Introducing a city hub for the zero-emission city center:
using a two-echelon vehicle routing problem with
compartment constraints
Master thesis
MSc. Technology and Operations Management & MSc. Supply Chain Management
Supervisor: dr. I Bakir
Co-assessor: prof. dr. K.J. Roodbergen
Annelotte Pool
S3451380
24-01-2021
1
Acknowledgement
2
Abstract
3
Content
1. Introduction ... 4
2. Theoretical background ... 7
2.1 City logistics ... 7
2.2 Existing mathematical models ... 9
3. Methodology ... 12 3.1 Research design ... 12 3.2 Model assumptions ... 12 3.3 Problem definition ... 13 3.4 Optimization model ... 16 3.5 Data ... 21 3.6 Solution method ... 23 4. Results ... 26 4.1 Experimental design ... 26
4.2 City hub vs. no city hub ... 28
4.3 Adding customers for vehicle utilization purposes ... 31
4.4 Rounding scenarios ... 33
4.5 Different city hub locations ... 35
5. Conclusion ... 39
6. References ... 41
7. Appendixes ... 44
A1: Input data ... 44
A2: Support of results 4.2 ... 45
A3: Support of results 4.3 ... 47
A4: Support of results 4.4 ... 48
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1. Introduction
By 2025, the main city centers in the Netherlands have to become zero-emission zones for logistics (Climate Agreement, 2019), so companies with customers in the city center need to use zero-emission vehicles. This final step in the distribution process, also called the last mile of the delivery process, is responsible for 75% of the costs of the distributer (Charisis et al., 2020). In those city centers, there are many restaurants, hotels and other companies that require food supplies. Food distribution involves the transportation of perishable products which usually need extra attention during transportation, for example, some products require cooling conditions in a truck (Musavi and Bozorgi-Amiri, 2017; Ostermeier and Hübner, 2018). Refrigerated trucks are more expensive than normal trucks, because a cooling installation need to be built into a truck and requires power. Therefore, costs of food distributors are higher compared to distributors of non-food products (Morganti and Gonzalez-Feliu, 2015). These elements show the complexity and expensiveness of food distribution in city logistics, creating an interesting area of research which is not studied extensively yet (Morganti and Gonzalez-Feliu, 2015).
To obey the regulation of the government, products of customers in the city center need to be delivered with electric vehicles. Currently, most companies travel to all destinations with trucks to deliver products in both urban and suburban areas (Charisis et al., 2020). This implies that
companies are going to use electric vehicles for the complete delivery, covering large distances and carrying large quantities. However, this causes problems with respect to the downsides of electric vehicles, which are a limited radius, a smaller capacity and an expensive purchase price (Sheth et al., 2019; Kumar and Alok, 2020). The smaller capacity results in less products that fit into a vehicle, so more vehicles are needed, or vehicles need to perform more rides. To compensate for the extra rides, the distance for an electric truck can be shortened by locating a small storage facility at the edge of the city center. Such a storage facility is called a city hub (Charisis et al., 2020). In this way, companies can bring all products to this storage facility with big, non-electric trucks, and electric trucks only need to drive between the city hub and the customers in the city center, which involves smaller distances. Thus, using a city hub may possibly increase performance of city logistics, by lowering distances or decreasing the number of vehicles needed, which is beneficial for food distribution companies. It may eventually provide the opportunity for companies to work together and create shared transport or storage, which is why this thesis links to the “Shared connectivity in Mobility and Logistics Enable Sustainability” project (Steeman et al., 2019).
5 example, frozen, cooled and non-cooled (Ostermeier and Hübner, 2018). Food distributors can use compartments in vehicles which can be equipped with different temperature conditions. The use of compartments in vehicles can be beneficial for food distributors (Derigs et al., 2011), because of the following two reasons. First, a customer may require products of different segments which, with the use of compartments, can be delivered in once. Second, hotels and restaurants in a city center require frequent deliveries of rather small quantities (Fancello, Paddeu and Fadda, 2017). When a separate vehicle is used for every product segment, there may not be enough products to fill the different trucks, leading to a small vehicle capacity utilization.
In order to optimize deliveries into the city center, a vehicle routing model can be used. Vehicle routing models determine the optimal routes of vehicles considering relevant constraints, such as compartment capacities. When a city hub is included in such a model, it becomes a “two-echelon vehicle routing problem” which splits the distribution into two steps: from a distribution center or warehouse to a city hub, and from the city hub to the final customer (Anderluh et al., 2019). Models for those routing problems are widely available (Anderluh, Hemmelmayr and Nolz, 2017; Anderluh
et al., 2019; Nolz et al., 2020), however, none of them include the perishability of products which is
an important element of food distribution in city logistics. Perishable products require different storage conditions during distribution, which is why compartments in vehicles are used.
Compartments can be incorporated into a model by adding capacity constraints for the different compartments, which is captured in other vehicle routing models (Derigs et al., 2011; Musavi and Bozorgi-Amiri, 2017; Wang et al., 2021), but the combination with a city hub is not found in literature yet. Combing these elements in a vehicle routing model provides the opportunity to investigate if a city hub improves performance for food distributors in the city center.
For investigating whether or not a city hub at the edge of the city center is useful, the research question is as follows:
“What are the effects on distance traveled when using a city hub for food distribution in order to obey the requirement of zero-emission vehicles in the city center?”
6 who distributes food products in the Netherlands and involves deliveries to customers of Bidfood in the city center of Groningen.
This thesis has some key contributions. Firstly, it extends an existing mathematical model to represent the real-life situation in the best way possible. The combination of elements of the research setting consisting of the use of a city hub, perishability of products and multi-compartment vehicles, has not been studied before. Secondly, results can be used for further research into city hubs and electric vehicles. And lastly, companies can use the results as they show the effects, measured as distance traveled, of using a city hub when obeying the new regulations in practice. With these results, Bidfood can decide on whether or not to implement a city hub for their
distribution process and where they should pay attention to regarding the location and customers. The rest of the thesis is structured as follows. Section 2 contains the theoretical background of the study which entails a review of literature and concepts that are relevant for this research. Section 3 comprises the methodology that is used for answering the research question, including a
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2. Theoretical background
This section provides the background for understanding the research topic and its importance. First, there is a discussion about city logistics with the use of definitions, problems to be addressed and possible solutions to those problems. This emphasizes the relevance of this study. Next, existing mathematical models for vehicle routing problems are elaborated upon and compared to each other, focusing on their relevance for this study, which shows the lack of availability of a suitable mathematical model.
2.1 City logistics
City logistics can be defined as transporting goods in urban areas in an effective and efficient way, whereby considering and minimizing the negative effects on the environment, congestion and safety (Savelsbergh and Van Woensel, 2016). There are other definitions for city logistics, for example Taniguchi (2014) who states that it contributes to a balance of economic vitality and an improved environment in the urban area. Yet this research focuses on the company perspective, so the definition by Savelsbergh & Van Woensel (2016) is more suitable. City logistics is sometimes also called city distribution, urban logistics or last mile logistics (Taniguchi, 2014). The latter can also comprise logistics in non-urban areas, however, for the purpose of this research the last mile is in the city center which is an urban area.
