Author: F. Nab Creating Flexibility for Synchromodal Transportation: The use of Revenue Management Techniques

Creating Flexibility for Synchromodal

Transportation: The use of Revenue

Management Techniques

Author: F. Nab

2

ABSTRACT

3

CONTENT

3.2.2 Case 1: Fare classes ... 9

3.2.3 Case 2: Dynamic Pricing ... 10

3.2.4 Case 3: Accept or Reject Order... 11

3.3 Experimental setting ... 12

3.4 Performance measures ... 13

3.5 Validation and Verification ... 13

4. SIMULATION RESULTS ... 13

4.1 Modal split... 13

4.2 Utilization ... 14

4.3 Financial performance ... 14

5. CONCLUSION AND FURTHER RESEARCH ... 17

REFERENCES ... 18

4

1. INTRODUCTION

Synchromodality is a logistics concept that tries to overcome challenges hinterland transport is facing due to growing freight flows, increasing road congestion and traffic emission issues. The concept was developed to manage the inflexibility of intermodal transport, where

different modalities (e.g. train, barge and truck) are decided upfront each shipment. The inflexibility of the predetermined modes gives rise to practical problems since barge and train services are highly sensitive to disruptions and varying transportation characteristics.

Synchromodality adopts a mode-free booking concept and allows flexible selection and real-time switching of modalities at any real-time during transportation (Van Riessen, Negenborn, & Dekker, 2015b). The concept offers the convenience to improve transportation services on aspects like costs, sustainability, duration and reliability (Mes & Iacob, 2016).

Synchromodality is accepted to be economic and environmental beneficial, but is not widely used in practice due to missing flexibility and pricing strategies. Only a few successful pilot studies are accomplished in the Netherlands (Pfoser, Treiblmaier, & Schauer, 2016), partly because of the missing flexibility to switch between modes and routes (van Riessen et al., 2015b). Service providers are limited in choosing the optimal transport mode because customers are very strict on aspects like departure time, arrival time and mode of

transportation, which seems strengthened by trends such as JIT and e-commerce. However, several studies have shown that customers are interested in transport services that offers more flexibility to the service provider, if they receive the right incentives (e.g. lower prices) (Verweij , 2011; Dong et al., 2017). In addition, it is difficult to set a price for the transports in a synchromodal framework, since the transport mode and the specific route are not

determined beforehand (Pfoser et al., 2016). Given these two aspects, it is important to develop an appropriate pricing strategy for synchromodal transportation in order to optimize revenue.

Revenue management (RM) is widely used in many different sectors to manage demand and prices. Interest in RM started after the success stories in American Aviation, where airlines experimented with differentiated fare products by offering discounts to seats that would otherwise fly empty (McGill & Van Ryzin, 1999). Furthermore, studies show that RM may be a desirable approach in freight transportation optimizing revenue (Van Riessen, Negenborn, and Dekker, 2015a; Liu and Yang, 2015; Bilegan, Brotcorne, Feillet, and Hayel, 2015; Wang, Bilegan, Crainic, and Artiba, 2016). Studies that focus on using RM aimed at facilitating flexibility for synchromodal transportation are scarce. We are therefore interested in finding how RM techniques can be used to create flexibility in the planning of a service provider. Explicitly, we study the flow of containers through a synchromodal transportation system with one arc. Using discrete event simulation we evaluate the use of two basic revenue management tools in terms of modal split. Furthermore we assess which tools can create flexibility and how this relates to the financial performance of the system. A stochastic setting is used, where departure time of services is uncertain. The remainder of this thesis is

5

2. LITERATURE OVERVIEW

2.1 Synchromodality

Synchromodality is a relatively new logistics concept where no uniform definition for exists yet. However, the general compliance exists that the logistics concept contains an integrated view of planning and usage of different transportation modes to provide flexibility in handling demand (Behdani, Fan, Wiegmans, & Zuidwijk, 2014). The concept differs from intermodal transport since it allows flexible selection and switching of modalities in real-time. The result is that modes can more easily deal with transportation disturbances, such as cancellations or service delay (Lucassen & Dogger, 2012). In synchromodal transport, the customer only determines basic requirements of the transportation in advance, such as costs, duration and sustainability aspects (Haller, Pfoser, Putz, & Schauer, 2015). This way the customer leaves the mode choice to the service provider.

