Supply Chain Article Summary


write a 2-page summary of the attached paper.Vol. 42, No. 1, January–February 2012, pp. 5–16
ISSN 0092-2102 (print) — ISSN 1526-551X (online)
© 2012 INFORMS
Achievement in Operations Research
A Strategic Empty Container Logistics
Optimization in a Major Shipping Company
Rafael Epstein, Andres Neely, Andres Weintraub
Department of Industrial Engineering, University of Chile, Santiago, Chile
Fernando Valenzuela, Sergio Hurtado, Guillermo Gonzalez,
Alex Beiza, Mauricio Naveas, Florencio Infante
Compañia Sud Americana de Vapores (CSAV), Valparaíso, Chile
Fernando Alarcon, Gustavo Angulo, Cristian Berner,
Jaime Catalan, Cristian Gonzalez, Daniel Yung
Department of Industrial Engineering, University of Chile, Santiago, Chile
In this paper, we present a system that Compañía Sud Americana de Vapores (CSAV), one of the world’s
largest shipping companies, developed to support its decisions for repositioning and stocking empty containers.
CSAV’s main business is shipping cargo in containers to clients worldwide. It uses a fleet of about 700,000
TEU containers of different types, which are carried by both CSAV-owned and third-party ships. Managing the
container fleet is complex; CSAV must make thousands of decisions each day. In particular, imbalances exist
among the regions. For example, China often has a deficit of empty containers and is a net importer; Saudi
Arabia often has a surplus and is a net exporter. CSAV and researchers from the University of Chile developed
the Empty Container Logistics Optimization System (ECO) to manage this imbalance. ECO’s multicommodity,
multiperiod model manages the repositioning problem, whereas an inventory model determines the safety stock
required at each location. CSAV uses safety stock to ensure high service levels despite uncertainties, particularly
in the demand for containers. A hybrid forecasting system supports both the inventory and the multicommodity
network flow model. Major improvements in data gathering, real-time communications, and automation of
data handling were needed as input to the models. A collaborative Web-based optimization framework allows
agents from different zones to interact in decision making. The use of ECO led to direct savings of $81 million
for CSAV, a reduction in inventory stock of 50 percent, and an increase in container turnover of 60 percent.
Moreover, the system helped CSAV to become more efficient and to overcome the 2008 economic crisis.
Key words: shipping; container repositioning; logistics; forecasting: applications; inventory; networks: flow;
uncertainty; collaborative planning.
ompañía Sud Americana de Vapores (CSAV) is
the largest logistics operator in Latin America and
one of the world’s largest shipping companies in terms
of capacity. Founded in 1872, it is the most global
Chilean firm. In addition to its headquarters in Chile,
CSAV operates seven regional offices: Valparaíso,
Chile; Sao Paulo, Brazil; Hong Kong, China; Hamburg,
Germany; New Jersey, United States; Barcelona, Spain;
and Mumbai, India. In 2010, CSAV had operations in
over 100 countries and more than 2,000 terminals and
depots worldwide.
CSAV’s main business is shipping cargo using containers, which are transported on ships operated
by both CSAV and other companies. The container
fleet consists of about 700,000 20-foot equivalent-unit
(TEU) containers of over 10 types in terms of size
and type of cargo (e.g., 20- and 40-foot dry vans,
reefers, and oil tanks). This fleet is valued at approximately $2 billion and serves customer needs of more
than 2.9 million TEU (about 50 million tons) per year.
CSAV owns only about 5 percent of its container fleet;
it charters the rest from leasing companies. In general,
CSAV rents containers on long-term contracts that
allow it to receive the containers at specific depots in
a specific time frame and return them to previously
specified locations within a predetermined period.
To cover its worldwide client needs, CSAV coordinates a multimodal network and offers about 40 container transport services. These services have fixed
routes and are carried out by more than 180 container
ships that have capacities ranging from 2,000 to 6,500
TEU each. Each week, CSAV handles approximately
400 vessel calls, requiring hundreds of thousands
of container logistics decisions. Intermodal services,
which include thousands of feeder ships, barges,
trucks, and trains both from CSAV and third parties,
complement CSAV’s transport services.
Managing this global operation requires 24/7 attention. CSAV employs more than 6,500 people worldwide, and its decisions impact workers at thousands
of suppliers. The CSAV professionals responsible for
operations are of different cultures, nationalities, and
backgrounds, and live in different time zones, thus
making it difficult for them to coordinate and plan
interconnected activities.
The company previously managed its container
fleet based on decentralized decisions from its
regional offices. The high level of interconnection
of these decisions, the empty container imbalance
among regions, and the uncertainty in main parameters, such as demand for containers, led to significant shortcomings in container management, reflected
mainly by CSAV’s high level of container safety stock.
In 2006, CSAV and researchers from the University
of Chile began a project to address this problem.
