Collaboration in last mile food deliveries: a multi-compartment vehicle routing problem

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Collaboration in last mile food deliveries: a

multi-compartment vehicle routing

problem

Master’s thesis

MSc Technology and Operations Management

MSc Supply Chain Management

University of Groningen

Ilse Attema

s3000036

First supervisor: dr. I. Bakir

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Preface

This thesis has been written as part of the Shared connectivity in Mobility and Logistics Enable Sustainability (SMiLES) project.

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Abstract

This thesis discusses a multi-compartment vehicle routing problem with time windows and flexible compartment sizes (MCVRPTWFCS) under horizontal collaboration in the context of food deliveries. In this sector, customer orders typically consist of two different product types that have to be transported in different compartments in the same vehicle. Collaboration in last mile deliveries can reduce total travel distance and thereby indirectly reduce the negative impacts of city logistics on urban life. A mathematical formulation established for the optimization problem is developed to quantify the impact of collaboration and flexible compartment sizes on total distance travelled, total time, number of routes needed, and vehicle utilization. Based on the delivery networks of seven food retailers operating in the city centre of Groningen, the impact of collaboration over no collaboration and the impact of having flexible compartment sizes over fixed compartment sizes is evaluated. Results show that food retailers benefit from collaborating in their last mile deliveries, but the magnitude of the savings obtained in the four performance metrics depends on the fleet composition used. This thesis shows that having flexible compartment sizes is the most beneficial collaborative scenario, but also with the companies’ current fleet considerable savings can be obtained. It is also concluded that, in terms of travelled distance, having a best fixed fleet can perform close to fleets with flexible compartment sizes when customer demand is not vastly different between the different days of the week. Furthermore, a collaboration between a large and small company turned out to be the most fruitful combination. Lastly, the benefits of collaboration are analyzed from a cost perspective, showing a significant cost reduction.

Keywords: multi-compartment vehicle routing problem, flexible compartment sizes,

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1. Introduction

Nowadays, city centres are exposed to many delivery vans, causing problems for citizens (Ranieri et al., 2018). Growth of freight transportation in urban areas has led to negative influences on city living conditions such as emissions, noise, congestion, and space consumption (Cleophas et al., 2019). Freight volumes have been growing rapidly and are expected to grow even further causing problems to arise in last mile deliveries (Charisis et al., 2020). Last mile deliveries refer to the last step of a delivery process, the transportation of products from a facility to the final customer (Charisis et al., 2020). Electric vehicles are considered as a promising alternative to fuel driven vehicles since they have no direct emissions and produce minimal noise (Muñoz-Villamizar, Montoya-Torres & Faulin, 2017). However, electric vehicles still cause congestion and consume space. City logistics addresses these challenges by finding efficient and effective ways to transport goods in urban areas (Savelsbergh & van Woensel, 2016).

Typically, each supplier transports their own products. This results in many freight operations and empty vehicle kilometers (Crainic, Ricciardi & Storchi, 2009). Horizontal collaboration, a collaboration between multiple logistics providers in the same tier of the supply chain, can increase the efficiency of last mile deliveries through sharing resources (Cleophas et al., 2019). To effectively collaborate in last mile deliveries, an optimized consolidation of goods of different suppliers within the same vehicles and an optimized coordination of resulting activities is needed (Crainic et al., 2009). In food deliveries, guaranteeing the quality of products during delivery and dealing with the negative impacts of deliveries, such as congestion, is a challenge (Musavi & Bozorgi-Amiri, 2017). Therefore, integrating the concept of city logistics has also attracted researchers in food supply chains (Musavi & Bozorgi-Amiri, 2017).

Food distribution, among other industries, use multi-compartment vehicles to allow for the transportation of inhomogeneous products on the same vehicle (Derigs et al., 2011). In city centres, food deliveries for restaurants, cafes, and hotels account for a significant part of the freight transportation. Vehicles for food deliveries typically have two compartments with different temperature zones, one for fresh products and one for frozen products (Hübner & Ostermeier, 2019). In addition to vehicle capacity, these compartments each have their own capacity restrictions (Derigs, et al., 2011). The capacity limits of each of these compartments limit the possibilities in optimizing the logistic movements and thereby the reduction of the negative effects of last mile deliveries.

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covered by a fleet while satisfying demand. Many extensions of the classical VRP that are relevant in the field of food distribution are considered in VRP literature as including capacity constraints, allowing vehicles to have multiple compartments, optimizing the compartment configuration, and including time windows (Braekers, Ramaekers & Nieuwenhuyse, 2016; Toth & Vigo, 2014). Besides, different objectives are considered as minimizing distance travelled, minimizing delivery times, minimizing cost, and minimizing total number of vehicles.

This research introduces a multi-compartment vehicle routing problem with time windows and flexible compartment sizes (MCVRPTWFCS), which is applied in the context of collaboration in last mile food deliveries. This allows to compare different scenarios in food deliveries, namely collaboration against no collaboration, and fixed compartment sizes against flexible compartment sizes. The aim is to minimize the total distance travelled for each scenario. Based on the proposed variant of the traditional vehicle routing problem, the following research question is addressed:

How much savings in travel distance can be obtained by horizontal collaboration of retailers in last mile food deliveries using multi-compartment vehicles compared to no collaboration? In this thesis, a mathematical formulation of the MCVRPTWFCS is developed. The developed model is different from the ones previously discussed in literature as it is a new combination of different VRP extensions and besides includes service times, capacity in number of products and weight, and a maximum time length for the routes. To evaluate the impact of collaborative delivery and flexibly sizeable compartments, the food deliveries of seven food retailers operating in the city centre of Groningen, the Netherlands are investigated. Based on the proposed mathematical model, both the non-collaborative and collaborative scenario with flexible compartment sizes are modelled. The models are solved heuristically to find the best possible compartment configuration that minimizes the travelled distance for the last mile deliveries. A multi-compartment vehicle routing problem with time windows (MCVRPTW), which is the proposed MCVRPTWFCS without flexible compartment sizes, is used to model the non-collaborative and collaborative scenario with fixed compartment sizes. The four scenarios are compared on total distance, total time, number of routes, and vehicle utilization to quantify the differences between them.

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collaboration is evaluated, which provides new quantitative insights on the benefits of collaboration in food retail. Finally, quantitative insights on the benefits of having flexible compartment sizes in non-collaborative and collaborative scenarios are given.

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2. Theoretical background

This section provides a literature review focussing on the main research areas combined in this thesis, collaborative transportation in city logistics and vehicle routing problems. First, the concept of collaboration is introduced to give some background on the setting of this thesis. Thereafter, several extensions to the classical vehicle routing problem are explained in order to introduce the modelling purposes of this thesis. Next, the use of meta-heuristics is introduced. Finally, a comparison between the current study and existing studies is given.

2.1 Collaboration in city logistics

Many researchers have addressed the negative impacts of freight transportation in urban areas. Congestion, emission, and noise are considered as the main factors influencing living conditions in cities (Charisis et al., 2020; Savelsbergh & van Woensel, 2016). Cleophas et al. (2019) add space consumption to this list. Most of the city logistics literature aims to reduce these impacts by streamlining distribution activities, resulting in fewer movements and a better use of vehicles (Crainic, Ricciardi & Storchi, 2009). Montoya-Torres, Muñoz-Villamizar & Vega-Mejia (2016) argue that for city logistics to improve the attractiveness of city centres, city logistics should be better integrated into the urban city planning.

