The impact of foldable containers on container fleet management costs in hinterland transport

Transportation Research Part E 46 (2010) 750–763

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Transportation Research Part E

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The impact of foldable containers on container fleet management costsin hinterland transport

Koichi Shintani a,*, Rob Konings b, Akio Imai c

a Department of Shipping Technology, Oshima National College of Maritime Technology, Suo-oshima, Oshima, Yamaguchi 742-2193, Japanb OTB Research Institute for Housing, Urban and Mobility Studies, Delft University of Technology, P.O. Box 5030, 2600 GA Delft, The Netherlandsc Graduate School of Maritime Sciences, Kobe University, Fukae, Higashinada, Kobe 658-0022, Japan

a r t i c l e i n f o a b s t r a c t

Article history:Received 6 March 2009Received in revised form 29 September2009Accepted 21 November 2009

Keywords:Container transportationContainer fleet managementEmpty containerFoldable containerHinterland transportation

1366-5545/$ - see front matter � 2010 Elsevier Ltddoi:10.1016/j.tre.2009.12.008

* Corresponding author.E-mail address: [email protected] (K. Shin

This paper analyzes the possibility to save container fleet management costs in reposition-ing empty containers through the use of foldable containers. We model this entire emptycontainer flow as an integer programming problem with different strategies in empty con-tainer flow itinerary. The model is used to carry out numerical experiments that optimizethe empty container repositioning in the hinterland, where there are serious empty con-tainer repositioning problems caused by extremely imbalanced trades. The study finds thatfoldable containers can substantially save on repositioning costs compared to the use ofstandard containers.

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1. Introduction

The introduction of the maritime container has induced great improvements in freight transport in many respects. Thetransfer of goods became much easier, cheaper and safer and the use of containers paved the way for intermodal transportdevelopment. At present, the maritime container dominates the shipping industry and the extent of its influence in landtransport is also abundantly clear. Most journeys of containers in deepsea shipping have a land leg, i.e. start or end in thenearby or more distant hinterland of a seaport.

An important downside of containerization however is that the place where containers are loaded and unloaded is oftennot the same, so transport movements of empty containers are unavoidable. Basically these unproductive journeys arecaused by trade imbalances which occur at a global level in the container trades and these imbalances have more or lessa structural nature, but the need to reposition empty containers also occurs at a regional level. In the transpacific tradethe imbalance in 2006 was 1:2.6 in favor of eastbound traffic, with demand for 14.3 million TEUs (Twenty-foot EquivalentUnit) eastbound, and 5.5 million TEUs westbound. Meanwhile, in the Asia–Europe trade the imbalance was 1:1.8, in favor ofwestbound with carryings of 7.5 million TEUs and 4.1 million TEUs eastbound (Robinson, 2007).

Large amounts of empty containers are being moved around the world both at sea and over land. The estimated share ofempty containers is estimated as 21% of all containers transported. For land transport the estimates are even higher (about40%). The total costs of these unproductive journeys are huge.

The cost structure of the total container transport chain indicates that in particular the costs of the land leg of the chainare high. The costs of hinterland transport accounts on average for about 40% of the total container transport costs, while

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deepsea shipping and handling costs in seaports both have a 30% share in the total costs (Notteboom and Winkelmans, 2001,and Rabobank, 2004). The ever-increasing scale of deepsea container vessels has reduced the deepsea shipping costs dramat-ically over the last decades, compared to the cost savings which could be achieved in hinterland transport. Consequently,carriers and merchants have shifted their attention to the hinterland transport in order to achieve cost savings in the totaltransport chain. Evidently, considering the large share of empty containers in inland transport movements, a reduction of thecosts of empty transport in the land leg of the chain could be a very cost-effective solution.

Although sophisticated information and communication systems are expected to improve the match of empty containersand cargo in order to reduce the number and distance of empty movements, transport movements of empty containers cannever be eliminated completely. So it would be worthwhile to consider also options which could reduce the actual costs ofempty movements in addition to the current strategies to avoid empty movements. From this perspective the use of foldablecontainers could be interesting. Empty containers which are folded enable to use transport capacity in a more cost-efficientway.

While their details will be provided in Section 3, foldable containers are not commercially available yet (except for flatracks). Moreover, though there are very few existing studies that address the economic and logistical viability of foldablecontainers, they at least give some indications of the conditions under which such containers could be operated successfully.However, these studies do not sufficiently cover the complexity of container transport chains.

The purpose of this paper is to contribute to the knowledge of empty container fleet management by analyzing the pos-sible cost savings of using foldable containers. In particular, this study builds on the previous work of Konings (2005) byfocusing on the cost saving potential of foldable containers in the land-based leg of the maritime container transport chain.Since this study analyzes multiple hinterland container transport chains simultaneously and enables us to include the inter-relations between these individual hinterland transport chains, it covers and demonstrates the potential cost savings of fold-able containers.

The remainder of this paper is organized as follows: Section 2 reviews the relevant literature. Some backgrounds and thestate-of-the-art foldable containers are discussed in Section 3. Section 4 presents a description and formulation of the prob-lems. Section 5 reports numerical experiments and their results. Finally, Section 6 provides major conclusions of this studyand discusses future research directions.

