Master’s Thesis in Supply Chain Management (SCM)
University of Groningen, Faculty of Economics and Business
Last-mile collaboration by a fixed transhipment point
June 22, 2018
Sietske Hoekstra
1
Supervisor
dr. I. Bakir
Co-assessor
dr. E. Ursavas
Acknowledgement
First, thanks to my supervisor dr. Bakir, who led me through this master’s thesis project by sincere guiding. Every meeting she helped me to convert my struggles into new ideas and motivation. I think she did more than can be expected from a supervisor in general. Also, I want to thank dr. Ursavas for the feedback on the first version of my thesis. Thereafter, thanks to drs. Vogelaar, who included me in his astronomy course and taught me the basics of Python in a very enthusiastic way and with personal advice. Next, I am grateful to my fellow students for their support and stimulating study breaks. In particular, Hugo, my programming friend, who alleviated the programming struggles, and Sanne, who helped me to improve my writing style. Finally, the completion of this project could not have been possible without my family. They supported me by words, writing feedback, car trips, postcards, and chocolate bars. In special, my eldest sister Maaike, who gave me very useful writing tips. I owe many thanks to my ‘little’ twin sister Gerbrich, my personal programming and LateX expert. Especially in the last period of the project, she reviewed my whole thesis, supported me in all Latex activities and improved my layout.
1 Student number: 2551241
Last-mile collaboration by a fixed transhipment point
Abstract
Contents
1 INTRODUCTION 4
2 THEORETICAL BACKGROUND 6
2.1 Horizontal cooperation . . . 6 2.2 Transfer options . . . 7 2.3 Fraction sharing and transhipment point . . . 8
3 PROBLEM DESCRIPTION 10
3.1 Illustrative example . . . 10 3.2 Problem setting . . . 12
4 METHODOLOGY 13
1
INTRODUCTION
Urban last-mile logistics, which consider the last step of business-to-consumer delivery service, are currently addressed as one of the ‘most expensive, least efficient and most polluting sections of the entire logistics chain’ (Gevaers, Van de Voorde, & Vanelslander, 2014: 398). As a result, human and business activities, and the environment are negatively effected in ways such as traffic congestion, noise and emission (Pronello, Camusso, & Valentina, 2017). Moreover, it is the most expensive stage of the whole e-commerce supply chain due to the personalised delivery desires and spatial distribution (Zhou, Wang, Ni, & Lin, 2016). Nowadays, there are many individual operating companies in this sector, each executing their own business involving simultaneous trips in common surroundings (Fern´andez, Roca-Riu, & Speranza, 2018). In order to make this process more efficient and to reduce the negative consequences for human and business activities, and environment, companies should strive for a common approach.
marked as ‘shared customers’. All in all, the following question is considered in this thesis:
Can companies, cooperating by the Shared Customer Collaboration concept, decrease their driving distance by using a transhipment point in urban last-mile distribution and what are the main effects on the collaboration value?
This thesis highlights the situation of existing companies which are operating from their own depot with the SCC approach, and make exchange of parcels possible by creating a fixed joint TP in the urban core area. Earlier studies with a TP dealt with the availability of sharing all customers (Mirzapour Al-e-Hashem & Rekik, 2014; Nadarajah & Bookbinder, 2013; Wu, Zhang, & Huang, 2017). None of the studies, that are included in the literature review of Fern´andez et al. (2018) (introducer of SCC) consider a setting in which only a fraction of the customers is shared. In their study, the real exchange of packages is organised by one-time trip each day between the two depots. However, this thesis investigates the cooperation by using a TP in order to allow for more flexibility between the companies. Therefore, to the best of my knowledge, this thesis is the first study that investigates the outcomes of a fixed joint transhipment facility combined with the SCC approach. This topic is modelled by an extension of the Vehicle Routing Problem, called Shared Customer Collaboration Vehicle Routing Problem with Transhipment (SCC-VRP-T), and implemented in Python. The model includes SCC (1), a TP (2), pickup and delivery (3), heterogeneous fleet (4), time windows (5), and heterogeneous products (6).
By exploiting the benefits arriving from this type of horizontal collaboration, I contribute to the existing literature in the following ways: (1) I develop a mixed integer programming formulation for horizontal collaboration with the Shared Customer Collaboration approach and a TP with potential applications in last-mile distribution. This is aimed at reducing driving distance (in units), and therefore indirectly also environmental effects, such as pollution. The achieved benefits are quantified with respect to the scenario in which carriers work independently from each other. Secondly, (2) I develop a route-first-cluster-second type heuristic for the model discussed in contribution (1). Lastly, (3) I provide an analysis of the derived computations.