Most research done on the topic of synchromodality is focused on planning aspects (e.g. Behdani et al., 2014; Mes et al., 2016). However, research focusing on creating flexibility with revenue management is scarce.

2.2 Revenue management

Revenue management (RM) is concentrated on three basic types of demand-management decisions: (1) structural decisions, such as selling format and differentiation mechanisms to use; (2) price decisions, as pricing policy over different product categories, discounting; and (3) quantity decisions, as accept or reject orders, and how to assign capacity to products, segments or channels (van Ryzin & Talluri, 2005). RM can either be qualified as price-based RM or quantity-based RM, this depends on whether it uses prices or capacity as the primary tactical tool, for managing demand (van Ryzin & Talluri, 2005).

Interest in RM started with the development of the model known as Littlewood’s rule. This model distinguished between two fare classes, which have a fare of p1 and p2, where p1 > p2

(Littlewood, 1972). The demand for class 2 arrives before demand for class 1. Using a simple rule, the incoming demand for class 2 is accepted until the revenue for class 2 is exceeded by selling the same space to class 1:

𝑝₂ ≥ 𝑝₁∗ 𝑃(𝐷₁ > 𝑥)

The model is limited to two classes, and can be extended to an n-class model using a dynamic programming approach (Belobaba, 1987).

6

Recently, RM has also been identified as a desirable approach in freight transportation. (Van Riessen et al., 2015b). RM can help service providers to better manage revenue and improve service by aligning prices and service levels to particular classes of customers (Wang, Bilegan, Crainic, & Artiba, 2016). Li et al. (2015) studied the effect of a cost-plus-pricing strategy to determine the service prices of transport operators under different transport

scenarios (i.e. self-transporting, subcontracting and a mix of these two). The service price was calculated by the sum of the operational cost and the targeted profit margin. Van Riessen et al. (2015a) studied a new set of two products with varying delivery times and prices. They

introduced a framework for the cargo fare class mix. The purpose of this framework is to set limits for each fare class such that the expected revenue is maximised. Liu and Yang (2015) developed a two-stage stochastic model based on Littlewood’s rule. They made a distinction between two types of customers: contract sale (large shippers) and free sale customers (scattered shippers). In the first stage of their model, capacity is reserved for all contract sale customers. In the second stage a dynamic pricing model is applied to reserve space for the free-sale customers.

Bilegan et al. (2015) proposed a RM policy to dynamically accept or reject transportation orders for rail container transportation based on achieving potential higher profit. Similarly, Wang et al. (2016) consider reject and accept decisions for an intermodal barge transportation system, by including different types of customer categories.

3. SIMULATION DESIGN

The main purpose of this thesis is to gain insight in how RM techniques can create the flexibility needed so that in a synchromodal setting more freight will be shipped by train or barge. The aim is to show how flexibility and revenue are interconnected and how these two concepts affect the modal split and total profit in a synchromodal transportation system. For this purpose, we adopt a discrete event simulation approach. Simulation models give the opportunity to compare different system designs, to predict the system performance and to evaluate different policies on the performance of a system (Robinson, 2004). The models are able to represent the variability, interconnectedness and complexity of a system. Many prior studies of RM in freight transportation used simulation as methodology (e.g. Liu & Yang, 2015; van Riessen, 2015a). The use of simulation as methodology has both advantages and limitations. An advantage of simulation is that it is less time consuming and costly in comparison with experimenting in a real situation. In addition, it allows testing of multiple scenario’s without interrupting day-to-day operations. Lastly, it enables monitoring many different indicators over time. Yet, it should be mentioned that one of the main shortcomings of a discrete simulation approach is that problems cannot be solved optimally and that there is a limited generalizability of the outcomes (Evers & Wan, 2012).