2. Related studies

Several studies have been performed on the subject of empty container management. Gavish (1981) developed a decisionsupport system for vehicle fleet management. Its adaptation to the container fleet problem is straightforward. In his study,prior to making a decision on empty container relocation, owned and leased containers are assigned to the demand pointsbased on the marginal cost criterion. Crainic et al. (1993) proposed dynamic and stochastic models for empty container allo-cation in a land distribution and transport system. Cheung and Chen (1998) developed a stochastic model for a sea-borneempty container allocation problem in which, owned and leased containers are considered to meet the total transport de-mand. Their model makes a distinction between long- and short-term leased containers, although it should be pointedout that in their model the constant leasing cost is assumed without consideration of the lease term. Imai and Rivera(2001) deal with fleet size planning for refrigerated containers where they determine the necessary number of containersrequired to meet predicted future transport demand. Choong et al. (2002) developed an integer programming (IP) formula-tion for empty container relocation with use of both long- and short-term leased containers. However, the treatment of theshort-term leased container in their study is not appropriate, since the cost of the short-term leased containers is indepen-dent of the lease term. Li et al. (2004) study the empty container allocation in a port with the aim to reduce redundant emptycontainers. They consider the problem as a non-standard inventory problem with a simultaneously positive and negativedemand under a general holding cost function. Erera et al. (2005) deal with a fleet management problem for a quite uniquetype of container: tank container. They formulate the problem as a multi-commodity flow problem. They solve the problemby using a commercial solver and demonstrate that by integrating container routing and repositioning decisions in a singlemodel, the total operating costs and fleet size can be reduced. Coslovich et al. (2006) discuss a container fleet managementproblem by formulating it as an IP model. They propose a decomposition method for solving that problem. From the originalformulation they generate three decomposed sub-problems: pairing definition, resource assignment and container reposi-tioning. They evaluate the quality of the solution by using upper and lower bounds. Jula et al. (2006) consider empty con-tainer repositioning, which they refer to as empty container reuse, from a different perspective than the above studies. Theiraim is to reduce traffic congestion in the Los Angeles and Long Beach port area, which is caused by heavy traffic of containertrucks. A network flow formulation is constructed, in order to optimize empty container movements from consignees toshippers directly and/or via inland depots. The problem is solved in two phases: the first phase deals with the model trans-formation to a bipartite transport network (i.e. a classical transport problem) and the second phase in solving the transportproblem by linear programming (LP).

Very few studies have been conducted in the past on the problem of empty container repositioning with foldable contain-ers. Konings and Thijs (2001), and Konings (2005) address the economic and logistical viability of using foldable containers.These studies give some indications of the conditions under which such containers could be operated successfully. Konings(2005) argues and demonstrates that the potential costs savings of using foldable containers in the land leg are larger than in

752 K. Shintani et al. / Transportation Research Part E 46 (2010) 750–763

the sea leg of the transport chain. However, although these studies are based on empirical data, they do not sufficiently coverthe complexity of container transport chains. To include this complexity the problem should be formulated and elaborated asa network flow problem.

3. Concepts of foldable containers

The idea of foldable containers is not so new. In the past several designs have been proposed, but none of them have beenintroduced to the market successfully. Reviews of previous designs show that the technical features of the foldable contain-ers could often not meet the requirements of users in the transport chain, being a major cause of failing market introduction(Konings and Thijs, 2001).

The tremendous growth of the Chinese economy over the last decade, which has boosted the imbalance of containerflows, has raised the interest in the foldable container again. Learning from past experiences there seems to be much moreattention now for the technical performance of the foldable container. This design, however, is indispensable related to itseconomic and logistical performance. It will influence the additional costs, which are inevitably associated with the use offoldable containers. These additional costs include the costs of folding and unfolding processes (hereafter referred to as F/UF)and higher exploitation costs of the foldable container. The latter is a result of higher manufacturing costs as well as highermaintenance and repair costs, because of a more complex construction of a foldable container. In order to make the use offoldable containers viable, these additional specific costs must be compensated by cost savings elsewhere in the transportchain, i.e. through costs savings in transport, storage and transshipment (in case of the possibility to bundle a number offolded empty containers into one package).

Among the more recent designs for foldable containers, currently, a foldable container is being developed in the Netherlandsby Holland Container Innovations (HCI). This box is a 40 ft high cube container, that once it is folded, stacked four high and inter-locked, it has exactly the same dimensions of a standard 40 ft high cube container (see Fig. 1). A 1:1 scale prototype of this con-tainer already exists. The next steps will be to get certification and to start a pilot with a small number of containers to test itsperformance. This pilot is scheduled to start in 2010. Parallel to this technical development and certification process differenteconomic studies are carried out, which should prove in which types of transport chains this foldable container would performbest. The current study described in this paper is part of this economic analysis. Therefore, in the models we use in this paper theparameters for foldable containers are derived from characteristics and economic data about the HCI foldable container.

4. Description and formulation of the problem

Motivated by the observation that the costs of repositioning empty containers are particularly high in hinterland trans-port, this study focuses on the movements of empty containers in the hinterland. The models we developed therefore applyto this part of the total container transport system and do not optimize the container fleet size. They deal with a static prob-lem; they provide an optimal solution for the repositioning of empty containers in the hinterland based on data regardingthe supply of and demand for empty containers on a 1 week basis.