Hubs are introduced as intermediate depots to make the logistics more efficient. Other researchers prefer to use the term urban consolidation centre (UCC) for these intermediate depots, based on the location of these facilities, namely close to the city border (Allen et al., 2012). Long-haul transportation vehicles unload their cargo at a hub, where freight is consolidated into smaller vehicles (Perboli, Tadei & Vigo, 2011). These vehicles distribute the goods to the final customer in a more efficient way. In a hub operation in the city of Belo Horizonte, Correia, Oliveira & Guerra (2012) show the use of hubs to be successful in reducing emissions, travelled distance, and number of vehicles used. Reduction of emissions and travelled distance was also found by Heeswijk, Larsen & Larsen (2019), who performed a similar study in the city of Copenhagen.

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Cleophas et al. (2019) describe horizontal collaboration as the situation in which multiple logistics service providers are working together in the same tier of the supply chain. Bahinipati et al. (2009) define it as “a business agreement between two or more companies at the same level in the supply chain or network in order to allow ease of work and co-operation towards achieving a common objective.” The latter definition is more comprehensive, and therefore better fits this thesis. In city logistics, two or more providers can collaborate horizontally by sharing a distribution centre or sharing a fleet of vehicles to perform their last mile deliveries (Cleophas et al., 2019). By collaborating, the partners aim to optimize vehicle capacity utilization, reduce empty kilometers, and cut costs (Cruijssen, Cools & Dullaert, 2007). Ideally, different service providers deliver their goods to the hub and organize last mile deliveries together (Cleophas et al., 2019). By combining their resources, additional opportunities for vehicle routing optimization appear because customers of different companies can be served by the same vehicle (Defryn, Sörensen & Cornelissens, 2016). The hub in the collaborative scenario can be a facility on a new location, but it can also be one of the collaborating retailers’ depot, which is the case in this thesis.

In a typical non-collaborative scenario, each service provider creates its own routes. Contrarily, in a collaborative scenario, deliveries to closely located customers can be combined regardless of the service provider. Figure 2.1 provides a first intuitive idea regarding the savings in travelled distance that can be obtained by collaboration. The figure represents the research setting as used in this thesis, where all food retailers are sharing a single hub in which their goods are consolidated for the last mile transportation.

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2.2 Vehicle routing problem extensions

Extensions to the classical vehicle routing problem are extensively studied in literature. Early work by Solomon (1987) considered the vehicle routing problem with time windows (VRPTW), as this emerged as an important development towards more realistic routing models. The VRPTW allows each customer to designate a time window in which they want to be served. Two variants of time windows exist: the hard time windows and the soft time windows (Chen & Shi, 2019). The hard time window refers to the situation in which the customer must be served in that time window, the soft time window implies that the window can be violated if a penalty in incurred (Chen & Shi, 2019). As an extension, Martins et al. (2019) introduce product-oriented time windows, where the time window in which a specific product will be delivered is a decision variable. The use of hard time windows is most suitable in food deliveries because of perishability of the products and because restaurants need to have their ingredients in time to process them.

Another extension to the classical VRP is the capacitated VRP (CVRP). This variant considers the maximum capacity of vehicles when determining optimal routes. Since in many practical applications, as in food deliveries, more than one type of products is involved, Brown and Graves (1981) introduced the multi-compartment VRP (MCVRP). Typical examples include fuel delivery, waste collection, and grocery distribution. The MCVRP was originally designed for fuel deliveries and many studies in this field are motivated by the same application area (Avella, Boccia & Sforza, 2004; Van der Bruggen, Gruson & Salomon, 1995; Cornillier et al., 2008). For fuel delivery, as well as waste collection, only one supply can be assigned to each department but the assignment of product types to compartments is not fixed (Henke, Speranza & Wäscher, 2015). However, in the food industry each type of product has special temperature requirements which make certain product-compartment combinations infeasible (Derigs et al., 2011)

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2.3 Meta-heuristics

Vehicle routing problems are one of the most well-known combinatorial optimization problems. Current VRP models increasingly aim to incorporate real-life aspects bringing along substantial complexity (Braekers, Ramaekers & Nieuwenhuyse, 2016). The VRP is an NP-hard problem, making exact algorithms only efficient for small VRP instances (Laporte, 2007). Heuristics and meta-heuristics are more suitable for real-life problems and have been widely developed. Meta-heuristics aim at improving the performance of heuristic methods in solving large vehicle routing problems (Voudouris & Tsang, 1999).

Local search is the foundation for most meta-heuristics (Voudouris & Tsang, 1999). It is the procedure of minimizing the objective function by replacing the current solution with a better solution (Voudouris & Tsang, 1999). The algorithm starts with an arbitrary solution and ends up in a local minimum, a solution where no further improvement is possible because the solution is better than all neighbours (Alsheddy, Voudouris & Tsang, 2016). The main problem with local search is that these local minima are not necessarily optimal solutions (Voudouris & Tsang, 1999). From a local minimum, there is no obvious way to find a better solution for the local search algorithm. To overcome this problem, and escape local minima, meta-heuristics are used. Well-known meta-heuristics based on local search for VRP’s are Tabu Search (TS), Simulated Annealing (SA), Guided Local Search (GLS), Variable Neighbourhood Search (VNS), and Adaptive Large Neighbourhood Search. Vidal et al. (2013) provides an in-depth analysis and comparison of these meta-heuristics. Next to local search, population search heuristics, and learning mechanisms can serve as foundation for meta-heuristics (Laporte, 2007). An example of a population search based meta-heuristic is Particle Swarm Optimization (PSO), which is intensively investigated in the paper of Wang, Tan & Liu (2018).

This thesis uses the meta-heuristic Guided Local Search (GLS) as several papers (Kilby, Prosser & Shaw, 1997; Voudouris & Tsang, 1999) have found GLS to be a good meta-heuristic for solving large VRP instances. Guided Local Search uses long-term memories for penalizing features of previous solutions to modify the search space and escape local minima (Vidal et al., 2013).

2.4 Collaborative vehicle routing problem

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in these studies are, however, still very general. This arises the need for more realistic ones. This thesis aims to model the collaborative as well as the non-collaborative scenarios more realistically by combining several extensions of the classical VRP model and including some additional aspects.

Table 2.1 presents features of studies discussed above and provides a comparison between these studies and the current study based on the following factors: whether horizontal collaboration is included or not, if multi-compartment vehicles are considered, if the models consider flexible compartment sizes, the number of compartments (fixed or variable), if time windows set by customers are included, the nature of the objective function, and the fleet composition used (homogenous or heterogenous). Since the savings in distance travelled is affected by the capacity of vehicles, and thus by the capacity of each compartment, the size of these compartments is a decision variable in this study. Besides, since the application in food deliveries is chosen, the number of compartments is fixed, and products are pre-assigned to a compartment. All compared existing studies, as well as this thesis, determine best possible vehicle routes. The current study uses a different perspective than most existing papers by aiming for minimum distance travelled, rather than cost minimization. This perspective is chosen since it enables to shed light on reduction of congestion and space consumption. These are indirectly reduced when travelled distance is reduced. This thesis quantifies the impact of collaboration under different vehicle compartment configurations.

