Crowd Shipping: A Vehicle Routing Problem with Compatibility Constraints and Restrictions for Occasional Drivers

Crowd Shipping:

A Vehicle Routing Problem with Compatibility

Constraints and Restrictions for Occasional Drivers

Msc Supply Chain Management, Msc Technology & Operations Management, Faculty of Economics and Business, Rijksuniversiteit Groningen

22th June, 2020

Jelle Nijboer S2561433

j.nijboer.4@student.rug.nl Supervisor:

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Abstract

The substantial growth of e-commerce is leading to logistics challenges in parcel industries. Crowd shipping is an innovative way of organizing the last mile delivery by making use of excess capacity on existing traffic flows. In this paper, a setting is considered where a company operates from a central store or depot and could make use of occasional drivers next to own personnel to perform deliveries. Occasional drivers have to travel to the depot to pick up parcels to perform deliveries. The willingness of occasional drivers is included by modelling the origin of occasional drivers and by denoting a minimum of visits, maximum detour and time windows. The model seeks to minimize costs by optimizing the assignment and routing of delivery tasks to occasional drivers and regular drivers. Time windows are considered for customers. We introduce restrictions for a set of delivery tasks to be carried out by occasional drivers to overcome trust and privacy issues. The problem is formulated mathematically and a computational study is conducted. The results show that substantial cost savings can be obtained when using occasional drivers. Especially in less dense areas where customers are randomly distributed and when there are sufficient occasional drivers.

Keywords: Crowd Shipping, Occasional Drivers, Vehicle Routing Problem, Restrictions,

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Contents

2.2 Vehicle Routing Problem with Occasional Drivers ... 10

3. Problem Description ... 12

4. Mathematical model ... 15

5. Computational Study ... 19

5.1 Instance Generation ... 19

5.2 Comparative Analysis on Number of Occasional Drivers ... 20

5.3 Analysis of Specific Instances ... 23

5.4 Sensitivity analysis and overall performance ... 26

6. Conclusions ... 28

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1. Introduction

The rapid growth of e-commerce and demand for short delivery lead times are leading to logistics challenges in the parcel shipment industry. The increase of small volume demands results in fragmentation of good flows and difficulties for shipping companies to transport in an efficient and sustainable way (Montreuil, 2011). However, technological developments and the importance of efficient delivery operations make creative concepts arise in the shipping industry such as crowd shipping.

Crowd shipping (CS) is built on the idea of outsourcing (a part of) the delivery operations to the crowd. It is making use of existing traffic flows of ordinary people driving their private cars rather than vehicles of shipping companies. Many people make daily trips towards their homes with excess capacity in their cars. By making a small detour, they could earn a little compensation by fulfilling a part of the delivery operations of a shipping company. For instance, they could pick up a parcel and deliver it to one of their neighbours by making a small detour. Crowd shipping requires a service platform in order to match parcel delivery tasks with drivers who are willing to pick it up and deliver it to customer locations (Arslan et al., 2018). The use of the crowd, in literature referred to as occasional drivers (ODs), can generate several benefits for different stakeholders. ODs can earn money by performing deliveries on a route that they are already traversing. For companies, the cost of compensating ODs could potentially be lower than the salary of traditional parcel delivery staff and improved efficiency could lead to faster deliveries for the customer. Besides, the replacement of traditional delivery vehicles by ODs could reduce the environmental impact in terms of CO₂ emissions and congestion.

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In 2013, shipping company DHL ran a pilot with a crowd shipping platform called ‘MyWays’. The company created an application serving as a digital platform, connecting individuals who were willing to transport a parcel along their route with customers asking for a flexible delivery. In 2015, Amazon launched a similar concept called (Amazon Flex) where people could become an occasional driver and have the opportunity to transport a parcel for a small compensation. See Table 1.1 for an overview of crowd shipping concepts from practice.

Although CS seems a good solution to improve efficiency and reduce negative environmental side effects, it is challenging to develop a system that actually realizes this. Profitability is a major issue in competing with fast delivery services (Dablanc et al., 2017) and only a fraction of the current systems succeed in maintaining a lasting crowd shipping market. Without sufficient demand, no profitable tasks can be offered to occasional drivers and without a large community of occasional drivers, it becomes complex to offer high quality to the customers (Raviv & Tenzer, 2018). In order to make crowd shipping a more efficient alternative for traditional delivery, more research on models is needed which consider the willingness to participate of drivers and customers. Especially the operational aspect of the service platform should be addressed since it plays a significant role to ensure capacity optimization and reduce CO₂ reduction (Rai et al., 2018).

