The open universal interconnected network of Physical
Internet: a model-based comparison
Master Thesis
MSc. Supply Chain Management
University of Groningen, Faculty of Economics and Business
June 22, 2018
Author: Johan Ziel
Student number: 2588846
E-mail: j.ziel.1@student.rug.nl
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ABSTRACT
Current logistic networks are dedicated, fragmented and overlapping networks in which physical objects are unsustainably moved, stored, realized, handled and supplied. To overcome these unsustainability issues, previous researchers have defined the innovative concept Physical Internet. This system defines an open interconnected logistic network where physical objects are transported in smart modular containers. The purpose of this paper is to determine the benefits in terms of distance and load of the open universal interconnected network of Physical Internet. Therefore, this study proposes a MILP model which embed the open universal interconnectivity and multi-segment transport characteristics of Physical Internet. This proposed model, called the reconsolidation routing problem, allows loads to be unloaded and loaded at hubs. For the comparison to Physical Internet, a computational study is performed to the vehicle routing problem with simultaneous pickup and delivery. Thereby, different network layouts and demand balancing cases are examined. Furthermore, a heuristic algorithm has been proposed for further insight. The outcomes of this study suggest that Physical Internet has relatively high potential benefits in terms of distance and load in comparison to the current logistics networks. Moreover, the type of network and the demand balancing throughout the network showed different insights into the benefits.
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ACKNOWLEDGEMENTS
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TABLE OF CONTENTS
1. INTRODUCTION ... 2 2. THEORETICAL BACKGROUND ... 4 2.1.PHYSICAL INTERNET ... 4 2.1.1. Characteristics ... 4 2.2.PRIOR RESEARCH ... 62.3.VEHICLE ROUTING PROBLEM WITH SIMULTANEOUS PICKUP AND DELIVERY ... 7
3. PROPOSED MATHEMATICAL MODEL ... 8
3.1.NOTATION ... 8 3.2.MODEL ASSUMPTIONS ... 9 3.3.RRP FORMULATION ... 10 4. PROPOSED HEURISTIC ... 12 4.1.MOTIVATION ... 12 4.2.ALGORITHM ... 12 5. COMPUTATIONAL STUDIES ... 15 5.1.RRP VERSUS VRPSPD... 15 5.1.1. Model inputs ... 15 5.1.2. Results... 18 Illustrative example ... 18 Model outputs ... 20
5.2PERFORMANCE PROPOSED HEURISTIC... 23
5.2.1. Model input ... 23 5.2.2. Results... 24 6. DISCUSSION ... 26 7. CONCLUSION ... 27 REFERENCES ... 28 APPENDIX ... 31
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1. INTRODUCTION
According to Montreuil (2011), the current manner in which physical objects are moved, stored, handled, supplied, realized and used is socially, environmentally and economically unsustainable. Montreuil (2011) supports his claim by identifying thirteen main unsustainability symptoms of the current logistic models. One of these symptoms, from an economic and environmental perspective, is that often half empty trucks departure. Another symptom, from a social and economic perspective, is that the truck drivers are often a long time away from home and as result have a precarious social life. Together, Montreuil termed these thirteen symptoms as “the global logistics sustainability grand challenge” (Montreuil, 2011, p. 71).
During the past years, several researchers have supported Montreuil’s (2011) claim and they (mainly) all opt to overcome this grand challenge by developing the Physical Internet (PI) concept (Pan, Ballot, Huang, & Montreuil, 2017; Treiblmaier, Mirkovski, & Lowry, 2016). This innovative concept can be defined as: “a global logistics system based on the interconnection of logistics networks by a standardized set of collaboration protocols, modular containers and smart interfaces for increased efficiency and sustainability” (Ballot, Montreuil, & Meller, 2014, p. 540). Mainly, this concept is based on the Digital Internet metaphor, which involves an interconnected network between all providers that is transparent to all its users (Pan, Nigrelli, Ballot, Sarraj, & Yang, 2015). Since 2009, PI concept has gained transdisciplinary interest from practitioners and researchers all around the world (Pan et al., 2017; Treiblmaier et al., 2016). The Alliance for Logistics Innovation through Collaboration in Europe (ALICE) even created a roadmap to reach the concept of PI in 2050 (ALICE, 2017). Therefore, PI has recently become a trending topic to research.
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Therefore, this paper addresses the research question: What are the benefits of the open universalinterconnected Physical Internet network compared to the current logistics networks in terms of distance and load?
According to Sternberg & Norrman (2017), several prior studies have already examined the potential benefits of the interconnected PI network. Mainly these publications consider the French retail supply and determine the benefits of PI by using simulations (Hakimi, Montreuil, Sarraj, Ballot, & Pan, 2012; Sarraj, Ballot, Pan, Hakimi, et al., 2014). Sarraj et al. (2014), for example, used a multi-agent simulation approach based on the shortest path algorithm to route vehicles. In their study the assumption is made to neglect fleet management. Furthermore, the study of Fazili et al. (2017) investigated the benefits of PI by applying a three phase routing optimization framework. In their study, the routing based-model was derived from the vehicle routing problem (VRP). One of the model assumptions in their paper is that consolidation of loads is possible at all nodes (Fazili et al., 2017).