3.1 Network setting

7

only one route exists between the two terminals. During transportation no exchange can occur between the modes. Each mode has different transportation costs, service capacities and transfer times. These numbers are however not direction dependent. Since the premise of synchromodality is based on the integration of schedules of multiple modes, at least one mode is available to deliver the container on time at the destination. Therefore, no delay is

considered in the system. Whilst the departure of trains and barges is based on a fixed

schedule, the number of trucks in the system is unlimited. Hence, the departure time for trucks is flexible. In this setting, we indicate customers as the one who places orders for

transportation in the system. Service providers arrange the transport of containers. We assume a so-called mode-free booking, which means that customers do not book transports on certain modes.

Figure 1: Representation of the synchromodal transportation system

Parameters regarding transportation costs, capacity and transit time indicated by prior

research of Behdani et al. (2014) are used. The assumptions on the transportation parameters are summarized in Table 1. We assume that the number of services from A to B and from B to A are the same. This means for instance that every 21 hours a barge departs from A to B and vice versa. In line with practice the truck is the most expensive mode of transportation per container, whilst the barge is the cheapest option. The transit time of the different modes is based on the connection between the Port of Rotterdam and Tilburg.

Table 1. Network parameters, based on Behdani et al. (2014) Mode Variable cost (€/container) Capacity (containers) Nr. of services (per week) Transit Time (hours) Barge 45 40 16 11 Train 60 110 2 6 Truck 90 1 Infinite -

Demand in the system is generated using the distributions given in Table 2. We assume for the parameters a discrete uniform distribution. Every 10 hours an order arrives in the system. Each order indicates a certain batch quantity, release time and delivery deadline. The release time of the batch of containers is generated by the sum of the order create time and a specified time which is uniformly distributed between a lower and an upper bound.

Table 2. Assumptions on demand parameters

Order frequency Quantity Release Time Delivery Deadline Constant every 10

hours

8

In the stochastic setting we assume a 25% chance of delay in departure time of barge and train. If deviations occur in the system the realized value is the value of the deterministic setting + the value for delay.

Table 3. Assumptions on stochastic parameters (p = 25%) Departure time

Train Departure time train + U{1;5}

Barge Departure time barge + U{1;10}

3.2 Experiments

Three different cases are compared with a base model. The first two cases are qualified as price based RM, as it uses prices as the primary tactical tool for managing demand. The third case can be qualified as quantity based RM since it uses simple accept and reject rules for orders. A stochastic setting is used to evaluate the performance of the cases. In this setting delay in departure time of barges and trains is considered.

3.2.1 Base model

The purpose of the base model is to transport as many containers as possible per barge or train. Orders enter the system with a certain frequency. Each incoming order specifies a certain destination, release time, batch quantity, delivery deadline and price. The price per container for each customer is the same.

9 Figure 2: Logic flowchart of base model

3.2.2 Case 1: Fare classes

Prior research of Wanders (2014) & Lin (2014) identified that the market for inland container transport can be segmented in groups of customers with different characteristics. These groups are sensitive to incentives that may allow more flexibility in the planning of a service provider. Related to their research, European Gateway Services (EGS) is considering to offer a differentiated portfolio of services to the market (van Riessen, 2018). The new portfolio consists of varying delivery lead times and prices. Here, this approach is adapted to identify the benefits of this new set of products on the performance of a synchromodal transportation system.

10 Figure 3: Logic flowchart of fare classes case

3.2.3 Case 2: Dynamic Pricing

The difference between the fare classes case and this case is that an order has no pre-determined price. In the dynamic pricing case, the price is pre-determined by the model using a few simple rules. For each incoming order it is checked if the order can be transported per barge or train. If this is not the case, the customer is offered the choice whether he is

11 Figure 4: Logic flowchart of dynamic pricing case

3.2.4 Case 3: Accept or Reject Order

In this case orders are accepted or rejected based on the capacity of barge and train and the profitability of the order. This model makes a distinction between two types of customers: flexible customers and non-flexible customers. Customers who allow a longer delivery lead time will get a discount on their transport price. For each incoming the model checks if the order can be transported per train or barge. If this is not the case and the order is from a flexible customer, it is rejected and deleted from the system. After acceptation of the order the containers are scheduled for a service as in the fare classes case. Figure 5 shows the logic flow chart of this case

Not all individual orders can be rejected, as long-term commitments are often made. Loads with that are part of a long-term commitment between customer and service provider and cannot be rejected in order to achieve modal shift to barge or train. Moreover, this case cannot be compared to the other cases since orders are deleted from the system. Therefore, the