Due to the novelty of crowd shipping, literature is limited. Nevertheless, a few scientist explored the field of crowd shipping. Several researchers studied the behavioural aspects of crowd shipping and concluded that a successful crowd shipping network requires a critical mass of users on demand and supply side who are willing to participate (Rouges & Montreuil, 2014, Punel & Stathopoulos, 2017, Rai et al., 2018). There are several models that complement the lack of supply of occasional drivers by adding a fleet of traditional drivers to perform the deliveries that are not viable for occasional drivers (Archetti et al., 2016, Macrina et al., 2017 and Arslan et al., 2018). The willingness of ODs to participate is mostly determined by

Table 1.1

Crowd shipping platforms

Name Segment Range

Amazon Flex B2C Last-mile

DHL MyWays B2C, P2P Last-mile

Nimber P2P Long distance

Parcify P2P Long distance

PiggyBee P2P Long distance

ShipperBee B2C Regional, Last-mile

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compensation and the opportunity to be your own boss (Le & Ukkusuri, 2018). Besides, the literature lacks models for assigning delivery tasks which consider the willingness of customers. Challenges on the demand side are related to trust and reliability issues (Erickson & Trauth, 2013, Le et al., 2019). Since occasional drivers are not employed by a company and assume their own liability, senders and receivers may question whether their parcels will be delivered on time and without damage. Besides, customers might be concerned about sharing personal information, home address and purchasing habits (Fatnassi et al., 2015).

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solve a Vehicle Routing Problem with Occasional Drivers, Time Windows and Compatibility Constraints (VRPODTWCC) and impose constraints for ODs to illustrate their willingness. The contribution of this paper is twofold. First, we provide quantitative insights for crowd shipping in order to generate better guidance for reliable crowd shipping concepts. Second, we enrich the current literature by extending the work of Macrina et al. (2017). More specific, this paper is adds compatibility constraints, involves previous locations of ODs before accepting a delivery request and introduces limitations that illustrate the willingness of ODs. Therefore we introduce a Vehicle Routing Problem with Occasional Drivers, Time Windows and Compatibility Constraints (VRPODTWCC). This problem differs from the classical VRPTWCC since the use of occasional drivers is added. A computational study is conducted to analyse instances, test sensitivity of parameters and derive practical insights.

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2. Literature review

This chapter is divided into two different sections. First an overview of literature on crowd shipping related to our work is provided. Second, literature on the vehicle routing problem is presented and adaptions needed for this study are discussed.

2.1 Crowd shipping

In recent years, crowd shipping has become an interesting topic in freight transportation. Despite the novelty, several scientist explored the possibility of crowdsourcing (a part of) the delivery process. Both, operational and behavioural aspects are investigated. However, the characteristics of each CS concept are diverse.

Archetti et al. (2016) developed a model where regular drivers are complemented by a set of occasional drivers. Occasional drivers are willing to perform a single delivery if the total route length does not exceed the initial route length multiplied by the detour parameter. They considered a ‘cost-to-serve’ compensation scheme and a cost scheme based on the total deviation. Especially for the latter cost scheme, they found that substantial cost savings could be realized by using occasional drivers.

Macrina et al. (2017) extended the work of Archetti et al. (2016) by addressing the availability of occasional drivers. More specific, they added time windows and allowed ODs to make multiple deliveries. Their results suggested improved routing plans and interesting cost savings. In both Archetti et al. (2016) and Macrina et al. (2017), customer locations are served from a central depot and the supply of occasional drivers is limited to drivers that declare their willingness to perform a delivery when they are already at the depot. While in reality, occasional drivers indicate their availability before reaching the depot.

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for regular drivers. While in reality, compensating ODs is likely to be less than compensating RDs since they pay for their own fuel, insurance and maintenance.

There are several scientists who addressed the non-operational aspect of crowd shipping. Rouges & Montreuil (2014) explored the stakeholder value creation and found that a critical mass of drivers and customers are needed to exploit the network effect of crowd shipping. Furthermore, they discussed characteristics of different business models and distinguished offer pole, creation pole, revenue model, couriers and character. In this paper we consider a crowd shipping model focused on the B2C segment in an intra-urban setting where occasional drivers are non-professional and professional couriers who are looking for additional revenues and who can self-determine their schedule.

Le et al. (2019) reviewed current practice and literature to come up with gaps for implementation. They found that there are concerns at supply and demand side on trust issues. This contains concerns about timeliness, parcel damage and privacy. Contrary to regular drivers, there is only little control on performance of occasional drivers since they are self-employed. Our work addresses these issues by introducing a set of customers which can only be served by regular drivers to ensure reliability.