Although city logistics is important for the economic development of cities, it is causing much congestion and air pollution (Lindawati et al., 2014). The rise in awareness and importance of sustainability forces companies to find solutions with the least negative environmental impact (Savelsbergh and Van Woensel, 2016). Especially the transportation sector is responsible for much air pollution, mainly in urban areas (Kumar and Alok, 2020). Those emissions can be effectively reduced by selecting the best transportation mode, making good routing decisions, consolidating transports and effective selection of storage locations (Das and Jharkharia, 2018). However, transportation mode choices in the urban areas are not that diverse, because city centers are only accessible by road (Kumar and Alok, 2020). When considering the new regulation that main city centers have to become zero-emission zones (Climate Agreement, 2019), the choice of
transportation modes in the city center is even limited to electric vehicles, such as an electric truck or cargo bike.
8 governmental regulations, but there are lots of barriers in using an electric vehicle. For example, electric vehicles have a limited radius and need to be charged regularly (Breunig et al., 2019). They often have a smaller capacity, especially when considering cargo bikes (Sheth et al., 2019), which increases the number of movements of vehicles. Moreover, the cost of acquiring such vehicles are high (Kumar and Alok, 2020). Due to the new regulation, companies are forced to use electric vehicles in city centers, but they can still use non-electric vehicles outside urban areas. In this way, there needs to be a storage location just outside the city center to which non-electric trucks can bring the products and from where on an electric vehicle can start driving. Such a small sized storage facility, also called a city hub, can be the solution to this problem (Charisis et al., 2020) as it shortens the distance to be covered by electric vehicles. That is why a city hub is a promising solution for companies that need to obey the new regulation in city centers.
City logistics regarding parcel deliveries is studied extensively in literature, however, food delivery is at least as important and lacking attention. More than half of the world’s population is living in cities (Schliwa et al., 2015) and in order to supply those city residents with food products, it is important to focus on perishable products in the field of city logistics (Lindawati et al., 2014). Perishable products have a limited shelf life and require a different focus while shipping to ensure product quality (Musavi and Bozorgi-Amiri, 2017). They can be divided into different product segments requiring a specific storage condition, namely frozen, cooled and non-cooled (Ostermeier and Hübner, 2018). Distributors of perishable food products have to pay attention to the storage conditions in order to preserve the quality of products, which requires temperature control facilities in vehicles. As hotels and restaurants in city centers require frequent deliveries of small quantities consisting of different product categories (Fancello, Paddeu and Fadda, 2017), this leads to many trucks driving through the city center when different vehicles are used for the different product categories. Therefore, the use of multi-compartment vehicles can be beneficial for those companies (Derigs et al., 2011), and also lead to less visits to customers, less vehicles in the city center and consequently, less traffic
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2.2 Existing mathematical models
The research question implies the use of a mathematical model to find vehicle routes. To gain a better understanding of already existing models and their limitations, this section discusses relevant models.
Perishable products require a time-related or storage requirement constraint to ensure product quality (Musavi and Bozorgi-Amiri, 2017). A time-related aspect can be captured in a model by adding a constraint that forces products to be delivered within a specified time. When a product requires a specific storage requirement, for example refrigeration, this is incorporated by using specific vehicles, as executed by Wang et al. (2021). They use a temperature control constraint, which leads to resource sharing of different logistic partners in the transportation phase so they can combine deliveries that require the same temperature while shipping. However, the model of Wang
et al. (2021) assumes there are different vehicles for the different temperatures, while the use of
multi-compartment vehicles is beneficial for companies delivering food products to the city center. This is discussed in the next paragraph.
There exist several models capturing “vehicle routing problems with compartments”, both for fixed compartment sizes (Derigs et al., 2011; Kabcome and Mouktonglang, 2015) and for flexible
compartment sizes (Henke, Speranza and Wäscher, 2015). As it is assumed that compartments for perishable products are fixed, that is where the focus is on. Derigs et al. (2011) consider an inhomogeneous product fleet that is delivered with a vehicle with several fixed compartments. Incorporating compartments into a model involves the addition of several capacity constraints, so there is one for every compartment in every vehicle. Kabcome & Mouktonglang (2015) also include multiple trips and a time window besides the multiple compartments aspect. Multiple trips can be integrated by adding more vehicles and creating constraints that only allow one vehicle to start after the previous has finished. Adding time windows involves creating constraints that force the delivery to be performed within a strict timespan. Both models focus on a delivery direclty from the
warehouse to the customer. They include valuable information regarding how to include
compartments, yet they lack the use of a city hub. As this is important for this research, the next paragraph sheds a light on two-echelon models.
10 second echelon after they are distributed in the first echelon and available at the city hub. The model by Nolz et al. (2020) is very useful for this thesis as non-electric trucks can perform the first echelon, and electric vehicles can perform the second echelon. A downside of this model is its focus on parcel deliveries, because the focus of this thesis is on food products requiring different storage conditions during shipment. Perishability of products is included in the research of Rohmer, Claassen, and Laporte (2019), who present a two-echelon inventory-routing problem. Such an inventory-routing problem focuses on holding inventory at the storage location in between the two echelons and accounting for the quality deterioration of products during storage. This is
incorporated into the model by incurring inventory holding costs and minimizing the time of storage, which highlights the differences with a vehicle routing problem. However, for this research setting, products are assumed to be of acceptable quality when leaving the company facility, and a time window for delivery to customers is used which forces same day delivery. This makes the inventory routing aspect and focus on inventory holding costs not necessary for the model to be constructed. Within a few years, the transportation to customers in the city center in the Netherlands is limited to electric vehicles. In mathematical models, different vehicle types can be implemented through differentiating in capacity and driving range constraints. Breunig et al. (2019) focus on the driving range constraints of electric vehicles for the two-echelon vehicle routing problem. Nevertheless, for the sake of this research, it is assumed the driving range is not a limiting factor, because electric vehicles do not have to cover large distances as they operate in the inner-city center. Therefore, the discussion about different vehicle types is focused on the capacity aspect. The capacity of electric trucks is higher than the capacity of cargo bikes, implying more vehicle movements when a cargo bike is used instead of a truck (Nolz et al., 2020). However, cargo bikes have less difficulty accessing small streets and parking in busy areas (Sheth et al., 2019), which is beneficial for the city center. There are several researchers that include cargo bikes in their models (Anderluh, Hemmelmayr and Nolz, 2017; Enthoven et al., 2020), but they can easily be implemented into any model by adjusting the capacity of the vehicle to the capacity of cargo bikes. This also implies that including electric vehicles in this thesis is not limiting, as the model can include any vehicle type by adjusting its capacity. A model can even include a vehicle fleet consisting of different vehicle types by having different vehicle capacities.
11 temperature storage conditions need multi-compartment vehicles as this positively affect vehicle capacity utilization and traffic congestion. The focus of this study can be summarized as the combination of a two-echelon vehicle routing problem with a storage location, and the use of multiple compartments to account for the temperature control constraints of perishable products. Besides, some less crucial, yet important elements of the research setting are the time window for delivery, the possibility of performing multiple trips, and a heterogeneous fleet. All relevant models discussed in this chapter include one or more of those elements but fall short on at least one other essential element. The most relevant studies are shown in Table 1 which displays the different features of the studies. The research contribution is to fill this gap in literature by providing a mathematical model including a city hub, electric vehicles for delivering the second echelon, service time windows, perishable products, and fixed compartment sizes with different temperature conditions. The next chapter gives this mathematical model.
