developed by Rytle is most appropriate to use within the context of this thesis. It should also be noted that the MD solution used by ‘Rytle’ also has a drawback, which is the scarcity of parking space within urban areas (Siemens AG, 2007).

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2.2 LOCATION ROUTING PROBLEM

This study pertains to the body of research commonly referred to as Location Theory, which focuses on solving a Location Routing Problem (LRP). A LRP is simply defined as a combination of the two major fields in operation management, namely Facility Location Problem (FLP) and a Vehicle Routing Problem (VRP)(Ghannadpour, Noori, Tavakkoli-Moghaddam, & Ghoseiri, 2014). Delving into the literature of both the FLP and VRP fields is deemed redundant, since LRP is a combination of both. Nevertheless, for more readings on FLP the following review papers are recommended: Farahani, Fallah, Ruiz, Hosseini, & Asgari (2019); Melo, Nickel, & Saldanha-da-Gama (2009); Owen & Daskin (1998) and for VRP: Braekers, Ramaekers, & Van Nieuwenhuyse (2016); Eksioglu, Vural, & Reisman (2009). Like VRP and FLP, LRP has a rich research history and has been around for half a century (Chan, Carter, & Burnes, 2001; Drexl & Schneider, 2015; Laporte & Nobert, 1987; Min, Jayaraman, & Srivastava, 1998; Nagy & Salhi, 2006; Prodhon & Prins, 2014). Throughout the years, many different extensions, algorithms and (meta)heuristics are developed. From the recent additions to the research, the most relevant extension for this thesis is the Mobile Facility Routing Problem, which is defined in the next section.

It should be noted that LRP is a NP-hard problem, as it contains two NP-hard problems namely the FLP and VRP (Nagy & Salhi, 2006; Prodhon & Prins, 2014). The combination of two NP-hard problems explains the decreased number of publications on exact algorithms (Laporte & Nobert, 1987; Prodhon & Prins, 2014). Solving an LRP that includes (fixed) multiple depots, multiple constraints and a large set of customers has not yet been accomplished. A few exact approaches are offered, but when increasing the number of customers above 50, the algorithm starts to fail (Prodhon & Prins, 2014). To be clear, this research examines multiple mobile depots within a large set of customers, and has no intention to solve for optimality. Therefore this thesis makes uses a (meta) heuristic(s) as a solution method, which according to Barreto, Ferreira, Paixão, & Santos (2007), has the following advantages: (i.) Getting good solutions within satisfactory time limit; (ii.) Producing several good solutions granting the user to select the most suitable corresponding to the scenario; (iii.) Easy to understand, modify and implement, and allow to deal with larger data sets. These advantages align with the objective of this thesis in the sense that a reasonable solution, but not necessarily the optimal solution, is of interest. It allows to test multiple scenarios with large sets of customers in a shorter time frame than exact algorithms, and the model is easy to use, so that future users can effortlessly use and tweak it to fit their research purpose.

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7 (iii.) Savings/Insertion, (iv.) Improvement/Exchange. The developed model uses the (i.) Location-allocation-first, Route-second heuristic, and in some way this heuristic bears a resemblance to the sequential routing method, which does not allow for feedback from the routing phase and can lead to suboptimal designs of the distribution system (Nagy & Salhi, 2006). However, this research derives its location-allocation from a clustering-based method, which means that the locations are built on the skeleton of a routing plan, so this is an improved effort at combining locational and routing decision (Nagy & Salhi, 2006). Again, this research is not solving for the optimal solution, and it should be noted that in some cases the sequential methods provided good quality solutions (Srivastava & Benton, 1990 IN Nagy & Salhi, 2006).

2.3 EXTENSIONS ON LRP

First, the dynamic location Routing Problem (DLRP) is explained, which covers a more modern-day way of solving the problem compared to the traditional LRP. This is followed by the most relevant extension: Mobile Facility Routing Problem (MFRP). A novice extension in location theory, which has been discussed in various forms by a few other scholars (Bashiri, Rezanezhad, Tavakkoli-Moghaddam, & Hasanzadeh, 2018; Güden & Süral, 2014; Halper & Raghavan, 2011; Halper, Raghavan, & Sahin, 2015; Lei, Lin, & Miao, 2014).

2.3.1 Dynamic Location Routing problem

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Figure 2 DLRP (Pillac et al., 2013)

2.3.2 Mobile facility routing problem

The Mobile Facility Routing Problem (MFRP) was introduced relatively recently by Halper & Raghavan (2011). Their research focused on maximizing the total demand serviced, they were the first to solve this NP-hard problem for a single mobile facility to optimality in polynomial time. Furthermore, the study presents various heuristics when solving with multiple mobile facilities. The authors made a distinction between Sequential Routing and Insertion Heuristics, and their results show that the former typically outperforms the latter. However, the insertion heuristic is quicker in finding a solution, as opposed to the Sequential Routing, which gives higher quality solutions. Overall, the effectiveness of these heuristics were verified against several data sets, and they concluded that mobile facilities are capable of serving larger and more fluctuating demand, better than an optimal fixed facility location (Halper & Raghavan, 2011).

