Collaborative location routing problem with pickups and deliveries

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Collaborative location routing problem

with pickups and deliveries

Master’s Thesis

MSc Supply Chain Management

University of Groningen, Faculty of Economics and Business

June 24, 2019

Andyna Giya Rosaputri Tarigan

Student Number: S3533816

Supervisor:

dr. I. Bakir

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ABSTRACT

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1. INTRODUCTION

Service quality improvement, operational cost reduction, and the environmental impacts awareness have been considered as the objectives of decision making by the current supply chain managers (Wang, Zhang, Assogba, Liu, Xu, & Wang, 2018). In achieving these goal, companies compete with each other to improve their distribution systems, comprising all operations related to the transportation of final products from factories to customers including all intermediate steps such as depots and distribution centers (Nadizadeh, Nasab, Sadeghieh, & Fakhrzad, 2014). Several companies in these recent years have adopted a new transportation model called collaborative transportation (CT) which has become increasingly popular in the road transportation industry, aiming to improve the overall performance of transportation planning by becoming partners in a horizontal logistic coalition, especially by solving a collaborative vehicle routing problem (Defryn, Sörensen, & Cornelissens, 2016; Liu, Jiang, Fung, Chen, & Liu, 2010).

Another improvement method of distribution network is the location-routing problem (LRP) optimization that has been recently used to simultaneously integrate the decisions of the strategic location and the tactical vehicle routes, in order to effectively optimize the cost savings and the service quality (Karaoglan, Altiparmak, Kara, & Dengiz, 2012; Rahmani, Oulamara, & Cherif, 2013). It is highly important to investigate the optimal location decision along with the distribution routing, particularly for the joint consolidation center in the collaborative environment, as it is described as an important factor to improve the logistic process in the cities to provide a conceivable solution to imposed time windows and vehicle restrictions on last-mile deliveries which complicate the operations of the deliveries and cause the receivers experiencing longer wait times then affect the service performance (Handoko & Lau, 2016).

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popular in these recent years due to its significant savings, as carriers who must serve common customers within the same time period could deliver part of the demand for other carriers without deteriorating their own routes and obtaining savings (Fernandez, Roca-Riu, & Speranze, 2018). The LRP can potentially be a suitable method to optimize the cost savings in the collaborative network by simultaneously selecting a subset of potential joint consolidation center used in the collaborative network and making the optimal routes by allocating the shared customers to the different consolidation center (Nadizadeh et al, 2014).

Combining the concept of collaborative transportation and the LRP, this thesis will aim to study about collaborative location routing optimization. This focus of research is currently still lacking in the existing literatures. To solve the problems, mathematical modelling method will be further developed in this research. As from a practical point of view, the collaborative among carriers seems to be most relevant in a pickup and delivery environment, given amounts of goods have to be transported from pickup points (customers) to corresponding delivery customers where shipments from different customers can be moved on the same vehicle (Gansterer et al, 2017), thus this specific environment will be taking into account. This leads to the following research question:

RQ : How to determine the optimal location for the joint consolidation center(s) in a shared customer collaboration network with pickups and deliveries? How does it benefit the collaboration network?

This study will have both theoretical and practical relevance. From the theoretical view, this study will fill the gap in the existing literatures in providing optimal location routing solutions in collaborative transportation environment, especially with the pickup and delivery problem. Moreover, in the practical application, the result of optimization in this study can be potentially used by the supply chain managers or decision makers related to transportation field in various kind of business to aim the optimal solution of the location routing in the carrier collaboration with the similar characteristics, considering that distribution system with pickup and delivery problems has been widely implemented in various kind of business. The flexibility of the proposed mathematical model to be applied in the real life business is further increased since two types of customer request (in regards to the pickup and delivery arrangements) will be

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2. THEORITICAL BACKGROUND

The collaborative location-routing problem with pickups and deliveries (CLRPPD) has not been previously addressed specifically in the existing literatures. Therefore, the most related literatures to this problem are reviewed in this section. The concept of collaborative transportation including its benefits, along with the use of consolidation center, is firstly elaborated here. Thereafter, the approach of location-routing problem, specifically with the scenario of customers’ pickup and delivery demand, is furtherly explained.