12 Figure 5: Logic flowchart of Accept or reject order case

3.3 Experimental setting

To illustrate how the proposed RM tools support flexibility in the planning of service providers and how this affect the modal split and financial performance of the system, we study scenario’s with different demand and cost parameters. Since exact numbers for demand distributions for both normal and flexible services are not known, the impact of using fare classes and dynamic pricing for a range of hypothetical demand scenarios is compared with the base model. In these scenario’s we will vary with the following three parameters: percentage of total demand that is flexible Nf, varying between 20 and 60% of the total

demand, delivery lead time for flexible customers DDf , varying between 200 and 300% of the

normal delivery lead time and discount price Pf varying between 60 – 100% of the normal

transport price. Table 4 shows an overview of the experimental setting of this research. Table 4. Experiment setting for different scenarios

Parameter Values

Percentage of total demand that is flexible Nf [20%, 60%] N

Discount price Pf [60%, 66%, …, 100%] P

13

3.4 Performance measures

Since literature states that environmental and economic benefits can be achieved by using synchromodality, the performance of the system will be evaluated on these two aspects (Rivera & Mes, 2016). To examine the economic benefits, total costs and revenue of the service provider will be evaluated for the different cases. Environmental benefits will be evaluated in terms of modal split and utilization.

3.5 Validation and Verification

Throughout the life-cycle of this simulation study, multiple techniques are used for validation and verification of the simulation model. Verification of the model is done by building the model step-by-step and testing it after each addition of modules. After the last addition the complete model is run through again to verify its completeness. Furthermore, the validity of the model is checked by assessing conceptual model validity, experimental validity and by performing black-box tests. Starting on the last aspect, when the model is runned using the input parameters described in section 3.1, the output of the model in the stochastic setting corresponds with the percentages of modal split of the port of Rotterdam (Port of Rotterdam, 2016).Conceptual model validity has been assessed through supervisory meetings discussing the scope, level of detail and correctness of the conceptual model. Moreover, the base model and network setting of this thesis are based on prior research of Behdani et al. (2014). To ensure experimental validity, Welch’s method was used to determine the warm-up length of this simulation (Law & Kelton, 2007).Using this method it has been determined that the simulation has reached a so-called steady state after 20 days. As recommended by Banks (2001) we use a run length of fifteen times the length of the warm-up period. This means a run length of 300 days. Moreover, the confidence interval method was used to determine the number of replications. It is set to eight replications in order to get a deviation of less than 1%. Figures A1 and A2 of the Appendix shows the graphs of these estimations.

4. SIMULATION RESULTS

This section analyses the results of the scenarios proposed in section 3.3. Next to that, a sensitivity analysis is performed to check the robustness of the results.

4.1 Modal split

The modal split of the base model for barge, train and truck is, respectively, 36%, 10% and 54%. Our simulation results show that there is an increased use of trains and barges for both RM tools, yielding that less containers are transported per truck (Table 5). The fare classes strategy shows the highest decrease in truck usage (from 54% to a range of 48%-24%), explained by the fact that the total amount of flexible customers is higher in comparison with the dynamic pricing case. Consequently, the service provider has more flexibility in

14

640 containers per week. Although the utilization of the train service increases (see section 4.2), the absolute increase of containers transported by trains is small in comparison with the absolute increase of transport by barges. In addition, for both RM strategies a longer delivery leadtime (DDf = U{96;144}) ensures a lower use of the truck (Table 5).

Table 5. Modal split for the different scenario’s

DDf Base model Dynamic 20% Dynamic 60% Fare classes 20% Fare classes 60% U{48;72} Barge 36% 38% 42% 41% 49% Train 10% 10% 11% 11% 13% Truck 54% 52% 47% 48% 38% U{96;144} Barge 36% 39% 47% 44% 57% Train 10% 11% 13% 12% 18% Truck 54% 50% 40% 43% 24%

4.2

Utilization

In the base scenario, barges and trains are only utilized for, respectively, 47.6% and 35%, meaning that the barges and trains of the service provider are often (half) empty during

transportation. Our simulation results show that the use of different RM strategies increase the utilization of barge and train services (Table 6). Utilization of the barge service is increased between 2.5 – 15.2 pp. by using dynamic pricing, and between 7.5 – 29.6 pp. by using fare classes. Moreover, the utilization of the train service is increased between 1.6 – 12.5 pp. by using dynamic pricing and 3.6 -29.9 pp. by using fare classes. The fare classes strategy proves to be a more effective tool for increasing the utilization of the services compared to the

dynamic pricing strategy (Table 6).