2
THEORETICAL BACKGROUND
First, this section explains the concept of horizontal cooperation and its categories, benefits and challenges. Thereafter, the options of transferring are addressed. Subsequently, fraction sharing and the different options of TPs are discussed.
2.1
Horizontal cooperation
Nowadays, a high number of small and medium-sized companies are involved in the urban last-mile delivery. The operations of these companies lead to emissions, noise, pollution and road congestion in urban areas (Anderluh, Hemmelmayr, & Nolz, 2017). Collaboration between different carriers can reduce all these nega-tive effects of logistics, and it reduces operational costs by combining the fulfillment of customers’ requests (Fern´andez et al., 2018). I refer the reader to the interesting survey of Verdonck et al., (2013) for an extensive and detailed discussion on collaboration in road transportation and carriers perspective. Cruijssen, Dullaert, & Fleuren (2007: 23) have defined ‘horizontal cooperation’ as: ‘identifying and exploiting win-win situations among companies that are active at the same level of the supply chain in order to increase performance’. Cooperation is possible between unrelated companies (i.e. companies operating in different supply chains) or competing companies (i.e. companies that are being active in the same supply chain).
2.1.1 Categories
2.1.2 Benefits and challenges
Cooperation in road freight transportation comes along with benefits, but also challenges. The main benefits and challenges are provided in Table 2.1. This study focuses on designing an appropriate cooperation frame-work. The recent literature review of Perez-Bernabeu et al. (2017) established three levels of cooperation development, namely (1) operational, (2) tactical, and (3) strategic. The key concept in this thesis, using transhipments as a collaborative strategy, is incorporated in the strategic level. Such a decision requires involvement of the whole company and is carried out for a long-time period (Perez-Bernabeu et al., 2017).
Table 2.1: Main benefits and challenges of cooperation Reference
Benefits Mitigating environmental impact Guerrero, Pedro, Garc´ıa, & D´ıaz-ram´ırez (2017) Reducing cost Vornhusen et al. (2014)
Reducing risk Perez-Bernabeu et al. (2017)
Enhancing market share Gou, Zhang, Liang, Huang, & Ashley (2014) Challenges Finding a suitable partner Lambert et al. (1999)
Establishing mutual trust between Schulz and Blecken et al. (2010) cooperating companies
Allocating profits Guajardo & R¨onnqvist (2016) Establishing an appropriate framework Perez-Bernabeu et al. (2017)
2.2
Transfer options
A literature review shows two different practical ways of transferring packages between companies; operating from their own individual depot and using (1) synchronisation for exchanging packages, or a (2) fixed storage TP. The second type is investigated in this thesis.
2.2.1 Synchronisation at location
Figure 2.1: An example of a transhipment point (Navarro, Furi´o, & Estrada (2016)).
2.2.2 Fixed transhipment point
The second type of package transhipment is a transfer facility (Vornhusen et al., 2014; Wu et al., 2017), which is applied in this thesis. Goods delivered by a carrier are stored in a storage room, awaiting their pick up by another carrier (Wu et al., 2017). Figure 2.1 shows an example of a possible joint fixed TP. The temporary storage leads to equipment, storage, and handling costs in this situation, which can be shared by the companies. To keep these costs as low as possible, the lead time in the centre should be as low as possible (Vornhusen et al., 2014). On the other hand, the main advantage of this type of transferring packages is the fact that a carrier does not have to wait for the connected carrier at the facility in order to drop or pick up the parcel (Wu et al., 2017). As a result, a precedence constraint is relaxed in the model; a particular parcel should be dropped by carrier 1 first, before it can be taken by carrier 2 (Vornhusen et al., 2014). A potential drawback of using a fixed TP is the availability of a temporary storage location in urban areas. However, by minimising the total inventory at all times, the total space needed is limited (Merch´an & Blanco, 2015). The synchronisation option is already investigated by Vornhusen et al. (2014), and therefore this thesis focuses on the fixed single TP which has not been investigated earlier with a location in the city core, to the best of my knowledge. In addition, a fixed TP lowers the collaboration barriers in a way that routes of carriers do not have to synchronise, and companies can make routing decisions independent of each other (Vornhusen et al., 2014).