Epstein et al.: A Strategic Empty Container Logistics Optimization
Interfaces 42(1), pp. 5–16, © 2012 INFORMS
As part of the project, we developed an operations
research (OR)-based system, Empty Container Logistics Optimization System (ECO), which optimizes
CSAV’s empty container logistics by integrating the
operational and business decisions of all regional
offices. Our objective was to minimize global empty
container-related costs while guaranteeing a high service level. ECO is also a collaborative Web-based optimization framework in which multiple agents who
have different local objectives and work in dissimilar
business conditions make decisions.
In late 2007, we implemented the first version of
ECO in Chile and Brazil. When the financial crisis
hit the shipping industry particularly hard in 2008,
CSAV decided to address the crisis by gaining a competitive advantage through excellence in managing its
container fleet; ECO played a key role in achieving
this goal. CSAV implemented the system rapidly and
implemented globally. In January 2010, ECO became
operational worldwide.
In this paper, we use the following structure. The
Empty Container Problem section presents the problem
that we address. In the Background section, we discuss
how CSAV handled empty container logistics decisions prior to implementing ECO. The Empty Container
Logistics Optimization System section explains the OR
features of ECO and how it improved coordination
and decision making by changing CSAV’s operational
strategy. Implementing the ECO System describes the
project’s history and how CSAV successfully implemented this tool to support its global operations.
We discuss quantitative and qualitative results in the
Impact section and present final comments in the Conclusions section.
The Empty Container Problem
The literature discusses container routing and repositioning problems as they relate to shipping and other
means of transportation. Movement of empty containers is usually the result of imbalances in moving
cargo. Models often take the form of multicommodity
flow problems to reflect the conservation of flow and
satisfaction of demand constraints. In Crainic et al.
(1993), the authors present one of the first characterizations of these problems, as they develop single and multicommodity network formulations. Erera
Epstein et al.: A Strategic Empty Container Logistics Optimization
Interfaces 42(1), pp. 5–16, © 2012 INFORMS
et al. (2005) present a large-scale multicommodity
flow problem on a time-discretized network model
developed for the chemical industry; the model integrates container routing and repositioning decisions.
Choong et al. (2002) discuss a tactical planning problem for managing empty containers on barges for
intermodal transportation. They use an integer program to analyze the effects of the length of the
planning horizon. Jansen et al. (2004) report an operational planning system used to reposition empty containers for a German parcel post firm.
In dealing with empty containers, the handling of
uncertainty, particularly of demand, can be a major
problem. Erera et al. (2006) propose a robust optimization approach based on the ideas of Ben-Tal and
Nemirovski (2000). Cheung and Chen (1998) handle
the uncertainty issue by using a two-stage stochastic
network flow model, and develop procedures to solve
this problem.
To define the empty container problem at CSAV,
we first describe its dynamics. The typical cycle of a
cargo container (see Figure 1) starts when a shipping
company takes an empty container from a container
depot. The empty container is loaded on a truck and
delivered to a shipper, who fills it with the merchandise to be shipped. Once the container has been filled,
the company transports it to its final destination, as
indicated by the consignee to whom the cargo is to
Empty container
from depot to shipper
be delivered. Typically the company uses multiple
types of transport. The filled container is transported
by truck to the main port, where it will be loaded
onto a vessel. Some shippers fill the container at the
port, saving the travel from the depot to the shipper’s location and then to the port. Once all customs
requirements for the filled container at the port have
been satisfied, the container is then loaded onto a vessel. Once loaded on the vessel, the filled container is
transported to the port at which it is to be unloaded.
The shipping process might also include transshipments, which involve moving the container from one
vessel to another before it reaches its final destination. The destination port is generally close to the
consignee’s location. The filled container is unloaded
from the vessel and is transported by truck, train,
or feeder ship to the consignee’s location, at which
the consignee receives the container, unloads the merchandise, and returns the empty container to the shipping company, which performs maintenance on the
container if it is damaged or dirty. Consignees sometimes use filled containers as warehouses, extending
the time they keep the containers before returning
them to the company, and paying fines for the late
We observed four main problems related to managing the fleet of empty containers. The first problem is an imbalance of demand among regions, as
Full container
from shipper to port
Port of
(includes several
Empty container
from consignee
to depot
Full container
from port to
Port of
Figure 1: The graphic depicts the typical cycle of a cargo container, which starts empty in the origin depot and
finishes empty at the destination depot.
we describe above. Some regions are net exporters of
empty containers; other regions are net importers. This
regional imbalance of supply and demand for empty
containers forces shipping companies to solve this
problem by efficiently repositioning the containers.
A company must consider several solutions to mitigate the imbalance. The most efficient and costeffective solution is to transport empty containers
from surplus to shortage locations using container
ships and other available transport modes. Empty
containers represent a firm’s biggest operational cost
after ship fuel; therefore, empty container repositioning is a key element in a company’s performance. For
example, during 2010 in one region in Asia, CSAV had
a container imbalance—a deficit of more than 900,000
TEU—that had to be repositioned empty to cover this
uneven demand.