The task of the models is to find optimal empty container movements in the hinterland in order to minimize the totalcosts. For the standard containers these costs consist of:

– Regional repositioning costs: the costs of transporting empty containers from the inland depot in the hinterland to theseaport.

– Local repositioning costs: the costs of the movements of empty containers in the hinterland.– Handling costs: the costs of loading and unloading containers to/from trucks.– Exploitation costs of the container.

For the foldable container there is in addition to these cost categories the F/UF costs, which also include inspection of thecontainers.

The models should include the possibility to reuse empty containers in the hinterland, because this also reflects whathappens in practice. A surplus of empty containers in the hinterland is returned to the seaport.

The comparison between the container fleet management costs of standard containers with foldable containers is carriedout in a comprehensive way by considering different options to reuse empty containers in the hinterland.

In addition to the container depot in the hinterland as a possible location to fold/unfold containers, the premise of ship-pers/consignees is also included as an option. This assumes that shippers/consignees have equipment at their site to handleempty containers. In general they do not have dedicated container handling equipment, but if only empty containers need tobe handled (i.e. fold/unfold and load/unload an empty container on/off chassis) a heavy forklift could perform these tasks aswell. This is the type of equipment some shippers/consignees have for their business undertaking. Although shippers/con-signees that have the required handling equipment are not numerous, we include this option to give an outlook on whatcould be the potential savings of using foldable containers under these specific conditions.

Based on the possible local repositioning movements of empty containers (i.e. direct or indirect interchange of containersbetween customers) and the locations where containers can be folded and unfolded (i.e. at the customers’ site or at the

Fig. 1. The folding process of the HCI foldable container.


inland depot), three scenarios are distinguished in order to compare container fleet management costs of standard contain-ers and foldable containers:

(1) Advanced direct interchange (ADI): empty containers are directly interchanged between customers where F/UF is pos-sible at the customers’ site (see Fig. 2a and b).

(2) Advanced indirect interchange (AII): empty containers are indirectly interchanged between customers via the inlanddepot and F/UF is possible at the customers’ site (see Fig. 2c and d).

(3) Simple indirect interchange (SII): empty containers to be reused by shippers in the hinterland are interchanged betweenthe customers via the inland depot where movements from the consignee to the depot and from the depot to the ship-per occur with unfolded (erected) containers (see Fig. 2e). Since it is assumed that F/UF of containers is only possible atthe inland depot, the potential benefit of using foldable containers in this scenario is limited to the cost savings on theroute between the inland depot and the seaport. The pattern of empty container flows with standard containers in theSII-scenario is the same as in the AII-scenario (see Fig. 2d).

The scenario SII seems the easiest way to use foldable containers. The inland depot is the only location where F/UF takesplace, which might offer possible scale advantages in F/UF. Since empty containers are bundled for just one route, i.e. fromthe inland depot to the seaport, it will be easier to bundle the folded containers into packages. Moreover, since shippers andconsignees are not involved in F/UF there are no logistical barriers for these customers to use foldable containers: since thecontainers arrive at and leave their site erected, the customers should virtually notice no difference in using a standard boxor a foldable container.

Fig. 2. Empty container flow patterns for local repositioning.


The most complex scenario is ADI. It assumes that the customers are willing and able to execute F/UF at their sites byusing their own simple handling equipment such as a forklift. ADI also assumes that unloaded containers at consigneescan be transported directly to shippers to load these containers, but this empty movement is more restrictive. In practiceit will be a barrier if consignees and shippers are served by different shipping lines, since a shipping line usually does notallow to use its containers for another shipping line, unless they have agreements. Moreover, as Hanh (2003) discusses,real-time information on export containers is often not available at the time when import containers become empty. Suchrestrictions could be mitigated to some extent if information systems and co-operation between shipping lines in inter-changing containers (the development of so called ‘gray boxes’) are improved and widely spread.

The scenario AII takes a middle position regarding the ease of implementation.


4.1. Assumptions

The assumptions in our models are as follows:

(a) Empty containers are assumed to be transported by truck only.(b) The total volume of import cargo exceeds the total volume of export cargo in the hinterland.(c) The volumes of import and export cargo of each customer, in number of containers, are given.(d) The model considers the use of one type of containers, i.e. 40 ft containers, only. This assumption excludes empty con-

tainer movements that arise from a mismatch in supply and demand for type of containers. Moreover, this assumptionlimits the complexity of the problem formulation.

(e) Four foldable containers can be bundled into one unit, which corresponds to the size of a 40 ft standard container, i.e.the foldable container is a four-in-one type of foldable container (see Section 3).

(f) Empty containers are transported in the folded state only with four empty ones. This offers the best net benefit intransporting empty containers folded and would fit the best to the requirements of deepsea shipping, when a bundleof foldable containers would continue its trip after arriving in the seaport.

(g) The exploitation cost of a foldable container is estimated twice as high as the one of a standard container, due tohigher purchase, maintenance and repair costs of the foldable container.