2.3
Fraction sharing and transhipment point
with requests of another company, and not beforehand as in the situation of decentralised planning. In addition, Fern´andez et al. (2018) did not detect fraction sharing by their literature review, only systems where all customers are available for sharing which seems rather unrealistic in practice. In their approach, called Shared Customer Collaboration (SCC), ‘shared customers’ can be exchanged. This are customers who are common among carriers or who are not adding an extra stop to the route of another carrier, because of the closeness to another customer in the planned route. The results of Fern´andez et al. (2018) showed savings in a collaboration setting in comparison with a non-collaboration setting. Their SCC concept comes along with two main benefits contrary to an ‘all-sharing’ principle. (1) Carriers do not have to deteriorate their own routes immensely, which decreases the number of collaboration barriers. Such that no large physical and technological investments are required, which implies that the consequences in case of failure are reduced (Simoni et al., 2017). Furthermore, (2) a company still retains visibility and control in the whole delivery process for the majority of the customers (Fern´andez et al., 2018; Merch´an & Blanco, 2015; Simoni et al., 2017). Fern´andez et al. (2018) established the real exchange of packages by a one-time trip each day between the depots. However, this thesis investigates company cooperation by using a TP in order to create more flexibility between the companies. All in all, it is expected that fraction sharing in combination with a TP results in distance savings for both companies.
Earlier research determined different types of TPs; suppliers, customers and independent third parties (Mirzapour Al-e-Hashem & Rekik, 2014; Nadarajah & Bookbinder, 2013; Rais et al., 2014; Wu et al., 2017). However, in a cooperation with customers or suppliers, willingness and enough space are needed for stocking transfer parcels, which can lead to an obstruction in that situation (Nadarajah & Bookbinder, 2013). Unlike the majority of earlier studies, but similar with this thesis, Nadarajah & Bookbinder (2013) made use of a single TP, namely an independent third party. This thesis assumes a TP which is owned by the cooperating companies, in order to be independent of another company (e.g. with respect to time windows). Moreover, Vornhusen et al. (2014) described this transhipment approach, but investigated, without further explanation, the other type of transferring, namely synchronisation.
3
PROBLEM DESCRIPTION
This section gives first an illustrative example of generating driving distance savings (in units) in a situation with shared customers. Thereafter, the problem setting is described.
3.1
Illustrative example
An illustrative example is given to show the approach and potential benefits of exchanging some customers. Within the concept of Shared Customer Collaboration, shared customers can be exchanged among two carriers. In this context, cooperation between two companies means that both are willing to exchange some of their demand with the other, if the overall driving distance is decreased. Figure 3.1 shows two depots of company A and B (viewed with a square), which have both one vehicle with a capacity of four and five packages, respectively. The companies have to serve together four different customers (C1, C2, C3, C4), denoted by dots. Demand d with respect to carrier c (c,d) could be either a delivery (in a pentagon) or a pick up request (in a ellipse), e.g. customer 3 has a delivery request of one to carrier B and a pickup request of two to carrier A. The Euclidean distance between the different customers and depots are provided in the arcs and are assumed to be symmetric (distance C1-C2 = distance C2-C1).
Figure 3.1: Situation with no collaboration
situation a transfer point T (denoted as triangle) is taken into consideration. C1 and C3 can be labelled as shared customers, because of having requests to both carriers. Hence, these two customers may exchanged between carrier A and B if it results in distance savings. In that situation the routes changes, as a result of a visit to the TP and due to the fact that fewer customers have to be served, because of the takeover. Figure 3.2 shows the optimal solution where collaboration is allowed. Carrier A visits C4, then goes to transhipment centre T, and lastly visits C1 (total route= C4-T-C1). On the other hand, carrier B visits C3, then goes to transhipment centre T, and lastly serve C2 (total route= C3-T-C2). Notice that in this case the order in which customers are visited does matter, because a carrier should first pick up a package from the transfer point before he can serve the particular customer of the other carrier. In the example, carrier A needs to pick up one package of carrier B for C1 at the transhipment centre, before he can visit C1. In order to satisfy this precedence constraint, carrier B has to visit the transhipment centre T before carrier A visits this point, in order to exchange the package of C1. Simultaneously, carrier B can drop the pickups of A from C3. This cooperation leads to a driving distance (in units) of 26 for carrier A and 21 of carrier B (total of 47). Concluding, total driving distance (in units) decreases from 60 to 47 due to the cooperation of the two carriers.