The second problem is the multiple sources of
uncertainty. The main source of uncertainty is the
demand for empty containers, which depends on
external factors such as market conditions. Thus, a
significant part of the challenge is forecasting the
demand for empty containers at each location, for
each equipment type, and for a specific date. The
time and place at which consignees will return empty
containers is uncertain because customers sometimes
delay returns. Travel times are also an element of
uncertainty. For example, the travel time from Shanghai, China to Port Elizabeth, New Jersey in the United
States is 37.9 days on average; the standard deviation
is 4.1 days, which represents a coefficient of variation
of 11 percent. A final source of uncertainty is the availability of vessel capacity allocated to move empty
containers. Filled containers have a higher priority
over empty containers because paying customers are
awaiting them. Empty containers do not necessarily
have a booking waiting for them at their destination; however, they must eventually be repositioned
to reduce the container imbalance.
A third major problem relates to handling and
sharing operations information. Tracking worldwide
container activities, compiling the information, and
making it available in real time to all decision makers are technological challenges. In one year, CSAV’s
tracking systems record over 18 million container
activities; these systems process over 400,000 transactions daily to update information related to the
Epstein et al.: A Strategic Empty Container Logistics Optimization
Interfaces 42(1), pp. 5–16, © 2012 INFORMS
container activities. At the beginning of the project,
the regional offices used different information, which
they obtained from various sources. This often forced
planners to make decisions using outdated or inaccurate reports. Moreover, data gathering and processing
were done manually, which forced logistics planners
to spend much of their time processing worksheets
and database extracts rather than making decisions
and coordinating empty container activities.
The fourth problem we faced was that the decision makers were distributed throughout the regional
offices. Each regional office can handle intraregional
decisions, which relate to trips between locations
within a geographic area. However, because interregional decisions relate to trips between geographic
areas, they require coordination between the regional
offices. Coordinating both intraregional and interregional decisions in real time for regions with different cultures and dissimilar operational practices was
a problem. Prior to the ECO implementation, each
CSAV regional office had a team responsible for coordinating and making empty container logistics decisions, which the headquarters office in Valparaíso
coordinated. Regional teams were supplemented by
over 30 logistics planners worldwide, who coordinated activities with people both within the company
and from third-party companies.
The imbalance, uncertainty, data, and coordination
problems inherent to CSAV’s business shaped the
problem. In addition, if we consider CSAV’s global
operations at thousands of points worldwide, hundreds of vessels with scheduled itineraries, multiple
container types, and hundreds of thousands of empty
container-repositioning routes, this problem is hard to
manage by even the most skilled team of professionals. Moreover, the seven regional offices coordinating
this operation are in different time zones, adding complexity to daily planning and decision making.
CSAV previously managed its container fleet using
a decentralized decision-making process through
regional offices, which have poor visibility of present
and future container flows and no clear definition
of stock levels. This process was the result of the
Epstein et al.: A Strategic Empty Container Logistics Optimization
Interfaces 42(1), pp. 5–16, © 2012 INFORMS
firm’s rapid growth, which made centralized control difficult given the complexity of global operations. Therefore, CSAV gave significant independence
to its regional offices. Decentralization, among other
factors related to the size and nature of the problem,
led to significant shortcomings in container management, mostly expressed by a high level of empty container safety stock held to satisfy expected demands.
This was aggravated by the lack of flexibility in combining containers in different regions, difficulties in
handling the natural fluctuations of market conditions, and the lack of tools to support global decision
making. Because of this inadequate knowledge about
container stocks and future container needs, empty
containers were not always repositioned efficiently.
Regional offices focused on finding the best local optimum instead of finding a company-wide optimum.
CSAV’s philosophy is to achieve a superior level
of service (i.e., close to 100 percent customer satisfaction). In the shipping industry, efficiency is important
because margins are small and the container fleet represents a firm’s major cost. Therefore, an optimized
policy for empty container storage and a smart strategy to reallocate the containers are crucial for operations. The uncertainty in the main parameters and the
lack of tools to quantify this uncertainty led decision
makers to hold high levels of stock of empty containers to maintain their high service standards.
Initially, we did not have a clear picture of the complexity, uncertainty, size, and required coordination of
the issues to be addressed. After some work, we realized that our main contribution would be to assist
CSAV in centralizing its empty container inventory
and repositioning decisions.
The Empty Container Logistics
Optimization System
We considered developing a single, integrated, and
robust optimization model that would address the
entire problem, including uncertainties (Bertsimas
and Sim 2004). When we did some tests with small
instances of the problem, we found that the time
required to find an optimal solution was too long for
our needs. Therefore, we opted for a two-stage solution approach, based on a network flow model and
an inventory model, as we describe below.
ECO is based on two decision models supported
by a forecasting system. First, an inventory model
addresses the uncertainty problem and determines the
safety stock for each point. Second, a multicommodity,
multiperiod network flow model addresses the imbalance problem and supports daily empty container
repositioning and inventory levels. The service quality is managed by imposing the safety stock as constraints in the network flow model. Finally, to address
the coordination problem, ECO uses a collaborative
Web-based optimization framework in which multiple
agents make decisions taking local objectives and dissimilar business conditions into consideration.