Table 2.1: features of existing studies

Research Collaboration vs non-collaboration Multi-compartment Flexible compartments Number of compartments Time windows

Objective Fleet Solution approach Chen &

Shi (2019)

✓

Fixed

✓

Cost Homogenous PSO, SA Derigs et

al. (2011)

✓

Variable Cost Homogenous SA, TS Henke et

al. (2015)

✓

Variable Cost Homogenous VNS Martins et

al. (2019)

✓

Variable Cost Homogenous ALNS

Montoya-Torres et al. (2016)

✓

Total distance Homogenous MILP

Current

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3. Problem setting

As stated previously, this thesis seeks to analyze the impact of horizontal collaboration between food retailers in city centres as well as the impact of having flexible compartment sizes by quantifying the reduction in travel distance. This section defines the non-collaborative and collaborative scenarios. Next, an illustrative example is given to visualize the differences between the scenarios.

The non-collaborative scenario with fixed compartment sizes (scenario 1), represents the current situation where companies are not collaborating and the compartments of each vehicle have a fixed capacity. In this situation, each company must define the routing of their vehicles to visit their own customers. Besides, the companies have agreements with their customers about delivery times. Therefore, for each company, the routing problem is modelled as a MCVRPTW. The sum of the distances of the final routes for all companies gives the total delivery distance for the non-collaborative scenario with fixed compartment sizes.

In scenario 2, the non-collaborative scenario with flexible compartment sizes, the capacity of the vehicle compartments can be adjusted by means of a movable divider. As in scenario 1, each company must define their own routes taking into account delivery time windows. For scenario 2, a MCVRPTWFCS is proposed to include the flexible compartment sizes.

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products. The most left vehicle is loaded with 4 products of type ‘green’ and one of type ‘orange’ and supplies the two most left red locations. Similarly, the other two companies do this for their own customers. In scenario 2, compartment sizes are flexible, allowing company 1 to visit all their customers with one vehicle instead of two, resulting in less distance travelled. In scenario 3, the compartment sizes are still fixed at 9 products each. The routes of the companies are now combined in three routes. Scenario 4 allows the compartment sizes of the vehicles to be flexible. This makes it possible to reduce travel distance since all customers can be visited with only two vehicles, both having a capacity of 12 ‘green’ and 6 ‘orange’ products.

This setting allows to compare the benefits of having flexible compartment sizes over fixed compartment sizes in a non-collaborative situation (comparing scenario 1 and 2), the benefits of collaboration over no collaboration (comparing scenario 3 and 4 with scenario 1), as well as the benefits of having flexible compartment sizes over fixed compartment sizes in a collaborative situation (comparing scenario 3 and 4).

Regarding the differences between collaborative scenarios and non-collaborative scenarios, it depends on the situation under study to what extent the companies will benefit from

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4. Methodology

Mathematical modelling is used in this thesis as it can represent real-world phenomena in mathematical equations, thereby making it possible to solve real-life problems and gain useful insights

(

Avula, 2001).

Because of the size of the problems, a heuristic method is used to find near-to-optimal solutions. In this section, the problem description, model assumptions, and mathematical formulation of the multi-compartment vehicle routing problem with time windows and flexible compartment sizes is given. Thereafter, the solution approach is explained.

4.1 Problem description

The MCVRPTWFCS can be defined as follows. An undirected graph 𝐺 = (𝐿, 𝐴) is given which consists of a set of locations, 𝐿 = {0, … , 𝑛}, where 0 is the location of the (shared) depot and 𝐿𝑐 = 𝐿\{0} the set of customer locations. 𝐴 = {(𝑖, 𝑗): 𝑖, 𝑗 ∈ 𝐿, 𝑖 < 𝑗} is the set of arcs which

represents the arcs that can be traversed between the different locations. The depot has a number of heterogenous vehicles, which are represented by the set 𝑉 = {1, … , 𝑣}. Each vehicle has two flexibly sizeable compartments, which allows for loading fresh and frozen products in the same vehicle while keeping them separated. The size of the compartments can be varied continuously. The set of products or compartments is given by 𝑃 = {1, … 𝑝}. Each product type is assigned to a compartment. The capacity of a vehicle is given by 𝑄𝑣. Each customer is

served exactly once by exactly one vehicle. The ordered products are delivered within a given time window. The time window is given by [𝑒𝑖, 𝑙𝑖] where 𝑒𝑖 is the earliest delivery time of a

location and 𝑙𝑖 the latest delivery time. The time for the retailer to unload their goods is

represented by 𝑢𝑖, which is referred to as service time. Each vehicle starts and ends at the

depot. Travel time between two locations is given by 𝑡𝑖𝑗. The objective is to determine a set of

vehicle tours, and the sizes of the vehicle compartments such that all customer requests are satisfied, capacity is not exceeded, and time constraints are not violated, at minimal distance travelled.

4.2 Model assumptions

For the formulation of the MCVRPTWFCS model, some reasonable assumptions are adopted: - The hub location is fixed and known beforehand, serving the whole area

- Each route starts and ends at the depot

- Each customer is served by a single vehicle, split deliveries are not allowed - Each vehicle performs one route per day, due to time windows

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incorporating the hub location decision. The second assumption is adopted because vehicles are loaded at the depot and should be positioned there when not driving. The third assumption is set since it is most compatible with food deliveries. All three assumption are common in the studies to which this thesis mostly relates (Chen & Shi, 2019; Derigs et al., 2011, Henke, Speranza & Wäscher, 2015; Martins et al., 2019). The fourth assumption is made since most customers require to get their products delivered in the morning, implying that all routes need to be performed simultaneously.

4.3 Mathematical formulation

The sets, parameters and decision variables used in the mathematical model are given in Table 4.1.

Table 4.1: sets, parameters, and decision variables

Description Sets

𝑳 = {𝟎, … , 𝒏} Set of locations, 0 is the depot, and 1, …, n are customers 𝑳𝒄= 𝑳\{𝟎} Set of customers

𝑨 = {(𝒊, 𝒋): 𝒊, 𝒋 ∈ 𝑳, 𝒊 < 𝒋} Set of arcs

𝑽 = {𝟏, … , 𝒗} Set of heterogenous vehicles

𝑷 = {𝟏, … , 𝒑} Set of products or compartments

Parameters

𝒅𝒊𝒑 Demand (units) of customer 𝑖 for product 𝑝

𝒘𝒊 Weight of demand of customer 𝑖

𝒆𝒊 Earliest delivery time of location 𝑖

𝒍𝒊 Latest delivery time of location 𝑖

𝒖𝒊 Service time at location 𝑖

𝒕𝒊𝒋 Travel time on arc (𝑖, 𝑗)

𝒂𝒊𝒋 Travel distance on arc (𝑖, 𝑗)

𝑸𝒗 Capacity (units) of vehicle 𝑣

𝑾𝒗 Maximum load of vehicle 𝑣

𝒔 Maximum route length (time)