3.2
Problem setting
In this thesis, I consider the SCC-VRP-T which combines routing aspects of collaboration with a TP. This is aimed at minimising driving distance in a cooperation situation between carriers, in which shared customers are exchanged. Vehicles are loaded with requests at their own depot and make their route through the city with probably one or more stops at the transfer location. After serving all customers and picking up all returns, the vehicles return to the depot of origin. It is assumed that packages that should be delivered in the city are coming from outside the city, and pickups always leave the city and therefore return to the carrier’s depot. The SCC-VRP-T has various characteristics (Fern´andez et al., 2018); First, carriers operate from different depots. However, the problem can not be applied to a multi-depot setting, because of the sharing aspect. Secondly, not all customers can be exchanged, only the shared customers. Lastly, the group of carriers that can provide a given shared customer is not fixed, as this depends on the customer. However, this thesis simulates a situation with only two companies, and therefore the number of carriers is known when a customer is shared.
4
METHODOLOGY
This section explains the quantitative modelling method that is used to solve the problem at hand. First, the mathematical model of the collaboration situation is discussed, followed by the introducing of a route-first-cluster-second type heuristic for the collaboration model.
4.1
The collaboration model
For the collaboration and the non-collabortion models the following assumptions are made: • No time windows at the TP and depots
• Pickup packages have to be transferred to the depot • Delivery packages come from the depot
• The exchange of packages is only allowed at the TP
• Each customer can be served by only one vehicle per company • Vehicles start and end at the same depot
• Vehicles are heterogeneous in capacity • Service time is neglected
• The travel time is proportional to the driving distance • The triangular inequality holds with respect to time
• Arcs are symmetric, i.e. the driving distance from node i to node j is equal to the driving distance from node j to node i.
Table 4.1: Sets, indices, parameters, and decision variables of the SCC-VRP-T. Sets
A Set of all arcs K Set of vehicles
K(r) Set of vehicles belonging to the company of request r R(d) Set of all delivery requests
R(p) Set of all pickup requests
R Set of all requests, i.e. R = R(d) ∪ R(p) S(d) Set of delivery requests able to transfer S(p) Set of pickup requests able to transfer
S Set of all possible transfer requests, i.e. S = S(d) ∪ S(p) N Set of nodes V Set of customers Indices i Node, i ∈ N j Node, j ∈ N k Vehicle, k ∈ K l Vehicle, l ∈ K r Request, r ∈ R Parameters uk Capacity of vehicle k ∈ K
dij Unit distance of driving from node i to j (with (i, j) ∈ A)
o(k) Initial depot of vehicle k ∈ K o0(k) Final depot of vehicle k ∈ K qr Quantity of request r ∈ R
p(r) Pickup node of request r ∈ R d(r) Delivery node of request r ∈ R
tij Time required driving from node i to j (with (i, j) ∈ A)
[ai, bi] Time window of customer i ∈ V
Decision variables Xk ij =
1, if vehicle k ∈ K uses arc (i, j) ∈ A 0, if not Ykr ij =
1, if vehicle k ∈ K carries request r ∈ R on arc (i, j) ∈ A 0, if not Skl ir =
1, if request r ∈ S is transferred from vehicle k ∈ K to vehicle l ∈ K, l 6= k, at i = T 0, if not
Tk
i The start and departure time of vehicle k ∈ K from customer i ∈ V
The mathematical model is as follows:
Constraint (13) maintains the request flow conservation at the TP in a way that a not-exchangeable request that is entering the TP must also leave the TP. Constraint (14) assures a vehicle flow on an arc if there is a request flow in the same vehicle and on the same arc. Constraint (15) states that the capacity of a vehicle may not be exceeded. Constraints (16), (17) and (18) requires that these decisions variables are binary, and constraint (19) is a non-negative condition. Constraint (20) holds the time triangle inequality, and therefore eliminates subtours. Constraints (21) and (22) guarantee the compliance with the time windows. Constraints (23) and (24) relax the precedence constraint, explained in Section 2.2.2. Lastly, constraints (25) and (26) guarantee that if a customer is exchanged, he is visited by the same vehicle as his sharing partner, in order to enforce that a customer is visited twice by the same company.
The model is extended in comparison to Rais et al. (2014) as follows: The objective value (ObV) is the driving distance times the used arcs, unlike Rais et al. (2014) it is assumed all vehicles have equal variable costs. Subsequently, a time decision variable is added as a result of time windows and the decision variable S is changed. Since only fraction sharing is allowed, and a single TP functions as exchange point instead of customers, like in the situation of Rais et al. (2014) constraints are added and changed. The following constraints are added: (3), (5), (6), (7), (8), (13), (19), (25), (26) and constraints (9), (10), (11), (12), (20), (21), (22), (23), (24) are modified. However, the single TP is duplicated in Python (as many times as the number of shared customers) in order to allow multiple visits at the TP. Ohterwise only one visit was possible, because of the time triangular inequality in constraint (20).