Another study by Lei et al. (2014) extended the MFRP by using a L-shaped algorithm to solve a Mobile Facility Routing and Scheduling Problem with Stochastic Demand (MFRSPSD). The objective of this study was to minimize the total costs generated during the planning horizon. The problem was divided into two stages, first the location and movements of the MDs were realized and the second stage dealt with how the MDs could serve customer demands.

The most recent paper of Bashiri et al. (2018) introduced a new p-mobile hub location problem. The study addressed an alternate mobility strategy that was benchmarked against a traditional DLRP, this was done by developing a mathematical model which was solved by genetic algorithm that included a local search for large instances. The authors concluded that their model outperforms the current status quo and that it is especially suitable for applications like mobile postal service, fire stations or medical facilities that require to reach final destinations as fast as possible.

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3 MODEL

Most of the papers published in the location and routing field adopt mathematical models to improve existing algorithms and heuristics. This thesis, however, does not aim to improve on any of the existing models. Instead it uses a simulation approach to obtain new insights on what effects can be measured when changing the frequency of relocating MDs. A simulation is defined as modeling the operation of “real-world” processes, events or systems by using computer software (Davis, Eisenhardt, & Bingham, 2007). This particular real-world system is related to the MD concept created by Rytle, and is built in Python. Sufficient relevant information was available on the structure of this freight distribution system to build it as discrete event simulation model in Python. This research makes use of experimental input parameters, since there was no generalizable empirically validated data readily available.

3.1 SIMULATION

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3.2 INPUT PARAMETERS

An overview of the parameters can be found in table 1. A distinction is made between fixed parameters and variable parameters. First, an explanation is given of why these fixed parameters have been selected. After that, the variables and the value selection is explained.

Table 1 Fixed and variable input parameters.

Fixed parameters Symbol Value

Number of Customers 𝑁𝐶𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠 1000

Number of Simulations 𝑄𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑠 50

Vehicle Capacity 𝑉𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 50

VRP Search Strategy 𝐺𝑠𝑡𝑟𝑎𝑡𝑒𝑔𝑦 Guided Local Search

Time Limit 𝑇𝑡𝑖𝑚𝑒_𝑙𝑖𝑚𝑖𝑡 120

Simulation Environment 12,25km2

Variable parameters Symbol Value

Cluster Intervals (in days) 𝑡𝑐𝑙𝑢𝑠𝑡𝑒𝑟_𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙 0, 7, 30, 90 Number of Mobile Depots 𝐾𝑚𝑜𝑏𝑖𝑙𝑒_𝑑𝑒𝑝𝑜𝑡𝑠 1, 2, 5, 10

Number of Vehicles 𝐶𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠 20

Error rate of driver 𝜖 1% - 75%

Additional error distance 𝐴𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 500 – 5000 meters

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11 The vehicle capacity is based on technical specifications of the Rytle box1_{, which measures an} approximate 1,7m3_{. The assumption is made that this system is most suitable to deliver small} packages2_{, which are on average 0,03m}3_{in size. With these measures, approximately 50 parcels would} fit in the Rytle box.

To achieve the most reliable results, a preliminary sensitivity analysis indicated that increasing the number of simulations to exceed 50 would not lower the coefficient of variation of the route distance and thus would not give more stable results. When converting the number of simulations to a time frame in reality, a single simulation would be equivalent to a single day in reality plus the additional days of historical data that are needed for creating the cluster centroids. The 50 simulations are actually the equivalent of simulating 140 days, existing of 90 days of historical data plus the 50 days of routing. The 90 days of historical data are related to the largest cluster interval, which is 90 days. The centroid locations are thus created based on the first 90 days of customer locations. Hence, no routing occurs until the first centroids are created. The cluster intervals are now set to four different intervals: 0 = daily, 7 = weekly, 30 = monthly and 90 = quarterly; the selection of these intervals are inspired by the existing MD implementations mentioned in the literature review. For instance, the daily interval relates to the case study of Arvidsson & Pazirandeh (2017). Whereas the 90 day interval reflects the scenario of the STRAIGHTSOL Project by TNT in Brussels. The cluster intervals in between are simply based on logics, and the Gregorian calendar which should align with most of the Western delivery companies.

Aside from a range of different cluster intervals, several different values for the number of MDs are selected, in this simulation the number of MDs automatically regulate the capacity of the MD, because the number of customers is fixed. It is simply adding more locations to start and return to, while delivering the same number of packages. The Rytle MD would have an approximate capacity of 500 parcels, which would mean that two MDs are needed to supply 1000 customers. Next to this base scenario, three additional scenarios are employed to see what the effects are of having more MDs with less capacity and the other way around having one larger MD with double the capacity to a 1000 parcels, which would sort of mimic the TNT project in brussels. The two scenarios with lower capacity have five MDs with 200 capacity, and ten MDs with only a 100 capacity. An oversimplistic overview of the different scenarios is given in figure 3. In total 16 different scenarios are simulated.