Research Routing type
Multi-echelon
City hub
Multi-compartment Multiple trips Service time windows Fleet Derigs et al. (2011) Vehicle routing ✓ Heterogeneous Kabcome et al. (2015) Vehicle routing ✓ ✓ ✓ Heterogeneous Anderluh et al. (2017) Vehicle routing ✓ Homogeneous Rohmer et al. (2019) Inventory routing ✓ ✓ Heterogeneous Nolz et al. (2020) Vehicle routing ✓ ✓ ✓ ✓ Homogeneous Current study Vehicle routing ✓ ✓ ✓ ✓ ✓ Heterogenous
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3. Methodology
In this chapter, the methodology of performing the research is described. First, the research design is explained which forms the basis for the model to be developed. The model’s assumptions are listed in the second section. The next section presents the problem description, for which an
optimization model is provided in the subsequent section. Further, the data used as the model input is described and limitations of this data are discussed. Lastly, the solution method is given, and its procedure is explained.
3.1 Research design
The goal of this research is to measure the effect in terms of travel distance when using a city hub. As this requires measurements of various elements, for example distances and amount of trucks, a quantitative model is needed (McCusker and Gunaydin, 2015). More specifically, a mathematical model should be build that represents this real life situation as accurately as possible by using mathematical formulations like parameters, constraints, and decision variables (Weare, 1982). This research is based on deductive thinking, as the mathematical model is based on proven theories and it provides conclusions that are only applicable when considering the specific characteristics of the model and the research setting the model is constructed for (Ormerod, 2010).
The model of Nolz et al. (2020) forms a basis for this study, and is extended to account for perishable products and multiple-compartment vehicles. These extensions are specified in Section 3.4. This model with its extensions is suitable to find the effects in terms of distance traveled when using a city hub, by determining vehicle routes for the scenarios with and without a city hub. It adequately reflects the real-life situation by incorporating the important elements, which are the two-echelon distribution in the city hub scenario, multi-compartment vehicles for perishable products, time windows for customers and the use of electric vehicles in the city center. These elements and their importance are explained in the previous section.
3.2 Model assumptions
13 Table 2 gives the assumptions made for developing the model and the research setting.
• There is only one truck available for the first echelon distribution.
• Vehicles for the second echelon are assumed to be available in the quantity needed. • Every customer is served in a single visit, so split deliveries are not allowed.
• Compartments in the vehicles are fixed in size and quantity: two compartments per vehicle.
• Vehicles start and end at the same place, which is the company facility location for the first echelon and the city hub for the second echelon.
• Products are always available at the company facility location.
• Loading and unloading times at the company facility and the city hub are neglected. The (un)loading times at the customers are covered in the service time of delivering to a customer.
• Distances are fixed: the locations of the company facility, city hub and customers are known and fixed.
• Enough employees are available to drive the vehicles.
• The way a vehicle is loaded (i.e., which products are in the back/front of the vehicle) is ignored, as it is not considered to be important for the sake of this research.
• Deterioration of the perishable products is ignored, as products are delivered the day they were picked up from the depot. The products are assumed to be of acceptable quality when leaving the depot.
• Charging breaks do not influence the model as there are charging stations at the city hub and the distances electric vehicles have to cover in the city center are small.
Table 2: Assumptions for developing the model and research setting.
3.3 Problem definition
The problem for optimizing vehicle routes is called the Two-Echelon Vehicle Routing Problem with Compartment Constraints (TEVRP-CC). It consists of a two-echelon distribution scheme with a single truck operating on the first echelon, conducting several trips from the depot to the city hub without visiting customers, and a fleet of electric vehicles operating on the second echelon performing trips from the city hub to the customers. The TEVRP-CC is defined on two complete directed graphs 𝐺1 and 𝐺2. For first level distribution, graph 𝐺1 is introduced: 𝐺1 = (𝑉1, 𝐴1). The set of vertices 𝑉1 of
14 level distribution is 𝐺2 = (𝑉2, 𝐴2), whereof the vertices 𝑉2 contain the city hub (𝑆) and the set of
customers (𝑁): 𝑉2= {𝐻} ∪ 𝑁.
The time horizon defines the working day, starting at 𝐸 and ending at 𝐿: [𝐸, 𝐿]. During this time window, the distribution needs to be performed. Each customer has its own time window during which deliveries can take place: [𝐸𝑛, 𝐿𝑛]. This time window means the earliest time of service to
customer 𝑛 is 𝐸𝑛. When a vehicle arrives earlier, it has to wait until 𝐸𝑛 to start the service. The latest
time a vehicle can arrive at customer 𝑛 is 𝐿𝑛. As vehicles have different compartments, each
customer 𝑛 requests 𝑄𝑛,𝑐 products transported in compartment 𝑐. When a vehicle travels arc (𝑖, 𝑗),
it induces a travel time of 𝑇𝑖𝑗 and a distance of 𝐷𝑖𝑗. Moreover, each vertex 𝑖 in both graphs has a
corresponding service time 𝑆𝑖. As the service time of the depot and the city hub are neglected, those
are equal to 0, but the service time of the customers is included in this parameter.
First-level distribution is organized with a single truck having different compartments of capacity 𝑄1𝑐. This truck starts at the depot at time 𝐸 and has to be back at the depot at time 𝐿. The vehicle
has to deliver all goods ordered by customers (𝑁) to the city hub, possibly in multiple trips. So, the city hub can be visited multiple times by the truck. An order of a customer cannot be split and has to be delivered to the city hub in a single trip. Time to load and unload the vehicle are neglected. Second-level distribution is organized with multiple electric vehicles: fleet 𝐿2. Each vehicle has
different compartments with capacity 𝑄2𝑐. The second-level vehicles start and return at the city hub.
Within the time window [𝐸, 𝐿] they serve all customers in 𝑁 without split deliveries in multiple trips. The goods that are delivered to customers from the city hub are only available when the first level truck has brought them to the city hub. This implies synchronization between the first level vehicle and the second level vehicle fleet (𝐿2). Moreover, the city hub is split into different compartments,
each having its own capacity 𝑄𝑆𝐻,𝑐.
The following tables give an overview of the sets, parameters (Table 3) and decision variables (Table 4) used in the model.
Sets
𝑉1 Set of vertices in graph G1: 𝑉1= {0, 𝑆𝐻}
𝑉2 Set of vertices in graph G2: 𝑉2= {𝑆𝐻} ∪ 𝑁
𝑁 Set of customers
𝐴1 Set of arcs in graph G1
15 𝐿2 Set of second level vehicles
𝜋1 Set of first level trips: 𝜋1= {1, … , |𝜋1|}
𝜋2 Set of second level trips: 𝜋2= {|𝜋1| + 1, … , |𝜋1| + |𝜋2|}
𝑇 Set of time periods 𝑇 = {𝐸, … , 𝐿}
𝐻 Set of copies of the city hub in a first level trip 𝑠ℎ ∈ 𝐻 𝑉̃1 Vertex set for the first level with city hub duplications
𝐴̃1 Arc set for the first level with city hub duplications
𝐶 Set of compartments
Parameters
𝑇𝑖𝑗 Time of traveling on arc (𝑖, 𝑗)
𝐷𝑖𝑗 Distance of arc (𝑖, 𝑗)
𝑆𝑖 Service time of vertex 𝑖 ∈ 𝑉1∪ 𝑉2
𝑄𝑛,𝑐 Quantity ordered by customer 𝑛 ∪ 𝑁 that is stored in compartment 𝑐 ∪ 𝐶
𝑄1𝑐 Capacity of compartment c in the first level vehicle
𝑄2𝑐 Capacity of compartment c in the second level vehicles
𝑄𝑆𝐻,𝑐 Capacity of compartment c in the city hub
[𝐸𝑛, 𝐿𝑛] Time window of customer 𝑛 ∪ 𝑁
𝐸 Start time of delivery
𝐿 End time of delivery
𝑀 Very big value
Table 3: Sets and parameters.