Table 6. Utilization barge and train services for different scenario’s

DDf Base model Dynamic 20% Dynamic 60% Fare classes 20% Fare classes 60% U{48;72} U{96;144} Barge 47,6% 51,0% 51,8% 56,8% 62,8% 55,1% 59,6% 66,7% 77,2% U{48;72} U{96;144} Train 35,0% 36,6% 38,8% 39,5% 47,5% 38,6% 44,3% 48,2% 64,9%

4.3 Financial performance

Figure 2 depicts the total revenue if 20% of the customers is flexible (Nf = 20%), assuming

15

Fare class U{96; 144}: 33988). One possible explanation of the increase in transported containers is that due the longer lead times, transportation scheduling is more optimal and therefore, less orders are in the queue at the end of the simulation. Yet, if there is a discount price for the flexible customers, the total revenue depends on the amount of discount given to the flexible customers (Figure 6). In other words, if the discount is too high, the revenue in the new scenario’s is lower than the revenue in the base model. However, if discount is below this threshold, the new scenarios outperform the base model since the flexibility of customers in lead times ensures that service providers create more effective schedules where more

containers can be transported in the given timeframe. Our results show that in the fare classes scenario, the price of a container has to be more than €135 for a delivery lead time between 48-72 hours and more than €138 for a delivery lead time between 96-144 hours. For the dynamic pricing case the price of the containers for the flexible customers can be lower, i.e. €96 per container for a lead time between 48-72 hours and €117 per container for a lead time between 96-144 hours. This can be explained by the lower number of flexible customers in the dynamic pricing strategy as only the customers with orders that cannot be transported per truck or barge get the offer to transport their freight for a discount price with a longer delivery lead time. When the number of flexible customers is 60%, the results show the same trend as for the case where only 20% of the customers is flexible. Using the fare classes strategy with 60% of the customers being flexible and a delivery lead time of 48-72 hours, the price of the container has to be more than €144 to outperform the base model in terms of revenue. Similarly, for a lead time of 96-144 hours, the container has to be more than €141 Using the dynamic pricing strategy, the thresholds are €144 and €135 for lead times of 48-72 hours and 96-144 hours, respectively, which is again lower than for the fare classes strategy.

Figure 6: Total Revenue for each scenario (Nf = 20%)

Total costs

Figure 7 and 8 depict the total variable costs for the base, fare classes and dynamic pricing models, using the different delivery lead times and the different percentages of flexible customers. The total variable costs in the system are reduced for each scenario except in the dynamic pricing case where delivery lead time is between 48 and 72 hours (DDf = U{48;72})

and 20% of the customers is flexible (Nf =20%). However, the variable costs per container in

the latter scenario are lower than in the base model, explained by the higher total number of containers transported compared to the base scenario (see subsection total revenue).

4.550.000,00 4.650.000,00 4.750.000,00 4.850.000,00 4.950.000,00 5.050.000,00 5.150.000,00 0% 8% 16% 24% 32% 40% Re ve n u e (€) Discount rate

16

Moreover, there is only a small decrease in the usage of trucks (Table 5), so not a lot of costs can be saved, resulting in higher total costs compared to the base scenario. In both scenario’s (Nf =20% and Nf = 60%) the fare classes strategy outperforms the dynamic pricing strategy.

When 60% of customers is flexible (Nf = 60%), costs are reduced because due to the higher

amount of flexible customers, the number of containers transported per barge and train is increased (Table 5), resulting in lower total variable costs. Moreover, an increase in the delivery lead time has a positive influence on reducing costs.