Punel & Stathopoulos (2017) investigated the acceptance of crowd shipping and state that the willingness of occasional drivers to detour from existing travel plans are fundamental and should be included in operational designs. Le and Ukkusuri (2018) found that two major motivations for ODs to participate are ‘to get paid’ and ‘to be your own boss’. To include these aspects in our study, our model considers requirements for acceptance or rejection. The occasional driver accepts to perform a delivery only if: 1) they do not exceed a maximum detour from their intended route; 2) a minimum number of deliveries can be performed to earn a minimum compensation; and 3) they can perform the deliveries within their own time windows.

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are added to overcome trust issues. Our work focusses on a hybrid CS platform with a central depot since crowd shipping is most promising in the B2C segment where retailers operate from a central depot or store (Rouges & Montreuil, 2014). Like Macrina et al. (2017) and Arslan et al. (2019), time windows are introduced to address the dynamic nature of occasional drivers and delivery windows for customers.

2.2 Vehicle Routing Problem with Occasional Drivers

According to Laporte (1992), the vehicle routing problem (VRP) is an appropriate method to optimize the assignment of delivery tasks from one or several depots to customers, subject to side constraints. Starting from the basic VRP introduced by Dantzig & Ramser (1959) there are many novel variants which extend the classical VRP. In this section, the characteristics of the VRP that are involved in this study are discussed.

Deliveries in crowd shipping are performed by regular drivers and occasional drivers. Characteristics of regular drivers are different from occasional drivers and therefore our fleet can be described as a heterogenous fleet. But for the sake of simplicity, we assume that constraints are the same among both groups. However, origins and destinations of occasional drivers are randomly generated and therefore different.

Although regular drivers start their trip from the depot, occasional drivers start their operations by travelling from the origin to the depot to pick up the parcels. Therefore, the behaviour of occasional drivers should be modelled as a pickup and delivery problem (PDP). This is a variant of the VRP that aims to transport goods or people between origins and destination (Berbeglia et al., 2007). In this paper, the aim is to transport parcels from the origin (depot) to the destination (customer).

We consider capacitated vehicles with a maximum number of parcels that can be transported on a single tour. This capacity constraint cannot be violated. Since a heterogenous fleet is considered, we assume different capacity limits for regular drivers compared to occasional drivers.

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(Voccia et al., 2019). Besides, all delivery tasks need to be served and cannot be rejected. This paper includes hard time window constraints. This means that drivers cannot violate the late boundary of the time window and have to wait if they arrive before the early boundary (Cordeau et al., 2000).

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3. Problem Description

We consider a setting in which parcels can be delivered to the customer by either a Regular Driver (RD) or an Occasional Driver (OD). While RDs can be characterized as a homogeneous pool of drivers, the pool of ODs is heterogeneous and varies in origin and destination. The objective is to assign delivery tasks such that the total travelling cost is minimized. Total cost is composed of the routing cost of RDs and the compensation paid to ODs. The cost of RDs is linearly related with the total distance. The cost of ODs is based on the distance they cover from the depot until the last customer that they visit. Thus, the distance from their origin to the depot and from the last customer to their destination is not reimbursed. The cost per kilometer for occasional drivers is assumed to be less since they pay for their own fuel, insurance and maintenance. Moreover, we neglect service time for stopping by the depot and customer locations. The main limitation of this cost scheme is that it neglects time consuming aspects like loading, visiting a customer location or traffic jams.

A single depot is considered as origin for all parcels. Regular drivers must start and end their journey at the depot. Since we consider crowd shipping for a shipping company, we assume that the supply of regular drivers is unlimited. For occasional drivers, we assume that they start their journey from their homes by travelling from their origin to the depot to pick up parcels. Therefore, the routing of ODs should be modelled as a pickup and delivery problem (PDP). After performing the deliveries, occasional drivers end their journey at their destination (this could be the same location as their origin).

Since having fast and timely deliveries is a competitive advantage, we consider time windows for customers where the service of each customer must be within an associated time window (Cordeau et al., 2000). Besides, all delivery tasks need to be served and cannot be rejected. In our problem we allow RDs and ODs to perform multiple deliveries. Since most parcel requests in the B2C segment are small to medium sized (Ermagun et al., 2019), we assume that parcels have a homogeneous size. There is a maximum number of parcels that drivers can transport, where RDs have a larger capacity than ODs.

