Internet
Master’s Thesis EORAS, Operations Research University of Groningen
March 11, 2018
A system design for the Physical
Internet
Ting An Phoa
s2381761
Abstract
In this research a system design for the Physical Internet (PI) is proposed, which is based on the public transport system. In this proposed system, an interconnected hub network will be extensively used and transportation services of various modes run on a fixed schedule between these hubs. The frequency and timing of the transportation services will be based on expected demand. Loads can then determine their route over the network to their destination based on easy decisions, much alike passengers in the public transportation system. Since there are no long-term contracts between shippers and transporters, the system is very flexible and should deal with unforeseen events better than the current transportation system. A numerical study is performed for a single arc of the network in a deterministic and a stochastic setting. In this study, we compare the performance of three cases: a decentralized optimization case where multiple transporters plan their transportation individually, a centralized optimization case representing full cooperation between these transporters and a PI case with a fixed schedule and simple protocols. Due to its greater flexibility, the PI system performs relatively well in the stochastic setting and encouraging results are obtained in terms of costs and environmental performance. Moreover, the results indicate that the PI case performs relatively better compared to the planned optimization cases as the number of participating transporters increases.
1
Introduction
The current way of transporting goods is not sustainable economically and environmentally (Montreuil, 2011). Sarraj et al. (2014) state that the logistics performance is limited by pur-suing two antagonist goals: just in time delivery and environmental performance. For just in time delivery, road transportation has advantages in terms of speed and flexibility. However, truck transportation has a more severe impact on the environment and is more expensive than barge or rail transportation, since the latter profit from economies of scale. According to the European Environment Agency (2013), CO2 emissions of trucks are around 75 grams
per transport unit (tonne-km), whereas for trains and maritime barges they are around 21 g/tkm and 14 g/tkm respectively. The transportation sector contributes a significant part of the GHG. In the European Union, the relative share of the transportation sector in total GHG emissions increased from 15% in 1990 to 22% in 2015 (Eurostat, 2015), emphasizing
the relevance of the problem. In our vision, there are several reasons why the current logistic performance is limited. First, planning all routes for the transportation services and the allocation of goods to those services is a difficult problem, which gets more complicated as the number of origins, destinations, vehicles or packages grows. Moreover, companies have unbalanced flows, which inherently causes underutilized transportation means. Cooperation with other companies might resolve this problem partially. By cooperating planning and activities, it is possible to share costs or to avoid unnecessary costs and obtain economies of scale. However, selecting partners is a difficult task since e.g. demands and capacities should match, quality requirements should be agreed on and costs have to be divided. Another way to obtain economies of scale is via third party logistic providers (3PL). A 3PL can plan all shipments based on all transportation demands. The above described planning problems become even more difficult, since in the real world deviations from the planning (e.g. delays, cancellation of services and change in demand) occur. Partial or full replanning (van Riessen et al., 2015) is necessary and re-allocating loads to other services might be impossible due to delivery deadlines or the fact that the services have been planned full, which will incur extra costs and GHG emissions.
To overcome these logistic problems, Montreuil (2011) envisions the Physical Internet (PI). The goal is “to enable the global sustainability of physical object mobility, storage, real-ization, supply and usage”. In his paradigm breaking vision, a Digital Internet inspired metaphor is exploited to envision a breakthrough concept for the physical transportation world. Montreuil, Meller, and Ballot (2010) describe the PI idea as: “Goods are container-ized in containers of modular dimensions and, as data packets in the Digital Internet, are routed using their PI identifier towards their destination using highly efficient, shared trans-portation, storage and handling means.” There should be a shift from fragmented, hard to optimize, closed operational networks, to a system like the Digital Internet, where networks are interconnected. An example by Montreuil of the difference between fragmented and in-terconnected networks is given in Figure 1. In this two company logistic network plants are represented by squares, warehouses by triangles and customer delivery points by circles. On the left side, it can be seen that the networks overlap, but are completely disconnected, re-sulting in a low efficiency. On the right side, in the connected network, products are shipped through the hubs of the network. This concentration of flows helps efficiency because of the economies of scale. Furthermore, as little as possible should be planned. Decisions should be taken on the spot, given current information on opportunities and containers should float seamlessly to their destinations.
Figure 1: Fragmented network (left) & Interconnected network (right) (Montreuil et al., 2012)
modes travel between locations on a predefined schedule. The services on this schedule are available for all shippers. The PI containers can then, much alike passengers in the public transport, determine their route through the network, based on current information and easy decisions. At all hubs, the PI containers can choose the most suitable transportation service towards their destination. We expect that for a large and dense enough system, there will be multiple suitable services for each container and enough containers for each transporter. Another advantage is that if any deviations occur, the container can determine a new route at any hub easily, without the necessity of replanning the route of other containers or the schedule of transportation services.
This leads to the following research question:
How can a Physical Internet inspired system be designed to overcome the current problems in logistics?
In order to answer this question the following sub-questions are defined:
• How can the network be strategically set up in terms of topology, information sharing, modes and loads?
• How do the stakeholders make their decisions at a tactical level?
– What services (origin, destination and mode) do transporters offer at what time and price?
– How do shippers determine the route of their loads over the network, given costs, times and delivery deadlines?
• How are operational problems handled?
– In case transportation means are full, how are loads prioritized?
For a system with two nodes, we will analyse how the proposed PI system performs compared to a system like the current system, where all departure times of services and assignments of loads to services are planned optimally, based on the realized demands. We will compare three ways of planning transportation: a decentralized optimization case, where transporters individually plan their schedule and container assignment, a centralized optimization case, where full cooperation is considered (like a 3PL) and the PI case with a fixed schedule. We will perform experiments and analyse the size effect by the varying the market size of demand and analyse the cooperation effect by varying the number of transporters. Furthermore, we will evaluate the performance of the three cases in a deterministic and in a stochastic envi-ronment, to analyse the flexibility effect.