𝑴 Sufficiently large number

Decision variables

𝒙𝒊𝒗 1 if customer 𝑖 is served by vehicle 𝑣, 0 otherwise

𝒚𝒊𝒋𝒗 1 if vehicle 𝑣 serves customer 𝑗 immediately after customer 𝑖, 0 otherwise

𝒃𝒊 Arrival time at location 𝑖

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With the notations shown in Table 4.1, the MCVRPTWFCS can be modelled as follows:

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Formulations of the different extensions of the vehicle routing problem have been widely studied. Therefore, existing models (Chen & Shi, 2019; Derigs et al., 2011; Henke, Speranza & Wäscher, 2015) are adjusted to fit this specific research setting. The objective functions of Chen & Shi (2019), Derigs et al. (2011), and Henke, Speranza & Wäscher (2015) are adjusted by replacing cost with distance, since the aim of this thesis is to minimize total distance travelled. Constraints (2), (11), and (12) are obtained from the model of Chen & Shi (2019). Constraint (6) is also obtained from this model, only minor changes are made to fit the flexible compartment sizes setting of this thesis instead of the fixed compartment sizes setting of Chen & Shi (2019). Constraints (3) and (5) are obtained from Derigs et al. (2011). Constraints (4) are added to explicitly address that vehicles must return to the depot. Constraints (13) and (14) are common in all three papers (Chen & Shi, 2019; Derigs et al., 2011; Henke, Speranza & Wäscher, 2015). Constraints (8) and (15) are inspired by Henke, Speranza & Wäscher (2015), only changed to fit the specific research setting of this thesis since Henke, Speranza & Wäscher (2015) consider discrete flexible compartment sizes, where this thesis considers continuous ones. Constraints (7) and (9) are unique constraints. Next, an explanation of all constraints is given.

The objective function (1) minimizes the total distance travelled. Constraints (2) ensure that each customer is visited by exactly one vehicle. Constraints (3) make sure that each vehicle starts at the depot and can only depart once from the depot. Constraints (4) ensure that each vehicle ends at the depot. Constraints (5) represent the vehicle flow constraints, which ensures that if vehicle 𝑣 arrives at location 𝑖, it should also leave that location. Constraints (6) guarantee for each compartment that the assigned products do not exceed its capacity. Constraints (7) ensure for each vehicle that the weight of the assigned products do not exceed the maximum load of the vehicle. Constraints (8) ensure for each vehicle that the sum of the compartment sizes is smaller than or equal to the vehicle capacity. Constraints (9) guarantee that each route does not exceed the maximum route length. Constraints (10) are classical subtour elimination constraints. Constraints (11) ensure that the arrival time at the next location 𝑗 considers the arrival time 𝑏𝑖 plus the unloading time 𝑢𝑖 of the previous location 𝑖 in addition to the travel time

between these locations 𝑡𝑖𝑗. Constraints (12) ensure the delivery to location 𝑖 to be within the

given time window. Constraints (13), (14), and (15) define the variable domains.

In MCVRPTWFCS, the compartment sizes are flexible. When the compartment sizes are fixed, 𝐶𝑝𝑣 is known for each vehicle and is no longer a decision variable. 𝐶𝑝𝑣 can therefore be

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4.4 Solution approach

To model the scenarios introduced, this thesis makes use of Google OR-tools (Perron & Furnon, 2020). Some modifications to the solvers of Google OR-tools are made to suit the specific setting of this thesis. These adjustments are explained first. Thereafter, the meta-heuristic Guided Local Search is explained.

4.4.1 Solver

Two different solvers of Google OR-tools are combined to develop the solver used in this thesis, namely the Google OR-tools solvers for VRPTW and CVRP. The VRP solvers of Google OR-tools are designed in such a way that each vehicle route starts and ends at the depot, and that each location is visited exactly once by exactly one vehicle, which are also two assumptions made in this thesis. Additionally, some enhancements are made to the Google OR-tools solvers. First of all, the Google OR-tools CVRP solver only considers one capacity constraint. The solver constructed for this thesis involves three capacity constraints, namely number of fresh products, number of frozen products, and total weight of these products. This was implemented by creating multiple capacity callbacks. Next to that, a constraint limiting the maximum route length was added. Besides, the Google OR-tools VRPTW only considers travel time between locations to ensure a customer is visited within its specified time window. The solver for this thesis adds service time at a customer to that.

To use a heuristic to find a near-to-optimal solution, an initial solution to the problem should be set. Google OR-tools uses a decision builder which returns the first solution found as the initial solution. The default settings of this decision builder are used in this thesis, implying that the solver selects the first available location from the location array and connects it iteratively to the first unbound successor. Before adding a location to the route, the solver first checks if no constraints are violated. If one of the constraints of the model is violated, a new route is started. In the Google OR-tools solvers for CVRP and VRPTW, the solver only checks one constraint before adding a location to a route, namely the capacity of the vehicle and the time window in which a customer must be visited, respectively. The solver developed for this thesis needs to check five constraints, to wit three capacity constraints, a time window constraint, and a route length constraint. The strategy to set the first solution used in this thesis is given as pseudo code in Figure 4.2.

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Figure 4.2: pseudo code first solution strategy

When modelling the scenarios with flexible compartment sizes, the set of vehicles changes compared to the scenarios with fixed compartment sizes. As can be seen in the pseudo code, the solver loops over all available vehicles. In the flexible scenarios, compartment capacities can be increased or decreased by one or multiple roll containers over a specified range. Increasing the fresh capacity leads to a decrease in frozen capacity. For each vehicle, all possible combinations of compartment sizes within the specified range are added to the model. Therefore, the set of vehicles is larger in the flexible scenarios. More details on the flexible fleet are given in Section 5.2.

Based on the initial solution created by the described strategy, Guided Local Search further optimizes the solution. This is explained next.

4.4.2 Guided Local Search

Guided local search (GLS) was proposed by Voudouris and Tsang (1996). GLS is a penalty-based method that sits on top of local search heuristics to guide these procedures in exploring the search spaces of combinatorial optimization problems (Voudouris & Tsang, 1999). This thesis uses the Google OR-Tools GLS meta-heuristic (Perron & Furnon, 2020). Next, the underlying procedure of this method is explained based on the Google OR-tools user manual of Omme, Perron & Furnon (2014).