16 𝜎𝑡𝑘 = { 1, 𝑖𝑓 𝑠𝑒𝑐𝑜𝑛𝑑 𝑙𝑒𝑣𝑒𝑙 𝑡𝑟𝑖𝑝 𝑘 𝑠𝑡𝑎𝑟𝑡𝑠 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝛼𝑛,𝑡𝑘,𝑠ℎ = { 1, 𝑖𝑓 (𝑓𝑖𝑟𝑠𝑡 𝑙𝑒𝑣𝑒𝑙) 𝑡𝑟𝑖𝑝 𝑘 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑠 𝑔𝑜𝑜𝑑𝑠 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 𝑛 𝑡𝑜 𝑐𝑖𝑡𝑦 ℎ𝑢𝑏 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝛿𝑛,𝑡𝑘 = { 1, 𝑖𝑓 𝑡𝑟𝑖𝑝 𝑘 𝑣𝑖𝑠𝑖𝑡𝑠 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 𝑛 𝑎𝑛𝑑 𝑠𝑡𝑎𝑟𝑡𝑠 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡 (𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑐𝑖𝑡𝑦 ℎ𝑢𝑏) 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝜔𝑘𝑘′ = { 1, 𝑖𝑓 𝑡𝑟𝑖𝑝 𝑘 𝑖𝑠 𝑓𝑜𝑙𝑙𝑜𝑤𝑒𝑑 𝑏𝑦 𝑡𝑟𝑖𝑝 𝑘′ 𝑜𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 (𝑠𝑒𝑐𝑜𝑛𝑑 𝑙𝑒𝑣𝑒𝑙) 𝑣𝑒ℎ𝑖𝑐𝑙𝑒 0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝑡𝑖𝑘 Time at which trip 𝑘 visits vertex 𝑖 (if present in the trip)
𝑡𝑓𝑘 Time at which trip 𝑘 is finished
𝑙𝑡,𝑐 Stock level at the city hub at time 𝑡 in compartment 𝑐
Table 4: Decision variables.
3.4 Optimization model
The Two-Echelon Vehicle Routing Problem with Compartment Constraints model is described with a mixed-integer linear programming formulation for which the sets, parameters and decision variables from the previous section are used. The model by Nolz et al. (2020) covers a few important
characteristics of the research setting: the two steps in the distribution process separated with a city hub, service time restrictions and capacity restriction to the vehicles. The model that is developed for this research is an extension of the model by Nolz et al. (2020). The following adaptions are made:
1. Nolz et al. (2020) include customers in the first echelon, however there are no customers in the first echelon in this research setting. Thus, the first echelon is simplified by excluding customers.
2. Extra capacity restrictions are required as the vehicles capacity is split in 2 compartments: fresh and frozen. This requires adding several constraints to the model.
3. The city hub also needs extra capacity restrictions related to the different compartments, which requires some extra constraints.
17 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 ∑ ∑ 𝐷𝑖𝑗× 𝑥𝑖𝑗𝑘 𝑘 (𝑖,𝑗)∪𝐴1 + ∑ ∑ 𝐷𝑖𝑗× 𝑥𝑖𝑗𝑘 𝑘 (𝑖,𝑗)∪𝐴2 (1) subject to:
First level constraints
∑ ∑ 𝑦𝑛𝑘,𝑠ℎ 𝑠ℎ∈𝐻 = 1 𝑘∈𝜋1 (𝑛 ∈ 𝑁) (2) ∑ 𝑦𝑛𝑘,𝑠ℎ ≤ |𝑁| × 𝑧𝐻𝑠ℎ 𝑘 𝑛∈𝑁 (𝑘 ∈ 𝜋1, 𝑠ℎ ∈ 𝐻) (3) ∑ 𝑥𝑗𝑖𝑘 𝑗∈𝑉1\{𝑖} = ∑ 𝑥𝑖𝑗𝑘 𝑗∈𝑉1\{𝑖} = 𝑧𝑖𝑘 (𝑖 ∈ 𝑉1, 𝑘 ∈ 𝜋1) (4) ∑ ∑ 𝑄𝑛,𝑐× 𝑦𝑛𝑘,𝑠ℎ 𝑠ℎ∈𝐻 ≤ 𝑄1,𝑐 𝑛∈𝑁 (𝑘 ∈ 𝜋1, 𝑐 ∈ 𝐶) (5) 𝑡𝑖𝑘+ 𝑆𝑖+ 𝑇𝑖𝑗≤ 𝑡𝑗𝑘+ 𝑀 × (1 − 𝑥𝑖𝑗𝑘) ((𝑖, 𝑗) ∈ 𝐴1: 𝑗 ≠ 0, 𝑘 ∈ 𝜋1) (6) 𝑡𝑖𝑘+ 𝑆𝑖+ 𝑇𝑖0≤ 𝑡𝑓𝑘+ 𝑀 × (1 − 𝑥𝑖0𝑘) (𝑖 ∈ 𝑉1{0}, 𝑘 ∈ 𝜋1) (7) 𝑡0𝑘≤ 𝑡𝑓𝑘 ≤ 𝑡0𝑘+1 (𝑘 ∈ {1, … , |𝜋1| − 1}) (8) 𝐸 ≤ 𝑡01 (9) 𝑡𝑓|𝜋1|≤ 𝐿 (10)
Second level constraints
18 ∑ 𝑄𝑛,𝑐× 𝑧𝑖𝑘 𝑛∈𝑁 ≤ 𝑄2,𝑐 (𝑘 ∈ 𝜋2, 𝑐 ∈ 𝐶) (13) 𝑡𝑖𝑘+ 𝑆𝑖+ 𝑇𝑖𝑗≤ 𝑡𝑗𝑘+ 𝑀 × (1 − 𝑥𝑖𝑗𝑘) ((𝑖, 𝑗) ∈ 𝐴2: 𝑗 ≠ 𝐻, 𝑘 ∈ 𝜋2) (14) 𝑡𝑖𝑘+ 𝑆𝑖+ 𝑇𝑖𝐻≤ 𝑡𝑓𝑘+ 𝑀 × (1 − 𝑥𝑖𝐻𝑘 ) (𝑖 ∈ 𝑉2{𝐻}, 𝑘 ∈ 𝜋2) (15) 𝐸𝑛× 𝑧𝑖𝑘 ≤ 𝑡𝑖𝑘 ≤ 𝐿𝑛× 𝑧𝑖𝑘 (𝑛 ∈ 𝑉2\{𝐻}, 𝑘 ∈ 𝜋2) (16) 𝑡𝑓𝑘≤ 𝐿 (𝑘 ∈ 𝜋2) (17) 𝑡𝑓𝑘≤ 𝑡𝐻𝑘 ′ + 𝑀 × (1 − 𝜔𝑘𝑘′) (𝑘 ∈ 𝜋2, 𝑘′∈ 𝜋2∶ 𝑘 < 𝑘′) (18) |𝜋2| − ∑ ∑ 𝜔𝑘𝑘′ 𝑘′∈𝜋 2,𝑘<𝑘′ 𝑘∈𝜋2 ≤ |𝐿2| (19) ∑ 𝜔𝑘𝑘′ 𝑘∈𝜋2,𝑘<𝑘′ ≤ 1 (𝑘′ ∈ 𝜋 2) (20) ∑ 𝜔𝑘′𝑘 𝑘∈𝜋2,𝑘′<𝑘 ≤ 1 (𝑘′∈ 𝜋 2) (21) Synchronization constraints 𝑡𝐻𝑘𝑠ℎ ≤ 𝑡𝐻𝑘 ′ + 𝑀 × (2 − 𝑦𝑛𝑘,𝑠ℎ− 𝑧𝑖𝑘 ′ ) (𝑘 ∈ 𝜋1, 𝑠ℎ ∈ 𝐻, 𝑘′∈ 𝜋2, 𝑛 ∈ 𝑁) (22)
Hub capacity management
20 𝛾𝑡𝑘,𝑠ℎ∈ {0,1} (𝑘 ∈ 𝜋1, 𝑠ℎ ∈ 𝐻, 𝑡 ∈ 𝑇) (44) 𝜎𝑡𝑘 ∈ {0,1} (𝑘 ∈ 𝜋2, 𝑡 ∈ 𝑇) (45) 𝛼𝑛,𝑡𝑘,𝑠ℎ ∈ {0,1} (𝑛 ∈ 𝑁, 𝑘 ∈ 𝜋1, 𝑠ℎ ∈ 𝐻, 𝑡 ∈ 𝑇) (46) 𝛿𝑛,𝑡𝑘 ∈ {0,1} (𝑛 ∈ 𝑁, 𝑘 ∈ 𝜋2, 𝑡 ∈ 𝑇) (47) 𝑙𝑡 ≥ 0 (𝑡 ∈ 𝑇) (48)
The objective function (1) aims at minimizing total travel distances of the first and second echelon. The formulation of the constraints is largely based on the formulation by Nolz et al. (2020); any changes are explicitly stated at the description of the corresponding constraint. The first level distribution is captured in constraints (2) – (10). A few constraints for the first level distribution are excluded as they incurred serving customers in the first echelon, which is not included in this study. Constraints (2) ensure that the goods requested by every customer are loaded in exactly one trip to the city hub. Constraints (3) ensure that all requested goods are unloaded at the city hub.
Constraints (4) ensure that the arc is visited when the vertex is present in a trip which conserves the flow in the model. Constraints (5) capture the capacity limitations of the vehicle compartments, whereof the compartment aspect is added to the model of Nolz et al. (2020). Time variables are evaluated in constraints (6) and (7). They ensure the arrival of a trip being later than the sum of the departure, service, and travel time. Moreover, constraints (8) ensure that a next trip can only be started after the previous trip is finished, because there is only one vehicle in the first echelon. Constraints (9) and (10) capture the time windows constraints of the working day.
21 The synchronization constraints (22) ensure that a second level trip to a customer can only start after the goods for the customer are delivered to the city hub.
Constraints (23) – (33) ensure the capacity limitations of the city hub and its compartments. First, arrival and departure times at the city hub are fixed in constraints (23) – (25). Constraints (26) ensure all second level trips to departure from the city hub. Constraints (27) and (28) enforce a trip to visit the city hub when it delivers goods to the city hub. Similar, constraints (29) and (30) enforce a trip to leave from the city hub when it visits a customer. Constraints (31) – (33) manage the