Based on previous research, this study contributes to literature by demonstrating the benefits of PI in relation to the current logistics networks by proposing an optimization model which takes into consideration different aspects. Specifically, the aim of this proposed model is to optimize vehicle routes by taking into consideration a network with shippers and hubs, where only consolidation of loads can take place at hubs. Furthermore, vehicles have to return to its origin. Since vehicles are allowed to consolidate its load multiple times during its route, this problem has been defined as the reconsolidation routing problem (RRP). To compare the performance of the proposed RRP model with the current logistics networks, this study has conducted a computational study. Thereby, the current logistics networks are represented by the vehicle routing problem with simultaneous pickup and delivery (VRPSPD). Besides this comparison, this study proposes a heuristic in order to solve large network problems.
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2. THEORETICAL BACKGROUND
In this section, the theoretical background is discussed which is relevant in order to create the optimization model. Since PI is at its infancy stage, the PI concept is first explained. Subsequently, the PI-characteristics and prior studies relevant to this research are discussed. Finally, the VRPSPD is shortly described.
2.1. Physical Internet
Recall from the previous section that PI is the movement of physical objects throughout a logistic network, which combines “standardized, modular, and intelligent containers with new logistic protocols and business models” (Montreuil, Meller, & Ballot, 2010, p. 306). This type of network should result in a collaborative, highly leveraged and distributed logistics system and distribution system (Montreuil et al., 2010). Ultimately, the objective of PI is to reduce the thirteen unsustainability symptoms present in the current logistics networks (Montreuil, 2011). To enable this, three key types of physical elements are required: π-containers, π-nodes and π-movers (Montreuil et al., 2010). Π-containers are the smart modular containers in which goods will be transported. The general idea is that these π-containers will become a world-standard in the PI network in terms of dimensions, fixtures and functions. Π-nodes are the nodes in an open universal interconnected network. These π-nodes will collaborate with each other in order to combine shipments. Π-movers are the transport modes which will move the π-containers through the open interconnected network (Montreuil et al., 2010).
2.1.1. Characteristics
Montreuil (2011) defined thirteen PI-characteristics and thirteen asserted unsustainability symptoms of the current logistics networks. Since the research objective is to compare the PI logistic network with the current type of network, only the relevant PI-characteristics are described in this sub-section. These characteristics are: (1) universal interconnectivity; (2) distributed segment intermodal transport; and (3) open global supply web. In the next two paragraphs, these three characteristic of Montreuil (2011) are discussed. In Appendix A, a complete overview of the characteristics and unsustainability symptoms can be found.
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logistics networks are fragmented, overlapping and dedicated to specific organizations, e.g. a supermarket chain (Montreuil, Ballot, & Fontane, 2012). However, the interconnected network implies a collaborative structured network which is accessible for everyone. This openness offers distributors, retailers and producers the option to traverse their products (embedded in π-containers) to a large range of geographically dispersed centers (Montreuil, 2011). One key objective, which has to be considered when realizing an interconnected network, is to ensure that load breaking becomes economically and negligible temporally (Montreuil, 2011). Load breaking is the time loads are sorted, stored and handled.Figure 2.1: Current logistic network versus PI logistic network (adapted from Montreuil et al. (2012))
Squares, triangles, and circles represent manufacturers, warehouses and customers respectively. (a) Current logistic network. The image illustrates two logistic networks. The grey triangles and squares, and plain arrows belong to one logistic network, while the black triangles and squares, and dashed arrows belong to the other network. The two networks are disconnected from each other. (b) PI logistic network. The image illustrates an interconnected network where the network is shared and open to everyone.
Besides this open interconnected network, the aim of PI is to distribute loads via multi-segment intermodal transport (Montreuil, 2011). Similarly as in the Digital Internet, loads should not be directly shipped form source location X to end location Y. Instead, loads should traverse different segments (arcs between two nodes) to reach its final destination. Thereby, the aim is that each vehicle remain active to a specific limited region in order to improve the current precarious social life of drivers (Montreuil, 2011). Moreover, it implies that loads should traverse one or multiple PI-hubs or PI-transit centers (Ballot, Montreuil, & Thivierge, 2012; Fazili et al., 2017; Montreuil, 2011). At these hubs or centers, consolidation and deconsolidation of loads should take place. Specifically, transport modes will be unloaded and reloaded with a new set of loads (depending on the vehicles next visit). In the current network, hubs will only consolidate loads with the same destination or origin (Fazili et al., 2017). Moreover, the current network is
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a combination of hub-and-spoke transport and point-to-point transport which implies that loads are mainly directly shipped to its destination. According to Montreuil (2011), transit nodes and hubs will become responsible for the transfer of π-containers between segments in PI.2.2. Prior research
Currently, the interest and literature in the PI concept is growing (Pan et al., 2017; Sternberg & Norrman, 2017; Treiblmaier et al., 2016). Therefore, researchers have investigated a range of subjects: smart modular π -containers, PI-facilities, potential benefits of PI, etc. This section reviews the main prior literature which examined the potential benefits of the PI network.