2.1. Collaborative transportation

Increasingly, collaborative transportation (CT) has been adopted by many transportation companies in these recent years, especially in the urban last-mile logistics. By cooperating together, multiple players in the field of logistics and transportation can increase their efficiency through sharing many resources such as vehicles, distribution centers, or other last-mile delivery services which could potentially lead to fewer vehicles utilization in urban areas, less pollution, and lower product prices (Cleophas, Cottrill, Ehmkec, & Tierney, 2019). Wang et al (2018) illustrates the benefit of CT in a diagram as shown in Fig. 1 which improves the fluidity and organization of the transportation network.

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2.1.1. Categories

According to Liu et al (2010), CT can be classified into two ways: the collaboration among shippers and carrier collaboration, yet carrier collaboration has received less research attention since most carriers currently only collect shipping requests from shippers and optimize the vehicle routing individually. In fact, carrier collaboration may result in significant savings since carriers who must serve common customers within the same time period could deliver part of the demand for other carriers without deteriorating their own routes and obtaining savings both in terms of distance travelled and utilized fleet due to better exploiting the vehicles capacity (Fernandez, Roca-Riu, & Speranze, 2018).

Cleophas et al (2019) argue that there are two vital types of CT, which are the vertical and horizontal collaboration. Transportation in the vertical collaboration environment is often organized along modes and service operators, for example, carrying out the first leg within the city by conventional trucks while operating the last mile delivery to the customers using environmental-friendly city freighters or freight bikes. On the other hand, in horizontal collaboration, multiple transport companies work together in the same section of the transport chain, potentially sharing orders and infrastructure. This thesis can be considered to focus on the horizontal collaboration environment, since the coalition between multiple carriers in the same stage of the supply chain is discussed.

2.1.2. The use of Consolidation Center

Along with the implementation of CT in the city logistics, a joint consolidation center (CC) is started to be used, which is well-known as the Urban Consolidation Centers in the city logistics. The initiative of a consolidation center can be considered as a system consisting of a logistic facility for consolidation process which is placed in an urban area, where multiple carriers or logistics service providers (LSPs) can drop off their products to be consolidated, and the outbound transport operators who can pick up and execute the deliveries of their products to the customers in the city area (Björklund & Johansson, 2018).

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on last-mile deliveries which complicate the operations of the deliveries and cause the customers experiencing longer waiting times and affect the company’s service performance (Handoko & Lau, 2016).

Collaboration in the city logistics has become particularly challenging when multiple companies jointly operate a consolidation center since significant efforts are required for the transshipment and consolidation process of the combined goods for the transport within subsequent tiers of the supply chain, especially for the synchronization of goods and establishment of transportation infrastructure between the coalition partners (Cleophas et al, 2019). Consequently, the studies of optimization modelling to overcome the challenges of CT in the city logistics have become increasingly popular in these recent years.

2.2. Location-routing optimization with pickup and delivery problem

The location-routing problem (LRP) deals with determining the location of depots or other facilities and the distribution routes of vehicles simultaneously for serving the customers under some constraints such as route distance, the capacity of vehicle and facilities, requested lead time, etc. to satisfy all customer demands while minimizing the total cost including transportation costs, fixed costs of the vehicle and other facilities, and facility operating costs (Karaoglan et al, 2012; Yu & Lin, 2016).

The LRP has been implemented successfully in numerous diverse fields from the online retailing business (Aksen & Altinkemer, 2008), bill delivery in telecommunication service (Lin, Chow, & Chen, 2002), glass recycling (Rahim & Sepil, 2014), to the military logistic system (Çetinkaya, Gökçen, & Karaoğlan, 2018), most of which do not consider the reverse flow of the supply chain that is regarded as an opportunity to gain higher profit (Yu & Lin, 2016). The general form of LRP assumes that customers have only delivery demand thus the LRP only focuses to analyze how to distribute the goods with a fleet of vehicles from the opened depots to customers, yet in practice, customers can have pickup and delivery demands where both demands should be met at the same time (Karaoglan et al, 2012).