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side of the customer about parcel timeliness, parcel damage and privacy (Le et al., 2019). Hence, we discuss the following elements which constitute the addition of this paper. We consider a set of delivery tasks that can only be carried out by RDs to overcome those concerns related to trust. This set contains requests from customers who explicitly indicated that they want their parcel to be delivered by a driver employed by the company. Therefore, the set of customers is divided into two subsets i.e. customer locations that can be visited by either an RD or OD and customer locations that must be served by an RD. However, we model the subsets in one problem since a tour of an RD can be composed of visiting customers from both sets. By means of this, a shipping company can get a holistic view on total cost, where the use of crowd shipping is integrated in their shipping operations.

Another novel aspect in our problem is that the we address the dynamic nature of ODs by including their origin in the routing problem. Previous work (Archetti et al., 2016, Macrina et al., 2017) assumes that ODs declare their willingness when they are at the depot. This is reasonable in a context where companies operate from a store where customers perform deliveries, but not for companies who operate from distribution centers (Archetti et al., 2016). Besides, participation of ODs is subject to three requirements to address their willingness:

1. Minimum number of visits

By performing deliveries as an occasional driver, it makes sense that participants would like a minimum number of visits in order to generate a minimum compensation. Therefore, our model introduces a parameter which denote the minimum number of visits for occasional drivers. If the requirement cannot be met, the occasional driver will not participate in delivery operations which results in visiting zero customers. 2. Maximum detour

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their intended route to ensure that delivery tasks are clustered together between the depot and their homes.

3. Hard time windows

Since occasional drivers can self-determine their schedule it is assumed that they are not inclined to work very long shifts and prefer to be at home before a certain time. Therefore, their availability is characterized by time windows.

Figure 3.1 presents an example of a possible routing plan where all customer locations are served by either an RD or OD. Figure 3.1a presents a scenario without ODs where all

customers are visited by RDs. Figure 3.1b presents a solution where a part of the delivery is outsourced to an OD. One trip of an RD can be replaced by an OD which can perform deliveries for less cost. It can also be seen that the requirement of certain customers to be served by an RD is still satisfied.

Figure 3.1

Possible routing plan with crowd shipping

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4. Mathematical model

In this section, an explanation on the translation of the problem into the mathematical model is provided. Our model is built based on the work of Macrina et al. (2017), who also consider occasional drivers and time windows.

We define a set of nodes and arcs where 𝐺 = (𝑁, 𝐴) denotes a directed graph. 𝑁 consists of 𝐶 ∪ 𝑅 ∪ {0} ∪ 𝑈 ∪ 𝑉. Let 𝐶 be the set of customers that can be served by either an RD or OD and let 𝑅 be the set of customers that can only be served by an RD. Regular drivers start their route from the depot {0}, serving a set of customers 𝑖 ∈ 𝐶 ∪ 𝑅 and return to the depot. 𝐾 is the set of occasional drivers where each 𝑘 ∈ 𝐾 has a corresponding origin 𝑢𝑘 ∈ 𝑈 and

destination 𝑣_𝑘 ∈ 𝑉. Note that occasional drivers start their route by traveling from the origin to the depot to pick up parcels, subsequently the OD is able to perform deliveries. For the sake of simplicity, the pickup operation of parcels at the depot is modelled in the travel time from the origin to the first customer. The origin (U) and destination (V) could be the same for occasional drivers. To improve the ease of use in the model, nodes for regular drivers are denoted as 𝑁 = 𝐶 ∪ 𝑅 ∪ {0}.

Furthermore we define a set of arcs 𝐴 = {(𝑖, 𝑗)}, where 𝑖 ∈ {0} ∪ 𝐶 ∪ 𝑅 ∪ 𝑈, 𝑗 ∈ {0} ∪ 𝐶 ∪ 𝑅 ∪ 𝑉 and 𝑖 ≠ 𝑗. For each arc (𝑖, 𝑗) ∈ 𝐴 there is a corresponding travel time 𝑡𝑖𝑗 based on

distance which reflect the total cost. The difference in compensation for ODs compared to RDs is denoted by 𝜌, where 𝜌 = 0,75 .