The research of Sarraj et al. (2014) investigated the benefits of the PI network via a multi-agent simulation. They included transportation protocols as well as the modular size π-containers in their model to demonstrate the benefits of such a network in the fast moving consumer goods (FMCG) industry. The objective of their simulation was to minimize the transport means by finding the best route via the shortest path algorithm. The research focused on the routing of containers but neglected the end-destination of the transport modes. Their experiments demonstrated that the fill rate of transportation modes increased by 17% and CO2 emission was reduced by 60% (Sarraj, Ballot, Pan, Hakimi, et al., 2014).
Hakimi et al. (2012) used holistic simulations to demonstrate the benefits of PI in terms of sustainability. Thereby, they exploratory examined the benefits of PI in an open logistics system in France. This study demonstrated that the overall travelled distance by PI is significantly lower and that the number of trips in the PI network is much higher (Hakimi et al., 2012).
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Moreover, Sohrabi and Montreuil (2011) and Ballot, Montreuil & Fontane (2011) examined the benefits of PI via an exploratory investigation and continuous approximation method respectively. Sohrabi and Montreuil (2011) examined the effect of an open supply web by sharing distribution centers all over the United States. Their research showed that strong reductions in customer service time can be achieved by sharing networks. However, the consolidation and deconsolidation at hubs is neglected. Moreover, the exploratory study of Ballot et al. (Ballot et al., 2011) stated that interconnection has a huge potential with respect to savings in distance. PI can decrease the overall traversed distance by 20% to 80%.As mentioned in the previous paragraph, several studies have already explored the potential benefits of a PI interconnected network. However, each study conducts its research by including different PI-characteristics and by using specific approaches. This research contributes to literature by determining the potential benefits via an optimization model. Thereby, different aspects and assumptions will be made, such as: consolidation and deconsolidation can take place only at hubs, and vehicle routes should start and end at its origin.
2.3. Vehicle routing problem with simultaneous pickup and delivery
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3. PROPOSED MATHEMATICAL MODEL
In this section, the mathematical model of the reconsolidation routing problem (RRP) is presented. This model is a mixed-integer linear programming (MILP) model which simulates the three PI-characteristics mentioned in the previous sections. Specifically, the RRP model optimizes the route distance of the vehicles by allowing unloading and loading, or in other terms reconsolidation, of loads at each hub. In this section, first a formal description of the RRP is given. Second, the model assumptions are discussed. Third, the mathematical formulation of the RRP is proposed and explained. For the formulation of the VRPSPD the model defined in the paper of Cordeau (2006) is used.
3.1. Notation
The reconsolidation routing problem (RRP) can formally be described as follows. Let there be an undirected graph 𝐺 = (𝑉, 𝐸). Let ℎ be the number of hubs and 𝑐 be the number customers. The vertex set 𝑉 is composed of two subsets 𝑉 = 𝐻 ∪ 𝐶, where 𝐻 = {0, … , ℎ − 1} is the set of hub vertices and 𝐶 = {ℎ, … , 𝑐 + ℎ − 1} is the set of customer vertices. 𝐸 is the set of edges defined as 𝐸 = {(𝑖, 𝑗): 𝑖, 𝑗 ∈ 𝑉, 𝑖 ≠ 𝑗}. The associated distance between each edge (𝑖, 𝑗) is denoted by 𝐷𝑖𝑗. Let 𝑑 denote the number of demands that needs to be traversed via graph 𝐺. The set of demands is denoted by 𝐷 = {0, … , 𝑑}. Associated to each demand 𝑑 ∈ 𝐷, an origin vertex 𝑜(𝑑) ∈ 𝐶 and end-destination vertex 𝑒(𝑑) ∈ 𝐶 \ {𝑜(𝑑)} are denoted to indicate the start and end customer vertex of each demand. Moreover, each demand 𝑑 ∈ 𝐷 has a specific demand quantity 𝑞(𝑑). Let 𝑘 denote the number of vehicles which are used to traverse the demands and let K = {0, …k} be the set of vehicles. Each vehicle 𝑘 ∈ 𝐾 has a capacity 𝐶𝑎𝑝 and is linked to a specific hub ℎ where it starts and ends its route.