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in terms of the customers’ demand (Karaoglan et al, 2012). In this case, Karaoglan et al (2012) proposed the polynomial-size mixed integer linear programming formulations for solving the LRPSPD, specifically node-based formulation and flow-based formulation.

According to Karaoglan et al (2012), LRPSPD can be considered as a special case of the many-to-many LRP (MMLRP) which was introduced by Nagy & Salhi (1998). While the LRP is an optimization approach to locate facilities, the MMLRP is an approach to locate hubs in which the flows between the hubs are permitted (Nagy & Salhi, 2007; Karaoglan et al, 2012). In the approach of LRPSPD, it assumes that customers could both send goods to other customers and receive goods at the same time where these pickup and delivery demands may be served by one of the potential hubs (Yu & Lin, 2016; Karaoglan et al, 2012).

The problem discussed in this study (CLRPPD) can be partly considered as the extension of LRPSPD approach. This study will contribute to build a mathematical model to solve location routing problem in the collaborative transportation network which involves the resources and (pickup and delivery) demands of multiple transportation companies, that is currently still lacking in the existing literature.

The proposed model in this study will also contribute to give a flexibility to be implemented in various kind of industries, since two types of customer request will be accommodated. The first one is the requests coming from customers with specific pickup and delivery locations which is a very common type of request applied in logistic service providers. The second one accommodates the requests in which the vehicle has to perform either a pickup or a delivery service at each customer and the depot is the origin and the destination of all the deliveries and the pickups. Having flexibility in such systems essentially offers incentive for multimodal planning and take advantage of all potential options for optimization which makes it has become

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3. METHODOLOGY

The purpose of the study is mainly to quantify the optimal location of consolidation centers, the optimal allocation of shared customers to the opened depots, and the corresponding vehicle routing at the same time, along with the affected cost savings. Therefore, the mathematical modelling method is used to solve the problem, in which two principal performance indicators will be considered: the total driving distances and the total costs in the distribution process. The mathematical modelling in this section will be further analyzed using computational study later in this study using the optimization programming software.

The mathematical modelling in this study is developed firstly by identifying the problem setting and all the related parameters. Subsequently, the mathematical formulation for the collaborative network will be discussed.

3.1. Problem Setting

In the collaborative network, the companies are willing to combine part of their demands in

order to decrease the total achieved distance which leads to the total distribution costs. Let 𝐴 = {(𝑖, 𝑗): 𝑖, 𝑗 ∈ 𝑁} be the set of arcs in the network with a set of nodes (𝑁 = 𝑁𝑘∪ 𝑁𝐶), where

𝑁_𝑘representing the nodes of potential depots and 𝑁_𝐶representing the nodes of customers. Each arc from i to j has a positive cost per unit time represented by 𝐶_𝑖𝑗 for the shortest path between them (𝑖, 𝑗 ∈ 𝐴). Next to this, each potential depot (𝑘 ∈ 𝑁𝑘) is associated with a fixed cost for

the operational activities (𝐹𝑘) and a positive capacity (𝐶𝐾𝑘).

A set of homogeneous vehicles (𝐿), in the sense that each vehicle may carry any type of request, is utilized in this network where each vehicle (𝑙 ∈ 𝐿) has a certain non-negative capacity (𝐶𝑉𝑙)

and a fixed cost for the operational activities (𝐹𝑉_𝑙). It is assumed in this case that the vehicles serve all of the pickup and delivery demands from the origin depot after which they return to the same depot. The origin depot of vehicle 𝑙 is represented by 𝑜(𝑙). The pickup node of request 𝑟is termed as 𝑝(𝑟) while the delivery node of request 𝑟is considered as 𝑑(𝑟).