(h) If the time at which empty containers become available after being unloaded at a consignee and the one at whichempty containers are needed by a shipper are matched, the empty containers are directly transferred between themin the hinterland. If empty containers are routed through the inland depot this assumption is not applied, because in acontainer depot there are always sufficient empty containers available to deliver in time.

(i) Empty containers at each site are transferred from consignees to the inland depot or are directly moved from consign-ees to shippers. Surplus containers, i.e. empty containers which cannot be reused in the hinterland, return from theinland depot to the seaport.

(j) A storage capacity at each site and a transport capacity of each link connecting a specific site pair are assumed infinite.(k) The storage costs of containers at each site are ignored. These costs are marginal, especially when the planning horizon

for empty container repositioning is long, e.g. 1 week.(l) To simplify the models, the routing optimization of truck transport services is not considered.

(m) Empty containers, regardless of standard or foldable, are handled in the same manner when shipped to consigneesfrom the places where they are stacked awaiting for the next shipment.

4.2. Formulations

This paper examines three scenarios for empty container local repositioning with two container types (foldable and stan-dard). Foldable containers may have two states: unfolded (erected) and folded. Since folded containers are bundled four toone, this state defines the number of foldable containers in transfer between nodes. We use three variables to represent thecontainer flow throughout the service network. In case of standard containers, only one variable is needed because they donot need any variables for F/UF.

In principle the definition of three scenarios for the two container types would require six different IP models. Note how-ever that since empty flow patterns in the AII- and SII-scenarios with standard containers are similar, five model formula-tions can cover these six cases.

4.2.1. Formulation for ADI with foldable containersThe model for this scenario is formulated as follows:

½ADIF� MinimizeX

i2N

X

j2N

ðCTij þ CH

ij ÞðXij þ YYijÞ þX

i2N

CUi Gi þ CFM ð1Þ

Subject toX

jð–TÞ2N

Yij ¼ Si 8ið–P; TÞ 2 N; ð2Þ

X

ið–TÞ2N

Yij ¼ Dj 8jð–P; TÞ 2 N; ð3Þ

YPT ¼X

kð–TÞ2N

YkP �X

jð–TÞ2N

YPj; ð4Þ

YYij ¼ Yij � 4Xij 8i; j 2 N; ð5ÞYYii ¼ Yii 8ið–P; TÞ 2 N; ð6ÞGP �

X

k2N

ðYPk � YYPkÞ �X

kð–P;TÞ2N

ðYkP � YYkPÞ; ð7Þ


� GP 6X

k2N

ðYPk � YYPkÞ �X

kð–P;TÞ2N

ðYkP � YYkPÞ; ð8Þ

Gi ¼ Si �X

k2N

YYik þ Di �X

k2N

YYki 8ið–P; TÞ 2 N; ð9Þ

M ¼X

i2N

Si; ð10Þ

M P 0 and integer; ð11ÞGi P 0 and integer 8i 2 N; ð12ÞXij; Yij;YYij P 0 and integer 8i; j 2 N: ð13Þ

where, N is the set of nodes of the inland depot, consignees and shippers, T is seaport’s node, P is inland depot’s node, CF isexploitation costs of containers, CT

ij is local repositioning cost of container from nodes i to j, CHij is handling costs of containers

at nodes i and j associated with local repositioning between these nodes, CUi is F/UF costs at node i, Di is number of required

empty containers at node i, Si is number of import containers at node i, M is number of transported containers in the hin-terland, Gi is number of folded and/or unfolded containers at node, Xij is number of folded and bundled containers from nodesi to j, Yij is number of foldable containers (regardless of folded or unfolded) from nodes i to j, YYij is the number of unfoldedcontainers from nodes i to j.

The objective function (1) minimizes the total costs, which consist of the regional and local repositioning costs, handlingcosts, F/UF costs, and exploitation costs of the containers. Eq. (2) guarantees that the total number of empties moved from aconsignee is equal to the empty container supply at that site. Eq. (3) ensures that the number of empties that arrive at a ship-per is the same as the demand for empties at that site. Eq. (4) defines the number of empties for regional repositioning fromthe inland depot to the seaport. Eq. (5) assures the flow conservation between folded and unfolded containers along a linkbetween sites such as sippers, consignees and the inland depot. The number ‘4’ in this equation means that four foldablecontainers are folded and bundled into one package that equals to the capacity of one standard container. Eq. (6) guaranteesthat reused empties at a site are unfolded ones. Constraints (7) and (8) define the number of containers that are folded and/orunfolded at the inland depot. At the inland depot, the difference between the number of incoming and outgoing containerswhich were folded and bundled is equal to the number of containers that are folded or unfolded at the depot. Whilst theycould be represented by one equation with an absolute value, the equation becomes non-linear and difficult to solve. Con-straint set (9) specifies the number of containers that are folded and/or unfolded at customers’ sites. If there is a surplus ofempty containers, they are repositioned to other sites. Reversely, in case of a deficit of containers, empties are collected fromother sites in order to compensate the deficit. Eq. (10) defines that the sum of import shipments corresponds with the totalcontainers in the hinterland. M, Gi, Xij and YYij are decision variables, and Yij are auxiliary variables to recognize the number offoldable containers in the network.