4.2
Heuristic
A route-first-cluster-second type heuristic is designed in order to develop a satisfying solution, which requires less running time (RT) than a model that generates the optimal solution (Afshar-Nadjafi & Afshar-Nadjafi, 2017; Pillac et al., 2013). A heuristic algorithm is the only feasible possibility for dealing with larger instances (Dragomir, Nicola, Soriano, & Gansterer, 2018), and is in this thesis implemented to instances of different sizes. The heuristic designed for the SCC-VRP-T, mentioned as future research direction by Fern´andez et al. (2018), takes the following steps to create a feasible, but not necessarily optimal, solution of the problem. Step 1 : Assign shared customers to a company
Step 2 : Solve a Travelling Sales Problem (TSP) for each company individually Step 3 : Split the TSP solution into multiple routes for multiple vehicles
5
COMPUTATIONAL STUDY
In this chapter the computational study of the various experiments is discussed. The problem is implemented in Python 3.6 (using software platform Spyder) and solved with Gurobi 7.5.2 optimisation software running on a personal computer with an Intel CoreR TMi3-4010U CPU @ 1.70GHz, 64-bit processor with 4 gigabyte RAM and Windows 10. All instances have a maximum time limit of 2 hours, in line with Dragomir et al. (2018) and Fern´andez et al. (2018). Three different experiments are conducted. The first experiment is conducted to investigate the effect of collaboration. The second experiment is used to get insights in the effect on collaboration of some parameters. The last experiment is conducted to test the performance of the heuristic for the collaboration setting. This section is organised as follows. First the way of generating data are discussed, followed by the expectations and the results of the experiments.
5.1
Data generation
Similar to Fern´andez et al. (2018), a customer is declared as shared customer with a probability of 0.25. Shared customers are assigned to both companies. Thereafter, the set of non-shared customers is split into two sets of equal size. In case the number of non-shared customers is odd, the first company is assigned one customer more than the second company. The request quantities are drawn from a discrete uniform distribution U (1, 5), which is consistent with Fern´andez et al. (2018) and Fikar, Hirsch, & Gronalt (2017). Since requests are assigned to a type (delivery or pickup) randomly, approximately half of all the requests are a pickup request in general. Each company has two vehicles available each with different capacities, where the total capacity is equal to 75% of the total request volume of the company. The volume of a company consists of both delivery requests and pickup requests. The total capacity is set equal to this limit such that some capacity is reserved for making sharing possible on the one hand, and companies can work efficient on the other hand. The capacity of at least one vehicle should be sufficient to transfer the largest request in order to ensure the feasibility of the model (Rais et al., 2014). The routing considers the morning route only, wherein each vehicle can depart once. Time windows have a length of two hours, and are as follows: 8-10 am, 9-11 am, and 10-12 am.
heuristic, which most likely results in larger RT compared to a situation where capacities were included in the heuristic as well. All other data (e.g. number and location of customers, and request quantities) is equal for the heuristic and the optimal model.
Figure 5.1: Geographical settings
Figure 5.2: Parameters to investigate
5.2
Expectations
5.2.1 Collaboration versus non-collaboration
In this experiment, the difference between non-collaboration and collaboration is investigated on four geo-graphical settings, presented in 5.1. On average, it is expected that the total driving distance of the collab-oration situation is lower than the non-collabcollab-oration situation, explained in Section 2. The expectations of the results belonging to the variety in locations of the customers, depots, and TP, is as follows. Locations of customers are generated in two ways; ‘random’ and ‘clustered & random’, according to the cases of Solomon (1987). The latter is expected to yield better results than the ‘random’ option. Since most customers are centred in the ’clustered & random’ setting the driving distance is already low. Consequently, (1) if a cus-tomer is shared outside the cluster region, it results most likely in a higher percentage of sharing savings than in the ’random’ setting, which already a relative high total of distance. In addition, (2) more distance is most likely saved in comparison with the ‘random’ situation, because of the lower probability of other customers nearby that need to be visited, as a result of the higher number of customers that are in middle of the square (centred). Concluding, it is expected that the ‘clustered & random’ option generates higher percentage of distance savings. For the two different options of the TP and depots, ‘centralised’ and ‘corner’ option, it is expected that the ‘centralised’ option yields for better saving results. In the non-collaboration setting, the ‘corner’ situation already has higher driving distance than the ‘centralised’ option, as a result of the more ‘non-added-value’ trips from the corner till the centre. Consequently, in case of collaboration, the ‘corner’ option has most likely lower percentage of distance savings, and therefore lower collaboration performance than the ‘centralised’ situation.