The main decision variables considered in the network flow model are (1) how and when CSAV should
reposition empty containers to fulfill its needs at
specific locations using the various transport modes,
(2) what the level of empty containers should be at
each point and period, including safety stock to handle the uncertainties, and (3) when and where CSAV
should lease and return containers.
Appendix A shows the multicommodity network
flow model. Its main constraints are container flowbalance equations, demand satisfaction, capacity constraints (defined by both weight and number of slots
available), safety stock limits, and initial conditions.
Because one goal of the model is to achieve a predefined service level, the inventory variables have the
safety stock as lower bounds. If the safety stock cannot be fulfilled with currently available empty containers, the variables representing shortages account
for the additional requirements for empty containers.
Finally, we consider other constraints such as unfeasible or undesirable repositioning options. The model’s
objective is to minimize costs associated with empty
container loading, transport, unloading, leasing, and
We determined that ECO should be run three times
per day to support regional offices located in different time zones. To achieve three runs per day,
we limited its run time to no more than two hours,
using warm starts and other speed improvements.
For example, the model incorporates only the main
location equipment-type combinations. The 2,000 terminals and depots are grouped into 600 locations.
From the 600 locations and 10 equipment types, 2,500
location equipment-type pairs account for more than
Epstein et al.: A Strategic Empty Container Logistics Optimization
Variation of safety stock on service level and demand
forecast error standard deviation
Safety stock (containers)
99 percent of the company’s operations. We considered only these combinations. However, this is one of
the many parameters that ECO system administrators
can fine-tune.
After logical preprocessing, which eliminates
unneeded constraints and variables, a typical instance
of the network flow model has approximately 3.7 million parameters, 1.2 million variables, and 600,000
equations. To reduce the solution time, we first run
a relaxed continuous version of the problem and
then round off the container flows. Given that these
are integer-friendly MIP problems, the error gaps
are small.
To address the problem of uncertainties, we developed an inventory model. We imposed the service
quality by including adequate safety stock in the network flow model at each location based on container
type and period. Both the network flow model and
the inventory model required that we generate empty
container demand and return forecasts.
After a lengthy analysis, we found that the best
forecasts required that we integrate time-series models with specific knowledge from the sales force and
local logistics planners. We based the safety stock on
the accuracy of the forecasts (Thomopoulos 2006). The
ECO system has a module that keeps track of historical demand and return-forecast accuracy, which
allows us to have updated estimators for the standard
deviation and the mean forecast error for each location, equipment type, and period.
An important part of the project was understanding the relationship between forecast error and safety
stock. In Figure 2, we present an example of a location and a specific equipment type in which we computed safety stock based on different service levels
and standard deviations of the demand-forecast error.
For example, for a service level of 99 percent, a forecast with a standard deviation of 12 units requires a
safety stock of 28; this rises to 77 when the standard
deviation is 33.
The results in Figure 2 showed CSAV management the importance of having the best possible
demand forecasts. After a long testing period, management agreed that the best possible forecasts could
be determined by a combination of approaches, as we
describe below.
Interfaces 42(1), pp. 5–16, © 2012 INFORMS
Demand forecast error
standard deviation
33 Units
18 Units
12 Units
Service level (%)
Figure 2: The safety stock depends on the demand forecast accuracy given
by the standard deviation of its error and the service level given by
the company. This example shows the values for one location and one
equipment type, assuming that the only source of uncertainty is given by
demand of empty containers.
1. Time-series forecasts: We tested several timeseries forecasting techniques, including ARIMA models (Box and Jenkins 1976). However, we obtained the
most accurate forecasts using seasonal and trended
moving averages. Therefore, ECO uses two types of
time-series forecasts: (1) a moving average forecast,
which uses the average of the past n days; (2) a
trended seasonal forecast, which uses past demand
from the same season and adds a yearly trend that is
computed from the previous year’s figures.
2. Sales force forecast: CSAV developed a qualitative sales forecast, the consensus forecast model
(CFM), in which the sales agents worldwide register their demand expectations; we elaborate on this
forecast, filter it to ensure its accuracy, and use it to
complement the time-series forecasts.
3. Logistics planners’ forecast: We realized that
logistics planners sometimes have information that
must be considered in the forecasts; therefore, we
included the option of introducing manual demand
forecast values.
To forecast returned containers, we consider the
first two methods. Note that in each instance, over
1,500,000 forecasts are calculated based on updated
information and new user settings. This calculation
considers both demand and return forecasts, the
length of the horizon (i.e., 128 days), and the main
location-equipment type combinations.
Epstein et al.: A Strategic Empty Container Logistics Optimization
Interfaces 42(1), pp. 5–16, © 2012 INFORMS
Logistics planners determine which forecast will
be used at each location based on the forecast accuracy and their own experiences. In addition, they
enter their demand expectations for specific locations,
equipment types, and dates, which can replace the
information in the ECO system forecasts. Then, the
forecast type that the planner in each region configured is used in the network flow model.
To calculate the safety stock, we included the
variance of the forecasts errors and the uncertainties because of repositioning travel times and capacity availability for shipping empty containers (see
Appendix B).