The error rate of the driver indicated by 𝜖 ranges from 1 to 75% chance that the driver takes a wrong exit when the routing is executed, nowadays there are enough technologies that would decrease this

1_{https://rytle.de/box/?lang=en}

2

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12 risk. However, it should be noted that when a more fixed location is used, the driver would become more familiar with this location and hence would have less trouble locating the MD. This error rate will invoke an additional distance, which will range between 500 and 5000 meters.

The remaining parameters, like time limit are used to test the robustness of the model. Regarding constraints in the model, it should be noted that all simulated scenarios need to supply all customers, and that a customer receives a single uniform parcel which does not differ in size. This means that the model makes use of deterministic demand which will not fluctuate during the simulations.

Figure 3 Simulated Scenarios

3.3 SIMULATION DESIGN

As previously described in the literature review, a sequential heuristic called cluster first, route second, is used in this thesis. This thesis employs k-means clustering to do so, due to its simplicity of implementation and fast execution (Davidson, 2002). K-means is a non-hierarchal clustering technique, which means that the number of clusters needs to be specified before the algorithm is executed. This also gives more freedom to discover what the effects are when employing multiple MDs. When the number of clusters is specified, the algorithm simply clusters all the generated customer X and Y coordinates, by trying to separate the customers in n groups of equal variance, minimizing a criterion known as the within-cluster sum-of-squares. The k-means algorithm splits a set of 𝑁 samples 𝑋 into 𝐾 separate clusters 𝐶, each described by the mean 𝜇𝑗 of the samples in the cluster, more commonly referred to as ‘centroids’. The aim of the algorithm is that the centroids minimizes the within-cluster sum-of-squares, which is mathematically expressed as:

∑ min 𝜇_𝑗𝜖𝐶 𝑛

𝑖=0

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13 A well-established Python package for data science is the Scikit-learn package3_{, which is used to} implement the k-means clustering technique in the model. A benefit of this package is that it actually uses k-means++ by default. K-means++ is a new version of the original k-means created by Arthur & Vassilvitskii (2007). Their empirical results show that k-means++ achieves improvements in both solution quality and running time (Shindler, 2008). Moreover, k-means clustering has been used in a similar DLRP study to identify the location of fixed depots (Gao et al., 2016). When the clustering is done, they are saved and then appended to a list. All customer locations and centroids are transformed into a distance matrix. This is done by calculating the Euclidean distances between all nodes in the model, by using the following formula: 𝐷 = √(𝑥2 − 𝑥1)2_{+ (𝑦2 − 𝑦1)}2_{. This distance matrix is used} to do the routing, which indicates the second phase in the model.

For the VRP part, the extension with capacity is chosen in order to force the model to use all assigned vehicles. A solver developed by Google, called Or-Tools4_{, is utilized to do so. According to Surana} (2019), the Google OR-Tools outperforms current best-known CVRP solutions 60% of the time. Google provides the user with the option to use various different first solution strategies and meta-heuristics. According to the developers of Google5_{, the meta-heuristic called Guided Local Search (GLS) is} generally seen as the most efficient meta-heuristic to solve routing problems. GLS is a high-level strategy that is applicable for solving routing issues and makes use of penalties to escape local minima. During Local Search, algorithms can get stuck in a local optima. The GLS then increases penalties for the features that are present in this local optimum, which forces the local search to escape the local optimum and it then continues to move again towards neighbour solutions that do not have these penalized features (Alsheddy & Tsang, 2011; Alsheddy, Voudouris, Tsang, & Alhindi, 2018). When employing this strategy, Google recommends to set a time limit, otherwise it shows the warning that the simulation can run forever. The next section will describe the robustness of the model, starting with this time limit as the first test.

3.4 ROBUSTNESS OF THE MODEL

In order to check robustness, multiple inputs have to be changed in succession of the other. This means that all inputs stay the same, except for one input which is changed multiple times in order to see what the effects are of only changing that particular input. In terms of validating the robustness of the model, it is important to use a logical sequence, because after each sensitivity analysis the starting set of inputs can change depending on the results. The input parameter time limit in particular has major

3_{https://scikit-learn.org/stable/modules/clustering.html#k-means} 4_{https://developers.google.com/optimization/routing/cvrp}

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14 effects on the outcome of all successive simulation. Assuming that setting a very low time limit could deliver poor results, while having a very high time limit would make it harder to rerun simulations sufficiently. Hence time limit is the first sensitivity analysis with the goal to identify at what time limit good quality results are achieved. Assessing the quality is done by looking at the average distance and standard deviation of the routing distance.

All robustness tests and used parameters are displayed in table 2. As can be seen in the table, it is sometimes necessary to change multiple parameters, because of capacity constraints. For instance, when decreasing the capacity of a vehicle, more vehicles are needed, or else the model is not able to supply all customers. In total three tests are proposed that could affect the routing distance.

Table 2 Overview input parameters robustness simulation

Analysis Customers Simulations Cluster

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4 RESULTS

In this chapter, the results of the aforementioned scenarios are presented. First, the robustness of the model is presented. Afterwards, the main results regarding the frequency of relocation are presented, which is followed by the trade-off between increased error rates and travelled distances.