inventory at the city hub whereby extra constraints were added to ensure the capacity restriction of the different compartments. Constraints (31) ensure the city hub compartments are empty at the start of the working day. Constraints (32) are the standard inventory balance constraints which updates the inventory level with the deliveries and pick-ups. The capacity of the compartments is limited with the use of constraints (33).
Constraints (34) – (48) define the decision variables that were explained in Table 4.
3.5 Data
The focus of this thesis is to investigate the effects of using a city hub for food distribution in the city center, so the scenarios with and without a city hub should be evaluated. This involves determining vehicle routes for those scenarios which requires several input data. This data is provided by the company Bidfood. The data is anonymized and comprises customers in the city center of Groningen. Vehicle routes consist of a starting point, visiting customers and going back to the starting point. For this, demand and service times of customers, locations of customers, Bidfood and the city hub, as well as the vehicle compartment capacities and vehicle speed are needed.
22 Distances are calculated using a tool provided by Bing Maps. After inserting addresses, the tool calculates the distances between two points as the lowest possible distance. A distance matrix was constructed for both scenarios: from Bidfood to the customers, and from the city hub to the customers. Travel times are calculated using an average travel speed. The speed in the city center was fixed to 15 km/h, based on research in Amsterdam (Grooten and Kuik, 2010). Outside the city center, the travel speed was fixed to 45 km/h, which is a little slower than the maximum allowable speed in that area, i.e., 50 km/h. So, travel times only depend on the distance that is covered and whether this occurs inside or outside the city center.
Although the input data is stochastic, meaning there is some unpredictability involved (Weare, 1982), it is modeled as deterministic. A deterministic model assumes to be completely based on previous behavior without any randomness (Weare, 1982). In this research, different input data is treated as deterministic, namely service time of customers, demand of customers and travel time. The service time of customers is modeled as an average of the service time of previous deliveries to the specific customer. Equivalent to this, demand of a customer is modeled as an average of
previous deliveries. In practice, customers may order a different number of products every time and service time may vary due to different ordering amount or whether the customer is present during the delivery. In the model, travel times are calculated using an average travel speed and the distance between two locations, whereas in practice, travel times may differ from this average due to traffic jams or road constructions. To obtain as reliable data as possible for the demand and service time, data over the period of half a year is used. This involves data from week 43 in 2019 till week 9 in 2020. More data was available, but experts from Bidfood said the data after week 9 in 2020 was not representative for their normal business practices due to the worldwide pandemic, i.e., Covid19. Also, it is past data, so it reflects the actual movements in the best way possible. Still, using
stochastic input data can result in different outcomes, because variation in demand and randomness are not included. Nevertheless, to compare both scenarios, the same input data is used, making the randomness affect both scenarios. As the goal of this thesis is to evaluate the effect of a city hub and not necessarily giving advice on specific routes, a deterministic model is expected to give a good indication about this effect.
23
3.6 Solution method
An optimization of the mathematical model developed in Section 3.4 might not be solved to optimality for a large number of customers, due to the increasing computational complexity. Therefore, a heuristic method was used to find near-to-optimal solutions. When deciding upon which heuristic to use, there is a trade-off between the quality of the solution and the running time (Bräysy and Gendreau, 2005). For vehicle routing problems as considered in this research, the guided local search heuristic is known to obtain good results in a reasonable amount of time
(Vansteenwegen et al., 2009). It is an improved heuristic compared to the general local search heuristics, to avoid it from getting ‘stuck’ in a local optima when searching for the optimal solution (Ruiz, 2018).
For the sake of this thesis, the solution method is developed using the packages of Google OR-Tools (Google Developers, 2020) and solved with the guided local search heuristic that is included in these packages. The idea behind this Google OR-Tools method is as follows. The heuristic finds a starting point, also called “first path”, which is the cheapest route. For this thesis, the cheapest route is the route with the least distance, as distances are minimized. From this first customer to visit, the method tries to find the cheapest route to the next customer. It tries to add the customer with the least distance from the first customer and checks if all constraints are satisfied. If not, the next best customer is added, and so on. A few constraints had to be developed, but most of them were captured in the different packages available by Google OR-Tools. The next part of this section outlines the elements of the solution method including the constraints.
