Business Models and Network Design in Hinterland Transport

Abstract

International container transport is the backbone of global supply chains. Hinterland transport, the transport from the port to the final destination and vice versa, is an important component of international container transport. However, academic attention to hinterland transport has emerged only recently. This chapter discusses business models and network design in hinterland transport. Understanding business models is relevant, as many different types of companies (e.g., shipping lines, terminal operating companies and forwarders) play a role in hinterland transport. Their business models influence how they position themselves in the market, their stance concerning cooperation and coordination in hinterland transport, and their scope in network design. Network design is a core issue in hinterland transport. New services need to be designed—and in such a way that they are expected to be profitable. Furthermore, current service patterns only change through deliberate redesign. So competition through the (re)design of transport services is a very important—perhaps the most important—form of competition in intermodal freight transport. One potentially promising innovation in this respect is the extended gate concept, where an inland hub becomes the ‘virtual gate’ of the deep sea terminal.

Appendix: Assumptions, the Formal Model and Relevant Parameters

1.1 Assumptions

• 1. Once a container is loaded on a truck in the port area, this truck directly drives to the shipper site, without intermediate handling at the hub or inland terminal, as truck transport is typically used when the container needs to be transported quickly.

• 2. All empty equipment that can be re-used in the H&S network, but which cannot be used for a terminal’s own service area, is transported back to the hub before it is re-distributed, i.e., no mutual empty equipment exchange between inland terminals is assumed.

• 3. All empty containers not being re-used are transported back to either a port terminal or an empty depot in the port area, but all full containers destined for export are transported back to a port terminal only.

• 4. Transportation is executed using only standard 20ft and standard 40ft containers. The impact of this assumption on eventual results is negligible. (The share of standard containers in total container volume is very substantial. Furthermore, other-sized containers only marginally influence costs or are not used for the operations under consideration.)

• 5. Empty and full containers are shipped between two nodes in the same barge.

1.2 Not Included in the Model

• 6. The handling costs and holding costs of the goods in the container. This follows from the assumption that the overall door-to-door time differs only marginally in both alternatives.

• 7. Container storage costs are not taken into account explicitly in the model; costs of additional storage capacity are in fact negligible compared to those of handling and transportation.

1.3 The Model

See Table 15.1 for a description of parameters and their ranges in value.

Table 15.1 Specification of parameters for the inland barge terminal network in the Netherlands

1.3.1 A: Direct Call (Base Case)

Volume calculation

The following formula was derived for determining the total volume of containers, ${\mathbf{V}}_{i}$, that needs to be transported between the port and the service area of a terminal:

$$ {\mathbf{V}}_{i} = {\mathbf{D}}_{i} - \min ({\mathbf{D}}_{i}^{f} *\alpha^{b} ,{\mathbf{D}}_{i} - {\mathbf{D}}_{i}^{f} ) $$

(15.1)

The minimum expression in this function needs to be included, as one cannot re-use more containers than the total demand for empty containers in the service area.

$${\text{Total truck volume}},\quad {\mathbf{V}}_{i}^{T} = {\mathbf{V}}_{i} *ut_{{P,i}}$$

(15.2)

$$ {\text{Total barge volume}}\quad {\mathbf{V}}_{i}^{B} = {\mathbf{V}}_{i} *\left( {1 - ut_{{P,i}} } \right) $$

(15.3)

Barge connection calculation

Based on an empirical analysis of a number of inland terminals, it is assumed demand is normally distributed. Thus, the required capacity, ${\mathbf{c}}_{i}^{\min }$, of the barge connection can be calculated as follows:

$$ {\mathbf{c}}_{i}^{\min } = \mu_{v,i} + z\left( {SL_{i}^{req} } \right)*\sigma_{v,i} , $$

(15.4)

where $\sigma_{v,i}$ is calculated as

$$ \sigma_{v,i} = \mu_{v,i} *cv_{v} $$

(15.5)

Using the value obtained for the required capacity, one can calculate the frequency, $f_{i} ,$ of the barge connection. However, that frequency must be high enough to offer a certain service. Therefore, the formula becomes

$$ f_{i} = \max \left( {f_{\min } ,\frac{{{\mathbf{c}}_{i}^{\min } }}{{C_{i} }}} \right) $$

(15.6)

The average total round-trip time between port and inland terminal, $TT_{P,i}$, was calculated as

$$ TT_{P,i} = 2tt_{P,i} + tw_{P}^{B} + tw_{i}^{B} + \frac{{4\left( {U_{i} *C_{i} } \right)/TEUF_{i} }}{{r_{i}^{B} + r_{P}^{B} }} $$

(15.7)

The final part of the formula shows the average handling time during one round trip.