Figure 7: Total costs (Nf = 20%) Figure 8: Total costs (Nf = 60%)

Total Profit

Figure 9 depicts the total profit for the base model and the two RM strategies, for different delivery lead times and a total percentage of flexible demand of 20% (Nf = 20%). The profit

in each scenario is higher than the profit of the base model if the total decrease in revenue is less that the total costs saved. In comparison with the revenue depicted in Figure 2, we see that the threshold to achieve a profit at least as good as the base scenario is located further on the horizontal axis for each scenario, except for the dynamic pricing case where the delivery lead time is between 48 and 72 hours. This is explained by the fact that in the latter scenario the total costs where higher than in the base scenario (Figure 3). Our result show that for the fare classes scenario (Nf =20%) approximately a maximum of 18% discount can be given for

a delivery lead time between 48 and 72 hours and 14% for a delivery lead time between 96 and 144 hours. For the dynamic pricing case this is respectively 28 and 26%. The same trend can be seen in the scenario’s where the percentage of total demand that is flexible is 60% (Nf

= 60%). In the fare classes case this is respectively 14 and 18% and 14 and 14%.

Figure 9: Total profit (Nf = 20%)

1800000 1900000 2000000 2100000 2200000 2300000 2400000 U{48;72} U{96;144} To ta l co sts in (€) DDf

Fare Classes Dynamic Pricing Base

2350000 2450000 2550000 2650000 2750000 2850000 0% 6% 12% 18% 24% 30% 36% Pro fit in (€) Discount rate

Base model Dynamic Pricing U{48;72} Dynamic Pricing U{96;144} Fare classes U{48;72} Fare classes U{96;144}

2150000 2200000 2250000 2300000 2350000 2400000 U{48;72} U{96;144} Tot al cos ts in (€ ) DDf

17

5. CONCLUSION AND FURTHER RESEARCH

Theoretical implications

Overall, this thesis illustrates how different RM techniques can stimulate customers to provide more flexible delivery lead times to allow for a better modal split under synchromodal

transportation. In this research two different RM techniques (i.e. fare classes and dynamic prices) were identified to decrease the total usage of trucks and to increase the use of barge and train services, respectively between 2.0-21.0 pp. and 0-8.0 pp. Moreover, higher utilization for train and barge services is accomplished by using these RM techniques in synchromodal transportation.

Practical implications

Our results show how a discount price can be offered to flexible costumers, still holding that the total profit in the system is higher than in the base model. Moreover, thresholds were identified for the minimum price of containers of customers with a flexible delivery lead time. We acknowledge that the numbers found in this research cannot be directly translated into practice, since the parameters used were based on assumptions and simplifications were made in the model. However, this research can provide insights for service providers who are facing problems by the strictness of customers and want to improve their modal split by offering discount prices.

Limitations and further research

Firstly, discrete event simulation cannot solve problems optimally and there is limited generalizability of the outcomes (Evers & Wan, 2012). However, the simulation gained insights which may be valuable for service providers in order to create more flexibility in their planning. Furthermore, due to time limitations, it was not possible to collect real case data. Therefore input parameters used were based on literature and assumptions. Next to that, sensitivity analysis for the research setting has not been done. The robustness of the presented results is therefore questionable and needs to be extended. Lastly, the dynamic pricing model proposed in this research does not treat each customer equally. Since only a certain set of customers is offered the adjustment of the order to a more flexible one with a longer delivery lead time. Moreover, no optimal prices were calculated, but we varied with certain prices between different ranges.

For further research it might be interesting to do empirical research in customers preferences regarding discount and longer delivery lead times, and to predict the number of customers that is interested in paying less for longer delivery lead times. Possibly, these concepts are

18

REFERENCES

Banks, J., Carson, J., Nelson, B. L., & Nicol, D. (2004). Discrete-event system simulation. Paperback:

Prentice Hall.

Behdani, B., Fan, Y., Wiegmans, B., & Zuidwijk, R. (2014). Multimodal schedule design for synchromodal freight transport systems. EJTIR, 16(3), 424-444.

Belobaba, P. (1987). Air travel demand and airline seat inventory management. Massachusetts Institute of Technology.

Bilegan, I. C., Brotcorne, L., Feillet, D., & Hayel, Y. (2015). Revenue management for rail container transportation. EURO Journal on Transportation and Logistics, 4(2), 261-283.