GLS requires to define a set of features for the candidate solutions, to distinguish between solutions with different characteristics. Each feature should be associated with a penalty cost, such that GLS can penalize some features of a local minimum. In this thesis, the chosen feature of solution is whether the solution traverses an arc (𝑖, 𝑗) or not. The penalty cost

First solution strategy

1. start a route with vehicle 𝑣

2. add the first unassigned location to the route 3. if all locations are assigned; go to step 6, else

if ∑𝑖∈𝐿𝑥𝑖𝑣𝑑𝑖𝑝 ≤ 𝐶𝑝𝑣 ∀ 𝑝 ∈ 𝑃

and ∑𝑖∈𝐿𝑥𝑖𝑣𝑤𝑖≤ 𝑊𝑣

and 𝑒𝑖≤ 𝑏𝑖≤ 𝑙𝑖 ∀ 𝑖 ∈ 𝐿𝑐

and ∑𝑖∈𝐿∑𝑗∈𝐿𝑦𝑖𝑗𝑣𝑡𝑖𝑗≤ 𝑠 are not violated do

select the first location with an unbound successor and connect it to the first available location

else go to step 5

4. update the capacities 𝐶𝑝𝑣 (∀ 𝑝 ∈ 𝑃), 𝑊𝑣; go to step 3

5. start new route with vehicle 𝑣 + 1; go to step 2

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associated with this feature is the distance between 𝑖 and 𝑗. Based on the penalties, GLS creates an augmented objective function:

𝑔(𝑥) = ∑ ∑ ∑ 𝑎𝑖𝑗𝑦𝑖𝑗𝑣 𝑗∈𝐿 𝑖∈𝐿 𝑣∈𝑉 + 𝜆 ∑(𝐼𝑖𝑗(𝑥)𝑝𝑖𝑗𝑎𝑖𝑗) (𝑖,𝑗)

Where ∑𝑣∈𝑉∑𝑖∈𝐿∑𝑗∈𝐿𝑎𝑖𝑗𝑦𝑖𝑗𝑣 is the original objective function as given in Section 4.3, 𝐼𝑖𝑗(𝑥) is

1 if solution 𝑥 traverses arc (𝑖, 𝑗), and 0 otherwise. 𝑝𝑖𝑗 is the penalty attached to traversing arc

(𝑖, 𝑗), 𝑎𝑖𝑗 the cost of traversing arc (𝑖, 𝑗). 𝜆 is called the penalty factor and can be used to tune

the search to find similar solutions (low 𝜆) or completely different solutions (high 𝜆). The penalty factor is set to 0.1 in this thesis, which is the default value used by Google OR-Tools. Penalties (𝑝𝑖𝑗) start with value 0 and are incremented by 1 with each local minimum. GLS only penalizes

a feature if its utility is large enough. The utility function used in this thesis for a feature 𝑖 in a solution 𝑥 is:

𝑈𝑖𝑗(𝑥) = 𝐼𝑖𝑗(𝑥)

𝑎𝑖𝑗

1 + 𝑝𝑖𝑗

If an arc (𝑖, 𝑗) is not present in a solution 𝑥, its utility is 0 since 𝐼𝑖𝑗(𝑥) will be 0. If arc (𝑖, 𝑗) is

present in a solution 𝑥, the utility is proportional to the cost of this feature. Since 𝑝𝑖𝑗 increases

with each local minimum, the utility tends to disappear when a specific feature is often penalized. This is done because a feature that shows up regularly in local minima, might be part of a good solution. Like this, costly features are penalized, but are not penalized too much if they often show up.

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Guided Local Search

𝑘 ← 0

{Generate a starting candidate solution heuristically}:

Generate 𝑠0

{set all penalties to 0}:

for 𝑖, 𝑗 ← 1 until M do

𝑝𝑖𝑗 ← 0;

end for

{define the augmented objective function}:

𝑔 ← ∑𝑣∈𝑉∑𝑖∈𝐿∑𝑗∈𝐿𝑎𝑖𝑗𝑦𝑖𝑗𝑣+ 𝜆 ∑(𝑖,𝑗)(𝐼𝑖𝑗𝑝𝑖𝑗𝑎𝑖𝑗)

{repeat the following until termination condition}:

while stopping criterion do

{find a local minimum using Local Search and 𝑔}:

𝑠𝑘+1← 𝐿𝑜𝑐𝑎𝑙 𝑆𝑒𝑎𝑟𝑐ℎ (𝑠𝑘, 𝑔);

{compute the utility for each feature 𝑖, 𝑗 present in 𝑠𝑘+1}:

for 𝑖, 𝑗 ← 1 until M do

𝑢𝑖𝑗 = 𝐼𝑖𝑗( 𝑠𝑘+1) × 𝑎𝑖𝑗/1 + 𝑝𝑖𝑗;

end for

{penalize each feature 𝑖, 𝑗 such that 𝑢𝑖𝑗 is maximum}:

for all 𝑖, 𝑗 such that 𝑢𝑖𝑗 is maximum do

𝑝𝑖𝑗 ← 𝑝𝑖𝑗+ 1;

end for 𝑘 ← 𝑘 + 1;

end while

𝑠∗_{← 𝑏𝑒𝑠𝑡 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑓𝑜𝑢𝑛𝑑;}

{return the best solution found so far according to the objective function 𝑔}:

return 𝑠∗_;

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5. Numerical experiments

This section is concerned with the numerical experiments performed in this research. First, the setup of the case study and the way of generating data is explained. Next, the experimental set-up is given. After that, the results of each experiment are presented.

5.1 Case study

This research is conducted in the city of Groningen. Groningen is the sixth largest city in the Netherlands (CBS, 2020a). This research focusses on the city centre of Groningen, which has a surface of 1.38 km2_{(CBS, 2020b). The city centre of Groningen is an environmental zone,}

restricting the access for specific vehicles on different times of the day. With environmental rules becoming stricter in the upcoming years, the need for more efficient ways of transportation in the city centre of Groningen arises.

The networks of seven food retailers operating in Groningen are analyzed. Bidfood, one of these food retailers, shared their real data on deliveries to perform this research. The other companies are referred to as company A, B, C, D, E, and F. Bidfood is a food retailer focussing on the professional world serving cafeterias, caterers, canteens, healthcare institutions, hotels, and restaurants (Bidfood, 2020).

Data about Bidfood’s deliveries from week 44/2019 till week 15/2020 is used for this research. Bidfood provided, for every delivery in the city centre in that period, the number of fresh products, number of frozen products, weight of those products, time window of the customer, and service time of the delivery. Service time is defined as the time needed to unload the goods at a customer. Bidfood has a total of XX1_{customers in the city centre of Groningen. Customers}

get delivered 1-6 times a week, making the routes different for every day of the week. If a customer got served on more than 50% of a specific day of the week in the 25-week period, it was considered as being part of the customers of that day. The customers that have very infrequent deliveries, were assigned to the day of the week on which most of their deliveries happened. If a customer was assigned to for example Monday, the demand and service time were determined as the averages over all of the customer’s deliveries on Monday. Like this, the same customer can have different demands on different days of the week, if they get delivered more than once a week. Because of this approach, no variation in demand is included between the same day every week. Therefore, the experiments performed in this research provide insights on the ideal situation, where demand is deterministic. Details on number of deliveries per week per customer and on demand ranges can be found in Table 5.1.

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Table 5.1: number of deliveries per week and demand ranges

Number of deliveries per week Percentage of customers

1 25 2 27 3 20 4 4 5 4 6 8 Infrequent 12 Parameter Range

Fresh demand 1 – 4 roll containers Frozen demand 0 – 2 roll containers

Next to this, Bidfood provided an overview of customers served by one of Bidfood’s competitors. For these customers, the serving company is known, however, no data on demand, time windows, and service time is available. To be able to involve these competitors in the research, data for these competitors was created based on the averages of Bidfood’s data. For example, the percentage of customers getting delivered twice a week is the same for every company and the ratio between number of customers each day of the week is the same for every company. Next to that, the same spread of demand as given in Table 5.1 is used for all collaborating companies. Service times for the competitors were generated as random numbers in the interval of the shortest and longest service times of Bidfood’s customers. Table 5.2 gives an overview of the number of customers visited by each company each day, their total number of customers, the total number of customers visited each day, and the weekly totals. Figure 5.1 shows the actual locations of each of the retailer’s customers.