Each customer 𝑖 ∈ 𝐶 ∪ 𝑅 has a demand of 𝑑_𝑖 and a time window with an early and late boundary which can be defined as [𝑒_𝑖, 𝑙_𝑖]. The same applies for each occasional driver 𝑖 ∈ 𝑈 ∪ 𝑉 since they state their availability by providing a time slot [𝑒𝑢𝑘, 𝑙𝑣𝑘]. The maximum detour

that ODs are willing to make is based on the detour coefficient ζ, where ζ > 1. ODs are willing to deliver a parcel when the length of the total tour does not exceed the length of the intended tour multiplied by the detour coefficient, 𝑡𝑢𝑘0+ 𝑡0𝑖+ 𝑡𝑖𝑗 + 𝑡𝑖𝑣𝑘 ≤ ζ(𝑡𝑢𝑘0+ 𝑡0𝑣𝑘). The

minimum number of visits that ODs demand is denoted by 𝑁𝑘. Note that if an OD cannot visit

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Let 𝑥𝑖𝑗 be the binary variable equal to one if an RD traverses arc (𝑖, 𝑗) and let 𝑟𝑖𝑗𝑘 be the binary

variable equal to one if OD 𝑘 ∈ 𝐾 traverses arc (𝑖, 𝑗). The arrival time of a driver at customer 𝑖 is denoted by 𝑠𝑖 and 𝑓𝑖𝑘 for RDs and ODs respectively. 𝑦𝑖 and 𝑤𝑖𝑘 denote the available capacity

of the vehicle after visiting customer 𝑖. In Table 4.1, an overview of sets, parameters and variables is given. Thereafter, the mathematical model is presented.

Table 4.1

Overview of sets, parameters and decision variables Sets

{0} Depot

C Customer locations served by OD or RD R Customer locations served by RD N Nodes for RDs where 𝑁 = 𝐶 ∪ 𝑅 ∪ {0} U Origins of Occasional Drivers

V Destinations of Occasional Drivers K Set of available Occasional drivers Parameters

𝑄𝑟 Maximum capacity regular drivers

𝑄𝑘 Maximum capacity occasional drivers

𝑁𝑘 Minimum number of visits occasional drivers

𝑑𝑖 Demand at customer location 𝑖

𝑡𝑖𝑗 Travel time for traversing arc 𝑖𝑗

[𝑒𝑖, 𝑙𝑖] Time windows of node 𝑖

𝑒𝑢𝑘 Time from which OD k is available at its origin

𝑙𝑣𝑘 Instant time before OD k must reach its destination

𝜌 Compensation coefficient for ODs ζ Detour coefficient for ODs 𝑀 A very large value (Big M) Variables

𝑥𝑖𝑗 Binary variable, 1 if traversed by regular driver, 0 otherwise

𝑦𝑖 Available capacity of RD after visiting node 𝑖

𝑠𝑖 Arrival time of RD at node 𝑖

𝑟𝑖𝑗𝑘 Binary variable, 1 if traversed by occasional driver 𝑘, 0 otherwise

𝑤𝑖𝑘 Available capacity of OD after visiting node 𝑖

𝑓𝑖𝑘 Arrival time of OD at node 𝑖

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𝑦0≤ 𝑄𝑟 (4)

𝑠𝑗≥ 𝑠𝑖+ 𝑡𝑖𝑗𝑥𝑖𝑗− 𝑀(1 − 𝑥𝑖𝑗), ∀𝑖 ∈ 𝐶 ∪ 𝑅, 𝑗 ∈ 𝐶 ∪ 𝑅, 𝑗 ≠ 𝑖 (5) 𝑒𝑖− 𝑀(1 − 𝑥𝑖𝑗) ≤ 𝑠𝑖 ≤ 𝑙𝑖+ 𝑀(1 − 𝑥𝑖𝑗), ∀𝑖 ∈ 𝐶 ∪ 𝑅 (6)

Expression (1) represents the objective of minimizing cost where the first term is related to the cost of regular drivers and the second term to the cost of occasional drivers. The letter ρ in the second term denotes the wage that occasional drivers receive compared to regular drivers. The last term subtracts the cost associated with the distance to reach the depot and the distance to reach the destination after the deliveries are done. Constraint (2) denotes the flow conservation for the nodes. Constraint (3) ensures that the demand at customer locations is satisfied and included in the available capacity of a vehicle. Constraint (4) sets the maximum capacity of RDs. Constraint (5) determines the arrival time at node 𝑗. Constraint (6) makes sure that the arrival time is within the associated time window of a customer. Constraints (7)-(18) are related to the behaviour of ODs and are modelled as follows:

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Constraint (7) assures the flow conservation for ODs. Constraint (8) makes sure that every OD performs not more than one trip. Constraint (9) assures the capacity and fulfilment of demand. Constraint (10) sets the maximum available capacity. Constraints (11)-(13) determine the arrival time at the first customer, next customers and destination respectively. Constraint (14) assures that customers are visited within their time windows. Constraint (15) guarantees that each regular customer is served by either an RD or OD. Constraints (16) and (17) assure that the variables are binary. Constraints 18 and 19 set the boundaries of the available capacity on a vehicle. Constraint 20 assures that arrival times are non-negative. Starting by the mathematical model introduced by Macrina et al. (2017), additional constraints are introduced. It is necessary to implement constraints that assure that every customer of set R is visited by an RD. Furthermore, we have to model the restriction on willingness of ODs to perform deliveries. Therefore, we set a minimum number of trips, a maximum detour and an ultimate arrival time at the destination of ODs. Hence, the following constraints are included.