The rest of this thesis is structured as follows. In the next section the relevant literature will be reviewed. In section 3 we describe the system design for the Physical Internet we propose. Then, in section 4 we elaborate on the methodology used to analyse the system performance of the PI compared to the current system. In sections 5 and 6 we perform a numerical study and present the results. Finally, in sections 7 and 8 we will draw conclusions and propose further research opportunities.
2
Literature review
In this section the relevant literature is reviewed. The focus of this research is on the PI system design. Therefore we consider work on PI network design and transportation planning and we do not evaluate e.g. hub design, urban logistics or the functionalities of PI containers. The PI is a relatively new concept and academic sources are scarce. Hence we review also related subjects to obtain interesting insights for the PI system design. For example, multimodal and especially synchromodal transport networks share the goal of the modal shift with the PI. Moreover, the literature regarding this subject is often categorised on decision horizon, which provides a framework to describe the system design of the PI. Also public transport models, by which our proposed system for the PI is inspired, could provide interesting insights and are reviewed here.
2.1
The Physical Internet
as a foundation for the PI infrastructure, like vehicles, hubs, etc. A key objective is to make load breaking almost negligible temporally and economically. So, with the Physical Internet, transportation would evolve from point-to-point hub-and-spoke transport to multi-segment intermodal transport, where nodes are openly accessible and service capacity is available on a per-use basis. Since a lot of actors are involved, there should be open performance monitoring and capability certifications.
The potential of the Physical Internet has been demonstrated by several simulation stud-ies with different focus, all using a set of actual flows from the fast-moving consumer goods (FMCG) market in France. Ballot, Gobet, and Montreuil (2012) focused on the PI open hub network design problem. They found that the PI open hub network reduces fuel consumption from 21 million to 17 million liters. Hakimi et al. (2012) focused on how the web simulator was designed and developed. Their proposed simulation model contains three main agents: a supply chain manager, a transportation agent and a routing agent whose behaviour can be adapted to target economical, social or environmental objectives. A PI scenario reduces the total travel distance from 54.7 million to 43.7 million kilometres. The work of Sarraj et al. (2014) concerned quantitative modelling aspects of routing of containers in the PI. A key aim is providing a primer on defining the protocols to find the best path routing for each container and minimise the use of transportation means. The path is made of several logistic services of potentially different modes. At each hub, there is a search for “the best fitting transportation means” for the next segment. The minimisation objectives are costs, time and environmental impact and the best route is based on shortest path algorithms. Next to the route decision procedure, a protocol is introduced that aims to fully load the selected transportation services. This protocol optimises the consolidation of containers by next destination while looking to have urgent containers to shipped first. They found that the fill rate increased from 59% to between 65% and 76% and combined with the higher usage of electric rail road this reduced CO2 emissions by up to 60%.
2.2
Multimodal, intermodal and synchromodal transportation
The literature on multimodal, intermodal and synchromodal transportation is relevant for this research since the goal of a modal shift is shared and explicitly considered. Moreover, according to ALICE, synchromodality can be seen as a step towards the Physical Internet since it offers flexible planning where routing decisions are made as late as possible. Stead-ieSeifi et al. (2014) define multimodal transportation as the transportation of goods by a sequence of at least two different modes. Intermodal transportation is defined as a type of multimodal transportation, where the load is transported from an origin to a destination in one and the same intermodal transportation unit, without handling the goods themselves when changing modes. Synchromodal transportation involves a structured, efficient and syn-chronized combination of two or more transportation modes. The carriers can independently and at any time select the best mode based on operational circumstances.
problems. Medium term, tactical, problems aim to utilize the given infrastructure optimally by an efficient allocation of existing resources and planning of routes and frequency. Short term, operational, planning deals with the real-time requirements of all stakeholders. The goal is still to find the best allocation of resources to the demand, however, this takes place in a highly dynamic environment where the time factor plays an important role and stochas-ticity is explicitly addressed.
Groothedde, Ruijgrok, and Tavasszy (2005) state that logistics costs can be decreased and service levels maintained in the FMCG market by shifting the stable part of demand to modes that profit from economies of scale such as rail and barge. There needs to be collab-oration between shippers to create a collaborative hub network and horizontal integration such that fast, flexible and expensive trucking and cheap, slow and inflexible modes (rail, barge) are used parallel. The development of the hub network is done by an improvement heuristic by stepwise adding hubs and capacity to the network. A similar procedure could be used in developing the hub network for the Physical Internet, especially since in this hub network design the change in modal split is considered.
Behdani et al. (2016) present a mathematical model for a synchromodal transport system between one origin-destination pair with delivery deadlines. The integrated service design model determines the optimal schedule and timing of services of all transportation modes (barges and trains) and the assignment of containers to each service simultaneously. Here the demand is known, where quantity, origin, destination, release time and due dates of contain-ers are given. Trucks are considered to be always available and able to deliver the loads before the due date, hence no overdue deliveries are allowed in the model. They compare this model in a deterministic setting to a service design without integration (barges and trains planned separately) and a fixed schedule of trains and barges, where every batch of containers takes the earliest available service that can deliver the batch on time. For our numerical study we will slightly adjust (we do not consider opening hours of terminals) their integrated service design to represent our centralized optimization case. We extend the research of Behdani et al. by considering multiple transporters in our decentralized optimization case to analyse the effects of cooperation and run experiments for different sizes of the problem. Moreover, for the PI system we propose, the selection of a service on a fixed schedule will also be based on costs, whereas Behdani et al. only base it on time. Furthermore, an important extension is that we introduce unexpected events to analyse how stochasticity influences the performance of the cases. To model this stochasticity, we follow the approach of van Riessen et al. (2015), who focus on the impact and relevance of transit disturbances on the network performance. They optimize the planning for a week of given demand, where all containers have a specified release and due time. Disturbances considered are late departure, early departure or cancel-lation and are known in advance (i.e. after the optimization, but before the first release or departure). After a disturbance, the planning can be updated optimally, called a full update, where all remaining transportation demands and the updated routes are considered, or, only containers planned on the disturbed service can be re-planned, which is called a local update.
and Macharis and Bontekoning (2004).