To avoid the model complexity with non-linear constraints (e.g. absolute and/or if-then-else conditions), the number offolded and/or unfolded containers at node i, Gi is considered in formulations regardless of folding and/or unfolding. Fortu-nately, Gi can be separated from variables for F/UF, and it can be incorporated in the formulations, respectively. Our inter-views with companies that have developed foldable containers learned that the costs for folding are about the same as thecosts for unfolding. So our assumption to give these processes the same parameter value in our model is justified.

4.2.2. Formulation for ADI with standard containersThe model for this scenario is built as follows:

½ADIS� MinimizeX

i2N

X

j2N

ðCTij þ CH

ij ÞWij þ CF M ð14Þ

Subject toX

jð–TÞ2N

Wij ¼ Si 8ið–P; TÞ 2 N; ð15Þ

X

ið–TÞ2N

Wij ¼ Dj 8jð–P; TÞ 2 N; ð16Þ

WPT ¼X

kð–TÞ2N

WkP �X

jð–TÞ2N

WPj; ð17Þ

M ¼X

i2N

Si; ð18Þ

M P 0 and integer; ð19ÞWij P 0 and integer 8i; j 2 N: ð20Þ

where, Wij is the number of standard containers from nodes i to j.The objective function (14) minimizes of the total costs that are comprised of the regional and local repositioning costs,

handling costs, regional repositioning costs from inland depot to seaport, and the exploitation costs of containers. Eq. (15)


guarantees that the total number of empties moved from a consignee corresponds to the supply of empties at that site. Eq.(16) defines that the number of empties arrived at a shipper’s site is the same as the demand for empties at that site. Eq. (17)defines the number of empties for regional repositioning from the inland depot to the seaport. Eq. (18) specifies that the sumof import shipments corresponds to the container fleet in the hinterland. M and Wij are decision variables.

4.2.3. Formulation for AII with foldable containersThe model for this scenario is constructed as follows:[AIIF] Minimize (1)

Subject toX

jð¼i;PÞ2N

Yij ¼ Si 8ið–P; TÞ 2 N; ð21Þ

X

ið¼j;PÞ2N

Yij ¼ Dj 8jð–P; TÞ 2 N; ð22Þ

(4)–(13)Eq. (21) guarantees that the total number of empties moved from a consignee corresponds to the supply of empties at that

consignee’s site. Some empty containers might be reused by this consignee and other empty containers will be transportedfrom this consignee to the inland depot. Eq. (22) ensures that the number of empties that arrived at a shipper’s site is thesame as the demand for empties of that shipper. Some empty containers might be reused by the shipper and other emptycontainers will be transported from this shipper to the inland depot.

4.2.4. Formulation for AII with standard containersThe model for this scenario is constructed as follows:[AIIS] Minimize (14)

Subject toX

jð¼i;PÞ2N

Wij ¼ Si 8ið–P; TÞ 2 N; ð23Þ

X

ið¼j;PÞ2N

Wij ¼ Dj 8jð–P; TÞ 2 N; ð24Þ

(17)–(20)Eq. (23) guarantees that the total number of moved empties from a consignee corresponds to the supply of empties at that

site. Some empty containers might be reused by this consignee and other empty containers will be transported from thisconsignee to the inland depot. Eq. (24) ensures that the number of empties that arrived at a shipper’s site is the same asthe demand for empties at that site.

4.2.5. Formulation for SII with foldable containersThe model for this scenario is as follows:[SIIF] Minimize (1)

Subject to YYPT ¼ YPT � 4XPT ; ð25Þ

YYij ¼ Yij 8i 2 N;8j 2 Qi; ð26Þ

GP ¼ YPT � YYPT ; ð27Þ
(4), (10)–(13).
where, Qi is a subset of N such that Q i ¼ fjji–P or j–T;8i; j 2 Ng.Eq. (25) defines the number of empties for regional repositioning from inland depot to seaport and allows that F/UF only

takes place at the inland depot. Eq. (26) assures that the unfolded containers can be reused at each customer’s site and betransported between the inland depot and customers. Eq. (27) specifies the number of containers that are folded and/or un-folded at the inland depot.

5. Case study

The models described in the previous section have been applied to a case study. To run these models a commercial math-ematical programming solver, LINGO version 10.0, is used on a DELL Optiplex GX620 computer. Each model can be solvedwithin 10 s. However, if the model size expands, the model requires a huge CPU time and it seems to need more powerfulsolvers and/or some other solution approaches.

5.1. Data: costs, container cargo flow characteristics and geographical features

The case study concerns the hinterland transport between the port of Rotterdam and a hinterland region that covers theeastern part of the Netherlands and the western part of Germany. Container Terminal Twente (CTT) has an empty container


depot in this region (at the country border in Hengelo) and acts as a road and barge transport operator for hinterland trans-port services. Data on container cargo flows of their customers and the location of these customers could be used to set upthe case study. In addition to this geographical setting and flow data, cost data have been collected. Data on regional andlocal repositioning costs by truck were derived from rates obtained from some trucking companies, The rate for handlingcontainers at inland terminals was assumed based on literature information and checked by an inland terminal operator.The cost of folding and unfolding containers was provided by a foldable container manufacture. The exploitation cost of afoldable container was assumed to be twice as high as for a standard container, taking in consideration the estimated addi-tional purchase, maintenance and repair costs of the foldable container. Based on these sources the following parameter set-tings were used for the numerical experiments:

(i) Numbers of sites: one seaport, one inland depot and 65 customers (shippers/consignees)(ii) Distance from inland depot to seaport: 160 km

(iii) Distance ranges: 1 to 120 km between the inland depot and customers, and 1 to 190 km between the customers(iv) Total cargo flow (imports and exports): 800 FEUs/week (FEU, Forty-foot Equivalent Unit)(v) The imbalance ratio of import (inbound) and export (outbound) cargo flows to the hinterland region is 2:1

(vi) Regional and local repositioning cost, CTij is defined as CT

ij ¼ 1:45 �distance +105 Euros/FEU (the distance is dependingon node pairs)

(vii) Handling cost, CHij ¼ 40 Euros/FEU (i–j), and = 0 Euros/FEU (i = j)

(viii) F/UF cost, CUi ¼ 40 Euros/FEU/process

(ix) Exploitation cost, CF ¼ 14 Euros/FEU/week for a foldable container, and = 7 Euros/FEU/week for a standard container.

5.2. Effects of the proposed scenarios for repositioning

We look at the difference in the total costs obtained in the three scenarios with two container types as mentioned in Sec-tion 4. In Table 1 the cost performances of these scenarios are presented.

In order to examine the influence of a specific data set on the results, a sensitivity analysis is carried out, in which somefactors are varied, i.e. the returning distance from the inland depot to the seaport, the imbalance ratio of cargo flow betweenimport and export in the hinterland and the distance range between the inland depot and the customers (customer density).

The returning distance is decreased to 0 and 80 km and increased to 320 km. Considering the imbalance ratio (2:1) as afundamental setting, we also two other settings such as ratios 1:1 and 3:1. Note that a ratio 1:1 assumes balanced flows at anaggregate level, but it may still involve a need of container reposition in the hinterland because export and import volumesof the individual customers are likely to be imbalanced. However, according to this setting empty containers do not have tobe transported from the hinterland to the seaport, unlike the settings of the imbalance ratio 2:1 and 3:1.

For the distance range between the inland depot and the customers the effect of a higher customer density on the totalcosts is analyzed. The current situation represents a distribution of customers at distances varying from 1 to 120 km betweenthe customers and the inland depot. In the alternative situation it is assumed that all the customers are located within 25 kmfrom the inland depot. This assumption corresponds well to the observation that most trucking operations around inlandterminals in Europe do not exceed 25 km (IMPREND, 1999 and Kreutzberger et al., 2006). Table 2 summarizes the resultsof this sensitivity analysis.

5.3. The impact of inland depot on cost savings

The results in the previous discussions show that the returning distance from the inland depot to the seaport predomi-nantly affects the container management costs. In order to examine the cost effects in this link of the hinterland transportchain in more detail, we prepared two other scenarios for regional repositioning from the hinterland to the seaport as shownFig. 3. Hence, the following three scenarios are distinguished:

(1) Repositioning and returning via inland depot (BASIC): this scenario corresponds to the one that is discussed in Section5.3. In this scenario the surplus of empty containers in the hinterland is temporarily stacked in the inland depot andthen it returns from the inland depot to the seaport. This scenario represents a common way for regional reposition-ing, particularly in the case when barge or rail transport is used for empty transfer from the hinterland to the seaport(see Fig. 3a).

(2) Repositioning and returning via seaport (SEAPORT): the surplus of empty containers in the hinterland directly returnsfrom customers to the seaport, bypassing the inland depot. The seaport can directly deliver empties to the next cus-tomers (see Fig. 3b).

(3) Repositioning and returning via inland depot or seaport (FLEX): literally this scenario is the most flexible method forregional repositioning, as it works as a combination of the scenarios BASIC and SEAPORT. Empty containers canreturn not only directly from customers to the seaport but also through the inland depot. Since the costs savingsby bundling empty containers in the inland depot (BASIC) can be traded off by the savings from avoiding detours(SEAPORT), flexible regional repositioning is expected to be the most advantageous for efficient empty containerrepositioning (see Fig. 3c).

Table 2The total costs (in Euros) by different distance ranges between inland depot and customers (imbalance ratio: 3:1, returning distance: 320 km).

(Foldable container/standard container)

Distance range Local scenariosADI AII SII

<=120 km 109,583.8/317,020.3 117,481.1/326,778.2 165,351.0/326,778.2<=25 km 107,375.2/312,282.2 114,016.3/319,594.0 158,166.8/319,594.0

Table 1The total costs (in Euros) by different imbalance ratios, returning distances and local repositioning scenarios.