The data problems mentioned above required significant changes in information quality and availability. CSAV undertook several projects to improve
container-activity gathering and data transmission in
its regional offices. Moreover, it designed several initiatives to improve information quality (e.g., regarding container activities, demand forecasts, and vessel
schedules). As a result, the information quality has
improved in both the ECO system and in many other
systems and business units in the company.
As a result of implementing ECO, the average computer time required to track container activities fell
from over 48 hours to fewer than 24 hours. In some
areas, this resulted in dramatic reductions in the time
between an activity’s occurrence and its entry into
CSAV databases. These reductions were the result of
projects that CSAV undertook to improve the process
that dictates how to gather and transmit information
from the agencies and depots worldwide.
Container activities also include the equipment ID,
the activity’s date and type (e.g., loading, discharge,
demand, drayage), and complementary information
such as booking numbers, ports, and schedules. The
quality of this information has also improved significantly, allowing the system to provide better information to the logistics planners about the status of
the containers and the time each is expected to be
available for use.
Data are sent to ECO directly from many of the
company’s core databases, which transfer updated
information every minute. However, we were aware
that information is not perfect; therefore, we integrated a data-cleansing module into ECO. Information quality has improved significantly because of
CSAV’s data-quality initiatives, some of which were
born out of problems that were detected during the
development and testing of this project.
To tackle the coordination problem, we designed
and implemented a framework that optimizes CSAV’s
global operations based on a collaborative and participative optimization model on the Internet. The team at
each regional office sets the parameters for each geographical area; the optimization model then considers all the settings simultaneously to deliver a global
result. For example, users can configure the type of
forecast to be used in the network flow model, set
the desired service level at each location for each
equipment type, and refine costs and some constraints.
The network flow model solutions are integrated with
updated business information, and several reports and
dynamic indicators are made available to all planners and logistics people worldwide. Users from all
regional offices review and share optimized plans and
use them as a common basis for planning, coordination, and decision making. Bulk upload functionalities and integration with common office software
allow parameter tuning and solution analysis in a
user-friendly and timely way, given the amount of
information available and considered in each instance.
Implementing the ECO System
Implementing the ECO system was a long process. In 2006, we evaluated the potential savings
to ensure that this approach would address CSAV’s
main problems, while improving efficiency and performance. Our first approach was to gradually
implement the system in all the regional offices,
starting with the headquarters office in Valparaíso.
We used a prototype-based development process,
which required a large amount of field work; however, it ultimately helped us to understand the major
decisions and problems that logistics planners faced.
It also allowed us to gradually improve the network
flow model, the inventory model, and the forecasting
At that time, CSAV empty container logistics operations did not include analysis of global processes
or global systems; therefore, each region used a different operational method to solve its logistics problems. This became one of the most difficult parts of
the implementation; we had to coordinate different
cultures, processes, concepts, and languages to implement a global unique process and tool.
Another challenge was implementing this new way
of handling empty container logistics simultaneous
with the existing process. The people who were testing, tuning, and starting to use ECO had to continue
doing their jobs as usual. We did not force its usage.
We trained the users in the methodology and basic
OR concepts, believing that using ECO would make
their jobs easier.
In early 2007, we tested the first prototype using historical data; our tests showed significant opportunities
for reductions in storing and shipping empty containers. This allowed us to move to the next step—using
dynamic information in the system and supporting
real decisions. In late 2007, we implemented a successful prototype in Valparaíso, Chile and Sao Paulo,
Brazil. This prototype allowed us to work with two
regional offices to understand how they used the system and determine any problems. For example, we
realized that coordinating the regional offices would
require a collaborative Web-based interface. Based on
the results of the prototypes developed in Chile and
Brazil, CSAV management committed to sequentially
installing the system in all regions.
In 2008, the financial crisis hit the shipping industry particularly hard; international trading fell significantly, and freight and charter rates plunged. The
shipping industry has a relatively large time lag
between economic cycles and shipping orders. Therefore, the crisis resulted in a large surplus of ships;
many shipping companies went bankrupt or became
insolvent; they were no longer able to make their
assets profitable, and therefore required complex debt
restructurings. Between July 2008 and March 2009,
CSAV’s freight cargo fell 18 percent, its sales dropped
38 percent, and its market value fell 66 percent.
To address the crisis, CSAV determined that it
would gain a competitive advantage through excellence in managing its container fleet. Radically changing its management strategy was imperative, and
ECO played a key role in achieving this goal. Management decided to improve CSAV’s operations and
instill a standard of excellence in staff at all regional
offices; it would be based on integrating and optimizing the decisions regarding managing its container
Epstein et al.: A Strategic Empty Container Logistics Optimization
Interfaces 42(1), pp. 5–16, © 2012 INFORMS
CSAV implemented ECO in 2009 and launched
it globally in January 2010. The plan required all
regional offices to implement ECO simultaneously.