∑ 𝑥𝑖𝑗 𝑗∈𝐶∪𝑅∪{0} = 1, ∀𝑖 ∈ 𝑅 (21) ∑ ∑ 𝑟_𝑖𝑗𝑘 𝑗∈𝐶 ≥ 𝑁𝑘∑ 𝑟𝑢𝑘𝑗 𝑘 𝑗∈𝐶 𝑖∈𝐶∪{𝑢𝑘}𝑗≠𝑖 ∀𝑘 ∈ 𝐾 (22) ∑ ∑ ((𝑡𝑢_𝑘0+ 𝑡0𝑖)𝑟𝑢𝑘𝑖 𝑘 _{+ 𝑡} 𝑖𝑗𝑟𝑖𝑗𝑘 𝑗∈𝐶,𝑗≠𝑖 ) 𝑖∈𝐶 ≤ ζ(𝑡𝑢_𝑘0+ 𝑡0𝑣_𝑘) ∀𝑘 ∈ 𝐾 (23) 𝑓𝑣𝑘_𝑘 ≤ 𝑙𝑣_𝑘, ∀𝑘 ∈ 𝐾 (24)

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5. Computational Study

In this section the proposed mathematical model will be validated. The objective is to gain insights in the potential benefits for the use of crowd shippers under different circumstances. Hence, several instances are used as input to check the behaviour of the model. The input for the study is the Vehicle Routing Problem with Occasional Drivers, Time Windows and Compatibility Constraints (VRPODTWCC) proposed in section 4. A comparative analysis is presented to examine the use of occasional drivers in different settings. The problem is solved using CPLEX 12.10.0 and run on a computer with an Intel i5 CPU-8265U with 1.80 GHz and 8GB of RAM.

5.1 Instance Generation

In this work, several instances are considered which reflect situations with different characteristics. The instances are generated based on the Solomon VRP benchmark set with time windows (Solomon, 1987). There are three types of classes (C, R and RC) which refer to different distributions of customer locations. Namely, clustered together, random and a mix of clustered and random respectively. We are using each class to see what the consequences are for different areas in terms of population density. Besides, each class is characterized by a short (C101, R101, RC101) or long planning horizon (C201, R201, RC201) for time windows. We use both types for each class type. For the distance between nodes, Euclidean distances are used.

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To reduce the complexity of the problem, the demand of customers is downsized. Furthermore, since the aim is to investigate the effect of occasional drivers and not the effect of variety in demand, we assume the same demand for each customer 𝑑𝑖 = 1. The vehicle

capacity varies in each specific set in the Solomon sets. However, we assume capacity of regular drivers homogeneous in each set. ODs are assumed to have smaller cars and therefore forced to rely on space in their trunk and back of the car. Hence their capacity is set as 𝑄𝑘 = 0,25 ∗ 𝑄𝑟. The minimum number of visits is set at 𝑁𝑘 = 0,1 ∗ |𝐶 + 𝑅| and the detour coefficient

(ζ) is set at 3.

Occasional drivers are assumed to prefer to do deliveries at convenient times. Hence, they have limited time slots in which they perform deliveries, starting from their origin at 𝑒𝑘=

0.2 ∗ 𝑙̅_𝑖 and reaching their destination before 𝑙_𝑘= 0.8 ∗ 𝑙̅_𝑖. In section 5.4, we take a closer look at the parameters to investigate the sensitivity of the model.

5.2 Comparative Analysis on Number of Occasional Drivers

In this section we analyse the problem in different ways. In particular, the performance of all six sets is tested for different values of K. First, we compare three values for K in all six sets:

1. |𝐾| = 0. The base scenario which reflects the situation where all deliveries are performed by regular drivers with a scenario where ODs are introduced.

2. |𝐾| = 2. A scenario where only a few ODs submit their availability. 3. |𝐾| = 10. A scenario where many ODs submit their availability.

CPLEX can solve instances with 30 customers and 10 occasional drivers mostly within 10 minutes. But when increasing the number of customers to 40, it becomes problematic for CPLEX to find optimal solutions within 30 minutes. Therefore, we

use |𝐶 + 𝑅| = 30 for the tests. The parameter settings are given in Table 5.1 and the results are presented in Table 5.2.