2.3
Public transport
We propose a system for the transportation of goods that is based on the public transport system. Instead of planning services and allocating containers as done at the tactical level in multimodal transportation, containers, much alike passengers in the public transport, find their way through the network to their destination based on a known schedule of transporta-tion services. The literature on public transportatransporta-tion could give insights on how to apply the PI. In public transport, two decisions are to be made. First, the timetable is determined by the transporter. Second, passengers in the public transport or containers in the PI choose the transportation services based on this timetable.
The literature reviews of Desaulniers and Hickman (2007), Guihaire and Hao (2008) and Ibarra-Rojas et al. (2015) give a good overview of problems, objectives and solution method-ologies for the frequency setting and timetabling. It should be noted that in public transport, there are two conflicting objectives. From the operator’s point of view, the goal is to make as much profit as possible or to reduce costs as much as possible. Whereas from the users’ perspective, the system should offer a good quality (comfortable, fast, direct, reliable) service to travel easily at low costs. This leads to multi-objective problems, quality requirements or budget constraints. In the PI setting, the main goal for the transporters and shippers will be to make as much profit as possible or to reduce costs as far as possible, at a high reliabil-ity level. Other differences between the PI and public transport networks are e.g. that we envision multiple competing transporters and no (governmental) quality requirements, but open performance monitoring.
Interesting insights for the frequency setting and timetabling of transportation services can be obtained from the research of Newell (1971) and Niu and Zhou (2013). Newell derived that for a single route with multiple stops and a given smooth arrival rate function, in order to minimize total waiting time for passengers, if capacity is sufficient and the number of vehi-cles is large, both the optimal flow rate of vehivehi-cles and the number of passengers per vehicle vary with time approximately as the square root of the arrival rate. Niu and Zhou optimize an urban rail timetable on a corridor under time-dependent demand and over-saturated con-ditions by minimizing overall passenger waiting times. They find that when the passenger arrival pattern follows a particular probability distribution, an even schedule with constant headway can reduce the total waiting time of passengers. So, with frequently enough service of vehicles and evenly distributed arrivals, an even schedule is optimal to minimize waiting time.
Several problem variants are available. Some examples are: earliest arrival, minimum travel time or number of transfers. For a more complete overview on route planning we refer to Bast et al. (2016).
3
Envisioned PI system
In this section, we describe our vision on how a Physical Internet based logistic system might work. The performance of the current logistic system is limited by, among other things, closed and private networks and poor cooperation and information sharing. This leads to very hard planning problems. Moreover, the ability to respond to unforeseen events and adapt the planning is poor, which causes low utilization of transportation means in case of high uncertainty and a prioritization of trucking over alternatives such as barges and trains. As a result, the current logistic system is unsustainable environmentally and economically.
We envision a system where shippers (companies with a transportation demand) and trans-porters (providers of transportation services) are two independent decision makers. Trans-porters of all modes (e.g. trains, barges and trucks) offer services between hubs on a fixed schedule and at a predetermined price. Loads can find their way over this schedule of services to their destination based on their preferences and requirements much alike people in the public transport system. In this PI system, goods are moved in PI containers to facilitate easy handling at all points in the system. Here we describe the system we propose in the context of strategic, tactical and operational levels from the viewpoint of both shippers and transporters.
3.1
Strategic level
We envision a network where hubs are extensively used and a lot of transportation services (barges, trains and trucks) are available between those hubs. Hubs can provide advantages to both shippers and transporters. If containers travel over hubs, this makes the bundling of loads easier since transportation is more concentrated on routes between hubs and hence could improve the utilization of transportation means, yielding more profit for transporters and/or lower costs for shippers. Also, since transportation is more concentrated, the fre-quency of services between two points in the network will be higher, yielding more options for goods to arrive on their destination without violating their delivery deadline. Moreover, transporters can focus on parts of the network they are specialized in, which could improve efficiency. Another improvement that can be obtained is that obligatory rest times for (truck) drivers can be avoided by transshipping the loads to another vehicle (Montreuil, 2011). The hub location problem is out of the scope of this research and we refer to Campbell and O’Kelly (2012) and Farahani et al. (2013) for reviews on this subject. Relevant research related to hub location problems and the PI is done by Ballot et al. (2012) and related to intermodal transportation by Groothedde et al. (2005).
handling of the PI containers at the hubs. This is described by Montreuil et al. (2010). An-other requirement is an information system where all offered transportation services (routes, times, prices) are given.
3.2
Tactical level
We envision that in the PI system shippers make decisions given the schedule of services and, in contrast to the current system, do not have long-term contracts with transporters. Hence transporters cannot determine the frequency and timing of the services they offer op-erationally, based on (contractually) realised demand. Rather, transporters will determine the services they offer tactically, based on expected demand. We envision this to be an evolutionary process. Transporters will add services of different modes to the network as long as they think a profit can be made by adding a service on that particular segment. An additional service between two locations can attract more demand and change the expected demand on this and other segments of the network. In order to model this evolutionary process we could look at the literature regarding public transport, where a similar evolu-tionary process was found. Nikoli´c and Teodorovi´c (2014) describe that passenger demand depends on the offered public transport network and that passenger flows depend on the transit network design. This process complicates the network design and scheduling. They overcome this problem by using the widely accepted frequency share method. We believe that the more shippers are participating in this PI system, due to size and density of the network, the closer the realized demands will be to the expected demand, which will improve decision making (size effect ). Moreover, we envision that because of the open, dense net-work, competition between transporters will lead to relatively stable market prices for the transportation services in the network.