This study uses the scenario that customers have pickup and delivery requests which are

represented by 𝑅𝑝 (set of pickup requests) and 𝑅𝑑 (set of delivery requests) where

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requests coming from customers where the pickup and delivery points are already decided. The second one is allowing some pickup requests (𝑅_𝑝), without specific pickup point, be picked up and transported to the depot as the delivery point, from where some random delivery requests (𝑅𝑑) independently will be delivered to the customers at final destinations. The quantity of

requests will be represented as 𝑞𝑟.

In addition, we will use a standard additional notation 𝛿+_{(𝑖) which denotes a single arc leaving}

node i, while 𝛿+(𝑖) denotes a single arc entering node i.

In developing the mathematical modelling for this study, several assumptions will be used in order to simplify the model. All transport companies in the collaborative network are assumed to have sufficient fleets to deliver the pickup and delivery demands. Next to this, the service time for each demands will be ignored.

3.2. Mathematical Formulation

The mathematical formulation of the (non-collaborative) location routing problem with pickups and deliveries is partly inspired from formulation from Karaoglan et al (2012). The formulation of constraints for the collaborative network, specifically for the vehicle routing problem, is based on Rais et al (2014), due to the similarity of the applied condition with the problem discussed in this study, with excluding the transshipment procedures.

The mathematical model in this study has several decision variables as below:

𝑥_𝑖𝑗𝑙 corresponding to 1 if vehicle l goes directly from arc i to j 𝑌_𝑘 corresponding to 1 if depot k is opened

𝑧𝑟𝑘 corresponding to 1 if request r is assigned to depot k

𝑠_𝑖𝑗𝑙𝑟 corresponding to 1 if vehicle l carries the request r from arc i to j 𝑢_𝑖𝑗𝑙 corresponding to 1 if node i precedes node j in the route of vehicle l where 𝑥_𝑖𝑗𝑙, 𝑌_𝑘, 𝑧_𝑖𝑘, 𝑠_𝑖𝑗𝑙𝑟, 𝑢_𝑖𝑗𝑙 are binary.

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throughout the delivery process, including the vehicle costs and operational costs of the consolidation centers.

The proposed mathematical formulation is as follows:

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13 ∑ ∑ 𝑠_𝑖𝑘𝑙𝑟 𝑖∈𝛿−_(𝑘) ≤ 𝑙∈𝐿 𝑧_𝑟𝑘 ∀𝑟 ∈ 𝑅_𝑝, ∀𝑘 ∈ 𝑁_𝑘 (13) ∑ ∑ 𝑠_𝑘𝑖𝑙𝑟 𝑖∈𝛿+_(𝑘) ≤ 𝑙∈𝐿 𝑧_𝑟𝑘 ∀𝑟 ∈ 𝑅_𝑑, ∀𝑘 ∈ 𝑁_𝑘 (14) ∑ 𝑧𝑟𝑘 𝑘∈𝑁𝑘 = 1 ∀𝑟 ∈ 𝑅 (15) 𝑧_𝑟𝑘 ≤ 𝑌_𝑘 ∀𝑘 ∈ 𝑁_𝑘, ∀𝑟 ∈ 𝑅 (16) ∑ 𝑞𝑟𝑧𝑟𝑘 𝑟∈𝑅𝑝 ≤ 𝐶𝐾𝑘𝑌𝑘 ∀𝑘 ∈ 𝑁𝑘 (17) ∑ 𝑞_𝑟𝑧_𝑟𝑘 𝑟∈𝑅𝑑 ≤ 𝐶𝐾_𝑘𝑌_𝑘 ∀𝑘 ∈ 𝑁_𝑘 (18) 𝑧_𝑟𝑘∈ {0,1} ∀𝑟 ∈ 𝑅, ∀𝑘 ∈ 𝑁_𝑘 (19) 𝑌_𝑘 ∈ {0,1} ∀𝑘 ∈ 𝑁_𝑘 (20) 𝑥_𝑖𝑗𝑙 ≤ 𝑢_𝑖𝑗𝑙 ∀(𝑖, 𝑗) ∈ 𝑁, ∀𝑙 ∈ 𝐿, 𝑜(𝑙) ≠ 𝑖, 𝑗 (21) ∑ 𝑢_𝑖𝑗𝑙 𝑙∈𝐿 = 1 ∀𝑖 = 𝑝(𝑟), ∀𝑗 = 𝑑(𝑟) (22) ∑(𝑢_𝑖𝑗𝑙 + 𝑢_𝑗𝑖𝑙) 𝑙∈𝐿 = 1 ∀(𝑖, 𝑗) ∈ 𝑁, 𝑜(𝑙) ≠ 𝑖, 𝑗 (23) 𝑢_𝑖𝑗𝑙 + 𝑢_𝑗𝑛𝑙 + 𝑢_𝑛𝑖𝑙 ≤ 2 ∀(𝑖, 𝑗, 𝑛) ∈ 𝑁, ∀𝑙 ∈ 𝐿, 𝑜(𝑙) ≠ 𝑖, 𝑗, 𝑛 (24) 𝑢_𝑖𝑗𝑙 ∈ {0,1} ∀(𝑖, 𝑗) ∈ 𝑁, ∀𝑙 ∈ 𝐿 (25)