Bitran, G., & Caldentey, R. (2003). An overview of pricing models for revenue management.

Manufacturing & Service Operations Management, 5(3), 203-229.

Dong, C., Boute, R., McKinnon, A., & Verelst, M. (2017). Investigating synchromodality from a supply chain perspective. Transportation Research Part D: Transport and Environment.

Evers, P. T., & Wan, X. (2012). Systems analysis using simulation. Journal of Business Logistics, 33(2), 80-89.

Haller, A., Pfoser, S., Putz, L.-M., & Schauer, O. (2015). Historical Evolution of Synchromodality: A First

Step Towards the Vision of Physical Internet. Paper presented at the Proceedings of the

Second Physical Internet Conference.

Law, A. M., Kelton, W. D., & Kelton, W. D. (2007). Simulation modeling and analysis (Vol. 3): McGraw-Hill New York.

Li, L., Lin, X., Negenborn, R. R., & De Schutter, B. (2015). Pricing intermodal freight transport services:

A cost-plus-pricing strategy. Paper presented at the International Conference on

Computational Logistics.

Littlewood, K. (1972). Forecasting and control of passenger bookings. Airline Group International

Federation of Operational Research Societies Proceedings, 1972, 12, 95-117.

Liu, D., & Yang, H. (2015). Joint slot allocation and dynamic pricing of container sea–rail multimodal transportation. Journal of traffic and transportation engineering (English Edition), 2(3), 198-208.

Lucassen, I. M. P. J., & Dogger, T. (2012). Synchromodality pilot study. Identification of bottlenecks

and possibilities for a network between Rotterdam, Moerdijk and Tilburg. Delft, The

Netherlands: TNO.

McGill, J. I., & Van Ryzin, G. J. (1999). Revenue management: Research overview and prospects.

Transportation science, 33(2), 233-256.

Mes, M. R., & Iacob, M.-E. (2016). Synchromodal transport planning at a logistics service provider

Logistics and Supply Chain Innovation (pp. 23-36): Springer.

Pfoser, S., Treiblmaier, H., & Schauer, O. (2016). Critical success factors of synchromodality: Results from a case study and literature review. Transportation Research Procedia, 14, 1463-1471. Port of Rotterdam, K. (2016). Modal split containers per jaar. Retrieved from

http://monitor.topsectorlogistiek.nl/indicator/modal-split-containers-per-jaar/

Rivera, A. P., & Mes, M. (2016). Service and transfer selection for freights in a synchromodal network. Paper presented at the International Conference on Computational Logistics.

Robinson, S. (2004). Simulation: the practice of model development and use. Chichester, UK: John Wiley & Sons.

van Riessen, B. (2018). Optimal Transportation Plans and Portfolios for Synchromodal Container

Networks: Erasmus University Rotterdam.

Van Riessen, B., Negenborn, R. R., & Dekker, R. (2015a). The cargo fare class mix problem-revenue management in synchromodal container transportation.

Van Riessen, B., Negenborn, R. R., & Dekker, R. (2015b). Synchromodal container transportation: an

overview of current topics and research opportunities. Paper presented at the International

19 van Ryzin, G. J., & Talluri, K. T. (2005). An introduction to revenue management. Tutorials in

operations research, 142-195.

Verweij, K. (2011). Synchromodal transport: Thinking in Hybrid Cooperative Networks. EVO Logistics

Yearbook, 77-88.

Wang, Y., Bilegan, I. C., Crainic, T. G., & Artiba, A. (2016). A Revenue Management Approach for

Network Capacity Allocation of an Intermodal Barge Transportation System. Paper presented

20

APPENDIX

Figure A1: Warm-up length (Welch’s method)

Figure A2: Number of replications (confidence interval method p = 95%)

0,0% 10,0% 20,0% 30,0% 40,0% 50,0% 60,0% 70,0% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Mo vin g av era ge :% o f co n ain ers tra n sp o rted p er tru ck Days w = 5 0,25 0,27 0,29 0,31 0,33 0,35 0,37 0,39 0,41 0,43 0,45 0,47 0,49 0,51 0,53 0,55 0,57 0,59 0,61 0,63 0,65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Cumu lat iv e m ean : Me an : % u sage tru ck Number of replications