The slack time, $tw_{P}^{B} ,$ required to achieve a certain service level, was found via the following formula

$$ tw_{P}^{B} = \,\left( {\frac{{\left( { - Ln\left( {SL_{i} } \right)} \right)^{ - \xi } - 1}}{\xi }} \right)*\sigma + \mu $$

(15.8)

The total barging costs per year, $TC_{P,i}^{B}$ for maintaining the barge connection between the port and terminal $i$ was then calculated as

$$ TC_{P,i}^{B} = \left( {FC_{c,i}^{B} + VC_{c,i}^{B} } \right)*nb_{P,i} , $$

(15.9)

where

$$ VC_{c,i}^{B} = P^{G} *\left( {tt_{P,i} *Gt_{c} + \left( {tw_{P}^{B} + tw_{i}^{B} } \right)*Gw_{c} } \right), $$

(15.10)

$$ FC_{c,i}^{B} = dc_{c}^{B} + pc_{c}^{B} + ic_{c}^{B} + mc_{c}^{B} , $$

(15.11)

and

$$ nb_{{P,i}} = \frac{{TO}}{{TT_{{P,i}} }}. $$

(15.12)

In the above, $dc_{c}^{B} ,pc_{c}^{B} ,ic_{c}^{B} ,mc_{c}^{B}$ stand for yearly depreciation, personnel, insurance and maintenance cost of a barge with capacity $c;\;nb_{P,i}$ represents the number of barges required per year; and $TO$ denotes the total yearly operating time of terminals and barges.

The total annual costs of barge transport for the base case were then obtained

$$ TC^{B} = \sum\limits_{i = 1}^{N} {TC_{P,i}^{B} } = \sum\limits_{i = 1}^{N} {\left( {\left( {FC_{c,i}^{B} + VC_{c,i}^{B} } \right)*nb_{P,i} } \right)} $$

(15.13)

Truck connection calculation

The yearly costs $TC_{P,i}^{T}$ of direct, unimodal transport between the port and the shippers in the service area of terminal $i$ are

$$ TC_{P,i}^{T} = tc_{P,i} *\left( {\frac{{{\mathbf{V}}_{i}^{T} }}{{TEU^{T} }}} \right) $$

(15.14)

With the following formula, the trip cost $tc_{P,i}$ between the port and inland terminal was calculated¹²:

$$ tc_{P,i} = vc_{d} *Td_{P,i} + vc_{h} \left( {\frac{{Td_{P,i} }}{{v_{gem}^{T} }} + tw_{P,i}^{T} } \right) $$

(15.15)

Here $Td_{P,i}$ represents the average total distance travelled for a round trip from the port to the service area of terminal $i,$ and was determined as:

$$ Td_{P,i} = 2d_{P,i} + d_{O} $$

(15.16)

The yearly costs of truck transport from the inland terminal to its service area, $TC_{t,i}^{T}$, were found similarly.

Adding these costs to the costs of direct trucking between the port and the hinterland, the total costs $TC^{T}$of truck transport were thus

$$ TC^{T} = \sum\limits_{i = 1}^{N} {\left( {TC_{P,i}^{T} + TC_{t,i}^{T} } \right)} $$

(15.17)

Handling costs calculation

The yearly amount of truck handlings, $h_{i}^{T}$, and the yearly amount of barge handlings at inland terminal $i,h_{i}^{B} ,$ were obtained using the following two formulas;

$$ h_{i}^{T} = \left( {\frac{{{\mathbf{D}}_{i} *\left( {1 - ut_{P,i} } \right)}}{{TEUF_{i} }}} \right)*2 $$

(15.18)

$$ h_{i}^{B} = \left( {\frac{{{\mathbf{V}}_{i}^{B} }}{{TEUF_{i} }}} \right)*2 $$

(15.19)

For terminal handlings, the assumption was made that barge handlings are more expensive than truck handlings, due to the use of more expensive equipment and additional resources when handling barges. It was therefore assumed the variable costs for barge handlings were a factor $\varepsilon$ larger than the variable costs of truck handling. The total handling costs for terminal $i,TC_{i}^{H} ,$ could then be calculated as

$$ TC_{i}^{H} = FC_{i}^{H} + SFC_{i}^{H} + VC_{i}^{H} *\left( {h_{i}^{T} + \varepsilon h_{i}^{B} } \right) $$

(15.20)

Let $h_{P}^{T}$ and $h_{P}^{B}$ respectively denote the truck handlings and barge handlings at the port. Equations. (15.21) and (15.22) were employed for the volumes of handling there.