Therefore, to test and use the system, the offices had
to be connected in real time. Once the main features were ready, a team from CSAV went to each
regional office to introduce the system and train logistics planners in the methodology and in using the
collaborative Web interface. In January 2010, testing
and revisions in all regions were completed and the
system became operational worldwide. The ECO system replaced the existing decision-making process,
thus globally optimizing CSAV’s large and complex
container shipping system.
To generate and implement a global process to support the tool that we were implementing worldwide,
we coordinated weekly logistics meetings with staff in
each region; in these meetings, we defined the empty
container flows for the following weeks and targeted
optimal levels of safety stock at each location. The
process also incorporated the best practices in using
the system. We consolidated all this information in an
operations manual that all CSAV offices use today.
ECO runs with the participation of all regional
offices. The results of the runs are incorporated with
business information and presented on a Web platform to which all logistics planners have access. They
consider the system’s suggestions and complement
them with their information on the status of ports,
ships, possible new demands, and other critical variables, and generate the final repositioning plan. The
planners create the inventory and shipping plans for
empty containers based on the system’s suggestions,
share them with the rest of the organization, and execute them on time.
ECO was implemented using four servers, each
with a specific function:
1. A database server stores and computes updated
parameters for the network flow and inventory models. More than 60 million container activities are
stored and used for computing necessary information
(e.g., historical demand, empty container returns, and
travel times). This server uses a marginal approach to
generate all the parameters based only on the changes
from the previous run.
2. A second database server stores the network flow model solutions combined with business
Epstein et al.: A Strategic Empty Container Logistics Optimization
Interfaces 42(1), pp. 5–16, © 2012 INFORMS
The project had both a wider and deeper impact
than originally intended. It led to significant improvements in data gathering, real-time communications,
automation of data handling, and quality of the decision processes; it allowed managers to make decisions
with better, standardized information. ECO allowed
for global decisions that were clearly superior to the
ones obtained locally by each region.
In quantitative terms, ECO resulted in savings of
$81 million in 2010, compared with the 2006–2009
average costs. In 2010, the cost reductions were
mainly the result of reducing empty container inventory stocks by 50 percent and increasing container
turnover by 60 percent.
Figure 3 shows the cost per full voyage, considering year 2010 as baseline with cost zero. The average cost in 2006–2009 was $35 per full voyage more
than in 2010; we used this value to estimate the ECOrelated savings. Considering the 2.9 million voyages
in 2010, the total savings were $101 million. We estimate the ECO-related impact to be 80 percent of
these savings, considering that the demand forecasts,
stocks visibility, return forecasts, and logistics solutions proposed are vital to the decision making. However, other minor projects were ongoing; we assign
them the remaining 20 percent. This results in the $81
million savings mentioned above.
CSAV’s flexibility to modify the size of its container
fleet shows that the savings come from improved efficiency because of better management of the fleet. The
company has the flexibility to return or hire leased
Cost per full voyage
3. A Web server generates dynamic Web pages to
meet user information needs.
4. An application server runs the network flow
model through GAMS/CPLEX software and includes
the ECO system application, which controls the flow
of information entered into the network flow model
and the database storing the solutions.
Today, ECO serves CSAV’s regional offices and is
used as a framework to support empty container
inventory and repositioning decisions. The head office
in Valparaíso uses ECO output as a common platform
for planning and coordinating interregional decisions
among the regional offices.
$ 51
$ 27
$ 32
$ 32
Average per voyage excess
cost 2006–2009:
Voyages 2010:
Total savings:
2.894 million
$35 · 2.9 = $101 million
Estimated ECO effect:
Total ECO savings:
$81 million
Figure 3: The graph shows the cost per full voyage from 2006 to 2009,
compared to 2010. The cost during 2010 was considered as level zero,
and marginal costs are shown.
containers and determine the size of the fleet based
on market conditions. Thus, the improved efficiency
in container management generates the savings.
The ECO implementation had an impact both by
reducing empty container logistics costs and by making CSAV more profitable than it had been in the
previous decade. Average net income for the years
2000–2008 was $60 million; however, CSAV lost $669
million in 2009 because of the financial crisis. The savings from this project are an important part of the
company’s 2010 net income of $170 million. If we consider that CSAV had a demand for 2.9 million TEU
in 2010, the net income per TEU was $59, an increase
of 91 percent over what it would have been without
the ECO-related savings. In addition, the savings generated by the ECO implementation surpassed by far
the average net income of CSAV in the previous four
years, even if we disregard the 2009 net income (see
Figure 4).
This efficiency improvements gave CSAV these savings and a competitive advantage, which were key
elements in helping CSAV to overcome the crisis and
position itself as one of the major carriers in the
world. According to CSAV CEO Arturo Ricke,
The ECO system allowed us to manage the highly
complex problem of our empty container fleet logistics very efficiently, which is fundamental in the global
management of the firm. This improvement was a
Epstein et al.: A Strategic Empty Container Logistics Optimization
Interfaces 42(1), pp. 5–16, © 2012 INFORMS
Net income (USD million)
– 39
– 58
– 200
– 300
– 400
– 500
– 600
– 700
– 669
– 800
Figure 4: The chart shows CSAV’s net income from 2006 to 2010.
major contribution in turning our company around
and is now one of the key elements in CSAV’s
operational strategy.