4.1 ROBUSTNESS OF THE MODEL

4.1.1 Time limit

Five different time limits were used to simulate the vehicle routing. The time limits were doubled every time, starting from 30 seconds until 480 seconds. This means that when simulating 50 days with a time limit of 480 seconds, the model would take approximate 6,67 hours to finish. All the time limits and the related distances are normally distributed and can be found in appendix 7.1 . As illustrated in the histogram in figure 5, the distribution of the average distance when adopting a time limit 120 is slightly skewed to the left but it falls within the boundaries of the empirical rule.

Figure 4: Distribution time limit: 120 seconds

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Graph 1: Average distance time Limits

As for the standard deviation displayed in graph 2, an expected drop is visible in the first minute, but then a surprising increase in the standard deviation occurs after the 60 second mark. This is surprising because it was expected that when giving the VRP solver more time, it would give more consistent results. No simulations were done above the 480 seconds, because this would not allow to run a valid number of simulations within the given time period. Based on both average distance and the standard deviation, the 120 second time limit is selected as the most consistent time limit for vehicle routing. All further simulations are executed with this time limit.

Graph 2: Standard deviation time limits

4.1.2 Vehicle capacity

The second robustness test was executed to check if the capacity parameters that were given by Rytle would give a reasonable output compared to other vehicle capacities. To test this, the capacity was both doubled to a 100 parcels and halved to only 25 parcels per vehicle. Table 3 displays the percentual

109000 110000 111000 112000 113000 114000 115000 116000 0 50 100 150 200 250 300 350 400 450 500 D is ta nc e in m eter s

Time limit in seconds

Average distance

2600 2650 2700 2750 2800 2850 2900 2950 3000 0 50 100 150 200 250 300 350 400 450 500 Sta nder devi at io n in m eter s

Time limit in seconds

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17 difference of travelled distances between the 50 parcel vehicle capacity and these other two scenarios. The 25 parcel vehicle capacity uses 40% more distance to deliver the same amount of parcels, whereas doubling the original capacity of fifty parcels to a hundred decreases the average distance travelled by more than 6%. These results were expected, because it is more suitable to use larger vehicles when drop zone density is relatively high (Marujo et al., 2018). However, on forehand It was not expected that reducing the capacity by 50% would increase the distance so significantly, thus employing cargo bikes with such little capacity would not be interesting to examine. Likewise, increasing the capacity of cargo bikes for the simulations would not mimic the Rytle system accurately, however, it should be noted that there are cargo cycles with supplementary trailers which could achieve this capacity and very well be an appropriate solution. Nevertheless, a vehicle capacity of 50 parcels is the most realistic scenario and is thus utilised in the following simulations.

Table 3 Vehicle capacity robustness test

Output 25 vehicle capacity 100 vehicle capacity

Average distance 39,82% -6,29%

Maximum difference 49,48% 2,66%

Minimum difference 29,43% -14,78%

4.1.3 Changing the customer locations

In the third robustness test, all the input parameters are the same except for the starting day. The starting day is an input parameter that simulates on which day the VRP solver is started for the first time, hence, when selecting a different starting day this would affect the random seed number that will generate the customer locations. It is interesting to know what the difference would be when using the exact same parameters with different customer locations, because this gives us in insight in how much deviation can be expected when executing the same scenario with different customers. Table 4 shows the average daily distance and the percentage of difference in distance between the original starting day that was set to 90, and starting days 180 and 270. The model shows no major deviations in average daily distance, with only 0,08% and 0,37% difference it is fair to say that the model functions properly. However, it is important to note that these deviations should be taken into account when assessing the percentage of difference of the average daily distances in the main results.

Table 4 Customer locations robustness test

Output Starting day 90 Starting day 180 Starting day 270

Average daily distance 116879,3 116783,8 117310,7

Average Percentage of difference - -0,08% 0,37%

Maximum percentage of difference - 8,86% 10,37%

Minimum percentage of difference - -9,13% -6,29%

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4.2 MAIN RESULTS

In this section, the results of the simulations are presented in subchapters that represent scenarios containing four different settings concerning the number of MDs, within these scenarios a total of four different cluster intervals: daily, weekly, monthly and quarterly are simulated. The corresponding input parameters for all these simulations can be found in appendix 7.2. Furthermore, it should be taken into account that this model only serves a thousand customers, which is a relatively small set of customers compared with the 8 million customers that are served every day within the Netherlands6_. Several additional calculations are done to give a better understanding of what the impact would be when expanding the model to a larger and presumably more realistic number of customers. It should be noted that these calculations are based on assumptions, and are not directly derived from the simulation.