For this RRP, five sets of decision variables are used: two binary (𝑥𝑖𝑗𝑘𝑑 and 𝑦
𝑖𝑗𝑘) and three nonnegative continuous variables (𝑠𝑖𝑘, 𝑞𝑖𝑑 and 𝑤
𝑙𝑚). For each edge (𝑖, 𝑗) ∈ 𝐸, each vehicle 𝑘 ∈ 𝐾 and each 𝑑 ∈ 𝐷, let 𝑥𝑖𝑗𝑘𝑑 = 1 if demand 𝑑 is traversed from node 𝑖 to node 𝑗 via vehicle 𝑘; otherwise, 𝑥
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3.2. Model assumptions
The RRP has two objectives: minimize the total route distance and the difference between the routes. Via the arcs and the vehicles, demands should be traversed from their origin vertex to its end-destination vertex. Thereby, demands are allowed to switch vehicles at hubs. Specifically, demands can be unloaded and loaded at each hub, or in other terms called reconsolidated. Besides, the demands are allowed to visit each vertex. The demands are carried to its end-destination vertex by a fleet of vehicles. Recall from section 2.1 that truck drivers preferably have to traverse loads in a restricted region to improve their precarious social life. To guarantee this social element, each vehicle should therefore start and end at the same hub and should approximately traverse the same route distance.
This RRP is a non-deterministic polynomial-time (NP) hard problem. Therefore, several model assumptions are proposed to reduce the computational complexity. Firstly, the number of vehicles is prefixed. It is set equal to the number of hubs, which implies that only one vehicle starts and ends its route at a specific hub. Nevertheless, vehicles are allowed to visit other hubs during its route as long as their start and end destination is at its allocated hub. Secondly, this model assumes a long-term type of planning problem rather than a short-term planning problem. Therefore, the assumption is made that customers and demands are continuously recurring. In fact, the model assumes a steady-state situation and therefore, also no due dates of demands are assumed. This implies that the order sequence of the demands at hubs can be neglected. Specifically, the consolidation of the demands at hubs can take place at any time, due to the fact that the demand is repeatedly appearing at the hub. In this situation, the vehicles do not have to wait for a demand at a hub arriving from a different vehicle. Thirdly, a penalty factor is introduced in the model to equal the different route lengths. Thereby, it guarantees that each vehicle driver traverse approximately the same distance in different settings.
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3.3. RRP formulation
Based on the two previous sub-sections, the RRP can be formulated mathematically as follows:
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𝑦𝑖𝑗𝑘 ∈ {0,1} ∀ 𝑖, 𝑗 ∈ 𝐸, 𝑘 ∈ 𝐾 (16)
𝑠𝑖𝑘 ≥ 0 ∀ 𝑖 ∈ 𝑁, 𝑘 ∈ 𝐾 (17)
𝑞𝑖𝑑≥ 0 ∀ 𝑖 ∈ 𝑁, 𝑑 ∈ 𝐷 (18)
The objective function (1) minimizes the total traversed distance of the vehicles. Thereby, the total distance is determined by summing up the edge distances used by the set of vehicles. The second term of (1) ensures, as long as the penalty factor 𝑃 is set properly, that the total traversed distance of each vehicle is forced to approximately similar values. Constraints (2) and (3) guarantee that each demand arriving at a hub or customer, which is not its origin or end-destination customer vertex, leaves the hub or customer. In case of a hub, the demand can leave the hub with any visiting vehicle. Constraints (4) and (5) ensure that each demand leaves its origin customer vertex and arrives at its end-destination vertex. The vehicle capacity is ensured by constraint (6). Constraint (7) ensures that each vehicle arrives and leaves a vertex it visits, while constraint (8) and (9) guarantee that each vehicle 𝑖 start and end its route at its allocated hub 𝑖. The two decision variables 𝑥𝑖𝑗𝑘𝑑 and 𝑦
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4. PROPOSED HEURISTIC
The RRP model, formulated in the previous section, is a problem with multiple decision variables with multiple indices. Test running this model showed that the RRP is computational demanding problem which can only run small data sets to optimality in reasonable time. Therefore, a main issue of this model is the computational complexity. However, to determine near-optimal or good solutions for larger data sets, a RRP-heuristic algorithm has been developed. In this section, this heuristic is provided and further enlightened.
4.1. Motivation
In the RRP model, the optimal route of the vehicles is decided by taking into consideration several aspects of PI. One major aspect in the network is the flow of demands. These demand flows can be traversed by multiple vehicles over multiple edges and can be consolidated at each hub. Hence, the search for an optimal route for the vehicle route becomes computational demanding. Therefore, the proposed heuristic is designed to simplify the vehicle routing. Specifically, a heuristic algorithm has been constructed to determine the vehicle route for each vehicle. This algorithm is based on the Nearest Neighbor Algorithm (NNA). Previous studies have demonstrated that NNA is a widely applied technique in VRP (Du & He, 2012; Gutin, Yeo, & Zverovich, 2002). Since the model is constructing routes on a symmetric network using Euclidean distances and contains aspects of VRP (e.g. hubs are set as the depot of each vehicle), NNA has been selected. In the next paragraph, a general description of the proposed heuristic algorithm is given.