The route of the loads over the network will be determined given the schedule of offered services. PI containers can determine their route based on different objectives. Costs and time (delivery time or lead time) will often be the main objectives. There is some literature regarding route selection given a fixed schedule. Often the schedule is transformed to a network representation and a version of the shortest path method is applied (e.g. Boardman et al. (1997), Ziliaskopoulos and Wardell (2000), Chang (2008) and Bast et al. (2016)). Shippers no longer negotiate price and timing in advance, but rely on offered services in the system. However, also from their perspective, if the system is large and dense enough, the number of offered services will limit the timing and pricing risks. We expect that since ship-pers can use the services of all participating transporters, they have more options to meet the delivery deadline. Moreover, this will yield a better allocation of containers to barge and rail services and hence a costs decrease (cooperation effect ).
3.3
Operational level
utiliza-tion will be a risk for the transporter, although if the system is large and dense enough this should hardly occur and transporters should be compensated, since on average utilization is higher. Moreover, a dynamic pricing policy might prevent low utilization at the cost of harder decision making. On the other hand, if there is more demand for a service than capacity, a simple First Come First Served (FCFS) policy could be used. The PI containers that cannot use the service should be able to find another “good” service fairly easily due to the density of the system and the possibility to go over other hubs. In other words, the load can either use the next service on the same route, which will often, due to the density of the system, not cause a drastic delay or be able to find an alternative route. Moreover, in a market situation we envision that a “first class” or a “Fare Class Mix” (van Riessen, Negenborn, and Dekker, 2017) might be used.
Unforeseen events, such as cancellation and delays of services or batches, also happen in the PI system. Moreover, a batch can turn out to be larger or smaller than previously thought. In case of unforeseen events, our hypothesis is that the envisioned PI system offers some advantages over the current (planned) logistics system since it is more flexible (flex-ibility effect ). In the current system, if a deviation from the planning occurs, a difficult replanning is often necessary since private transportation means are often planned full or have contracts assigning loads to specified services and service frequencies are relatively low, leading to the necessity to use trucking to meet delivery deadlines. In the PI based system however, the schedule of offered services has to be updated given the deviation information and the PI containers, individually, determine their new route through the system. More-over, because of the density in the system and the frequency of services, a delay leading to a missed connection should have less severe consequences.
4
Methodology
In this section we describe how we test the performance of the PI system as described in section 3. First, we describe the general network setting. Then, we explain three ways to plan transportation and how they respond to unforeseen events. Lastly, we outline our performance criteria.
4.1
Network
the arc itself and on other arcs make the planning very hard to optimize. To test the performance of our proposed PI system we need a good benchmark for the current system. We want to test PI system against a current planning system which gives an optimal schedule of services and allocation of loads to these services. Therefore we choose to consider only a single arc of the network, where we can obtain an optimal transportation planning for the current system in deterministic setting. Hence we only consider the transportation between two locations, which we call A and E. Goods travel in both directions and can use barge, train and truck services. Considering a single arc is limiting in a sense that containers do not have the possibility to go via other arcs and nodes. However, this set-up is still relevant since nodes A and E can be seen as hubs, with connections to local suppliers and receivers, as can be seen in Figure 2. An example of such a network is a port terminal and an inland terminal connected by road, railway and waterway.
Figure 2: The single arc network where trucks, barges and trains run between A and E, where A and E could be seen as hubs (Figure derived from Behdani et al. (2016))
4.2
Three ways to plan
We will use this single arc network to analyse three ways to plan transportation. The decen-tralized optimization case considers multiple (F ) transporters that plan their transportation of containers individually, based on their own agreements with shippers regarding transporta-tion demands and using their own resources. The centralized optimizatransporta-tion case represents a 3PL or full cooperation between these F transporters to optimize their planning. Hence all transportation demand is combined and all resources are shared. The third case is the PI case where a fixed schedule of transportation services is based on expected demand and all resources are shared such that all containers can access all services. For the three cases some assumptions are made, which are enlisted here.
as unit measure. It should also be noted that no transfers between modes can occur during transportation.
2. For barge and rail services the departure times are planned and there is a maximum amount of services over the planning horizon. Trucks are considered to be always available, i.e. the number of trucks is not limited and no constraints are imposed on departure time.
3. Transportation demand is considered as an input for the process. The demand is assumed to be known when the schedule is made for the decentralized and centralized optimization cases. We consider batches of containers. For each batch of containers, volume, release time (the time a batch is ready for transportation at its origin) and delivery deadline at destination are defined. Since we do not allow the late arrival of loads, the time between release time and delivery deadline should be larger than the shortest transit time of the transportation services.
4. Batches of containers can be split, such that a part of a batch uses one service and another part of this batch uses another service. Hence, a batch can be split over different modes or over sequential services of a mode.
5. We assume that the number of transportation services (barges and trains) moving back and forth between A and E is equal.
Decentralized optimization case
For the decentralized optimization case, all F transporters individually optimize the schedule of their services and allocation of loads to those services, based on actual demand and where a specified number of barges and trains is available. All containers that are not transported by barge or train are transported by truck. The optimization model is derived from the model presented by Behdani et al. (2016) and explicitly contains delivery deadlines where delay is not allowed. It is assumed that loads can always go by truck to arrive at their destination on time. We have adjusted Behdani’s model such that opening hours of terminals no longer are considered. The optimization model can be found in appendix A. To obtain the total costs of the decentralized optimization case, the individual total costs of the F transporters are summed.