(i) Imbalance ratio: 1:1Returning distance Local scenarios

ADI AII SII0 km 33,452.2/37,156.4 49,073.0/73,536.6 76,336.6/73,536.6a

80 km 33,452.2/37,156.4 49,073.0/73,536.6 76,336.6/73,536.6a

160 km 33,452.2/37,156.4 49,073.0/73,536.6 76,336.6/73,536.6a

320 km 33,452.2/37,156.4 49,073.0/73,536.6 76,336.6/73,536.6a

(ii) Imbalance ratio: 2:1Returning distance Local scenarios

ADI AII SII0 km 45,441.2/72,453.9 56,728.6/92,534.3 96,272.3/92,534.3a

80 km 60,149.4/131,286.4 71,556.7/151,366.9 113,660.5/151,366.9160 km 67,848.9/162,084.4 79,256.2/182,164.9 121,360.0/182,164.9320 km 83,324.6/223,987.5 94,732.0/244,068.0 136,835.7/244,068.0

(iii) Imbalance ratio: 3:1Returning distance Local scenarios

ADI AII SII0 km 53,041.3/90,850.7 60,738.7/100608.6 104,808.6/100,608.6a

80 km 74,993.8/178,660.5 82,891.1/188,418.4 130,761.0/188,418.4160 km 86,485.6/224,627.6 94,382.9/234,385.5 142,252.8/234,385.5320 km 109,583.8/317,020.3 117,481.1/326,778.2 165,351.0/326,778.2

Bold: The optimal solutions.The distance range between inland depot and customers: actual.

a Standard container is lower than foldable one.


Note that each formulation for these scenarios is built with three scenarios of local repositioning ADI, AII and SII for twocontainer types of foldable and standard containers. Hence, totally 18 models were formulated for these numerical experi-ments. The formulation of these models mainly require changes of the constraints regarding flow conservations (Eqs. (2) and(3)) from/to the customers and additional constraints like as constraints (7) and (8) to define the number of containers thatare folded and/or unfolded at the seaport. For practical reasons we will not elaborate and further discuss these models here,but only present the results of the numerical experiments incorporating these scenarios of regional repositioning (Fig. 4).

Comparing the scenarios of regional repositioning, the scenario FLEX with foldable containers offers the minimum totalcost for each local scenario of ADI, AII and SII. As a result, the scenario FLEX has the best potential cost savings over the otherregional scenarios, i.e. BASIC and SEAPORT. In the actual situation, the scenarios BASIC and FLEX with foldable containershave similar costs.

Tables 3 and 4 summarize the total costs for various imbalance ratios and scenarios of regional and local repositioningunder the actual situation with varying returning distances. Looking into these tables, we observe that the combinationswith foldable containers of both scenarios SEAPORT and ADI, and FLEX and ADI offer the minimum cost in every case.The results show that the possibility to interchange empty containers directly between customers leads to the most cost-effi-cient solution. However, the scenario BASIC does not provide the minimum cost. Since in case of BASIC every empty con-tainer indirectly returns from the customers to the seaport via the inland depot; the intermediary at the inland depotrequires significant costs of handling and transport for such a detour. Moreover, in the local scenarios AII and SII the regionalscenarios SEAPORT and FLEX give the same total costs with the returning distance of 0 km. On the other hand, the total costsof the regional scenario SEAPORT rapidly increase with an increase of the returning distance; the regional scenarios BASICand FLEX have the same total costs. The reason envisaged is that when the returning distance is 0 km, the scenarios SEAPORTand FLEX directly return empties from the customers to the seaport without passing through the inland depot for cost sav-ings. Reversely, when the returning distance is longer, the scenario SEAPORT results in higher total costs, suffering from long-er distances for direct interchange of empties between customers. Hence, the scenarios BASIC and FLEX give less cost thanSEAPORT.

(a) BASIC (b) SEAPORT

(c) FLEX

: inland depot : shipper/consignee : container flow of

regional repositioning

Seaport

1

5

4 3

2

Seaport

1

5

4 3

2

Seaport

5

4 3

2

1

Fig. 3. Empty container flow patterns for regional repositioning.

Imbalance ratio: 2:1, returning distance: 160 km,the distance range between inland depot and customers: actual

0

50,000

100,000

150,000

200,000

250,000

ADI AII SII ADI SII

Scenarios of local repositioning

Tota

l cos

t (Eu

ros)

BASICSEAPORTFLEX

foldable container standard container

Fig. 4. The total costs by different scenarios of regional repositioning.


6. Conclusions and future research perspectives

This study addressed the problem of empty container management and the possible contribution of using foldable con-tainers to the cost savings in empty container repositioning. In light of the high costs of empty container management in

Table 3The total costs (in Euros) by different imbalance ratios and repositioning scenarios (returning distance: 160 km).


(i) Imbalance ratio: 1:1Regional scenarios Local scenarios

ADI AII SIIBASIC 33,452.2/37,156.4 49,073.0/73,536.6 76,336.6/73,536.6a

SEAPORT 33,452.2/37,156.4 84,574.6/163,608.1 166,408.1/163,608.1a

FLEX 33,452.2/37,156.4 49,043.1/73,536.6 76,336.6/73,536.6a

(ii) Imbalance ratio: 2:1Regional scenarios Local scenarios

ADI AII SIIBASIC 67,848.9/162,084.4 79,256.2/182,164.9 121,360.0/182,164.9SEAPORT 57,667.9/121,182.7 91,516.3/182,001.1 185,739.1/182,001.1a

FLEX 57,667.9/121,182.7 68,792.0/139,404.9 121,360.0/139,404.9

(iii) Imbalance ratio: 3:1Regional scenarios Local scenarios


FLEX 71,676.3/165,100.3 79,476.8/173,738.6 142,216.8/173,738.6



Table 4The total costs (in Euros) by different returning distances and repositioning scenarios (imbalance ratio: 2:1).