4.2. Algorithm
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If there are any unvisited customer, the next step has to be performed. This procedure is iterative and will stop when all customers are visited. In this step, each unvisited customer will be allocated one-by-one to a specific vehicle route. This unvisited customer will be determined by calculating the distance from each unvisited customer to each visited end-customer. End-customer is defined the customer at the end of the vehicle route. Since the end-customers of each vehicle route are not yet connected, each vehicle route will contain two of these end-customers. After determining all the distances from each unvisited customer to each visited end-customer, the distances are ranked at ascending order. Next the shortest distance pair is selected (unvisited customer, visited end-customer). In case multiple vehicle routes have the same visited end-customer at the end of their route, the customer will be added to the vehicle route which has at that moment the shortest routing distance. Consequently, the unvisited customer becomes visited. This procedure of allocating unvisited customers is iterative and is finished if every unvisited customer is allocated to a vehicle route. Notice that during this procedure the end-customer changes due to the allocation of unvisited customers to vehicle routes.To ensure that demands can reach its end-destination customer and demands can be consolidated at hubs, the vehicle routes should be set up accordingly. Specifically, all vehicle routes should be interconnected to each other via hubs. Since connecting each vehicle route to every other vehicle route is not preferable with respect to minimizing the overall distance, each route will be connected to one other route via a hub. To guarantee that all the routes are interconnected and therefore demands can reach its end-destination customer, each route will be connected to one hub. To prevent sub-tours of vehicle routes, the NNA is used to determine the allocation of hubs.
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Figure 4.1: Flowchart of the RRP heuristic algorithm
Start
For each vehicle route m, link hub m to the two nearest
customers
The number of vehicle routes is equal to the number of hubs. At hub m, vehicle route m starts. Besides, set S is an empty set
For each vehicle route m, start at hub m
Are all customers linked / visited?
Determine the unvisited customers
Determine for each unvisited customer the distance to each visited end-customer of each
vehicle route m
Is this visited end-customer in multiple
vehicle routes?
For the specific vehicle route m, link the visited
end-customer to the unvisited customer Select the unvisited customer and visited end-customer pair
with the shortest distance Determine the two visited end-customers of each vehicle
route m
For the vehicle route with the shortest route distance, link the visited end-customer to the
unvisited customer
h vehicle route with the
longest route distance. Set S: S = S U {h}
n nearest hub to h
not in S
S S U {n} h n Does set S contain
each hub?
Determine the two visited end-customers of vehicle
route h
Link both visited end-customers of h to n.Vehicle
route is complete Link both visited
end-customers of n to the first entrance in set S. Vehicle
route is complete Determine the two visited
end-customers of n End No No Yes Yes No Yes
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5. COMPUTATIONAL STUDIES
In this research, two computational studies have been conducted. First, to determine the benefits of the PI-related RRP in comparison to the VRPSPD. Second, to evaluate the performance of the proposed heuristic. The next two paragraphs describe the performance measurements as well as the software and computer specifics which have been used to solve the models. The remaining section discusses the model inputs as well as the results of each computational study.
Regarding the aim of this research, the next three performance measurements are selected: total
traversed distance, average load and total distance traversed empty. These measurements can be defined
respectively as: the sum of all the vehicle routes, the average load carried by a vehicle during its route, and the sum of all the distances vehicle carries no load. Specifically, the average load has been calculated by taking the sum of the demand traversed over an arc times the corresponding distance of the arc and divide this number with the total traversed distance.
Both the RRP and VRPSPD model have been solved using the commercially available solver Gurobi Optimizer. Thereby, Python has been used as programming language and Spyder (Scientific python development environment) has been used as the integrated development environment (IDE). Similarly, Python and Spyder have been used for the heuristic. However, Gurobi Optimizer has been used as a tool to check the proposed routes of the heuristic to ensure that all the demands can reach its end-customer vertex. Moreover, these models have been solved by running the software on a MacBook Air with CPU Intel Core i5 1.6 GHz and 4GB RAM.
5.1. RRP versus VRPSPD
5.1.1. Model inputs
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Figure 5.1: The two logistic network layouts: (a) clustered; (b) scattered
Another main aspect is the effect of balanced and unbalanced demands. Balanced is defined as: each customer receives the same amount of demands as it ships, while unbalanced is defined as: the inbound and outbound demand are different. For clarity, amount of demands does not refer to the volume of the demands, but to an order. Regarding the PI concept, transport of air by transport modes should be minimized. Therefore, it is preferable that a vehicle should pass a shipper if it also can fill-up its truck. By setting up a balanced network situation, this characteristic can be stimulated. Nevertheless, an unbalanced situation is more a real-life scenario, due to the fact that not every customer receives the same amount of demands as it ships. Therefore, this study has investigated both cases.
Based on these two main aspects, the computational study could be composed out of four instances: scattered network with unbalanced and balanced demands, and clustered network with unbalanced and balanced demands. Since this study is mainly interested in the benefits of PI and running experiments is computational demanding, a clustered network with unbalanced demands is omitted. The decision to exclude this type of network is because, out of the four instances, these settings are the least representative of a PI-network. Therefore, this computational study consists out of the next three main instances: scattered network with balanced demands (SNBD), scattered network with unbalanced demands (SNUBD), and clustered network with balanced demands (CNBD). Each of these main instances have been examined on three sizes of networks (A, B and C) with specific settings. Table 5.1 shows the size of each network. The number of hubs/vehicles (H / K), customers (C) and demands (D) vary in size per network. Due to the computational complexity of the model, these networks are set small.