We estimate that the ECO system will generate an
additional $200 million in savings during 2011–2012.
On the qualitative side, OR made CSAV’s tracking
and information systems useful; the optimization system tells operators what to look for and focus on in
a global, complex, and changing network. ECO provided decision makers with a robust and trustworthy
methodology that gives them target inventory levels.
In addition, the optimization model provides them
with a reliable source of alternative repositioning
options, which can sometimes suggest new solutions
that they have not considered.
ECO made contributions in at least four areas:
• Data quality, management, and availability: ECO
development required a dramatic improvement of
information quality, management, and availability.
These improvements positively affected other areas of
the firm.
• Personnel efficiency: Before its ECO implementation, CSAV used approximately 30 logistics planners
to manage the container fleet. In August 2008, these
planners managed 550,000 TEU in the container fleet.
During 2010, the 30 logistics planners used ECO to
manage and coordinate empty container logistics of a
700,000 TEU fleet. These planners were able to absorb
this higher workload because the system significantly
reduced the time required to gather and process the
information they used.
• Unification of processes: Prior to creating and
implementing ECO, each regional office used different
information and procedures to plan and coordinate
empty containers logistics, thus making the coordination and tracking of logistics decisions difficult.
Today, ECO serves as a common platform for analysis and coordination, providing a standardized empty
container planning process.
• Better reporting and control: Prior to the ECO
implementation, empty container logistics planning
required a mostly manual gathering of information
from different sources. ECO allowed operators more
time to focus on core tactical and strategic decisions.
Logistics planners now spend most of their time making decisions and coordinating activities rather than
processing data and reports.
In addition, in the past five years, CSAV’s container
business has increased significantly. Its use of ECO
has allowed CSAV to maintain the same quality of
service while incrementing the number of empty containers provided to customers well below the increase
in the number demanded. The overall environmental
and economic effects have been positive.
This project and the resulting OR-based solution provided a decision support framework that changed
how logistics planners make their decisions and coordinate empty container logistics. This change produced important qualitative and quantitative results
and also plays a key role in CSAV’s operational strategy today. OR allowed CSAV to coordinate empty
container logistics and support decision making
under uncertainty, changing conditions, and imperfect information.
The ECO implementation demonstrated important
features of OR usage—how it must integrate with
information technology, data handling, and communications. Most importantly, it fostered a genuine
partnership between the researchers at the university
and the users at CSAV throughout the entire development process. As CSAV managers became convinced
of the significant benefits of an OR approach, we were
able to align the organization behind a change in
its operational strategy, which led to the significant
positive benefits described.
Epstein et al.: A Strategic Empty Container Logistics Optimization
Interfaces 42(1), pp. 5–16, © 2012 INFORMS
The use of prototypes was also an important part of
the project; at an early stage of the project, it allowed
us to understand the real needs and challenges faced
by logistics planners.
ECO enabled CSAV to make the organizational
changes needed to centralize the coordination of
empty container decisions. The collaborative Web
interface assisted the distributed planning process
over distinct time zones. The optimization of the network flow and the inventory levels subject to safety
stock constraints proved to be the right approach to
support the decision-making process. The improvement in data gathering and management needed to
run ECO provided high value for users in other
functional areas at CSAV.
We believe that the main lesson of this project was
how OR at CSAV facilitated a structural change that
had very significant positive results.
Appendix A. The Multicommodity
Network Flow Model
We present a simplified version of the network flow
model considered in ECO. Neely (2008) provides a
detailed description.
gtik ∈ + : Number of containers of type k already
scheduled to arrive at location i on day t and in
t ∈ + : Safety stock for containers of type k at
location i on day t.
lD ∈ + : Lead time for unloading containers, number of days required to make containers available.
lU ∈ + : Lead time for loading containers, number
of days required to prepare containers for loading.
Main Constraints
The difference in the number of containers that are
loaded and unloaded from a vessel in a given call is
equal to the difference of containers that arrive and
leave the location on this vessel.
X jik X ijk
∀ i1 k1 t1 s1 v ytsv
− ȳtsv
= xrtv − xsrv
j1 r
j1 r
Inventory dynamics account for flow conservation,
including lead times when loading and unloading
X ik
∀ i1 k1 t wt+1
= wtik + gtik + rtik − dtik − ȳ4t+l
U 5sv
v1 s
D 5v + z̄t − zt 0
v1 s
Decision Variables
wtik ∈ + : Number of containers of type k in inventory
at location i on day t.
xtsv ∈ + : Number of containers of type k that are
moved by vessel v when it departs from location i on
day t and arrives at location j on day s.
∈ + : Number of containers of type k that are
unloaded from vessel v at location i when it arrives
on day t and departs on day s.
∈ + : Number of containers of type k that are
loaded into vessel v at location i when it arrives on
day t and departs on day s.
t ∈ + : Number of additional containers of type k
that are required at location i on day t.
t ∈ + : Number of containers of type k that are no
longer required at location i on day t.
dtik ∈ + : Expected demand for containers of type k at
location i on day t.
rtik ∈ + : Expected return of containers of type k at
location i on day t.