5.2.2 Effect of parameters
Percentage of sharing. It is expected that by increasing the number of shared customers, the driving dis-tance decreases, as a result of the more options of reducing disdis-tance (Fern´andez et al., 2018). Consequently, the percentage of distance savings increases.
Time windows. Time windows specify the earliest and latest times at which customers need to be served (Afshar-Nadjafi & Afshar-Nadjafi, 2017). According to the VRPFlexTW of Tas, Jabali, & Woensel (2014), vehicles are permitted to deviate from a customer’s time window by a given tolerance with no negative con-sequences. This corresponds to expanding time windows. Their research showed that the driving distance lowers by using flexible time windows, as a result of increased freedom and decision possibilities, and therefore improved routes (Tas et al., 2014). Wider time windows is expected to increase the distance savings. On the other hand, if time windows are smaller, it is more difficult to combine customers, which results in longer routes.
Pickup and delivery ratio. In a balanced situation (50% pickup/50% delivery) the vehicle capacity should at least be equal to the highest sum of these two types. However, this sum is much higher in a situation of ‘75% pickup/25% delivery’, and therefore more capacity is needed than in the balanced option. When comparing the performance of each scenario, equal vehicle capacity should be used. As a result in the ‘50% pickup/50% delivery’ situation pickups and delivers are easier to put in one vehicle than in a ‘75% pickup/25% delivery’ or in a ‘25% pickup/75% delivery’ situation. Therefore, it is expected that a non-balanced situation has a negative effect on the solution.
Request quantities. It is expected that modification in the request quantity distribution has effect on the distance savings. When a distribution is higher, most likely packages are more difficult to combine in the vehicle capacities. For instance in a setting where the vehicle capacity is 10, a customer with a request of 2 and a customer with a request of 8 is more difficult to combine with other requests than two customers with each a request of 5. On the other, when the distribution is made smaller, it is expected that the distance savings increases. The request quantities distribution of U (3 − 8) is expected to have no effect on the distance savings, as a result of the same distribution as the basic situation (with a distribution of U (0−5)).
pickup requests) such that the model is feasible, it is expected that the solution quality is worse, because of the more limitations capacity imposes on the route.
5.2.3 Optimisation versus heuristic method
A heuristic should be able to solve the model in less RT than the optimal model. In this thesis, the optimal model is split in different stages and simplified by reducing the number of decision variables and the number of feasible solutions. Therefore, it is expected that the heuristic takes a reduced amount of time in order to create a feasible solution.
5.3
Results
5.3.1 Collaboration versus non-collaboration
For the overall analysis of distance savings between the non-collaboration and collaboration option, a basic situation is conducted for all the four settings with data generated as explained in Section 5.1. The results of this collaboration experiment are presented in Table 5.1 and show the change of distance in percentage with respect to the non-collaboration situation.
Table 5.1: Relative differences (in %) between the collaboration and non-collaboration situation ‘corner’ ‘corner’ ‘centralised’ ‘centralised’
‘random’ ‘clustered & random’ ‘random’ ‘clustered & random’ Mean
Basic situation -5.4 -7.8 -7.8 -9.8 -7.5
From Table 5.1, it can be concluded that in all situations the distance has improved as a result of decreased driving distance. In line with the expectations, the ‘centralised’/‘clustered & random’ setting (−9.8%) has the highest alteration, followed by ‘corner’/’clustered & random’ (−7.8%) and ‘centralised’/’random’ (−7.8%), and ending with ‘corner’/‘random’ situation (−5.4%). Table 5.1 shows no difference between ‘corner’/’clustered & random’ and ‘centralised’/’random’ setting. In this experiment only one aspect can be compared, and therefore no conclusions can be made if one of these two settings is dominant over the other.
5.3.2 Effect of parameters
the expectations, as such that by increasing the number of shared customers, more distance savings can be achieved. The reason of stagnating the increase of savings (N =4 and 5) deals with the aspect that the increased number of shared customer not results in an increase of exchanged customers.