4.2.1 Two mobile depot scenario

This scenario can be seen as the baseline for all upcoming scenarios, because it reflects the capacity specification of the Rytle MD the most accurate. In this scenario and all the following scenarios, the percentage of differences are calculated as followed: ∑

𝐷𝑎𝑖𝑙𝑦 𝑑𝑎𝑦𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 − 𝑤𝑒𝑒𝑘𝑙𝑦 𝑑𝑎𝑦𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐷𝑎𝑖𝑙𝑦 𝑑𝑎𝑦𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

140 90

𝑄𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑠 × 100%, in

which the daily and weekly indicate the scenario, and weekly is interchangeable with monthly and quarterly, but daily stays on the same location within the equation. Thus, all day distances ranging from the starting day, 90 to 140 are summed and divided by the number of simulations which is equal to fifty, in order to derive the average difference between the scenarios. The calculations were done from the daily cluster interval perspective, because it was expected that when the location was determined on a daily basis it would generate the least amount of distance. The reason for this is that the daily cluster interval only uses customer locations that are actually routed on that day. In table 5, the differences in distance between the cluster intervals are presented in meters. Surprisingly, it is not the case that the daily scenario is the most efficient in terms of distance covered. The quarterly scenario actually outperforms the daily scenario by 0,23%, a possible reason for this could be that the quarterly scenario uses the most historical customer location data to determine the MD locations. This difference actually falls within the deviation of the customer location robustness test, which means that the percentual difference is not large enough to actually state with any certainty that there is an effect visible between the scenarios. Nevertheless, when converting the daily results to a monthly and yearly period it becomes apparent that the results would have more impact than expected on first sight. The absolute differences between the scenarios were multiplied by 30 and 365 days to get the monthly and yearly difference in meters. Furthermore, when converting the daily difference back to a

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19 single customer it would mean that 0,27 meters can be saved on each customer. When the quarterly scenario would be adopted instead of the daily scenario when serving all 8 million addresses of PostNL, it would account for a substantial saving of 216 kilometres on a daily basis. The percentages of difference between other scenario, such as weekly to quarterly can be found in appendix 7.3. This yields for all following scenarios that are displayed in the results section.

Table 5 results two MD scenario

Output Daily - Weekly Daily - Monthly Daily - Quarterly

Daily percentage of difference 0,40% 0,27% -0,23%

Daily difference in meters 471 323 -270

Monthly difference in meters 14128 9676 -8105

Yearly distance in meters 171894 117722 -98605

Savings per customer 0,471 0,323 -0,270

Daily savings 8 million customers 3767535 2580214 -2161201 4.2.2 Single mobile depot scenario

In the single MD scenario, the MD capacity is double compared to the previously presented base scenario and stores 1000 parcels. This means that in terms of technical specifications it also doubles in size and it sort of represents the TNT project in Brussels, which also only deployed a single MD which was much larger than the MD proposed by Rytle.

First, when comparing this scenario to the base scenario it is 6,92% less efficient on a daily basis, which means that on average the distance would increase with 8,2km per day. This can most probably be assigned to the increase of distance between the MD and the customer locations. More interestingly, the daily clustering interval is the least efficient in the single MD scenario and a trend is visible in table 6, indicating that the longer the cluster interval is, the less distance is required for the routing. A reason for this could be that the longer the cluster interval, the more customer locations are used to determine the location. Only having a single MD location in a squared environment with random distributed locations, would always locate the MD in the centre of the area, even more accurately when using more customer locations to determine this. The differences are a little larger than the previous scenario, but again, this distance is within a kilometre, which is relatively small. This makes it questionable if it would have a noticeable effect on last-mile deliveries in reality.

Table 6 results single MD scenario

Daily percentage of difference -0,31% -0,59% -0,73%

Daily difference in meters -390 -753 -920

Monthly difference in meters -11688 -22585 -27611

Yearly distance in meters -142202 -274790 -335937

Savings per customer -0,390 -0,753 -0,920

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20 4.2.3 Five mobile depot scenario

This scenario deploys five smaller MDs with a capacity of 200 parcels. Having smaller MDs has some consequences in terms of additional routing from a central warehouse to the designated location, which is not taken into account in this thesis. This additional distance could maybe be made up by one truck that drops off multiple MDs in one route instead of only one MD which is the case in the previous scenarios. An advantage of these MDs is that they are more flexible in finding available parking space due to the smaller size, which can be a benefit within crowded city environments.

When comparing the average distances of this scenario to the two MD scenario, it would generate 6,78% savings, which is equivalent of saving 8,2 kilometres in route distance. Simply adding more MDs to the model while supplying the same amount of customers would decrease the distance understandably. A similar saving was registered earlier when increasing the number of MDs from a single MD to two MDs, this means that the deployment of more MDs in relation to savings in distance are not linear, it rather is a positively diminishing relationship.

For the first time, daily location determination is the most efficient, as shown in table 7. A possible explanation for this could be that when deploying multiple MDs at the same time, the model has enough freedom to locate the MDs closer to the customer locations. The percentual differences is still under 1%, but the differences are slightly bigger compared to previous scenarios. The aforesaid trend regarding increasing the cluster interval and increasing efficiency is also visible in this scenario. After the daily cluster interval, the quarterly is the most efficient, followed by monthly and finally weekly.