Centralized optimization case
For the centralized optimization case, all demand and transportation means of the F different transporters are combined. Then the model given in appendix A is solved as if there is one firm. The objective value that is obtained represents the total cost if all F firms cooperate perfectly.
Physical Internet case
envision that the services offered by transporters are realized by an evolutionary process. In this setting however, since we only consider a single arc, we use the results found by Newell (1971) and Niu and Zhou (2013) that the optimal flow rate of vehicles varies with the arrival rate distribution. So for our PI case, if we assume a constant arrival rate distribution of demand, we will schedule the barges and trains evenly over the time horizon. For example, if there is a time horizon of 100 hours and there are ten barges, the barges leave every ten hours, where the first barge departs after ten hours and the last one after 100 hours. Since barges and trains have different capacities and transit times, their schedule is determined independently, which could lead to trains and barges departing or arriving at the same time.
Given this created schedule, the loads determine which service to use. The sequence of releases of batches is simulated (FCFS), so the batch with the earliest release time has the first choice of service. A container uses the cheapest service that departs after its release time, arrives before the delivery deadline and has space remaining. Note that batches can be split over multiple services in case the batch quantity exceeds the remaining space on a service. In case multiple cheapest options are available, the service which departs the earliest is chosen.
4.3
Uncertainty and recourse action
In the real world deviations in demand and in the schedule of transportation services occur. Because of its flexibility, we believe that the PI system performs relatively well in a stochastic environment. In this research, we consider batch quantity and release time to be stochastic. Transportation services can depart later than planned and will have the same delay upon arrival. We follow the approach of van Riessen et al. (2015), where disturbances are consid-ered to be known in advance, i.e. after the planning is optimized in the decentralized and centralized optimization cases, but before the first departure or release time.
For the decentralized and centralized optimization cases, we consider a local update ac-cording to van Riessen et al. (2015). Hence, the entire remaining planning will not be re-optimized. The scheduled departure times of transportation services are not changed and the containers that were planned to be on specific services remain to be planned on those ser-vices. If allocations of loads to services have become infeasible, i.e. the release time exceeds the departure time or the arrival time is later than the delivery deadline, the load is removed from the planning and the space becomes available. Since we consider disturbances to be known in advance, this is done for the entire planning horizon. Then for each batch, in order of release time, it is checked if there is space on a feasible service, where cheaper services are prioritized. If this is the case, the load is added to the planning and the remaining space decreases. Note that this is not only done for the loads that were removed or not assigned yet, but for all batches. Hence also loads that still had a feasible assignment to a service can now be transported by a cheaper service if space has become available on this service because of an infeasible allocation. However, if no cheaper service is available, the original feasible allocation of the load is guaranteed.
situa-tion that batches can determine which service they use based on the realized release time and with knowledge of delays of services. The same procedures as in the deterministic PI case can be applied, where the schedule is adjusted for all delays of services and the actual demand is used. A flowchart of the process for all cases including recourse actions is given in Figure 8 in appendix B.
4.4
Performance measures
The PI should be a step towards making the transportation system more sustainable eco-nomically and environmentally. We evaluate the performance of the PI system based on total costs per container (total costs/ total demand) and modal split. The lower the total costs in the system, the more economically sustainable the system is. Moreover, in order to change to a PI based system, no group of stakeholders should be worse of compared to the current system since then they will not cooperate. The modal split can be used to approximate environmental performance. In order to remain sustainable environmentally, the usage of trucks should be low, since the CO2 emission of trucks is higher than of barges and trains.
5
Experimental setting
In this section we present the experimental setting we use to evaluate the performance of the PI case compared to the decentralized and centralized optimization case. We follow the case study of Behdani et al. (2016), who evaluate the design of a synchromodal service schedule for transportation of containers between the Port of Rotterdam and Tilburg. In their study they present cost and time parameters for transportation services which are based on scientific literature and expert evaluations. We use these parameter values as well. We also follow their assumption that demand is uniformly distributed over all weeks. Since we also want to evaluate the performances when unforeseen events occur, we add uncertainty to the process. The inputs are discussed in section 5.1. After the discussion of input variables, we will discuss the experiments we perform.
5.1
Input
In this study three groups of parameters are considered. First, we discuss parameters for transportation cost and time, then the distributions defining demand characteristics are given. Lastly, we discuss the stochastic parameters.
Deterministic setting
The parameters regarding transportation costs, transit times, the capacity and number of services are provided in Table 1. Note that since we assume that trucks are always available, no number of services has been defined. Moreover, no transit time has been defined since we assume that trucks can always deliver the goods on time.
Table 1: Transportation parameters
Mode Cost Capacity Nr. of services Transit time
(e/container) (Containers) (Per transporter) (Hours)
Barge 45 40 20 11
Train 60 110 6 6
Truck 90 1
Table 2: Demand distributions
Batch size (Q) Release time (T R) Delivery deadline (T D) U {20; 120} U {1; 168} T R + T T , T T ∼ U {24; 48}
where U {a, b} represents a discrete uniform distribution. Note that the delivery deadline is modelled as a moment in time, computed as the sum of the release time and a time available for transportation (T T ) which is uniformly distributed between a lower and an upper bound, which are set to 24 and 48 hours respectively.
Stochastic setting
We consider batch size (Q), release time of batches and departure time of transportation services (t) to be stochastic. It should be noted that the transit time is modelled to be fixed, hence a delay in departure time will result in the same delay upon arrival. The realized batch size, release time and departure time are modelled such that there is a probability of a deviation. If no deviation occurs the realized values are the same as the generated values in the deterministic setting. If a deviation does occur, it follows a specified distribution. The probabilities and distributions are described in Table 3, where U (a, b) represents a uniform distribution and the realized batch size is rounded to the nearest integer.