The packages for capacity constraints and time window constraints are combined, as those elements are both important for this thesis. Capacity constraints are captured by a maximum capacity for every vehicle and the demand of customers. The solution method contains a callback to check whether adding a customers’ demand to a vehicle still fits into the corresponding vehicle when it wants to add this customer to the route. Time window constraints are included into the solution method by a time window for every customer and a time for traveling between locations. This time includes the travel time between the two locations, and the service time of the location that is left. The callback for time windows forces the heuristic to check the earliest and latest time a customer can be visited when it wants to add a customer to the route. So, it sets a range in which the
24 routing problem, yet Google OR-Tools does not allow this. The solution for including a city hub is splitting the distribution into two parts: from the depot to the city hub and from the city hub to the customers. The two parts are treated separately, so an additional assumption needs to be made. It is assumed that the distribution from the depot to the city hub is finished before the distribution from the city hub to the customers starts. As the first part consists of a non-electric truck driving back and forth from Bidfood to the city hub in order to bring all products, this involves visiting a single
destination by multiple trips. Therefore, this is calculated by hand. The second part of the
distribution involves multiple vehicles visiting all customer in the city center, which is solved by the solution method described. In this way, no additions to the solution method need to be made to include the city hub.
Including the use of compartments in vehicles into the solution method involves adding extra capacity restrictions. Currently, the capacity constraint involves a single capacity limit for every vehicle. With the use of compartments, there needs to be a single capacity constraint for every compartment, which is two in this research. Moreover, the customers’ demand needs to be split by compartment, resulting in two demands for every customer. So, when a customer is going to be added to a route, two capacity restrictions should be evaluated. Therefore, there are two callbacks induced when adding a customer, checking both compartments’ capacity with the demand of the customer. To ensure all products of one customer are transported into one vehicle, both capacity checks should be satisfied before adding a customer.
The solution method assumes that each route is performed by one vehicle and it does not consider one vehicle consecutively traversing multiple routes. There is no limitation on the number of vehicles that the solution method can use, because the focus is to find the routes with the least distance and when limiting the number of vehicles, routes may become different. An addition made to the solution method ensures that the starting time of a new route is compared to the ending times of previously used vehicles, so that the same vehicle can be used for the new route if possible. In this way, as few vehicles as possible are used without limiting the solution method to a certain amount.
25 minutes. Therefore, all customers needed to be served between t=0 and t=720, whereby t is the time in minutes. The time windows for vehicles force the vehicle to be back at the starting point at the specified time, so a new ride can start. The solution method iterates over different time windows for the vehicles, in order to imitate the flexible time windows in practice. This iteration is given in Table 5 and involves time windows with the combination of every i and j in the ranges specified. The minimum time for a vehicle to visit one customer is 40 minutes, which includes the travel time to a customer, its service time, and the travel time back. The maximum is set to 100 minutes, because that was the maximum route length, due to the limited capacity of an electric vehicle. To prevent impossible time windows containing values larger than 720, a minimization function is included in the last few time windows.
For i in range(40, 100):
For j in range(40, 100):
Time window vehicles = (0, i), (i, i+j),
(i+j, i+2*j), (i+2*j, i+3*j), (i+3*j, i+4*j), (i+4*j, i+5*j),
(i+5*j, i+6*j), (i+6*j, min(720, i+7*j)),
(min(720, i+7*j), min(720, i+8*j)), (min(720, i+8*j), 720)
26
4. Results
This chapter gives the results from the experiments conducted. The first section outlines the different experiments performed of which the results can be found in the subsequent sections.
4.1 Experimental design
The experiments that are conducted can be divided into four different groups. In this section, the purpose of each group of experiments is explained, including the way data is used.
27
Figure 1: Customers with zip code 9712 and initial city hub location for experiments.
The customer base of zip code 9712 was selected based on their location close to the pilot of Bidfood. However, no attention was paid to the order quantities of those customers when selecting them. This could lead to an order quantity that is too much for one truck or too little for multiple trucks, resulting in a low vehicle utilization. The utilization is the rate to what extent a vehicle is filled, calculated by dividing the number of roll containers that are in the truck by the capacity of the truck. This utilization can also be calculated for a compartment in a vehicle, i.e., compartment utilization. It is interesting to investigate whether more customers can be served with the vehicles needed to serve the customers of zip code 9712. If extra customers can be served with the same number of vehicles, it might be beneficial because vehicle utilization increases. Therefore, the second group of experiments focuses on the capacity of the vehicles and adjusting the number of customers accordingly. The current customer base of zip code 9712 was the starting point.
Customers were manually added to this base when the capacity of the trucks permitted this. In case there was unused capacity in the trucks, the customer of Bidfood with the lowest distance to the city hub was added. Then again, it was checked whether there was spare capacity, and a customer was added when possible. As soon as no customer could be added without exceeding the capacity, the procedure was stopped, and the customer base was formed. This was executed for every day of the week separately, and experiments were conducted with the corresponding customer base. The results of these experiments are in Section 4.3.
Order quantities of customers comprise of roll containers, because the separate products are loaded on roll containers for distribution. A certain number of containers can be placed into a truck,
28 can be unloaded and delivered. However, this is not necessarily the case in practice, because
customers order the products they need which may comprise part of a container. Therefore, companies can round up order quantities to simplify the distribution, leading to containers that are partly empty. The set of experiments of which the results are presented in Section 4.4, are about three different rounding scenarios. The first scenario is rounding order quantities up to an integer number. This means when a customer orders 2.40 containers, 3 containers are used for that customer. As one can imagine, this has a negative effect on the number of customers that can be served with a certain vehicle, because part of some containers may be empty. The second scenario concerns the current practice of Bidfood. They split roll containers in 3 or 4 parts which means products of multiple customers can be placed on one roll container. The following example shows how this works. When there are four customers requiring an amount in between 0.01 and 0.25 containers, those orders can be combined in 1 container, so the order quantity of the customers is rounded up to 0.25 container. The same holds for containers that are split in 3 parts, but then the order quantities are rounded up to 0.33 (i.e., ⅓) container. This practice increases the number of customers that can be served with a vehicle, but may also increase service times as containers need to be split for the different customers. The third scenario involves not rounding order quantities at all. This results in products of numerous customers being distributed on one container and may lead to larger service times due to splitting the roll container during deliveries. Although there might be an increase in service time when semi- or not rounding containers, this is not included in the experiments. The three scenarios described are compared to investigate the effect of rounding and possibilities for companies to improve their rounding practice.
The last group of experiments is focused on the location of the city hub. The initial location was based on an intended pilot study of Bidfood, yet they do not have a concrete location. It seemed of added value to consider different city hub location, in order to find possible reasons for a difference in performance between locations. The results are presented in Section 4.5.
4.2 City hub vs. no city hub
29 hub, those large distances are covered by the bigger non-electric trucks and electric trucks only perform the smaller distances in the city center, so the total distance decreases.
The total time also decreases when a city hub is used, with 10% on average (Table 12, Appendix A2). Total time comprises of the travel time and service time. The travel time is based on the distance covered and the travel speed, while the service time is based on customers served. For both scenarios, the service time is the same as the same customers are served. Therefore, it is more interesting to look at travel time, which decreases with 41% when using a city hub. The saving in travel time is larger than the saving in distance, because of the different travel speeds explained in Section 3.5. The distance to travel is based on the minimum distance between two points, so without a city hub, the trucks enter the city center at the side of Bidfood, which is the opposite side of the city hub and the customers. Then, a truck has to drive a larger distance in the city center with lower speed, which increases the travel time, leading to a bigger travel time decrease compared to the distance decrease.