Several constraints are applied in this case. Constraint (1) ensures that each customer node must be visited only for once. Constraints (2) guarantee that each vehicle must have only one route from its initial depot. Constraint (3) and (4) maintains the flow conservation of the vehicles through the nodes in the network such that the vehicle which enters a certain node, either a depot or non-depot node, must also leave that node.

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request to happen by ensuring that each pickup request goes on an arc directing to the company’s depot and each delivery request travels from corresponding depot in vehicle l which belongs to that depot’s company. Constraints (9) states a vehicle flow on a certain arc if there is some request flow using the same vehicle and on the same arc, while constraint (10) guarantees that the load of requests on any point of the route do not exceed the vehicle capacity. Constraints (11) and (12) state that these decision variables are required to be binary.

Constraints (13) and (14) ensures all pickup requests must be delivered to a certain depot as their destinations and all delivery requests have to be transported from a depot as their origin. Constraints (15) ensures that each request must be allocated only to one depot. Constraint (16) imposes that request r is not allocated to the depot k if the depot is not opened. Constraints (17) and (18) guarantee that the total quantity of pickup and delivery demands allocated to a certain depot do not exceed the capacity of corresponding depot. Constraints (19) and (20) state that these decision variables must be binary.

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4. COMPUTATIONAL STUDY

In order to get insight about the implementation of the proposed mathematical model to solve the collaborative location routing problem, computational study is conducted which will be further explained in this section. The model is implemented in Python 3.7 (as the programming language) using Spyder software platform and solved with Gurobi 8.1.1 optimization software. The optimization software is run on a personal computer with an Intel® Core™ i5-8250U CPU @ 1.80GHz, 64-bit operating system with 4 GB RAM and Windows 10.

Two experiments are conducted in this study. The first experiment is aimed to understand the effect of the collaboration network. Meanwhile, the second experiment is for getting insight about the benefit of considering the location decision in the efficiency of the collaborative transportation process.

4.1. Data Generation

As the purpose of this computational study is to understand the effect of optimal location decisions and the effect of collaboration network, a set of random data, which is inspired by the real-life transportation networks, is generated in the programming process. The generated data includes a set of candidate depot nodes (including its capacities and fixed costs), a set of customer nodes (along with its request type and quantities), and a set of vehicles (associated with its capacities and fixed costs). The generated data can be found in Appendix A.

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Since two types of customer requests are studied in this study (pickup request and delivery request), the customer request data is generally divided into these two requests. The illustration

of the generated nodes for customer locations and depot locations is shown in Figure 2. The locations of customer nodes can be considered quite spread in a 10 x 10 square coordinates,

where the four depot locations are sited further away from the customer nodes.