Table 7 results five MD scenario

Daily percentage of difference 0,94% 0,47% 0,30%

Daily difference in meters 1037 521 329

Monthly difference in meters 31106 15641 9860

Yearly distance in meters 378452 190297 119967

Savings per customer 1,037 0,521 0,329

Daily savings 8 million customers 8294848 4170891 2629410

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21

Graph 3 Distances of daily versus weekly scenario

4.2.4 Ten mobile depot scenario

This last scenario deploys ten MDs to supply the same 1000 customers. As previously described, increasing the number of MDs automatically reduces the total distance due to smaller distances between the MDs and the customer locations. This scenario is 7,34% more efficient than the base scenario. However, these MDs have a very small capacity of only 100 parcels, which would be the equivalent of the capacity of two cargo bikes. This would again increase the routing distance from a central warehouse to the inner-city, but will even have more flexibility regarding parking in public space.

The results shown in table 8 have a substantial difference between the cluster intervals. This scenario indicates that the daily clustering interval is by far the most efficient compared to all other cluster intervals. The savings are two to seven times higher than previous scenarios, and this large difference is allocated to the deployment of more MDs. Allowing the model to determine more MD locations at the same time gives it the ability to better optimize MD locations based on the customer locations. Until now, the influence of vehicle routing on the differences in distance was not quantifiable, but since the only parameter that was changed is the number of MDs, it can be argued that within this scenario the vehicle routing has less of an influence on the distance compared to the MD locations.

Table 8 results ten MD scenario

Daily percentage of difference 6,85% 6,11% 2,00%

Daily difference in meters 7925 7066 2316

Monthly difference in meters 237758 211973 69487

Yearly distance in meters 2892718 2579005 845426

Savings per customer 7,925 7,066 2,316

Daily savings 8 million customers 63402030 56526147 18529874 100000 105000 110000 115000 120000 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 D is tanc e in m e te rs Time in days

Daily vs Weekly

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22 4.3 NAVIGATION ERROR CORRECTION

The simulations that are executed above, assumed perfect information and did not allow for any errors to occur. In reality, the routing is done by humans, which allows human error in the form of navigation errors. This section will correct the previous results by adding additional routing distances. This study assumes that when a MD re-location frequency is lower, meaning that the MD is located at a single location for a longer period of time, this would lead to less navigation errors. It is important for logistics companies to know at what error margins the previously described scenarios would outperform each other. The insights of this trade-off allow companies to make a better decision regarding choosing a relocation frequency strategy.

A navigation error exists of two parameters, the error margin and subsequently the additional meters it needs to cover. These two variables are greatly influenced by the infrastructure that the driver is in, which can result in that the parameter values are sensitive to large fluctuations. For instance, in a large city with a lot of traffic and one-way roads, the chance of missing an exit is considerably greater than in a small village where there are multiple possibilities to restore the navigation error. The vehicle type also has an effect on restoring the navigation error. This thesis uses cargo bikes which have a greater maneuverability than traditional delivery vans and often are able to use alternative infrastructure. However, no historical data is available that indicates which values for error-margin or additional meters are acceptable for these cargo bikes. Therefore, I decided to simulate a large range of values to make sure that every possible outcome would be captured, even if it is an exaggeration of reality. Twenty different scenarios of which the ranging values are displayed in table 9. The simulations calculated the average additional meters per day over the course of a hundred years. The number of simulated days used was rather large, because it gave the most consistent results.

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23

Table 9 Overview of simulated scenarios.

Five MD scenario

Daily Weekly Monthly Quarterly Scenario Additional meters Error margin Average additional meters Error margin Average additional meters Error margin Average additional meters Error margin Average additional meters 1 500 1,00% 4,68 1,00% 4,68 0,10% 0,49 0,01% 0,07 2 500 10,00% 50,44 2,50% 12,37 0,50% 2,32 0,05% 0,19 3 500 25,00% 125,00 5,00% 26,10 1,00% 4,96 0,10% 0,55 4 500 50,00% 249,58 10,00% 50,77 2,50% 12,59 0,50% 2,71 5 500 75,00% 375,01 25,00% 125,93 5,00% 25,62 1,00% 4,99 6 1000 1,00% 10,03 1,00% 10,03 0,10% 0,88 0,01% 0,19 7 1000 10,00% 100,93 2,50% 24,08 0,50% 5,04 0,05% 0,49 8 1000 25,00% 251,32 5,00% 49,86 1,00% 10,58 0,10% 0,82 9 1000 50,00% 501,84 10,00% 101,73 2,50% 25,84 0,50% 5,40 10 1000 75,00% 746,88 25,00% 250,36 5,00% 50,08 1,00% 9,84 11 2500 1,00% 24,59 1,00% 24,59 0,10% 3,29 0,01% 0,21 12 2500 10,00% 243,84 2,50% 59,38 0,50% 10,89 0,05% 1,23 13 2500 25,00% 627,19 5,00% 121,78 1,00% 24,38 0,10% 2,33 14 2500 50,00% 1247,05 10,00% 249,25 2,50% 60,82 0,50% 11,99 15 2500 75,00% 1871,23 25,00% 625,89 5,00% 124,73 1,00% 26,44 16 5000 1,00% 47,81 1,00% 47,81 0,10% 5,62 0,01% 0,41 17 5000 10,00% 506,03 2,50% 126,44 0,50% 27,40 0,05% 2,33 18 5000 25,00% 1236,03 5,00% 251,23 1,00% 50,82 0,10% 5,48 19 5000 50,00% 2489,18 10,00% 495,89 2,50% 119,59 0,50% 24,25 20 5000 75,00% 3741,64 25,00% 1229,86 5,00% 242,88 1,00% 49,32