The differences in demand on the days of the week influence the performance, especially when using a city hub. On Wednesday and Saturday, the demand of customers fits into one non-electric truck, whereas on the other days, demand exceeds the capacity of a non-electric truck, so two trucks are needed in the first echelon. This causes the distance of the first echelon on those days to be twice as high compared to Wednesday and Saturday. The distance in the second echelon depends on the number of customers, so the larger the number of customers, the larger the distance. The same holds for the total time, as its main element is the service time and for every customer a service time is induced.
This difference in performance between Wednesday/Saturday and the other days is also visible in the vehicle utilization. On the days that demand exceeds the capacity of a non-electric truck, the second truck is not filled at all, as demand is slightly above the capacity. This means that the
30 These experiments show that the change in the vehicle utilization mainly depends on whether or not the demand fits into the non-electric vehicle. This assumes that choosing customers only based on their geographical location, as is the case in these experiments, may not be beneficial for the vehicle utilization. Therefore, the second set of experiments (Section 4.3) investigates whether including some customers may be beneficial for companies due to an increased vehicle utilization.
When splitting the vehicle utilization in the utilization per compartment, there are some interesting insights. The utilization of the frozen compartment is on average 25% lower than the utilization of the fresh compartment, for both the electric and non-electric vehicle (Figure 8, Appendix A2). This assumes a company would benefit from a shift in compartment capacities: increasing the fresh compartment and simultaneously decreasing the frozen compartment size. A high utilization is beneficial for a company because vehicle space is used properly. However, the outcomes provide results based on averages, while in practice, uncertainty and variation in demand can lead to different outcomes as demand can be lower or higher than expected. This should be kept in mind when deciding upon changing the compartment capacities.
As electric vehicles are extremely expensive to acquire (Kumar and Alok, 2020), it is interesting to investigate the minimum number of electric trucks needed to serve all customers with a city hub. The heuristic finds near-to-optimal routes for serving all customers with an unlimited number of vehicles available, which results in the need for 3 electric vehicles on all days of the week. The heuristic can be forced to only use a limited number of vehicles and allow multiple trips with the same vehicles, of which the procedure is explained in Section 3.6.
First, the heuristic was limited to one electric vehicle, which resulted in a solution for Monday. For the other days, the heuristic gave a solution when using two electric vehicles. The downside of using fewer vehicles is an increase in distances and time, caused by the change in routes. Vehicles have to perform multiple rides which can only start after the previous ride is finished. In order to respect the time windows for delivery and the capacity restrictions of the vehicle, the sequence in which
31 time increase, and vehicle utilization decreases, needing fewer vehicle to serve the customers might be beneficial for a company, as they are expensive.
The main limitation for a company when trying to perform the routes with the least number of vehicles possible are the time windows of customers. Most time windows of customers only allow visits in the morning, making it impossible on most days to perform routes with one vehicle.
Therefore, a company can benefit from re-discussing the time windows with its customers and trying to create more flexible time windows.
4.3 Adding customers for vehicle utilization purposes
The focus of these experiments is on making better use of the vehicles initially needed by adding customers to the customer base. The experiments in Section 4.2 showed that a minimum of 2 non-electric and 2 non-electric vehicles are necessary to serve the customers for most days. Therefore, the scenarios are as follows:
Scenario 1: Original customer base (i.e., zip code 9712). Scenario 2: Adding customers to fill 2 non-electric trucks.
Scenario 3: Adding customers to fill 2 non-electric trucks but limited to 2 electric vehicles. Scenario 1, which comprises the customer base of the previous experiments, is compared to two different cases. The second scenario considers a customer base that fits into the 2 non-electric trucks which involves adding customers to fill these trucks. When solely focusing on filling the non-electric trucks, it is expected that more non-electric trucks are needed. That is why the third scenario involves adding customers to fill 2 non-electric trucks but limiting the number of electric trucks to 2. Figure 2 shows the number of customers served for the different scenarios. As expected, the
32
Figure 2: Number of customers that are served in the three different scenarios that consider adding customers to make better use of the vehicles.
Of course, total distance and time increase when adding customers. More interesting is the relative increase of distance and time. The experiments show that the average distance and time per
customer decreases when adding customers in both scenarios. The percentual changes are shown in Table 6. Scenario 2 performs best when looking at the number of customers served, but led to a minimal amount of 3 electric vehicles on every day of the week. Depending on the trade-off
between the number of electric vehicles to acquire and the increase in distance/time, both scenarios are beneficial for the company as average distance and time per customer decrease. As electric vehicles are expensive, it is expected that a company prefers scenario 3. However, when a company already has more electric vehicles or need more for other purposes, scenario 2 is beneficial. The vehicle utilization increases for both scenarios, whereby the increase for scenario 2 is larger.
Customer Distance Time Utilization
Scenario 1 -> 2 116% 95% 88% 26%
Scenario 1 -> 3 67% 53% 35% 13%
Table 6: Percentual changes in number of customers, distance, time, and utilization when comparing the different scenarios.
A sidenote for these experiments is that they are focused on filling vehicles and achieving a high vehicle utilization without paying attention to uncertainty in demand. Filling a truck and increasing vehicle utilization led to a better outcome for the experiments yet can lead to a worse outcome when there is variation in demand, for example when there is more demand than the average.
0 5 10 15 20 25 30 35 40 45
Monday Tuesday Wednesday Thursday Friday Saturday
N u m b er o f cu sto m ers
Adding customers
33 Companies can predict the variation in demand by looking at previous data and use this to
investigate a safe vehicle utilization. Such a safe vehicle utilization would be a utilization level up to which the vehicle can be filled with having enough spare capacity for the moments that demand is higher than expected. Of course, this never is an exact prediction, but it includes some demand variation and gives more realistic outcomes for practice.
In short, Bidfood can benefit from adding more customers to the customer base of zip code 9712. Then, they increase the number of customers that can be served with the same number of vehicles, decrease the average distance and time per customer, and increase vehicle utilization. However, they must pay attention to the uncertainty in demand which forces them to have spare capacity in the trucks. So, in practice, the improvements from adding customers are probably less compared to these results. As the previous experiments show that a company can benefit from a city hub, these experiments add that a company should focus on the geographical location of the customers, their demand and the vehicle utilization when deciding upon which customers to serve from the city hub.
4.4 Rounding scenarios
In these experiments, three different rounding scenarios for order quantities are investigated (Table 7).
Scenario Short explanation Numerical values Rounding Rounding roll containers up to
an integer number of containers.
Any integer: 1, 2, 3, 4, etc.
Semi-rounding Rounding roll containers up to ¼ or ⅓ of a container which is the current practice of Bidfood
0.25, 0.33, 0.5, 0.67, 0.75, 1, 1.25, 1.33, etc.
Not rounding Not rounding roll containers and using averages.
Any number with 2 decimals
Table 7: Rounding scenarios for order quantities, their explanations, and examples of corresponding numerical values.
34 with using one non-electric vehicle driving from Bidfood to the city hub (Figure 3). Obviously, more customers can be served when quantities are not rounded, as more products fit into the vehicle. Rounding up to whole containers has most impact on the number of customers served, because the difference between the actual order quantity and the rounded quantity can be high, whereas for semi-rounding, those differences are smaller.