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Since this computational study takes into consideration different network layouts, demand balancing and network sizes, different data inputs are required. For each network size (A, B and C) and specific instance (SNBD, SNUBD and CNBD), case specific input is required. Table 5.2 presents the nine different cases and the corresponding inputs. Each case has been run for both unlimited (UL) and limited (L) capacity. Furthermore, the table shows that different inputs are required for specific cases (A, B and C). Thereby, the geography sets (SCA, SCB, SCC, CLA, CLB, and CLC) are representing the coordinates of the customers and hubs for a specific case. Depending on the network size and layout, a specific geography set is used. The demand sets (α, β, γ, and δ) represent the origin, end-destination and quantity of each demand for a specific case. Due to the network size and (un)balancing of demands, different demand sets are defined. Lastly, the allocation sets (λ, ρ, and μ) represent the dedication of demands to specific hubs for a specific case and are depending on the network size.Moreover, to give an indication of the input parameters: the quantity of the demands has been randomly generated between 20 – 100; limited capacity has been set to 200; allocation set have randomly be allocated; customer locations are located between x,y-coordinates 15-70, depending on network layout.
Table 5.1: Network sizes
Network
A B C
H / K 3 2 2
C 5 5 7
D 10 10 14
Table 5.2: Model inputs
Specifications Cases
1a/b 2a/b 3a/b 4a/b 5a/b 6a/b 7a/b 8a/b 9a/b
Network A B C
Instance SNBD CNBD SNUBD SNBD CNBD SNUBD SNBD CNBD SNUBD
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5.1.2. Results
Illustrative example
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Figure 5.2: Output results of an illustrative example: the RRP (a) and VRPSPD (b)-(d) model for a scattered network with balanced demands.
In this example, the routes for network A (3 hubs, 5 customers, 10 demands) with limited vehicle capacity has been optimized (case 1b). In this example, Hn is the hub vertex, Cn is the
customer vertex, and dn is the demand traversed over an edge. Vehicle route 1, 2 and 3 are
colored blue, red and green respectively. In this figure, the flow of the demands d1 (origin:
C1; end-destination: C4; quantity 64), d2 (origin: C2; end-destination: C5; quantity: 49) and
d4 (origin: C3; end-destination: C4; quantity: 70) are displayed as an example.
(a) RRP: vehicle routes 1-3 (b) VRPSPD: vehicle route 1
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Model outputs
The results of the entire comparison are presented in table 5.3. In case of the RRP model, the results have been obtained by running each case (both unlimited and limited) with two different configurations with respect to geography. The VRPSPD model has been run six times. Three different hub allocation sets for each geographical configuration. The underlying reason therefore, is the sensitivity of the VRPSPD model to the hub allocation of demands. In the table, the columns of the three performance measures are representing the averages of the outputs per case. Since the average total distance traversed empty for RRP was for each case equal to zero, this column has not been included in the table.
Table 5.3. Comparison of RRP and VRPSPD per network type
Model input Model output
Case
Net-work Cap Instance
Average total
distance traversed Average load Average total
distance traversed empty by VRPSPD VRP-SPD RRP Diff. VRP-SPD RRP Diff. 1a A UL SNBD 429 182 -58% 53 169 219% 97 2a CNBD 430 225 -48% 56 156 179% 82 3a SNUBD 402 184 -54% 55 164 200% 109 1b L SNBD 429 195 -55% 53 111 109% 97 2b CNBD 430 228 -47% 56 122 118% 82 3b SNUBD 402 225 -44% 55 125 128% 109 4a B UL SNBD 313 155 -50% 54 182 237% 39 5a CNBD 320 173 -46% 55 186 238% 41 6a SNUBD 309 160 -48% 55 207 274% 45 4b L SNBD 313 158 -50% 54 141 161% 39 5b CNBD 321 177 -45% 49 143 192% 49 6b SNUBD 309 201 -35% 55 133 136% 45 7a C UL SNBD 339 156 -54% 76 303 299% 51 8a CNBD 292 163 -44% 58 196 238% 39 9a SNUBD 329 161 -51% 79 346 337% 58 7b L SNBD 365 199 -45% 66 152 130% 59 8b CNBD 295 199 -33% 51 130 155% 40
9b SNUBD 382 N.A. N.A. 58 N.A. N.A. 75
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The output results in the table show that the differences between RRP and VRPSDP model are significant for each performance measurement and for each case. The difference in average total distancetraversed ranges from -58% to -33%, while the difference in average load ranges from 109% to 337%. The
final column shows that the average total distance traversed empty ranges from 39 to 109 for the VRPSPD cases, while this number is equal to zero for each RRP case. Therefore, the output results imply that a PI-network is significantly performing better in comparison to the current logistics PI-networks simulated by VRPSPD, which confirms previous literature. First of all, this indicates that reconsolidation at hubs guarantees that the average total distance traversed by each vehicle is shorter. Second of all, this implies that each vehicle will carry a larger average load. Third of all, this means that each vehicle will never traverse an edge distance without a load.