Figure 2. Illustration of the generated customer location nodes and depot nodes (Dataset 1)

The fixed operational cost of each depot is generated to be relatively proportional to its corresponding capacity, which is also similarly applied for the fixed cost of the vehicles (proportional to its load capacity). Additionally, it is assumed that the transport cost between two nodes is considered equal to its distance, which is calculated by the Euclidean distance formula.

4.2. Experiments

4.2.1. Non-Collaborative VS Collaborative LRP

In this first experiment, the performances of the two companies when working isolated is analyzed. The model used in this experiment is also given an opportunity to choose for the most efficient depot that will be opened for the distribution activities. Four customer requests are given to each company in each dataset which are then divided equally to both pickup and delivery requests. The quantity of each customer request is considered to be moderate to large,

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compared to the operated vehicle capacity, where one vehicle is set to be able to carry 5 – 6 units of customer requests in this case. After running this experiment (using Dataset 1), the illustrated comparison of both company’s performances and their collaboration is shown in Table 1 below.

Table 1. Results of Experiment 1 (Dataset 1)

Performance Indicator Company 1 Company 2 Coalition

Total costs (€) 419.324 439.324 568.552

Number of depots used (units) 1 1 1

Number of vehicles used (units) 1 2 2

In order to assure the validity of this experiment, two more datasets are created and used to do the repetitions for the experiments. The characteristics of the generated data for the second and third dataset is fairly similar to the first one, where only the range of the customer and candidate depot locations differs. The second dataset is done in a 20 x 20 square coordinates, while the third one is created in a 50 x 50 square coordinates. Figure 2 & 3 below shows the illustrations of the second and third dataset.

Figure 3. Illustration of Dataset 2

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Figure 4. Illustration of Dataset 3

The summary of this experiment after running the model using Dataset 1, 2, & 3 is shown in Table 2 as follows.

Table 2. Summary of Experiment 1

Performance Indicator

% Difference Between Collaboration Scheme and Non-Collaboration Scheme

Dataset 1 Dataset 2 Dataset 3 Average

Total costs -33.79% -28.01% -30.82% -30.87%

Number of depots used -50.00% -50.00% -50.00% -50.00% Number of vehicles used -33.33% -75.00% -50.00% -52.78%

In above summary, the % difference of total cost is calculated by comparing the total cost caused by the collaboration to the sum of total costs of each company when working isolated. The same scheme applies to calculate the difference of the number of utilized depots and vehicles. Subsequently, the averages of % difference for each performance indicator are calculated to get the general conclusion of this experiment.

The result of this experiment shows the significant potential saving in the total distribution cost from doing the collaboration, with the average of 30.87%. This is might be due to the decrease

number of opened depots (by approximately 50% in average) and the utilized vehicles (by around 52.78% in average) for the distribution process of the companies. Besides sharing

costs for the operational activities of the distribution, this might be also because of the decreased travel distance caused by the facility sharing. Based on these reasons, it can be concluded that the coalition plays beneficial role for the two companies in this network.

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4.2.2. Fixed Location VS Location Decisions

In the second experiment, the proposed model is run twice with different scenarios in order to get insight about the impact of adding location decisions to a collaborative routing problem. The first scenario applies fixed locations of the depots, while the second scenario is given options whether to use which depot candidate locations to operate. The locations of the candidate depots, along with its capacity and fixed operational costs, are set to be in the same condition with the previous experiment. After running these two scenarios in the programming for Dataset 1, the illustrated results is compared as shown in Table 2.

Table 3. Results of Experiment 2 (Dataset 1)

Performance Indicator Fixed Depot

Locations

Variable Depot Locations

Total costs (€) 1,628.55 568.552

Number of depots used (units) 2 1

Number of vehicles used (units) 1 2

The model is also run using Dataset 2 & 3 in order to ensure the validity of the experiment. The summary of this experiment is shown in Table 4 as follows.