The inventory must at least include the safety stock.
t ≤ wt 0
The model also considers capacity constraints for
the various means of transport and the initial inventory available at each location, among other operational constraints. In particular, given the detailed formulation of the model, containers might be unloaded
at a given port and then loaded again at this port
in some instances. To avoid this nonlogical step, we
introduced binary variables. The objective function is
to minimize operational costs.
Appendix B. The Inventory Model
We consider safety stock requirements—at period t,
with orders at each period, and with a single source
of uncertainty—in demand for empty containers. The
safety stock depends on the demand forecast error
and is given by
St = max4‘Œˆ e1
+ z ‘ˆ te1 D ’1 051
Epstein et al.: A Strategic Empty Container Logistics Optimization
Interfaces 42(1), pp. 5–16, © 2012 INFORMS
with the following notation:
Œˆ e1D
t : Estimator of the mean demand forecast error
t days ahead.
‘ˆ te1D : Estimator of the standard deviation of the
demand forecast error t days ahead.
z : Safety factor to achieve a service level of  percent in demand forecast coverage.
The previous model was enhanced by assuming that
orders are placed at periods in which main vessels call
and that demand is not the only source of uncertainty.
Then, the safety stock in period t is given by
& q4t5
‘ !
u q4t5
X e1D
= max
4Œˆ l − Œˆ l 5+z t 4‘ˆ l + ‘ˆ l 5 10 1
with the following notation:

q4t5 = p4t5 + d + Œˆ N 4t5 + z‚ ‘ˆ N 4t5 .
Œˆ e1D
l : Estimator of the mean demand forecast error
for day l.
Œˆ e1R
l : Estimator of the mean return forecast error for
day l.
Œˆ e1D
l : Estimator of the standard deviation of the
demand forecast error for day l.
Œˆ e1R
l : Estimator of the standard deviation of the
return forecast error for day l.
z : Safety factor to achieve a service level of  percent in demand and return forecast coverage.
z‚ : Safety factor to achieve a service level of ‚ percent in the coverage from estimated times of arrivals.
d: Number of days required to unload containers.
p4t5: Day of arrival of next vessel, after day t.
N 4t5: Next vessel, after day t.
Œˆ N 4t5 : Estimator of the mean error of the time of
arrival of vessel N 4t5.
‘ˆ N 4t5 : Estimator of the standard deviation of the
time of arrival of vessel N 4t5.
In the previous expression, q4t5 represents the day
of the next call plus the time needed to cover for
uncertainty in this next call. In addition, note that we
assumed that the demand and return forecast errors
have normal distributions and are independent variables. We also assumed that delay times have normal
distributions. To achieve a specified service level, we
needed to calculate both  and ‚.
To include the uncertainty in empty container
capacity on vessels, we added a procedure in the
inventory model. Safety stocks are adjusted using a
factor calculated using the standard deviation of the
empty container capacity of each vessel that has calls
at each location considered.
This inventory model was used to provide daily
safety stocks, which were included as the minimum
empty container requirements at each location in the
network flow model. The basics of inventory management are in Silver and Peterson (1985). Neely (2008)
gives a detailed description of the model used.
Ben-Tal, A., A. Nemirovski. 2000. Robust solutions of linear programming problems contaminated with uncertain data. Math.
Programming 88(3) 411–424.
Bertsimas, D., M. Sim. 2004. The price of robustness. Oper. Res. 52(1)
Box, G., G. Jenkins. 1976. Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco.
Cheung, R., C. Chen. 1998. A two-stage stochastic network model
and solution methods for the dynamic empty container allocation problem. Transportation Sci. 32(2) 142–162.
Choong, S. T., M. H. Cole, E. Kutanoglu. 2002. Empty container management for intermodal transportation networks.
Transportation Res. E 38(6) 423–438.
Crainic, T., M. Gendreau, P. Dejax. 1993. Dynamic and stochastic
models for the allocation of empty containers. Oper. Res. 41(1)
Erera, A., J. C. Morales, M. Savelsbergh. 2005. Global intermodal tank container management for the chemical industry.
Transportation Res. E 41(6) 551–566.
Erera, A., J. C. Morales, M. Savelsbergh. 2006. Robust optimization
for empty repositioning problems. Oper. Res. 57(2) 468–483.
Jansen, B., P. Swinkles, G. Teeuwen, B. van Antwerpen de Fluiter,
H. Fleuren. 2004. Operational planning of a large-scale multimodal transportation system. Eur. J. Oper. Res. 156(1) 41–53.
Neely, A. 2008. Políticas de inventario de contenedores vacíos en la
industria naviera. Unpublished master’s dissertation, Department of Industrial Engineering, University of Chile, Santiago,
Chile. [English translation: Inventory policies for empty containers in the shipping industry.]
Silver, E. A., R. Peterson. 1985. Decision Systems for Inventory Management and Production Planning. John Wiley & Sons, New York.
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