4.3.1 Trade-off between daily and weekly scenario

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24

Graph 4 Daily corrected distance versus weekly initial saving

4.3.2 Trade-off between daily and monthly scenario

In graph 5 it is visible that seven scenarios exceed the 521 meters initial savings that was given in table 7. Of these seven scenarios, the most likely scenario to occur would be scenario 13, because it has the lowest error rate: 25%, and invokes an additional 2500 meters. It should be noted that scenario 13 only exceeds the initial savings by 82 meters. The corresponding error margins for the other exceeding scenarios range from 50% to 75% with additional distances varying from 1 to 5km. These scenarios are still very unlikely, nevertheless, when they occur it would initialize a surpassing of the initial saving by approximate 200 to 4000 meters. The results indicate that the corrected error distance would not compensate enough to switch to monthly location determination.

Graph 5 Daily corrected distance versus monthly initial saving

0,00 500,00 1000,00 1500,00 2000,00 2500,00 3000,00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Daily - weekly

Initial savings vs correction for error

Additional distance Intial saving

0,00 500,00 1000,00 1500,00 2000,00 2500,00 3000,00 3500,00 4000,00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Daily - monthly

Initial savings vs correction for error

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25 4.3.3 Trade-off between daily and quarterly scenario

The initial savings of the quarterly scenarios is significantly smaller than the daily scenario, only 329 initial savings were recorded in table 7. The consequence of this smaller initial savings are that ten of the twenty scenarios surpass the initial savings. The most plausible scenario would be scenario 17, with an error margin of 10% and additional distance of 5km. An error margin of 10% over twenty vehicles means that two vehicles would make a navigation error that day. However, it would be a bit farfetched to say that they also need to correct this error by cycling an additional 5km. Conclusively, similar to comparisons with the other cluster intervals, it is not likely that the additional distance retrieved from the navigation error would compensate the initial savings, when reasonable error margins of 1 to 10% are realised and the corresponding additional distance stays below the 2,5km.

Graph 6 Daily corrected distance versus quarterly initial saving

0,00 500,00 1000,00 1500,00 2000,00 2500,00 3000,00 3500,00 4000,00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Daily - quarterly

Initial savings vs correction for error

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26

5 DISCUSSION AND CONCLUSION

5.1

THEORETICAL IMPLICATIONS AND CONTRIBUTIONS

Prior research focused mainly on the development of new heuristics and algorithms to solve the MFRP more efficiently and accurately. During this development, the scholars did not take into account the effects of frequency of relocation of the MDs, the focus was mostly on the development of new algorithms and heuristics that could achieve lower cost and serve more demand. During the literature review it became apparent that there are various types of MDs, which varied in mobility. A number of case studies were examined which mostly focussed on the performance of a specific type of MD in terms of financial viability and sustainability. These case studies also neglected the frequency of relocation and focussed specifically on one type of MD without assessing different alternatives in terms of the mobility of the MD.

At the time of writing, this thesis is the first simulation study assessing the performance of different quantities and capacities of MDs in combination with changing frequencies of re-location. Since there is no literature available that allows to recall any contradictions or similarities with the results, this research proposes several propositions that can function as new avenues for future research.

Proposition 1: The frequency of relocation has a marginal effect on the efficiency of last-mile deliveries when deploying up to two mobile depots.

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27

Figure 5 visualization of two MD scenario

To better understand the variance of the MD locations, figure 6 displays all MD locations of the daily and quarterly cluster interval. It is visible that the model chooses to locate the MDs in the daily scenario in four areas, and it is evident that geographical spread is very slim. In the quarterly scenario only two locations are determined based on 90000 customer locations which are then adopted for the next 50 days. The location is dead centred, surprisingly, over the course of fifty days the quarterly locations are more efficient, which is unusual because it was expected that the clustering algorithm would still have enough freedom to determine a more optimal location for the 1000 customers that need to be served that day. The reason that this is not the case, could actually be due to the number of customers that need to be served. The difference in location determination based on 1000 customers that are served that day or 90000 customers of historical data within an area of 12,25km2_{are not large enough to} acquire a lower average daily routing distance.

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28 Proposition 2: A lower frequency in relocation of MDs is slightly more efficient in last-mile delivery. In all tested scenarios, a similar pattern is visible which indicates that the longer the cluster interval is, the shorter the routing distance becomes, apart from the five and ten hub scenario where the daily clustering is more efficient, the quarterly cluster interval follows quickly after.

In figure 7, the average distance of the five MD scenarios are given, here it is visible that after the daily clustering, the quarterly cluster interval is the most efficient. This pattern is consistent over all scenarios and it can be concluded that when excluding daily clustering from the equation, it is more efficient to determine the location on a quarterly basis due to the use of more customer locations.