(i) Returning distance = 0 kmRegional scenarios Local scenarios

ADI AII SIIBASIC 45,441.2/72,453.9 56,728.6/92,534.3 96,272.3/92,534.3a

SEAPORT 42,761.2/61,733.9 53,657.5/81,814.3 85,552.3/81,814.3a

FLEX 42,761.2/61,733.9 53,657.5/81,814.3 85,552.3/81,814.3a

(ii) Returning distance = 80 kmRegional scenarios Local scenarios


FLEX 50,014.3/90,593.3 61,178.9/109,127.2 111,381.3/109,127.2a

(iii) Returning distance = 160 kmRegional scenarios Local scenarios


FLEX 57,667.9/121,182.7 68,792.0/139,404.9 121,360.0/139,404.9

(iv) Returning distance = 320 kmRegional scenarios Local scenarios


FLEX 73,100.0/182,910.1 84,200.6/200,972.4 136,835.7/200,972.4




hinterland transport particularly, the study focused on the land-based leg of maritime container transport chains. Althoughthere is much literature on empty container repositioning, few studies consider foldable containers and none of them suf-ficiently cover the complexity of container transport chains. For this reason integer programming models were developed inthis paper to analyze the possible cost savings by using foldable containers in a more comprehensive way. The contributionof this paper to the literature is twofold: (1) providing knowledge about the possible cost effects of foldable containers oncontainer fleet management costs, as the existing literature does not cover the potential cost savings to its full extent, and (2)giving new insights in modeling these potential cost savings.


Based on the computational experiments that we conducted, the following conclusions can be drawn. The foldable con-tainers can contribute to substantial cost savings in empty container repositioning between the seaport and its hinterland.Especially in the situation of a long returning distance from the inland depot to the seaport with a largely imbalanced trade,the foldable containers can lead to significant cost reductions. In addition, the effect of foldable containers on the cost savingsdepends on surplus and shortage situations in the hinterland where empty containers are distributed. The possibility tointerchange empty containers directly from consignees to shippers in the hinterland leads to the most cost-efficient solution.These benefits can of course only arise if containers can be folded and unfolded at the sites of consignees and shippers. More-over, the opportunities for this direct interchange are limited because of different ownerships of containers and insufficientquality of information about short-term demand for empty containers in the region at the level of individual shippers. Ofcourse, these conditions are also barriers to improve the efficiency of repositioning with standard containers.

The interchange of containers between consignees and shippers via an inland depot has fewer restrictions. However, togain benefits of using foldable containers it still requires the possibility to fold/unfold containers at the sites of consigneesand shippers, e.g. the availability of handling equipment. The most realistic and easiest way is to implement foldable con-tainers where the folding and unfolding is only carried out at the inland depot. Consequently, cost savings by using foldablecontainers could only be realized in a transport segment between the inland depot and the seaport. Nevertheless, the resultsof this study show that using foldable containers could still be worthwhile.

The results of this study are founded upon European hinterland transport characteristics, but the major conclusion thatusing foldable containers can be beneficial will also be valid for regions like Asia or United States. Looking at the hinterland ofports in these regions the density of container inland depots is much lower than in Europe. This means less possibilities totransport empty containers bundled in folded state (if fold/unfold operations only can take place in depots) and hence thebenefits of foldable containers will be smaller. However, the distance in hinterland transport in these regions may be largermaking the benefits of foldable containers in this link of the transport chain greater. Since the largest cost savings of foldablecontainers can be reaped in repositioning of containers between hinterland and seaport, and considering that the volumes ofthese regional repositioning flows are larger than local repositioning flows, the use of foldable containers will also be ben-eficial in Asia and United States.

This paper has provided some evidence for the economic viability of foldable containers to save repositioning costs. How-ever, it would be interesting to extend the scope of this kind of analysis to the shipping network in future research. Further-more, the analysis on repositioning costs could be further refined. This study assumed empty repositioning only by trucks;barges and trains would be interesting alternatives to examine. Moreover, in order to limit the complexity of the reposition-ing models, the routing problem of truck services was not considered in this study. Also no comparisons between handlingprocesses of foldable and standard containers at customers’ sites were made. Adding these elements in the analysis as well asthe dimension of time in the demand for and supply of empty containers would further enhance the value of this study.These tasks remain a challenge for future work.

Acknowledgements

The authors wish to thank Dr. Milan Janic from OTB Research Institute for Housing, Urban and Mobility Studies, Delft Uni-versity of Technology, for his suggestions to improve the paper. The main stage of this study was carried out while the firstauthor of this paper, Koichi Shintani, was at Delft University of Technology as a visiting researcher with a support by theInstitute of National Colleges of Technology (Japan). This study was financially supported by the Japan Society for the Pro-motion of Science (Grant-in-Aid for Young Scientists (B) No. 20710124 and Grant-in-Aid for Exploratory Research No.19656232), Academic Centre of Transport in Rotterdam (The Netherlands), and SenterNovem in Utrecht (The Netherlands).

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The impact of foldable containers on container fleet management costs in hinterland transport