5.2
Experimental design
In order to evaluate the performance of the PI case compared to the decentralized and centralized optimization cases, several experiments will be performed. We define a stan-dard experiment, which is used as a starting point to analyse the effect of changing various parameters. For the standard experiment we use the transportation parameters, demand distributions and stochastic parameters as described above and assume there are K = 60 batches per origin and F = 3 transporters (hence 20 batches per transporter). For this ex-periment the expected demand is 1400 per origin and transporter (K × expected batch size)
Table 3: Stochastic parameters Element Probability of change Realized value
Batch size (Q) P(pQ = 1) = 0.5 Qold× pQ× φ + Qold(1 − pQ), φ ∼ U (0, 75; 1, 25)
Release time (T R) P(pT R = 1) = 0.5 T Rold + pT R× ρ, ρ ∼ U {−4; 10}
and the total capacity of barges and trains is 1460 per origin, yielding a coverage ratio of 104% (total expected demandtotal capacity×100% ). Since there are many parameters, we cannot perform a full facto-rial study and we focus on the cooperation effect, size effect and flexibility effect. Moreover, we analyse how the coverage ratio affects the performance.
Cooperation effect
To evaluate the cooperation effect, we analyse experiments with F = 2, F = 3 and F = 6 transporters and where K = 60 batches. As the number of transporters (F ) increases, the total costs of the decentralized optimization case are expected to increase, since all trans-porters serve a smaller part of the demand and have less resources, which complicates the planning. This effect is expected to be stronger in the stochastic setting due to the decreased number of recourse possibilities if the number of transporters is increasing. The centralized optimization case and PI case are not influenced by the number of transporters and hence we expect a bigger benefit of cooperation for the PI case relative to the decentralized op-timization case as F increases. The setting of these experiments can be found in Table 4, under cooperation effect.
Size effect
To analyse the size effect we perform experiments with a varying number of batches (K). We set K to 30, 60 and 90, keep F = 3 transporters and adjust the number of services to keep the coverage ratio at 104%. This yields that we analyse how the size of the transporters affects the results. As there are more batches, it is expected that the realized demand is closer to the expected demand and the PI case should perform better. However, since the transporters are bigger and have more planning options, a part of the cooperation benefit could be lost. The setting of these experiments can be found in Table 4, under size I effect.
In order to see the effect of an increasing number of batches and number of transporters simultaneously, we evaluate the performance with F = 2, F = 3, F = 4 and F = 5 trans-porters and keeping the size of the transtrans-porters equal at K = 20 batches per transporter, which hence increases total demand. Here, we expect that the PI performs relatively better compared to the decentralized optimization case as the problem size increases. We expect the costs per container for the decentralized optimization case to remain equal and the costs for the PI case to decrease with size in both deterministic and stochastic setting, due to both cooperation benefit and size effect. The setting of these experiments can be found in Table 4, under size II effect.A graphical representation of market size and number of transporters for the cooperation and size effect is given in Figure 9 in appendix C.
Coverage ratio
Table 4: Overview of experiments
Experiment K F Barges Trains Coverage ratio
(Per transporter) Standard experiment 60 3 20 6 104.3% Cooperation effect 60 2 30 9 104.3% 60 3 20 6 104.3% 60 6 10 3 104.3% Size I effect 30 3 10 3 104.3% 60 3 20 6 104.3% 90 3 30 9 104.3% Size II effect 40 2 20 6 104.3% 60 3 20 6 104.3% 80 4 20 6 104.3% 100 5 20 6 104.3%
Coverage ratio effect 60 3 17 6 95.7%
60 3 18 6 98.6%
60 3 19 6 101.4%
60 3 20 6 104.3%
60 3 21 6 107.1%
per container is likely to decrease for all cases. The setting of these experiments can be found in Table 4, under coverage ratio effect.
Flexibility effect
6
Results
In this section we provide and analyse the results we found. We first focus on costs per container and discuss the modal split later. The results for the standard experiment are presented in Table 5. The 95% confidence intervals are based on a t-distribution with 49 degrees of freedom since we performed 50 replications for our experiments. The con-fidence intervals are fairly tight, e.g. the width of the 95% concon-fidence interval of the av-erage costs per container for the centralized optimization case yields 0.9% of the mean ((upper bound CI - lower bound CI)cumulative mean × 100%), which indicates that we have enough scenarios.
We can conclude that the PI case has significantly higher total costs per container than the decentralized optimization case or centralized optimization case in the deterministic set-ting. For the stochastic setting however, the PI case is no longer significantly more expensive than the decentralized optimization case. This could be because of the flexibility effect. The centralized optimization case still outperforms both the decentralized optimization case and PI case in this setting. In Figure 3, the total costs per container for the three cases are shown for all 50 runs in the stochastic setting. The centralized optimization case has often the lowest total costs per container and is always better than the decentralized optimization case. However, the PI case outperforms the centralized optimization case once, illustrating that the performance for the centralized optimization case is no longer at least as good as the for the PI case in stochastic setting.
Cooperation effect
In Figure 4, the total costs per container for a varying number of transporters (F ) for the three cases in deterministic and stochastic setting and 60 batches are shown, where the experiments are as defined in Table 4, under cooperation effect. It can be seen that for the decentralized optimization (DO) case the total costs per container increase with the number of transporters since transporters become smaller and cannot use their resources as efficiently. The cost increase is stronger in the stochastic setting, which could be explained by the decreased number of recourse possibilities if there are smaller transporters. The costs for the centralized optimization (CO) case remain fairly constant since perfect cooperation is assumed and hence the planning is not influenced by an increasing number of transporters. Also for the PI system, since the services of all transporters are available to all shippers, the number of transporters is irrelevant. These results support the hypothesis that the PI system performs relatively better if the number of transporters increases due to its inherent cooperation. Tables 7 and 8 provide the results for F = 2 and 6 transporters respectively and can be found in appendix D. For this numerical study, if there are 6 transporters, the average costs per container are decreased from e57.30 to e55.07, which is a decrease of 4%, if the PI system is applied compared to the decentralized optimization case in stochastic setting.