Table 5.2: details on number of customers2

Total Monday Tuesday Wednesday Thursday Friday Saturday Weekly stops

Bidfood XX XX XX XX XX XX XX XX Company A XX XX XX XX XX XX XX XX Company B XX XX XX XX XX XX XX XX Company C XX XX XX XX XX XX XX XX Company D XX XX XX XX XX XX XX XX Company E XX XX XX XX XX XX XX XX Company F XX XX XX XX XX XX XX XX Total XX XX XX XX XX XX XX XX

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Figure 5.1: actual locations of customers of the seven food retailers (created with Google My Maps™) 3

5.2 Experimental set-up

The mathematical models used in this thesis are modelled using Google OR-Tools and Python 3.7 on Spyder platform. The models ran on a personal computer with Intel® Core™ i5-7200U 2.5GHz, a 64-bit processor, 4 GB RAM, and Microsoft Windows 10.

For each scenario, the origin–destination distance matrices were obtained using actual driving distances using Bing Maps mapping service. The shortest path option was used for distance calculations in this thesis. The average vehicle speed used is 15 km/h, based on a study on travel speeds in the inner city of Amsterdam (DIVV, 2010). Travel times between locations were indirectly calculated using the distance between these locations and this average vehicle speed of 15 km/h. Travel times between the collaborating companies’ depots and Bidfood’s depot were indirectly computed using the actual driving distance between the depots and an average vehicle speed of 45 km/h, which is slightly lower than the maximum permitted speed outside the city centre. Legal working time without breaks in the Netherlands of 4.5 hours (Your Europe, 2020) was considered, meaning that routes cannot exceed this.

Bidfood’s fleet consists of 13 vehicles, with different compartment configurations, and different maximum loads. Bidfood uses its 13 vehicles for all its deliveries, so also for the deliveries outside the city centre. It is assumed that all 13 vehicles are available to use for inner city

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deliveries. All Bidfood’s competitors are assumed to have the same fleet composition. This is assumed since the capacity of this fleet is sufficient for each company to do the city centre deliveries. However, in reality the fleet sizes and compositions are probably not identical for every company because of company preferences and insights in demand. Using the fleet of Bidfood might be too restrictive for the large company F, thereby limiting the optimization options. The smaller company might have excessive capacity due to this modelling decision, however, these companies have more customers outside the city centre. Details of the used fleet are given in Table 5.3, as well as the other parameters explained.

Table 5.3: characteristics of the fleet with fixed compartment sizes and parameters used

Parameters

Average vehicle speed city centre 15 km/h 45 km/h Average vehicle speed outside city centre

Maximum route length 270 minutes

Vehicles Maximum load (kg) Capacity fresh (roll containers) Capacity frozen (roll containers) Total capacity (roll containers) Type 1 (1x) 7313 20 16 36 Type 2 (2x) 8815 28 8 36 Type 3 (7x) 7919 25 7 32 Type 4 (2x) 7685 22 10 32 Type 5 (1x) 8990 20 12 32

Table 5.4 gives the specifications of the flexible fleet used for modelling scenario 2 and 4. The two different maximum capacities of Bidfood’s current vehicles (32 and 36 roll containers) are maintained in the flexible scenarios. The maximum load is based on the average maximum load of the current vehicles. The range of compartment sizes is motivated by the existence of cooling systems in the vehicles that limit the possibilities to have compartment capacities close to zero. Since there are now considerably more vehicles added to the model than in the scenarios with fixed compartment sizes, the model was able to select more than three 36-capacity vehicles. Although this is not possible with the current fleet of Bidfood, this was done to get the best possible configuration.

Table 5.4: characteristics of the fleet with flexible compartment sizes

Flexible compartment sizes fleet

Maximum load (kg) Range compartment sizes (roll containers)

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Four experiments are executed based on this data. The first experiment compares the four scenarios as introduced in Section 3 to investigate the distance savings that can be obtained by collaboration and to investigate the influence of having flexible compartment sizes. The second experiment examines the impact of having a best fixed fleet. The third experiment involves evaluating the benefits of collaboration based on company size. The fourth experiment evaluates different locations for the depot.

5.3 Results

This section further explains the experiments performed and provides the results of them. Different performance metrics are used to quantify the impact of collaboration and having flexible compartment sizes. The first performance metric, distance, gives the total distance travelled in kilometers, and is thus the sum of all vehicle routes. In the collaborative scenarios, this includes the distance to bring the products from the companies’ depots to Bidfood’s depot. Time is the total length of all routes, thus the sum of travel times and service times. In the collaborative scenarios, it includes the travel time to bring the products from the companies’ depots to Bidfood’s depot. Number of routes indicates the number of vehicle tours that are needed to serve all customers. Lastly, vehicle utilization is computed by dividing the number of roll containers in a vehicle by the total capacity for roll containers of that vehicle.

5.3.1 Comparison of the four scenarios

The first experiment compares the four scenarios introduced in Section 3. Table 5.5 shows the results of the first experiment in terms of the four performance metrics. The numbers represent weekly totals. Table 5.6 shows the relative differences between the scenarios, so the percentage difference for each metric when going from one scenario to the other scenario. Several insights can be derived from this experiment, these are explained next.

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of the collaborating retailers are closely located, meaning that the distance travelled to bring all the products to one depot (11.4 kilometers per day) is not a significant part of the total distance travelled per day. Situations in which the depots are much more dispersed will therefore obtain a lower relative distance reduction. The benefits obtained by collaboration in terms of distance travelled are nearly the same for each day of the week for both fixed and flexible compartment sizes, despite the different customer base and different customer demand between these days. Figure 5.2 shows these reductions being stable for each day of the week. The reduction in total time and number of routes needed follow a similar pattern. The reduction obtained in time is less than the changes obtained in the other metrics. An explanation for this is that service time has a large share in total time, and the service time is not considered to change when collaborating.

The second insight resulting from this experiment is about the impact of flexible compartment sizes. Flexible compartment sizes turn out to be more effective in a collaborative setting than in a non-collaborative setting. Comparing scenario 1 and 2 shows that having flexible compartment sizes leads to a distance reduction of only 0.98% in the non-collaborative setting, while having flexible compartment sizes in a collaborative setting leads to a distance reduction of 14.70%. The two larger companies (Bidfood and company F) are the only two companies benefitting from having flexible compartment sizes in the non-collaborative situation. For companies B, D, and E, only one vehicle is needed each day, which is not even used to half capacity. Therefore, flexible compartment sizes do not make a difference in their situation. Company A and C did also not benefit from being able to adjust their compartment sizes, this was due to maximum driving time and time window constraints. However, these results are partly influenced by the setting of this research. For example, if a delivery network has more large companies than in the current setting, the network can profit more from having flexible compartment sizes in the non-collaborative scenario. However, still the collaborative scenario is expected to benefit more from the flexible compartment sizes as there are much more possibilities for optimization with a larger customer base.