$$ h_{P}^{T} = \sum\limits_{i = 1}^{N} {\frac{{D_{i} *ut_{P,i} }}{{TEUF_{i} }}} + \beta *\sum\limits_{i = 1}^{N} {\frac{{ut_{P,i} *\left( {2V_{i} - D_{i} } \right)}}{{TEUF_{i} }}} $$

(15.21)

$$ h_{P}^{B} = \sum\limits_{i = 1}^{N} {\frac{{D_{i} *\left( {1 - ut_{P,i} } \right)}}{{TEUF_{i} }}} + \beta *\sum\limits_{i = 1}^{N} {\frac{{\left( {1 - ut_{P,i} } \right)*\left( {2V_{i} - D_{i} } \right)}}{{TEUF_{i} }}} $$

(15.22)

Now consider the empty-depot handlings, where $h_{E}^{T}$ and $h_{E}^{B}$ represent truck handlings and barge handlings at the empty depot respectively:

$$ h_{E}^{T} = \left( {1 - \beta } \right)*\sum\limits_{i = 1}^{N} {\frac{{ut_{P,i} *\left( {2V_{i} - D_{i} } \right)}}{{TEUF_{i} }}} $$

(15.23)

and

$$ h_{E}^{B} = \left( {1 - \beta } \right)*\sum\limits_{i = 1}^{N} {\frac{{\left( {1 - ut_{P,i} } \right)*\left( {2V_{i} - D_{i} } \right)}}{{TEUF_{i} }}} $$

(15.24)

In those equations, $\beta$ is the fraction of empty containers brought back to the port terminal.

The total annual handling costs for the port terminal and the empty depot can then be found from Eqs. (15.25) and (15.26):

$$ TC_{P}^{H} = VC_{P}^{H} *\left( {h_{P}^{T} + \varepsilon h_{P}^{B} } \right) $$

(15.25)

$$ TC_{E}^{H} = VC_{E}^{H} *\left( {h_{E}^{T} + \varepsilon h_{E}^{B} } \right) $$

(15.26)

Total costs calculation

The total yearly costs, $TC^{tot}$of the base case can be obtained using the following formula:

$$ TC^{tot} = TC_{P}^{H} + TC_{E}^{H} + \sum\limits_{i = 1}^{N} {\left( {TC_{i}^{H} + TC_{P,i}^{T} + TC_{t,i}^{T} + TC_{P,i}^{B} } \right)} $$

(15.27)

1.3.2 B: The hub-and-spoke model

Volume calculation

Because the volumes transported between the port and inland terminals are consolidated at the hub terminal, determination of those volumes differ considerably from that of the base case. The annual volume transported directly between the port and terminal $i$ is given by

$$ {\mathbf{V}}_{P,i}^{T} = {\mathbf{V}}_{i} *ut_{P,i}^{H} $$

(15.28)

The remaining volume that needs to be transported towards the service area of terminal $i$, ${\mathbf{V}}_{i}^{T,B} ,$ was calculated as:

$$ {\mathbf{V}}_{i}^{T,B} = \left( {{\mathbf{D}}_{i} - \min \left( {{\mathbf{D}}_{i}^{f} *\alpha^{h} ,{\mathbf{D}}_{i} - {\mathbf{D}}_{i}^{f} } \right)} \right)*\left( {1 - ut_{P,i}^{h} } \right) $$

(15.29)

The yearly volume transported by truck between the hub and the service area of a terminal is then

$$ {\mathbf{V}}_{H,i}^{T} = {\mathbf{V}}_{i}^{T,B} *ut_{H,i} $$

(15.30)

For yearly volume transported by barge between the hub and terminal $i$, the following equation is used:

$$ {\mathbf{V}}_{H,i}^{B} = {\mathbf{V}}_{i}^{T,B} \left( {1 - ut_{H,i} } \right) $$

(15.31)

For the yearly volume transported by barge between the port and the hub terminal, ${\mathbf{V}}_{P,H}^{B}$, the calculations are somewhat more difficult, and are based on Eq. (15.32):

$$ V_{P,H}^{B} = \sum\limits_{i = 1}^{N} {\left( {D_{i}^{f} *\left( {1 - ut_{P,i}^{h} } \right)} \right)} + \max \left( {0,\sum\limits_{i = 1}^{N} {\left( {\left( {1 - ut_{P,i}^{h} } \right)*\left( {D_{i} - \left( {1 + \alpha^{h} } \right)D_{i}^{f} } \right)} \right)} } \right) $$

(15.32)

Barge connection calculation

The frequency of the barge connection between the port and hub, and the number of port calls per visit, differ from the base case. This is because the connection needs to be point-to-point in the H&S network, to reduce the uncertainty and risk. That frequency was therefore calculated as follows:

$$ f_{i}^{h} = \max \left( {2f_{\min } ,\frac{{{\mathbf{c}}_{i}^{\min } }}{{C_{i} }}} \right) $$