Figure 3: Number of customers that are served with one non-electric vehicle for the different rounding scenarios.
Total distance and time are obviously higher when more customers are served (Figure 12&13, Appendix A4), because when a customer is added to a route, it involves a distance and time
increase. Distances in the city center are low, so only a small distance increase occurs when adding a customer, making the average distance per customer decrease. Time increases with both travel and service time. The main increase in time is caused by the service time, because for every customer a service time incurs. The service time comprises of the time to unload the truck and bring the products from the truck to the customer. In practice, service times may be higher for splitting containers in case of semi- or not rounding, but this is not included in these experiments.
Table 8 shows the percentual changes between the different scenarios. These show that when more customers are served, the time increases in proportion to the customer increase, whereas the distance increase is less. As more customers are being served with the same number of vehicles, a company may need less vehicles to serve all of their customers. Besides, there is a distance gain as the average distance per customer decreases. Improving from semi-rounding to not rounding does not seem to be worthwhile. However, these results strongly depend on the unrounded order
0 2 4 6 8 10 12 14 16 18 20
Monday Tuesday Wednesday Thursday Friday Saturday
N u m b er o f cu sto m ers
Rounding scenarios for order quantities
35 quantities which were mostly close to the semi-rounded values in the case of Bidfood. Other
companies may have customers that order only a few products, e.g. 0.05 roll container, and then, not rounding order quantities probably differs more in performance.
Customers Distance Time Rounding -> semi-rounding 55% 29% 55%
Semi-rounding -> not rounding 7% 6% 7%
Rounding -> not rounding 66% 38% 64%
Table 8: Percentual changes between the different rounding scenarios, for the number of customers served, distances and time.
A remark concerns the uncertainty in demand, as the vehicle is filled without paying attention to variation in demand. Although the number of customers to be served are lower when vehicles are filled to a certain percentage of their capacity, it is expected to get the same relative results as distance and time probably are lower as well. More research is needed to verify this assumption, and before implementing it in practice.
Summarizing, it does not seem to be worthwhile for Bidfood to consider not rounding order
quantities, as there is a small gain in the number of customers, but a possible service time increase. For companies suffering from extremely small order quantities, it may be worthwhile to consider not rounding. Also, companies currently rounding up to whole containers can benefit from considering another rounding practice as this improves performance in terms of the number of customers served and distance traveled.
4.5 Different city hub locations
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Figure 4: Possible city hub locations for the experiments in Section 4.5.
The experiments show that total distance and travel time differ between the different locations for the city hub, however, they all perform better than without a city hub. Table 9 gives an overview of the percentual changes in distance and travel time for every location, compared to not having a city hub.
Location 1 Location 2 Location 3 Location 4 Location 5 Distance -25.1% -19.3% -15.7% -24.9% -8.7%
Travel time -41% -39% -30% -33% -29%
Table 9: Percentual changes in distance and travel time when using the corresponding city hub locations compared to not using a city hub.
On average, distance and travel time decrease with 19% and 34%, respectively. This shows that a company may benefit from having a city hub, regardless of its location. Again, travel time decreases more due to differences in travel speed inside and outside the city center. Utilization does not change between the different locations, as the same customer base with constant demand is used and the same number of vehicles is needed.
37 part of the distance is caused by the number of customers to serve and their order quantities, because that is what differs between the days of the week. There is a clear pattern in the distances of the second echelon over the days of the week that follow the same pattern as customers to serve and their order quantities.
The larger the distance from the company to the city hub location, the larger the proportion is of the first echelon in the total distance. Locations 1 and 4 have the lowest distance to the company facility, and therefore also the lowest total distance when comparing all locations (Figure 5). So, it can be concluded that when choosing a location, the distance from the company facility to the city hub is more important than its location with respect to the customers. Of course, the city hub should also be located around the customer base and at the edge of the city center, because otherwise, the overall benefit from having a city hub is diminishing.
An unexpected result is the performance of not having a city hub on Friday, which is better than city hub locations 2, 3 and 5 (Figure 5). Although this slightly worse performance in distance is
compensated with the positive result on other days, there is no reason for this occurrence in the data. The only explanation is that the heuristic finds near-to-optimal solutions but can with some luck suddenly finds a better solution. Therefore, the relatively good performance of Friday without a city hub is probably caused by the heuristic and would not have occurred when optimal results were obtained. This highlights the fact that a heuristic does not always find the best solution, so for future work, it might be interesting to consider other heuristics or other research setting that provide the opportunity to solve a model to optimality.
Figure 5: Total distance for different city hub locations per day of the week.
0 10000 20000 30000 40000
Monday Tuesday Wednesday Thursday Friday Saturday
Dis ta n ce (m eters )
City hub locations
38 Currently, mobile city hubs are being developed and already used in some areas. A mobile hub can have a different location every day. Based on the previous experiments, there are two possibilities for an optimal mobile hub location set: minimizing distances and minimizing travel times. Figures 16&17 (Appendix A5) show the distance and travel time for the two mobile hubs.
Mobile hub one considers minimizing distances and leads to the following optimal locations: Location 1 on Monday, Tuesday, Wednesday and Saturday, and Location 4 on Thursday and Friday. The mobile hub performs better than no city hub, however, when the distances and time are compared to a fixed city hub at location 1, the differences are rather small. The distance to be traveled decreases with 1.38%, while the travel time increases with 2.12% on average.
Mobile hub two considers minimizing travel times and leads to Location 1 on Monday, Tuesday, Wednesday and Friday, and Location 2 on Thursday and Saturday. Of course, this mobile hub performs better than no hub. However, the additional benefit of having a mobile hub instead of a fixed hub at location 1 is small as well. While travel times are decreased with 0.74%, distances are increased with 1.12%.
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5. Conclusion
City logistics is a large cause of traffic congestion and air pollution, which is why city centers in the Netherlands have to become zero-emission zones, forcing companies to use electric vehicles for serving their customers in city centers. In order to cope with the downsides of electric vehicles, the use of a city hub seems promising. Besides being forced to reduce emissions, food distributors can reduce traffic congestion and make more efficient use of their vehicles by using compartments with different temperature control facilities. That is why the following research question was formulated:
“What are the effects on distance traveled when using a city hub for food distribution in order to obey the requirement of zero-emission vehicles in the city center?”. To answer this question, a
mixed-integer programming model has been developed and solved with the use of a guided local search heuristic.
The computational experiments showed that, for all days of the week, distances and travel times can be reduced by using a city hub. More specifically, the location of the city hub is not binding as all locations showed an improved performance in terms of distance and time. The locations are relatively close to the customers base at the edge of the city center; however, results show that the locations closest to the company facility perform best. This implies the largest proportion of distance is caused in the first echelon, i.e., from the company facility to the city hub. Further, when selecting the customers to be served from the city hub, not only the geographical location should be
considered. Vehicle utilization can easily be improved by adding customers to the customers base, which decreases average distance and time per customers and thus improves performance. So, when selecting a customer base to serve from a city hub, attention must be paid to the vehicle capacity and its utilization, as well as the location of the customers.
Besides the theoretical implications, this thesis offers some practical implications for Bidfood and other food distribution companies. It shows the benefits of using a city hub when companies are forced to use electric vehicles, whereby all locations considered showed improvements compared to not having a city hub. This means that even though there are restrictions with respect to the