Table 5.2: Effect of sharing percentage
N Sharing percentage (in %) Running time (s) ObV. (u) Exchanged Savings (in %)
0 0.0 12.2 421.2 0 1 16.7 19.1 421.2 0 0.0 2 33.3 54.9 392.9 2 -6.7 3 50.0 108.0 383.1 3 -9.0 4 66.7 159.8 383.1 3 -9.0 5 83.3 336.3 383.1 3 -9.0 6 100.0 1032.4 353.3 4 -16.2
Table 5.3: Relative effect (in %) of several parameters in the collaboration situation
‘corner’ ‘corner’ ‘centralised’ ‘centralised’
‘random’ ‘clustered & random’ ‘random’ ‘clustered & random’ Mean
TW small 3.5 0.6 3.2 3.3 2.6
TW large 0.0 -0.2 -0.2 0.0 -0.1
Ratio P/D= 25/75 4.6 5.5 10.3 -1.3 4.8
Ratio P/D = 75/25 4.7 4.0 7.2 -2.3 3.6
Request quantities low -21.6 -26.9 -7.8 -18.2 -19.6
Request quantities moderate -1.3 0.9 1.5 0.8 0.5
Request quantities high 7.1 3.8 5.7 -4.7 3.0
Vehicle capacity low 16.8 14.6 17.8 12.0 15.4
Vehicle capacity high -21.8 -28.8 -9.2 -18.9 -20.6
Outstanding results are found in the ‘centralised’/‘clustered & random’ case, in which more deliveries, more pickups, and higher distribution of request quantities (−1.3%, −2.3%, and −4.7%, respectively) have a positive effect on the collaboration, contrary to expectations and other three settings. Probably this can be explained by the number of customers in the experiment. A peculiar situation of customers’ locations in combination with the action (more deliveries, more pickups or higher distribution of request quantities) results in an unique savings outcome. This leads to a high percentage of distance savings as a result of the small number of customers. In case of higher number of customers this effect would be decreased.
5.3.3 Optimisation versus heuristic
in Section 5.1, is unclear which decreases the reliability of the experiment. Table 5.4: Heuristic results
Optimal Heuristic Rel. difference (in %) N ObV.(u) Time (s) ObV.(u) Time (s) ObV. Time
10 234.0 10.0 264.3 4.4 13.0 44.0
15 298.8 100.8 320.7 7.7 7.3 7.6
6
CONCLUSION
Last-mile distribution feels the pressure of efficiency and complying to the regulations in order to mitigate environmental and social footprints of distribution operations in congested and dense areas (Guerrero et al., 2017). Although literature on collaboration in last-mile distribution is evolving, only a few studies have been conducted on sharing just a fraction of their requests in order to lower collaboration barriers. Therefore, this thesis examined the Shared Customer Collaboration concept combined with a transhipment point (TP), directed by the following question: Can companies, cooperating by the Shared Customer Collaboration concept, decrease their driving distance by using a transhipment point in urban last-mile distribution and what are the main effects on the collaboration value? Therefore, a linear program has been formulated to investigate the profitability of this concept and the effect of some parameters on this collaboration. Computational results support the profitability of sharing by TP and show savings in distance, and indirectly in emissions, congestion, and noise relative to a situation of non-collaboration. With this thesis a new view and way is given to the existing collaboration literature. In addition, the heuristic for the Shared Customer Collaboration Vehicle Routing Problem with Transhipment shows a decreased running time compared to the optimal model. However, the costs of the TP are not taken into consideration, as a result of the difficulty of calculation and untraceable in earlier research, because of using other types of TPs such as customers or public areas (Rais et al., 2014; Vornhusen et al., 2014; Wu et al., 2017). This is a limitation of the thesis in a way that no hard statement can be made of real profits of this cooperation and could provide further research opportunities. Besides that, data is generated in this thesis, which makes the results less reliable. In addition, the experiment of the effect of parameters on collaboration shows three actions (increase vehicle capacity, smaller distribution of request quantities or make time windows bigger) that increase the distance savings in a collaboration situation. However, it is observed that the size (number of customers) of the experiments (in order to keep running times acceptable) could be an obstruct of reliable results. By running each element of the experiment multiple times, I tried to increase the reliability. This limitation could be an opportunity for future research. In addition, companies have control over only some investigated parameters, namely location of depot and TP, time windows and the vehicle capacity. Being aware of this fact moderates the practical implicates of this thesis.
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A
NON-COLLABORATION MODEL
The non-collaboration model can be defined on a graph G(N, A), where N is the node-set and A the arc-set. In Table A.1 sets, indices, parameters, and decision variables are showed for the non-collaboration model.