Size effect
We also expected to see that the PI system works better as more shippers participate. In Figure 5, the total costs per container are shown for a varying number of batches K as defined in Table 4, under Size I effect. The computation time of the centralized optimization case and 90 batches was too large and hence this setting was omitted. The PI however, has low computation times, benefiting from its simple protocols. It can be seen that for all settings and cases the costs decrease as the number of batches increases. Surprising is that the costs of the decentralized optimization case decrease faster in the stochastic setting than the costs of the PI case. This could be due to the loss of cooperation benefit since the individual transporters serve more loads each and have more resources (barge and train services), creating more recourse possibilities.
which yields an improvement of 1.8%. The results for the experiment with K = 100 and F = 5 can be found in Table 9 in appendix D. It can be concluded that the more trans-porters and shippers participate, the better the PI performs relative to the current situation due to the size and cooperation effect.
Coverage ratio
All the previous experiments were done with a coverage ratio of 104%. Now we evaluate the results for the experiments with varying coverage ratio, as given in Table 4, under coverage ratio effect. Figure 7 demonstrates the average cost per container varying the number of barges from 17 to 21. The costs decrease for all cases as the coverage ratio increases, since no fixed costs for services were considered. More interesting is that the costs decrease faster in the PI case than in the decentralized and centralized optimization cases. The results for the stochastic setting and all considered coverage ratios are given in Table 10 in appendix D. For all cases the percentage of barge transportation increased by around 10 percent points (p.p.) as the number of barges increased from 17 to 21. For the PI case, this increase is mostly caused by a decrease of 9 p.p. in trucking and train transportation decreases only 2 p.p.. Whereas for the decentralized optimization case, trucking decreases by 4% and train transportation by 6 p.p. and for the centralized optimization case, the decrease of truck and train transportation is 4% and 7 p.p. respectively, explaining the faster decrease in costs for the PI case. This is also reflected in the utilization of services. The utilization of barges is fairly stable for the different coverage ratios. The utilization of trains however, decreases far more (12 p.p. and 16 p.p.) for the decentralized and centralized optimization case than for the PI case (4 p.p.) as the number of barges increases. These results give an indication that for the PI system it is favourable to have a relatively high coverage ratio.
Flexibility effect
Figure 4: The total costs per container as function of the number of transporters (F ) for the three cases in deterministic (left) and stochastic (right) setting and K=60 batches
Figure 5: The costs per container as function of the number of batches (K) for F =3
Figure 7: The costs per container as function of the number of barges, where the number of trains is fixed to 6
Modal split
So far we have focussed on the average costs per container. Now we discuss the modal splits that were obtained in the various experiments. For the standard experiment and in deter-ministic setting, the main difference between the cases is in the use of trains and trucks, as can been seen in Table 5. Trains are used 41% and 42% in the decentralized and central-ized optimization case and only 33% in the PI case and this is compensated by the usage of trucks. There is no significant difference in the usage of barges. This can be explained since in the PI case containers first check if a feasible barge is available before looking for a more expensive feasible train. In the stochastic setting however, the difference in truck usage between the decentralized optimization case and the PI case has disappeared and only a slight difference in train and barge usage persists, making the difference in environmental performance negligible. The centralized optimization case still has significantly higher train usage and lower truck usage than the decentralized optimization case and the PI case and hence is more sustainable environmentally.
7
Conclusion
In this research a possible system design for the Physical Internet was proposed. This system is based on the public transport analogy and was presented at strategic, tactical and opera-tional level. We envision a hub network where transporters offer services on a fixed schedule based on expected demand. Containers can then, based on easy decisions, determine their route over the network to their destination. Since there are no long-term contracts between shippers and transporters, the system is very flexible and expected to deal better with un-foreseen events than the current system.
A numerical study was performed on a single arc of the network to compare the perfor-mance of the proposed PI system to a decentralized and centralized optimization system in deterministic and stochastic setting. It was found that in the deterministic setting the PI case was always outperformed by the decentralized optimization case and the centralized optimization case.
Encouraging results in terms of costs and modal split were found for the stochastic set-ting. When batch size, release time and departure time were modelled to be stochastic, the PI system performed relatively better. This indicates that the flexibility effect exists and the PI system has a better response to unforeseen events than the current system. The results of the numerical study also show the existence of a size and a cooperation effect. This indicates that the PI performs relatively better as the total transportation demand and number of participating transporters increases. This is caused by the inherent cooperation of the PI and the fact that as more shippers participate, the realized demand will be closer to the expected demand. From these results we can conclude that for large and dense enough systems, the Physical Internet can make transportation more sustainable economically and environmentally.
8
Discussion and further research
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Appendix
A
Optimization model
In this section we present the mathematical model for the decentralized and centralized optimization cases. This model determines the optimal schedule of services for trains and barges and the container assignment to these services for a single arc (A, E), given the demand quantities, release times and delivery deadlines and the available resources and is derived from the model of Behdani et al. (2016). Demand is considered to arrive in batches of containers B(k,i,j), where i ∈ {A, E} represents the origin, j ∈ {A, E} the destination and
i 6= j, k indicates the kth batch of containers in this direction.
Notation
The following notation is used in the model.