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customers than without collaboration. Appendix A gives the average route length in distance and time for each day of the week. The modelled reductions in number of routes, time, and distance do not include demand uncertainty, which influences the numbers obtained.

Another insight gained by this experiment is that empty kilometers are reduced. In the non-collaborative scenarios, vehicle utilization ranges from 0.22 to 0.80, indicating that there are many empty vehicle kilometers. When looking at the collaborative scenarios, it can be seen that the vehicle utilization is increased, thereby having less empty vehicle kilometers. Collaboration with flexible compartment sizes resulted in an average vehicle utilization of 0.93 compared to 0.75 when having fixed compartment sizes under collaboration. With flexible compartment sizes, the vehicles are therefore almost completely filled. Since demand uncertainty is not considered in this thesis, it might be possible that when using this fleet in real-life situations, the products do not fit in the vehicles anymore. Therefore, more vehicles are needed to visit the customers, or routes need to be adjusted, leading to more travelled distance.

Table 5.5: weekly results for the four scenarios in terms of the different performance metrics Non-collaborative scenarios

Distance (km) Time (min) Number of routes Average vehicle utilization

Fixed (scenario 1) Bidfood 125.30 3005 15 0.68 Company A 168.41 2433 12 0.47 Company B 82.33 1225 6 0.47 Company C 76.21 1655 7 0.79 Company D 64.30 929 6 0.35 Company E 83.40 655 6 0.22 Company F 215.11 5474 22 0.80 Total 815.06 15376 74 0.61 Flexible (scenario 2) Bidfood 118.31 2872 13 0.79 Company A 168.41 2433 12 0.47 Company B 82.33 1225 6 0.47 Company C 76.21 1655 7 0.79 Company D 64.30 929 6 0.35 Company E 83.40 655 6 0.22 Company F 214.10 5498 22 0.80 Total 807.06 15267 72 0.63 Collaborative scenarios

Fixed (scenario 3) 535.48 14320 61 0.75

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Table 5.6: relative differences between the scenarios

Scenario 1 → scenario 2 -0.98% -0.71% -2.70% +3.28% Scenario 1 → scenario 3 -34.30% -6.87% -17.57% +22.95% Scenario 3 → scenario 4 -14.70% -11.06% -21.31% +24.00% Scenario 1 → scenario 4 -43.96% -17.17% -35.14% +52.46%

Figure 5.2: distance reduction per day of the week

5.3.2 Flexible fleet

The best possible travel distance for the case setting found in the first experiment is obtained by using a specific fleet configuration each day of the week. This flexible fleet is evaluated in this section. With the current fleet of Bidfood, it turned out that in most cases the frozen compartment was restrictive and thereby limiting the possibilities for consolidation. In the flexible collaborative situation, the best fleet consisted of vehicles with more frozen capacity (10-14), resulting in even more distance reduction. Furthermore, reductions in time (11.06%) and number of routes needed (21.31%) are obtained by having flexible compartment sizes in the collaborative scenario. The best possible compartment sizes for each day of the week are given in Table 5.7.

Even though the model was able to select more than three 36-capacity vehicles per day, this did not happen for three of the days. It turned out that 32-capacity vehicles were in most cases sufficient, since further extending the routes of these vehicles did violate the maximum route length constraint. For Tuesdays, Wednesdays, and Saturdays, the network benefits from

0 20 40 60 80 100 120 140 160

Monday Tuesday Wednesday Thursday Friday Saturday

Dis ta n ce tra ve lle d (km' s)

Distance reduction

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having more than three 36-capacity vehicles as they were selected by the model. By allowing the model to select more than three 36-capacity vehicles, a secondary advantage to the flexible model was given. Table 5.7 shows that on Saturdays three extra 36-capacity vehicles are needed, on Wednesdays two extra 36-capacity vehicles are needed, and on Tuesdays one extra 36-capacity vehicle is needed. If this was not allowed, on all three days one extra vehicle tour is needed to serve all customers since the extra created capacity by using more 36-capacity vehicles is 4, 8, and 12 roll containers for Tuesdays, Wednesdays, and Saturdays, respectively. This fits in a single vehicle. Since the average route length of a tour is 8.1 kilometers, about 24.3 extra kilometers are travelled per week when only three 36-capacity vehicles are available. The distance savings for scenario 4 thus slightly reduce.

Table 5.7: best fleet composition for each day of the week

Best fleet composition

V eh ic le 1 (fr es h/f roz en ) V eh ic le 2 (fr es h/f roz en ) V eh ic le 3 (fr es h/f roz en ) V eh ic le 4 (fr es h/f roz en ) V eh ic le 5 (fr es h/f roz en ) V eh ic le 6 (fr es h/f roz en ) V eh ic le 7 (fr es h/f roz en ) V eh ic le 8 (fr es h/f roz en ) V eh ic le 9 (fr es h/f roz en ) Monday [25,11] [20,12] [18,13] [24,12] [18,13] [21,11] [20,12] Tuesday [24,12] [23,13] [20,12] [24,12] [20,12] [22,14] [20,12] [20,12] [22,10] Wednesday [24,12] [22,10] [22,10] [24,12] [23,13] [22,14] [23,13] Thursday [25,11] [25,11] [22,10] [22,10] [22,10] [24,12] [21,11] [21,11] Friday [20,12] [20,12] [21,11] [21,11] [21,11] [24,12] [20,12] [22,10] Saturday [25,11] [23,13] [22,14] [20,12] [21,11] [20,12] [24,12] [23,13] [23,13]

To be able to execute the best fleet composition on each day, the network needs six 36-capacity vehicles and three 32-36-capacity vehicles. By comparing the fleet composition of a specific day of the week and the day before that day, it can be determined how often compartment sizes need to be changed in the proposed situation. Table 5.8 gives the results. For example, on Mondays, there is excessive capacity available. In the best possible configuration, only 32-capacity vehicles are needed on Mondays. The needed 32-capacity configurations fit in the 36-capacity vehicles of Saturday, implying that no changes have to be made to the compartment sizes. On the other hand, on for example Tuesdays, two vehicles need a change in their compartment sizes to create the best possible configuration of that day.

Table 5.8: number of compartment size changes needed each day of the week

Change of compartment sizes needed

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5.3.3 Best fixed fleet

The second experiment evaluates the impact on travelled distance of having a best fixed fleet. The first experiment determined the best possible fleet composition for each day of the week. This involves that the companies have to be able to alter the size of the compartments in their vehicles every day. Since this is technically a challenging idea, a compartment configuration that fits every day of the week is investigated in this section. This best fixed fleet can be used throughout the whole week, which eliminates the need to change the compartment sizes every day.

Since on Saturday the most vehicle capacity is needed, the fleet composition of this day is considered as the best possible fixed fleet that can be used during the whole week. The configuration of every other day of the week can be created from the fleet of Saturday, which is not possible using the fleet of any other day of the week. Therefore, using the fleet of one of the other days of the week as a fixed fleet can never perform better than the fleet of Saturday. The fleet composition of Saturday is compared with the current fixed fleet and with the flexible fleet proposed in experiment 1. Figure 5.3 shows the distance travelled each day of the week with the three different fleet configurations considered.