The total routing cost for compensating regular and occasional drivers can be found under column cost. Under column #RD and #OD, the number of RDs and ODs are shown that are used in the optimal solution. Note that #OD denotes the total number of ODs that are actually matched with delivery tasks and could be different

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from |𝐾|, which denotes the total number of ODs that are available. Column %d denotes the percentage of total demand that is satisfied by ODs for each class. The formula 1 −𝐶𝑜𝑠𝑡𝑉𝑅𝑃𝑂𝐷

𝐶𝑜𝑠𝑡𝑉𝑅𝑃

is used for Gap%. Which reflects the potential benefit compared to the base scenario where all deliveries are performed by regular drivers.

Table 5.2

Results for the VRPODTWCC with 0 ODs, 2 ODs and 10 ODs

K=0 K=2 K=10

Set Cost #RD Cost #RD #OD %d Gap% Cost #RD #OD %d Gap% C101 327 5 311,75 3 1 13 5 311,75 3 1 13 5 C201 291 2 291 2 0 0 0 291 2 0 0 0 R101 690 8 630 6 2 23 9 591,5 5 4 40 14 R201 520 4 497,5 4 1 13 4 389 2 5 57 25 RC101 597 6 573 5 2 23 4 512,75 4 3 33 14 RC201 577 4 559 4 1 13 3 536,75 3 3 33 7 Average 500,3 4,8 477,0 4,0 1,2 14 5 438,8 3,2 2,7 29 12

The aim of these tests is to analyse the benefit of introducing ODs in delivery operations. Overall, it can be seen that cost reductions (5% and 12%) can be accomplished by using occasional drivers. The potential savings are highly dependent on the size of K since a scenario with many ODs (K=10) outperforms the scenario with a few ODs (K=2) with a 7% higher cost reduction. The cost reduction goes along with a decrease in the number of RDs when relying on more ODs performing delivery tasks. Furthermore, when two occasional drivers are available, 14% of the total demand can be satisfied by ODs. When 10 occasional drivers are available, 29% percent of the total demand is satisfied by ODs.

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cheap and assigning delivery tasks to RDs to improve efficiency. This can be seen in Figure 5.1 and 5.2.

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Figure 5.2 represents the percentage of the total demand that is satisfied by ODs while increasing K. This figure shows similar trends as figure 5.1. However, it can now be seen what ratio in assigning delivery tasks to RDs and ODs yields to the best solution. In an area where customers are randomly distributed (R101, R201, RC101 and RC201), up to 57% of all customers can be served by ODs. When observing both graphs, it can be seen that the total savings for each instance increase when increasing K, but stops increasing after K=10. Except, for R101 and RC201 which show a slight improvement when K>10. Most occasional drivers that can contribute to a cost saving are within the first 10 occasional drivers. Increasing this pool (K), does not result in substantial marginal savings. At this threshold, 29% of all demand is satisfied by ODs.

5.3 Analysis of Specific Instances

In this section we analyse specific instances in order to get a better understanding of the model and the influence of specific characteristics. Figure 5.3 represents the optimal solution for set C101 (top) and R201 (bottom) respectively. On left side, the situation without ODs is presented, the right side shows the solution when there are 10 ODs. The performance of these specific analyses can be seen in Table 5.3 and 5.4.

Table 5.3 Instance performance K=0 Set Cost #RD C101 327 5 R201 520 4 Table 5.4 Instance performance K=10

Set Cost #RD #OD %d Gap%

C101 311,75 3 1 13,3 5

R201 389 2 5 56,7 25

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Overall analysis. Capacity is set at 20 and 5 for RDs and ODs respectively and does not affect

the outcome. In 4 of the OD trips that can be seen in Figure 5.3, exactly the minimum number of customers is visited. Besides, routing is affected by the time windows since RD trips consist of illogical sequences. The ODs which have a destination relatively far from the depot seem more likely to be used in the model than others. This is declarable since the maximum absolute detour is too small to visit multiple customers when the OD lives relatively close to the depot.

Analysis on C101. This is an interesting instance because adding one occasional driver leads to

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constraints. In Figure 5.3b, it can be observed that three customers in that area are supplied by an OD in the optimal solution. However, there is another customer relatively near the destination of the OD which is still served by an RD. Looking at this specific customer, we find out that this customer has a time window that is quite early. This time window cannot be met by an OD without violating its own time window.

Furthermore, the OD starts by serving a customer which is located near other customers who are all served by RDs. Looking at this specific customer, it can be seen that the customer also has a relatively early time window. However, it can still be served by an OD and removing this customer from the trip of an RD can lead to efficiency improvements. All other areas where customers are clustered together are not profitable for crowd shipping. RDs already have to visit that area to serve customers with compatibility constraints. Using ODs in that area will then be inefficient.