Index:
m Transportation mode of service, barge (B) or rail (R); m ∈ {B, R}
V Truck service
i, j Origin and destination; i, j ∈ {A, E}, i 6= j k Number of batch; k ∈ {1, . . . , K}
l Service number l of a mode; l ∈ {1, . . . , L}
Parameters:
Cm(i,j) Cost per unit for transport mode m that departs from i to j
CV Cost per truck
Tm(i,j) Transit time of mode m that departs from i to j
Um Service capacity of mode m
LMm(i,j) Maximum number of mode m service from i to j over the planning
horizon, where LMm(i,j)≤ L ∀(i, j) ∈ {A, E} where i 6= j, m ∈ {B, R}
Inputs
Q(k,i,j) Volume (number of containers) of batch B(k,i,j) T R(k,i,j) Release time of batch B(k,i,j) at i,
T D(k,i,j) Delivery deadline of batch B(k,i,j) at destination j Decision Variables:
t(i,j)ml Departure time variables representing the departure time of service number l of mode m from i to j
y(i,j)ml Binary variables representing whether the service l of mode m from i to j is operated
D(k,i,j)ml Binary variable indicating whether a part of batch B(k,i,j) is delivered
by service l of mode m from i to j
Objective function
The objective of the model is to minimize the total costs of transportation, given the demands with corresponding release times and delivery deadlines. The objective function is given by
M in Z = X k∈{1,...,K} X (i,j)∈{A,E} X m∈{B,R} X l∈{1,...,L} Cm(i,j)· x(k,i,j)ml + X k∈{1,...,K} X (i,j)∈{A,E} CV · Q(k,i,j)− X m∈{B,R} X l∈{1,...,L} x(k,i,j)ml . (1)
The first term in equation (1) represents the total transportation costs of barge and train service. The second term represents the transportation cost of truck services. It should be noted that truck volume follows from the difference between total demand and the volume transported by barge and train.
Constraints
There also are some constraints, which are presented here.
Capacity constraints
Constraints (2) limit the capacity of the services. If service l of mode m is not operated (i.e. yml(i,j)=0), no volume can be transported on this service. If the service is operated (i.e. y(i,j)ml =1), the total volume transported on that service cannot exceed the maximum capacity of the corresponding mode Um
X
k∈{1,...,K}
x(k,i,j)ml ≤ Umy (i,j)
ml , ∀(i, j) ∈ {A, E}, m ∈ {B, R}, l ∈ {1, ..., L}, (2)
Maximum flow constraint
To ensure that the volume transported by trucks is not negative, constraints (3) state that, for each batch, the volume transported by barge or train should not exceed the demand. Recall that the total volume transported by trucks is the difference between the total demand and the total volume transported by barge or train.
Q(k,i,j)− X
m∈{B,R}
X
l∈{1,...,L}
Time constraints
The following constraints consider the timing of departure and delivery for the batches and the services. Constraints (4) state that if any part of batch k is transported from i to j by mode m and service l, D(k,i,j)ml should equal 1.
x(k,i,j)ml ≤ M · D(k,i,j)ml ∀k ∈ K, (i, j) ∈ {A, E}, m ∈ {B, R}, l ∈ {1, ..., L}, (4) Constraints (5) state that if any part of batch k is transported from i to j by mode m and service l, this service cannot leave before the batch has arrived at origin i. If Dml(k,i,j) equals 0, these constraints will always be true because of the big M.
t(i,j)ml ≥ T R(k,i,j)− M ·1 − Dml(k,i,j)
∀k ∈ K, (i, j) ∈ {A, E}, m ∈ {B, R}, l ∈ {1, ..., L}, (5)
The delivery deadlines are considered in constraints (6). Note that the sum of the departure time and the transit time (t(i,j)ml + Tm(i,j)) yields the arrival time. If any part of batch k is
transported from i to j by mode m and service l, the arrival time of this service should be smaller than the delivery deadline. Again, if Dml(k,i,j) equals 0, these constraints will always be true because of the big M.
T D(k,i,j)≥ t(i,j)ml + Tm(i,j)− M ·1 − Dml(k,i,j)
∀k ∈ K, (i, j) ∈ {A, E}, m ∈ {B, R}, l ∈ {1, ..., L}, (6)
Service constraints
For every mode, the number of services from A to E should equal the number of services from E to A. This is stated in equation (7).
X
l∈{1,...,L}
yml(i,j)= X
l∈{1,...,L}
yml(j,i) ∀(i, j) ∈ {A, E}, m ∈ {B, R}, (7)
Constraints (8) state that for every mode, the total number of services should be less than or equal to the maximum number of services.
X
l∈{1,...,L}
yml(i,j)≤ LMm(i,j) ∀(i, j) ∈ {A, E}, m ∈ {B, R}, (8)
Non-negativity and binary constraints
Furthermore constraints (9) and (10) ensure that the decision variables are non-negative or binary respectively.
B
Flowchart of the planning process
In Figure 8, a flowchart of the transportation planning process is given. The top part repre-sent the deterministic setting, the bottom part the setting where uncertainty is introduced. Demand is created, where for each batch the number of containers, release time and deliv-ery deadline are known. Given these demands and the number of available transportation means, an optimal schedule and allocation of loads to this schedule is computed for the decentralized and centralized optimization cases. Also the PI schedule is computed given the time horizon and number of transportation services and each batch can find its preferred service. For the (de-)centralized optimization and PI cases, this results in a schedule of services and corresponding flows of containers. With this information costs and modal splits are computed.
C
Experiments
Figure 9 gives a representation of the experiments that are performed to analyse the cooper-ation, size I and size II effects. The large circles represent the the total demand or the total number of batches (K) and the smaller circles represent the demand served per individual transporter.
Figure 9: Overview of the cooperation, size I and size II effect experiments, where the large circles represent the total demand or total number of batches (K) and the smaller circles represent the demand served per individual transporter