Table A.1: Sets, indices, parameters, and decision variables for the non-collaboration model. Sets
A Set of all arcs N Set of all nodes V Set of all customers K Set of all vehicles
S Set of all possible transfer requests = 0 Indices i Node, i ∈ N j Node, j ∈ N k Vehicle, k ∈ K Parameters uk Capacity of vehicle k ∈ K
cij Distance units of transport from i to j ∈ A with vehicle k ∈ K
o(k) Initial depot [0] of vehicle k ∈ K o0(k) Final depot [n-1] of vehicle k ∈ K p(i) Pickup request of customer i ∈ V d(i) Delivery request of customer i ∈ V tij Time required from node i to j ∈ V
[a(i), bp(i)] Time window of customer i ∈ V
M A large number, M > 0 Decision variables Xijk =
1, if vehicle k ∈ K uses arc (i, j) ∈ A 0, if not
Dk
i The amount of the remaining deliveries carried by vehicle k ∈ K when departing from
customer i ∈ V
Pik The amount of the collected pick-up quantities carried by vehicle k ∈ K when departing from customer i ∈ V
Tk
the other hand, constraints (A.8) and (A.9) ensure that by leaving the depot, the vehicle is fully loaded with the products to be distributed, while the pick-up load is zero. Constraints (A.10) and (A.11) ensure that if arc (i, j) is visited by a vehicle, the quantity to be delivered by the vehicle has to decrease by di in case
customer i has a delivery request, while in the other situation the pick up quantity has to increase by pi.
Constraint (A.12) holds the time triangle inequality, and therefore eliminates subtours. Constraints (A.13) and (A.14) ensure that a customer is served in his own time window. Lastly, constraints (A.15), (A.16) and (A.17) are non-negative conditions, and constraint (A.18) requires that the decision variable is binary.
The time constraints are written done differently, as a result constraints (A.13) and (A.14) are changed, and (A.16) is added in contrast to the model of Angelelli & Mansini (2002).
B
HEURISTIC
B.1
Pseudo code
Algorithm 1 General outline of the Route-first-cluster-second type heuristic
1: for customers (p, l) ∈ S do 2: Find nearest customer i
3: Allocate (p, l) to the company of customer i
4: end for
5: for company c ∈ {1, 2} do
6: Solve the TSP of company c
7: Split the TSP route into K vehicles
8: end for
9: for k ∈ K do
10: Optimise the route of k
B.2
Model
Table B.1: Sets, indices, parameters, and decision variables of the SCC-VRP-T.
Sets
A Set of all arcs K Set of vehicles
K(r) Set of vehicles belonging to the company of request r
K−0 Set of vehicles that has no ’taken-over-customer’ with a delivery request
K−1 Set of vehicles that has no ’taken-over-customer’ with a pickup request
K0 Set of vehicles that has a ’taken-over-customer’ with a delivery request
K1 Set of vehicles that has a ’taken-over-customer’ with a pickup request
KA Set of vehicles of company A
KB Set of vehicles of company B
R(d) Set of all delivery requests R(p) Set of all pickup requests
R Set of all requests, i.e. R = R(d) ∪ R(p) N Set of nodes V Set of customers Indices i Node, i ∈ N j Node, j ∈ N k Vehicle, k ∈ K r Request, r ∈ R Parameters uk Capacity of vehicle k ∈ K
dij Unit distance of driving from node i to j (with (i, j) ∈ A)
o(k) Initial depot of vehicle k ∈ K o0(k) Final depot of vehicle k ∈ K qr Quantity of request r ∈ R
p(r) Pickup node of request r ∈ R d(r) Delivery node of request r ∈ R
tij Time required driving from node i to j (with (i, j) ∈ A)
Decision variables Xk ij =
1, if vehicle k ∈ K uses arc (i, j) ∈ A 0, if not Ykr ij =
1, if vehicle k ∈ K carries request r ∈ R on arc (i, j) ∈ A 0, if not
Tk
i The start and departure time of vehicle k ∈ K from customer i ∈ N
The mathematical model of solving the TSP (Step 6 of Section B.1) is as follows: minX k∈K X (i,j)∈A dij· Xijk, subject to constraints (1)-(8), (12), (14), (16), (17), (19), (20).
To ensure TP visits before a vehicle can visit a ’taken-over-customer’ with a delivery request, the following constraints are added. Constraint (B.1) ensures that at least one vehicle that coming from the depot and has not a ’taken-over-customer’, visits the TP first, in order to drop the packages that are taken over by the other company. Thereafter, a vehicle of the other company (other vehicle than constraint (B.1)), comes and drops their packages that are taken over. Constraints (B.3) and (B.4) guarantee this. For ’taken-over-customers’ with a pickup request, the following constraints guarantee a visit at the TP in order to drop their taken over pickups. Constraint (B.2) denotes that at least one vehicle of each company visits the TP which has no taken overs. Constraints (B.3) and (B.4) ensure that at least one vehicle of each company visits the TP. Constraints (B.5) and (B.6) require that all vehicles with a ’taken-over-customers’ (pickup request or delivery request) has to visit the TP ones or twice.