Moreover, the output shows that the average total distance traversed and the average load decreases per network size if the capacity changes from unlimited to limited. This can logically be explained due to the fact that vehicles can carry an infinite load. Besides, the output results show that increasing the number of hubs increases the difference in average total distance traversed. This result suggests that a PI network is preferred for a higher ratio of hubs with respect to the number of customers.
Scattered versus clustered
Out of table 5.3, the effect of a scattered versus a clustered network can be determined for each network size (A, B, and C). Table 5.4 presents the comparison between scattered and clustered networks with balanced demands and shows which network saves more in terms of distance and load if the PI-network is compared to the current logistics networks. The column of the relative difference of the average total
distance traversed shows that in a scattered network more savings with respect to distance can be obtained
than in a clustered network. This holds for both limited and unlimited capacity. Therefore, this result suggests that the PI-network is more beneficial in a scattered than in a clustered geography with respect to total distance.
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traversed. Since in a clustered network, the distances to other clusters are relatively long, it is optimal to cross this edge distance up to a minimum. Therefore, the load will be relatively high in case of these edge distances resulting in a high average load. In the case of the unlimited capacity, this relative difference inaverage load numbers can be explained due to the objective function of the RRP model. The objective
function is minimizing the total distance. In case of unlimited capacity, it only ensures that demands reach end-destinations. Therefore, it does not take into account the flow of demands. Hence, the average load is depending on the network size.
Table 5.4 Scattered versus clustered network with balanced demands
Case Cap
Net-work
Diff. (RRP-VRPSPD) average total distance
traversed Diff. (RRP-VRPSPD) average load Average total distance traversed empty by VRPSPD SN-BD CNBD Rel. diff. SN- BD CNBD Rel. diff. SN- BD CNBD Diff. 1 vs. 2 UL A -58% -48% 10% 219% 179% -40% 97 82 -15% 4 vs. 5 B -50% -46% 4% 237% 238% 1% 39 41 5% 7 vs. 8 C -54% -44% 10% 299% 238% -61% 51 39 -24% 1 vs. 2 L A -55% -47% 8% 109% 118% -9% 97 82 -15% 4 vs. 5 B -50% -45% 5% 161% 192% -31% 39 49 26% 7 vs. 8 C -45% -33% 12% 130% 155% -25% 59 40 -32% Abbreviations: vehicle capacity (Cap); difference (Diff.); unlimited (UL); limited (L); scattered network with balanced demands (SNBD); clustered network with balanced demands (CNBD); relative difference (Rel. diff)
Balanced versus unbalanced
Besides scattered and clustered, the effect of unbalanced and balanced demands can be compared for each network size (A, B and C). Table 5.5 presents this comparison. The relative difference in average total
distance traversed shows that more savings with respect to distance can be obtained by applying the RRP
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Nevertheless, the table shows no trend for the average load. For unlimited capacity, the same reason applies as in the scattered versus clustered comparison. However, this time the average load is depending on the demand set. In the limited capacity cases, the results are unexpected. As in the scattered versus clustered comparison, an increase in average load was expected. This result can be explained by the definition of average load and the demand set. Because of the specific demand set, the sum of edge distance times demand traversed over edge varies depending on the network size. The average load is sensitive to the origin and end-destination customers of each demand, as well as the network size.Table 5.5 Scattered network with balanced and unbalanced demands
Case Cap
Net-work
Diff. (RRP-VRPSPD) average total distance
traversed Diff. (RRP-VRPSPD) average load Average total distance traversed empty by VRPSPD SN-BD SN-UBD Rel. diff. SN- BD SN-UBD Rel. diff. SN-BD SN-UBD Diff. 1 vs. 3 UL A -58% -54% 4% 219% 200% -19% 97 109 12% 4 vs. 6 B -50% -48% 2% 237% 274% 37% 39 45 6% 7 vs. 9 C -54% -51% 3% 299% 337% 38% 51 58 7% 1 vs. 3 L A -55% -44% 11% 109% 128% 19% 97 109 12% 4 vs. 6 B -50% -35% 15% 161% 136% -25% 39 45 6%
7 vs. 9 C -45% N.A. N.A. 130% N.A. N.A. 59 75 16% Abbreviations: vehicle capacity (Cap); difference (Diff.); unlimited (UL); limited (L); relative difference (Rel. diff.) scattered network with balanced demands (SNBD); scattered network with unbalanced demands (SNUBD); not available due to computational limitations (N.A.).