Figure 7 Average distance of all cluster intervals in the Five MD scenario.

Proposition 3: The effect of frequency of relocation has an considerable effect on the efficiency of last-mile delivers when deploying more than five mobile depots.

As displayed in figure 7 above, the daily scenario is the most efficient in terms of routing distance. At this point, the effect is still marginal and it cannot be concluded that this would actually have an effect in a real life environment. However, due to the fact that the ten MD scenario actually shows a greater difference, it can be assumed that the deployment of five MDs is the tipping point at which the daily scenario outperforms the quarterly scenario. Furthermore, the results of the ten MD scenario are the most interesting findings of this thesis because its difference would have an impact in a real life setting. To gain a deeper understanding of why this happens, all daily and quarterly cluster locations are again visualised in figure 8. The locations in the daily cluster interval adopt the same pattern as the quarterly locations determination. However, the geographical spread of the MD locations is far greater than the earlier visualization of the two MD scenario in figure 6. This insight indicates that when giving the model the task to determine more locations at once, it has more flexibility, meaning that the effect of

109600,00 109800,00 110000,00 110200,00 110400,00 110600,00 110800,00 111000,00 111200,00 111400,00

Daily cluster interval Weekly cluster interval Monthly cluster interval three months cluster interval

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29 optimizing the MD locations to the customer locations is higher, which results in a significantly lower routing distance.

Figure 8 Daily and quarterly mobile depot locations

Proposition 4: Only high error rates would influence the initial savings

Based on the results it is safe to say that the error rate would not affect the entire distribution system when keeping the navigation errors below 10%, of which I believe that this should not be an issue for logistics companies due to current navigation systems. Moreover, if a navigation error occurs, the current GPS systems would notify this almost instantly, which consequently limits the additional distance to a lower value than the proposed 2,5km or 5km that were utilised for the daily scenario. Additionally, the use of electric cargo bikes has an advantage over traditional delivery vans in terms of manoeuvrability which allows the drivers to adjust the routing and restore the navigation error quite easily.

5.2

PRACTICAL IMPLICATIONS

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30 The results suggest that the daily scenario could be the most efficient when deploying more than five MDs, and therefore some practical barriers need to be addressed when adopting this daily scenario. The first barrier is the available parking space and the ability to claim it in advance has to be in place before this system could be implemented. Moreover, daily clustering would suggest that the number of parking spaces that need to be controlled and monitored for by a logistics company, would be extremely large compared to the quarterly scenario for instance. Besides, not knowing if the parking space is available up to the moment of arrival would bear a risk which can increase variability of the entire operation, due to the fact that there would be no place to park the MD. In order to lower the variability of having vacant parking spaces, it can be considered to use a limited amount of candidate locations. A downside of these candidate locations is that it would limit the mobility of the MDs and thus potentially increase the routing distance. In short, determining the location on a daily basis requires a lot more man power to plan and orchestrate the delivery of parcels successfully. The question that arises is then: “would the savings in distances between the daily and quarterly location determination be enough for a transportation company to consider doing daily location determination?”. A clear and concise answer without exact calculations can be given and it is: ‘no’. Simple logics would already determine that only the daily location determination is 90 times more time consuming compared to quarterly location determination, without even considering additional activities, such as checking the vacancy of the parking space and the invoked costs of controlling considerably more parking spaces. Hence, in the long run, the operational cost would skyrocket compared to the quarterly scenario.

Therefore, based on the low percentage of difference within the first three cluster intervals, I would suggest to determine the locations on a quarterly basis. Additional benefits of a longer cluster interval would be the increase in standardizing the operation, which will lower the overall variability regarding the routing from the main warehouse located outside of the city. Moreover, determining the location once every three months allows the company to acquire a parking space for the long term, which would in turn decrease the costs of parking.

5.3

LIMITATIONS AND FUTURE RESEARCH

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31 particular setting. In addition, this study makes a few assumptions which should be interpreted with caution.

First of all, the model is built in a squared environment of 3500 by 3500 meters, and does not use an existing city infrastructure. This means that it does not take into account any traffic congestion, road blockings or numerous other factors that may influence the routing distance. Second, the location determination is done through clustering without any constraints regarding the actual possibility to locate an MD on that location. If the cluster locations would be placed on a real city map, there is a chance that the MD would be located on top of a building or in the middle of a river. The developed model does not identify the nearest parking space so to say, and future research could extend the current model by doing this. Third, the simulations that were run were performed with deterministic demand, where every customer only has one parcel and they are all equal in size. Fourth, the simulations that were run applied parameters that force the model to use all vehicles and their capacity, but in reality a situation like this this would not be realistic, due to the overcapacity that is needed to cope with fluctuating stochastic demands.

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32

5.4

CONCLUSION

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33

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7 APPENDIX

7.1 appendix time limit normal distribution

` Figure 9 - 30 second time limit Figure 10 - 60 second time limit

Figure 11 - 240 second time limit Figure 12 - 480 second time limit

The effects of relocating mobile depots on last-mile delivery