It is shown that using a best fixed fleet is a good compromise as it still significantly outperforms the current fixed fleet and only performs slightly worse than having flexibly sizeable compartments. The experiment shows that using the fleet of Saturday the other days of the week performs slightly worse than the flexible fleet and better than the current fixed fleet. The performance of the Saturday fleet is close to the flexible fleet, as the best fleet compositions are not that different throughout the whole week. The weekly total extra distance using the Saturday fleet compared to the best flexible fleet is 2.61 kilometers (+0.57%).

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This experiment only tests the fleet of Saturday as option for a best fixed fleet. Therefore, it is probably possible to find a fixed fleet for the current research setting, that is not the best possible fleet on any separate day, that overall performs even better than the fleet of Saturday. Next to that, there is the possibility that the current fleet of Bidfood, or another fixed fleet composition, outperforms the fleet of Saturday when demand uncertainty is considered.

Figure 5.3: travelled distance per day of the week with the different fleets considered

5.3.4 Cost savings

Previous sections have shown the benefits that can be obtained by collaboration in terms of distance, time, number of routes, and vehicle utilization. Another interesting measure for practice is cost. Based on cost indications obtained from experts in the field (Bidfood) an indication of the cost savings that can be obtained by collaboration can be given. Costs for fuel and use of vehicle are €1.40 per kilometer and personnel costs are €22.50 per hour.

Savings that can be obtained between the different scenarios considered in this research are given in Table 5.9. Calculations of the savings are given in Appendix B. The most beneficial scenario in terms of travelled distance, scenario 4, also leads to the largest cost savings. The large difference in cost reduction between collaboration with fixed compartment sizes and collaboration with flexible compartment sizes is because of the reduction in total time, which is the most expensive factor in the calculations. Furthermore, only a slightly lower yearly savings is obtained by using the fleet of Saturday than by using the flexible fleet. This corresponds to the small increase in travelled distance. In the most beneficial collaborative scenario, a cost reduction of 22.09% can be obtained compared to the current situation.

65 70 75 80 85 90 95 100 105

Di sta n ce trav ell ed (km 's )

Distance reduction

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Table 5.9: cost savings between different scenarios

Scenarios Yearly savings

Scenario 1 → scenario 3 €42719.93 Scenario 1 → scenario 4 €79336.56 Scenario 1 → scenario with best fixed fleet €79322.05

5.3.5 Company sizes

The third experiment evaluates the differences between collaborating with large- (>50 customers), medium- (13-15 customers), or small- (3-7 customers) sized companies in terms of distance travelled and number of routes. It is evaluated whether it is more beneficial for Bidfood to collaborate with large- (company F), medium- (company A and C), or small- (company B, D and E) sized companies. This is done by investigating scenario 4 for Bidfood combined with large, medium, or small companies. Scenario 4, collaboration with flexible compartment sizes, is evaluated as it was the most beneficial scenario in the first experiment. Table 5.10 presents the results for this experiment. Results are given for the situation in which Bidfood is collaborating with all companies of a category together. For example, results for ‘medium’ show the results of a collaboration between Bidfood, company A and company C. Numbers shown are weekly totals.

Interesting to see is that collaborating with the smaller companies leads to the largest distance reduction and to the largest reduction in number of routes. The small companies have to drive into the city centre to visit only a few customers, which makes the distance they travel per customer larger than for companies with more customers. Experiment 1 already showed that Bidfood needs 15 routes per week to serve their customers. Since on weekly basis six extra routes are needed to serve the customers of the small companies, Bidfood only needs to perform on average one extra route per day.

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Table 5.10: impact of company size on travelled distance and number of routes needed

Distance no collaboration (km) Distance collaboration (km) Reduction

Large 340.41 264.28 -22.36%

Medium 369.92 239.99 -35.12%

Small 355.32 213.07 -40.04%

Number of routes no collaboration Number of routes collaboration Reduction

Large 37 30 -18.92%

Medium 34 26 -23.53%

Small 33 21 -36.36%

5.3.6 Locations of city hub

This section evaluates different locations that can be used to consolidate the products of the food retailers. Three locations close to the city centre are chosen as it is more likely competitors are willing to bring their products to a shared facility than to Bidfood’s depot. These locations are visualized in Figure 5.4. The depots of the collaborating companies are all located to the east of all candidate hub locations. Again, as scenario 4 turned out to be the most favourable scenario in the previous experiments, this experiment is based on scenario 4.

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This experiment demonstrates that both location 1 and 2 are more beneficial than using Bidfood’s depot as consolidation point, and thus achieve relatively higher savings. Location 3 performs slightly worse.

Table 5.11: impact of hub location on travelled distance

Distance hub → city centre (km) Distance individual depots → hub (km) Total distance (km)

Bidfood 388.39 68.4 456.79

Location 1 315.65 115.20 430.85

Location 2 194.82 162.60 357.42

Location 3 259.91 205.20 465.11

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6. Discussion

By studying the delivery networks of seven food retailers in the city centre of Groningen, this thesis aimed to answer the research question: ‘How much savings in travel distance can be obtained by horizontal collaboration of retailers in last mile food deliveries using multi-compartment vehicles compared to no collaboration?’. The experiments performed in this research revealed different aspects that influence the savings in distance that can be reached. This section discusses the implications of these results.

6.1 Theoretical implications

First of all, this thesis proposed a mathematical formulation of the multi-compartment vehicle routing problem with time windows and flexible compartment sizes (MCVRPTWFCS). It thereby elaborates on existing models of Chen & Shi (2019), Henke, Speranza, Wäscher (2015), and Derigs et al. (2011) by making a unique combination of classical VRP extensions as flexible compartment sizes and time windows, and adding some novel elements as including a heterogenous fleet, legal working hours, and two-fold capacity constraints to make the model more realistic.

The experiments performed confirm the findings of Montoya-Torres, Muñoz-Villamizar & Vega-Mejia (2016) that collaboration improves the performance of the network. This research even found a larger reduction in travelled distance. Where Montoya-Torres, Muñoz-Villamizar & Vega-Mejia (2016) consider fixed compartment sizes, this research is the first to quantify the impact of using flexible compartment sizes in practice. The cost reduction based on benchmark data showed by Pérez-Bernabeu et al. (2015) is supported by this thesis. Moreover, it even strengthens their findings since partly real data is used in this thesis. Next to that, a best fixed fleet for the setting under study was proposed in this thesis, providing the insight that from the best possible fleet configurations needed each day, an almost identical performing fixed fleet can be found when demand is not vastly different between the different days of the week. This thesis found that having flexible compartments sizes did not make a significant difference in the non-collaborative scenario, but it did make a significant difference in the collaborative scenario in terms of distance travelled and indirectly cost. It thereby partly confirms the findings of Henke, Speranza & Wäscher (2015), adding that the cost reduction depends on the specific situation in which the flexible compartment sizes are applied.

Collaboration in last mile food deliveries: a multi-compartment vehicle routing problem