5.2 Performance proposed heuristic
5.2.1. Model input
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5.2.2. Results
The results of this computational results are presented in table 5.6. Thereby, the performance measurement
total distance traversed empty and average load are eliminated, since the objective function of RRP
minimizes only the average total traversed distance and does not take into consideration the flow of demands in unlimited capacity cases. Out of the table can be concluded that the performance of the heuristic in time is good. On average the heuristic solves the vehicle routing in 0.309 seconds, while without the heuristic the average computational time was 92.7 seconds. Therefore, the heuristic decreases the computational time on average with 99.1%. Moreover, the results show that the heuristic takes the same amount of time for each network type A and C.
Regarding the average total distance traversed, the heuristic creates a solution with on average a 24% optimality gap. However, the table suggests that for a closed balanced network, the heuristic is closer to optimality than for the other types of networks layouts. Moreover, depending on the size of the network, the performance of the heuristic differs. In network A, the performance of the average total distance traversed is significantly lower than in network C. Despite the fact that the overall performance of the heuristic is not close to optimality, the gaining in computational time is high.
Table 5.6. Performance of the proposed heuristic
Model input
Model output
Case
Network
Instance
Average total distance
traversed
Computational time
(sec.)
RRP
Heur.
Diff.
RRP
Heur.
Diff.
1a
A
SBN
182
220
21%
75.9
0.288 -99.6%
2a
CBN
225
235
5%
237
0.299 -99.9%
3a
SUBN
184
220
20%
88.9
0.271 -99.7%
7a
C
SBN
156
221
42%
18.7
0.312 -98.3%
8a
CBN
163
195
20%
119
0.297 -99.8%
9a
SUBN
161
221
37%
16.5
0.385 -97.7%
Abbreviations: difference (Diff.); heuristic (Heur.); scattered network with balanced demands (SNBD); clustered network with balanced demands (CNBD); scattered network with unbalanced demands (SNUBD)
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an hour, the heuristic only took 0.393 and 0.417 seconds respectively. Analyzing these two examples, shows that the clustered balanced network has a better output than the scattered balanced network (as table 5.5. already suggested). While figure (a) shows crisscrossing routes and difference in route lengths, figure (b) illustrates approximately similar route lengths and an almost none overlapping network. Therefore, example (b) illustrates more PI characteristics. Furthermore, both examples show that the whole network is interconnected: the flow of demands from origin to end-customer is ensured.Figure 5.3. Illustrative example of the proposed heuristic for large network sizes: (a) scattered and (b) clustered network with balanced demands example.
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6. DISCUSSION
As is shown in the previous section, the main result of this study is that the PI-related RRP model is significantly performing better than the current logistics-related VRPSDP model with respect to distance and load. In case of limited capacity, the average decrease in distance is 44%, while the average increase in load is 144%. These numbers confirm the statements in literature that a PI-interconnected network has high potential benefits with respect to load and distance. Furthermore, it meets the expectations that consolidation at hubs improves the total traversed distance and load of transport modes. This can be explained due to the fact that shippers can share vehicles and hubs. Thereby, it can save shippers additional vehicle trips.
Moreover, the output results suggested that the most savings in distance can be generated by applying PI to a scattered network with balanced demands. Due to this scattered network, hubs will probably be located closer to each other than in a clustered network. Therefore, the effect of reconsolidation between hubs can increase between shippers. Moreover, a balanced network ensures the distribution of loads over different vehicle routes.
The results of this study look promising. However, the computational numbers and statements should be interpreted with some caution. First of all, because the proposed model is a simple version of the whole interconnected network of PI. One of the assumption that is made in this model is long-term planning scheduling. It neglects order sequence and assumes that vehicles can be shipped as soon as they arrive at a hub. Therefore, the results are limited to situation in which demands and customers are continuously recurring. Furthermore, it should be noted that the average load is not taken into the objective function. This implies that the average loads have not been optimized, only the total traversed distance. Therefore, the average load values for each case can be put into discussion.
Another limitation of this research is that a limited set of experiments with limited data sets have been used due to computational complexity. Therefore, the numbers only present indication of the benefits. Furthermore, it should be noticed from table 5.3 that the average total distance traversed empty by the VRPSPD is high, especially for network A. Since in network A ten demands are assigned to three dedicated hubs, the amount of demands dedicated to a hub can become not representable for reality. Particularly, when comparing these values with network B (one hub less), it can be seen that the difference in empty travel is large. Moreover, it should be taken into account that the dataset only considers the simplest version of inputs.
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7. CONCLUSION
In conclusion, this study proposed and preliminary tested a reconsolidation routing problem for the PI network. By performing a computational study of this model, and comparting it to the results of the current logistics networks represented by VRPSPD, the potential benefits of PI were obtained. The result suggests that this PI-related RRP model decreases the total distance with an average of 44% considering long-term planning. Furthermore, this computational study suggested an increase in average load. Besides, it examined the effect of network layout and balancing of demands in case of PI. Thereby, the results suggest that the most savings by a PI-network compared to the current network can be achieved, with respect to distance, in a scattered network. Furthermore, this research proposed a heuristic to illustrate the problem in a larger data set.
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