(15.33)

(Note the difference from the number of port calls per visit as given by Eq. (15.6)). Because of the accumulation of demand for inland terminals at the hub, there is decreased variation for the connection between the port and the hub. The expression becomes

$$ C_{H}^{\min } = \sum\limits_{i = 1}^{N} {\mu_{i}^{V} } + z\left( {SL_{i}^{req} } \right)*\sqrt {\sum\limits_{i = 1}^{N} {\left( {\sigma_{i}^{V} } \right)^{2} } } $$

(15.34)

Truck connection calculation

Obtaining the costs of truck transport here is completely similar to the base case, with the exception that the costs of transporting containers between the hub and terminal $i$ must be added. To determine these costs, $TC_{H,i}^{T} ,$ the following equation was used:

$$ TC_{H,i}^{T} = tc_{H,i} *\left( {\frac{{V_{H,i}^{T} }}{{TEU^{T} }}} \right) $$

(15.35)

One can find the trip costs between the hub and inland terminal, $tc_{P,i}$, with the formula

$$ tc_{H,i} = vc_{d} *Td_{H,i} + vc_{h} \left( {\frac{{Td_{H,i} }}{{v_{gem}^{T} }} + tw_{H,i}^{T} } \right) $$

(15.36)

Here $Td_{P,i} ,$ represents the average total distance travelled for a round trip from the hub to the service area of terminal $i$ and is calculated

$$ Td_{H,i} = 2d_{H,i} + d_{O} $$

(15.37)

Following this extra container flow by truck between hub and the service areas of inland terminals, the annual costs of truck transport for the H&S network is expressed as follows:

$$ TC^{T} = \sum\limits_{i = 1}^{N} {\left( {TC_{P,i}^{T} + TC_{t,i}^{T} + TC_{H,i}^{T} } \right)} $$

(15.38)

Handling costs calculation

The yearly amount of truck and barge handlings at the hub terminal, $h_{H}^{T}$ and $h_{H}^{B} ,$ are given by Eqs. (15.39) and (15.40):

$$ h_{H}^{T} = \left( {\frac{{{\mathbf{D}}_{H} *\left( {1 - ut_{P,H}^{H} } \right) + \sum\limits_{i = 2}^{N} {{\mathbf{V}}_{H,i}^{T} } }}{{TEUF_{i} }}} \right) $$

(15.39)

$$ h_{H}^{B} = \frac{{2*\left( {{\mathbf{V}}_{P,H}^{B} + \sum\limits_{i = 2}^{N} {{\mathbf{V}}_{H,i}^{B} } } \right)}}{{TEUF_{i} }} $$

(15.40)

The total amounts of truck and barge handlings at the port terminal and the empty depot, respectively, $h_{P}^{H,T} ,h_{P}^{H,B} ,h_{E}^{H,T}$and $h_{E}^{H,B}$ were found via Eqs. (15.41)– (15.44):

$$ h_{P}^{H,T} = \left( {\frac{{\sum\limits_{i = 1}^{N} {ut_{P,i}^{H} *\left( {2{\mathbf{V}}_{i} - {\mathbf{D}}_{i} } \right)} }}{{TEUF_{i} }}} \right)*\min \left( {1,\frac{{E_{tot}^{C} *\beta }}{{E_{tot}^{H} }}} \right) $$

(15.41)

$$ h_{P}^{H,B} = \left( {\frac{{2{\mathbf{V}}_{P,H}^{B} - \sum\limits_{i = 1}^{N} {\left( {{\mathbf{D}}_{i} *\left( {1 - ut_{P,i}^{H} } \right)} \right)} }}{{TEUF_{i} }}} \right)*\min \left( {1,\frac{{E_{tot}^{C} *\beta }}{{E_{tot}^{H} }}} \right) $$

(15.42)

$$ h_{E}^{H,T} = \left( {\frac{{\sum\limits_{i = 1}^{N} {ut_{P,i}^{H} *\left( {2{\mathbf{V}}_{i} - {\mathbf{D}}_{i} } \right)} }}{{TEUF_{i} }}} \right) - h_{E}^{H,B} $$

(15.43)

$$ h_{E}^{H,B} = \left( {\frac{{2{\mathbf{V}}_{P,H}^{B} - \sum\limits_{i = 1}^{N} {\left( {{\mathbf{D}}_{i} *\left( {1 - ut_{P,i}^{H} } \right)} \right)} }}{{TEUF_{i} }}} \right) - h_{P}^{H,B} $$

(15.44)

In those equations, $E_{tot}^{C}$and $E_{tot}^{H}$ represent total numbers of available empty containers in the base case and in the hub-and-spoke case.