Performance Indicator

% Difference Between Fixed Depot Location and Variable Depot Locations

Dataset 1 Dataset 2 Dataset 3 Average

Total cost -65.09% -67.04% -65.92% -66.02%

Number of depots used -50.00% -50.00% -50.00% -50.00%

Number of vehicles used 100.00% 0.00% 0.00% 33.33%

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optimization can be achieved from the variable depot location scenario. This might be because of the vehicle capacity that is set to be moderate to large in the datasets, which is then expected to give less impact on the routing decisions in this collaborative network. Increasing the total vehicle’s capacity is predicted to decrease the total travel distance as there is less limitation that enforces the optimized routes.

4.2.3. The Effect of Cost Parameter

Next to the previous two experiments, the effect of cost parameter is also investigated in this study in order to further comprehend whether the changes of some costs will either improve or decrease the benefit of the collaboration. In this experiment, the amount of depot opening costs will be manipulated. Three level of depot fixed costs amount (low, moderate, and high level) will be set in order to see the differences in the results.

The default fixed costs for depot opening used in previous experiments are considered to be in moderate level, which is proportionally similar to its corresponding capacity. For the low level, the depot opening costs in each dataset are reduced to only 1/3 of the default amount. Meanwhile, this fixed cost is also increased with the extreme amount which is ten times of the default amount, considered as the high level.

After running this scenario using the three datasets, the results indicate that there are no significant changes in the optimal solutions caused in all datasets when the depot opening costs are altered. The priority for the opened depot basically will be given to the depot with the lowest fixed cost. Therefore, the result will remain the same when the fixed costs are changed proportionally. The only difference is the objective function value which follows the changes of its corresponding depot opening cost, as shown in Table 5 below.

Level of Depot Opening Cost

Objective Value (€)

Dataset 1 Dataset 2 Dataset 3

Low 368.55 468.55 458.55

Moderate 568.55 668.55 718.55

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5. CONCLUSION

5.1. Summary

Collaborative transportation (CT) has become increasingly popular in the transportation industry, aiming to result in considerable savings in transport operating costs as well as reduced emissions and noise from cargo vehicles by reducing the number of vehicles required and its distance travelled for the distribution process (Thompson & Hassall, 2012). However, the existing literature discussing about the vehicle routing problem in the collaborative network is still very limited, especially when also considering the optimal location decisions in order to maximize the cost savings in the collaboration. Therefore, this thesis studied about the collaborative location-routing problem (CLRP) among transportation companies and its affected cost savings which lead to this research question: How to determine the optimal

location for the joint consolidation center(s) in a shared customer collaboration network with pickups and deliveries? How does it benefit the collaboration network?

A mathematical model to solve the location-routing problem in the collaborative network is proposed in this study. The results, based on the computational study, confirmed the efficiency of the CLRP concept by comparing its cost savings. Comparing the results between the non-collaborative and collaboration network, there are significant cost savings affected by the coalition. On the other hand, the CLRP concept also result significant cost savings when comparing its total cost with the vehicle-routing problem without the location decisions which is also related to the efficiency in the depot operation.

5.2. Limitation and Recommendation for Further Research

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APPENDIX A

DATASET USED FOR EXPERIMENTS

Dataset 1

Company 1 Company 2

Depot locations [(2, 2), (3, 8)] [(7, 6), (10, 2)]

Depot capacities [300, 230] [200, 230]

Fixed costs (depot) [400, 330] [300, 330]

Pickup nodes [(1, 1), (4, 4)] [(5, 2), (8, 5)] Quantity of pickup requests [8, 12] [10, 10] Delivery nodes [(6, 7), (2, 5)] [(6, 7), (2, 5)] Quantity of delivery requests [9, 10] [9, 10]

Vehicle capacities [30, 40] [60, 55]

Fixed costs (vehicle) [30, 40] [60, 55]

Dataset 2

Depot locations [(7, 5), (18, 17)] [(20, 2), (1, 12)]

Fixed costs (vehicle) [50, 40] [65, 45]

Dataset 3

Depot locations [(8, 12), (45, 40)] [(18, 35), (40, 5)]

Collaborative location routing problem with pickups and deliveries