Next, we take a look at the choice of the specific OD. In figure 5.3a, it can be seen that there are two OD destinations in the area in the top. Although only one can be used(top right figure). Removing the current OD which is performing the deliveries from the list (K=9), leads to performing the same delivery tasks by the other OD. Thus, it is possible that delivery tasks can be offered to multiple ODs for the same cost. However, removing this OD as well (K=8), leads to another routing plan with lower cost savings since no OD can serve these customers without exceeding their maximum detour.

Analysis on R201. Then, the specific solution obtained for set R201 is examined. While set

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looking at the compensation scheme. ODs are not compensated from the distance from the last customer that they visit to the destination. Therefore, these two customers to the trip of an RD results in less marginal costs.

5.4 Sensitivity analysis and overall performance

In this section, the average performance of all instances is examined. Furthermore the sensitivity of the minimum number of visits and the maximum detour of occasional drivers is tested. These parameters are interesting because it is observed that most ODs that are employed are serving exactly the minimum number of customers (𝑁𝑘). Besides, in section 5.3

it can be observed that trips of ODs highly depends on the maximum detour. Therefore, we use different values for 𝜁 and 𝑁𝑘. Other parameters remain the same (see Table 5.3). The

results are presented in Table 5.6. The values are averages over all 6 instances (C101, C201, R101, R201, RC101, RC201). The superscripts in column cost denote the number of instances for which CPLEX cannot solve the problem within 900 seconds. In that scenario, the objective after 900 seconds is given.

Table 5.6

Analysis of all instances for different values of 𝑁𝑘 and ζ

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Overall, it can be seen that cost savings can be accomplished. In traditional settings (K=0), an average cost of 500,3 is obtained by using 4,8 regular drivers. But when 22% of the total demand is outsourced to 1,9 occasional drivers, a cost saving of 8,7% on average can be obtained. Also the average number of regular drivers that are needed decrease with more than 1,1 when using occasional drivers.

To obtain cost savings, a certain flexibility of ODs in deviating from their intended route is required. Because when ODs are less flexible in deviating from their intended route(ζ = 1,5), cost savings are low for most values of 𝑁𝑘. While extending the maximum detour results in

substantial higher savings.

Varying the minimum number of visits that ODs want to perform affects the potential cost reduction. Although a lower minimum number of visits increases the cost reduction, it is also leading to a more fragmented fulfilment of demand by different drivers. When ODs have a minimum number of visits of only 1 or 2, many ODs are deployed. But on the other hand, the percentage of total demand (%d) that is satisfied by ODs does not necessarily increase. It should also be mentioned that the capacity of ODs is assumed to be fixed at 5. This limits the feasible routes for ODs since they can only visit between N_k and Q_k customers.

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6. Conclusions

Existing literature already shows potential benefits for the use of crowd shipping (Archetti et al., 2016, Macrina et al, 2017, Arslan et al., 2018). However, literature is lacking models which include the willingness of customers and drivers (Le et al., 2019). This is important to obtain a sufficient amount of participants. We have introduced a new variant of crowd shipping where willingness of crowd shippers and customers is addressed. Our goal was to obtain insights in the settings in which crowd shipping with time windows, compatibility restrictions and restrictions for occasional drivers is profitable compared to traditional delivery operations. Therefore, we introduced and modelled a VRPODTWCC, analysed specific instances and conducted a sensitivity analysis.

The contribution of this paper is twofold. First, it enriches the literature by providing analytical results of an extension of the vehicle routing problem with occasional drivers. The extension is based on modelling origins of occasional drivers, adding compatibility constraints and restrictions for occasional drivers. Second, it gives quantitative insights in the profitability of using occasional drivers which are limited by several restrictions. This could be interesting for shipping companies and retailers with their own delivery service.

We present results of crowd shipping with 30 customers in three different geographical settings. The results are encouraging since a cost reduction of 19% can be accomplished when there are 10 occasional drivers. The potential benefit is more evident in less dense areas where customers are more randomly located. Furthermore, savings highly depend on the number of occasional drivers that are available until 30% of all delivery tasks are outsourced to occasional drivers. When analysing the sensitivity of parameters, it must be highlighted that, a minimum willingness of occasional drivers to deviate from their intended route is required to obtain a cost benefit. Occasional drivers which have destinations relatively far from the depot are more likely to be used since their willingness to deviate from their intended route is higher (in terms of absolute distance).

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