Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call

International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

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Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call q Maxim A. Dulebenets Department of Civil & Environmental Engineering, Florida A&M University-Florida State University, 2525 Pottsdamer Street, Building A, Suite A124, Tallahassee, FL 32310-6046, USA

a r t i c l e

i n f o

Article history: Received 9 May 2017 Received in revised form 16 September 2017 Accepted 20 September 2017 Available online xxxx Keywords: Liner shipping Environmental sustainability Green vessel scheduling Carbon dioxide emissions Energy efficiency

a b s t r a c t Considering a substantial increase in volumes of the international seaborne trade and drastic climate changes due to carbon dioxide emissions, liner shipping companies have to improve planning of their vessel schedules and improve energy efficiency. This paper presents a novel mixed integer non-linear mathematical model for the green vessel scheduling problem, which directly accounts for the carbon dioxide emission costs in sea and at ports of call. The original non-linear model is linearized and then solved using CPLEX. A set of numerical experiments are conducted for a real-life liner shipping route to reveal managerial insights that can be of importance to liner shipping companies. Results indicate that the proposed mathematical model can serve as an efficient planning tool for liner shipping companies and may assist with evaluation of various carbon dioxide taxation schemes. Increasing carbon dioxide tax may substantially change the design of vessel schedules, incur additional route service costs, and improve the environmental sustainability. However, the effects from increasing carbon dioxide tax on the marine container terminal operations are found to be very limited. Ó 2017 Tongji University and Tongji University Press. Publishing Services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Introduction Maritime transportation is vital for the global trade with more than 10 billion tons of cargo transported by vessels (UNCTAD, 2015). However, the maritime transportation sector is responsible for a significant quantity of greenhouse gas (GHG) emissions, which are mainly represented by carbon dioxide (CO2) emissions (Lindstad et al., 2011, 2012). According to the third GHG study, conducted by the International Maritime Organization (IMO), the overall CO2 emissions from the international maritime shipping comprise approximately 2.2% of the global CO2 emissions (IMO, 2014). If no actions are taken, the total production of CO2 emissions can increase by 150–250% by 2050 due to increasing volumes of the international seaborne trade (Lindstad et al., 2012). The United States Environmental Protection Agency (EPA) underlines that CO2 is a primary GHG that causes the climate change (EPA, 2017). CO2 and other GHGs absorb the energy from sunlight and prevent loss of heat to space (Sun and Wang, 1996; Feroz et al., 2009; Sharma et al., 2012; Tseng and Hung, 2014; Stewart, 2015; Levin et al., 2017). The latter phenomenon is also known as ‘‘GHG effect”. The average global temperatures are expected to increase between 1.4 °C and 5.8 °C by 2100 due to the GHG effect (Live Science, 2017). A rapid increase in the average temperatures due to CO2 emissions may result in catastrophic consequences at the global level.

Peer review under responsibility of Tongji University and Tongji University Press. E-mail addresses: [email protected], [email protected] https://doi.org/10.1016/j.ijtst.2017.09.003 2046-0430/Ó 2017 Tongji University and Tongji University Press. Publishing Services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003

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M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

To alleviate negative externalities and reduce CO2 emissions produced by oceangoing vessels IMO enforced a number of regulations. In 2011, IMO developed a new chapter with amendments to MARPOL Annex VI, entitled as ‘‘Regulations on energy efficiency for ships” (IMO, 2017). According to those amendments, the vessels are obligated to attain a specific ‘‘Energy Efficiency Design Index”, which is computed based on the vessel technical characteristics (i.e., rated installed shaft power, deadweight tonnage, and vessel speed at the designed load) and fuel type. Furthermore, liner shipping companies are required to comply with ‘‘Ship Energy Efficiency Management Plan”. The latter aims to improve energy efficiency of vessels in a cost-effective manner (e.g., improve planning of the vessel voyage, proper cleaning of propellers, implementation of new technical measures, etc.). In order to ensure a proper planning of the vessel voyage and improve energy efficiency, liner shipping companies have to directly account for the cost of CO2 emissions, produced in sea and at ports of call (Schroten et al., 2011; Tran et al., 2016). Throughout scheduling of vessels, the liner shipping company is required to identify the arrival times at ports of call, vessel handling times at ports of call, departure times from ports of call, and vessel sailing speeds at voyage legs of the liner shipping route. This paper proposes a novel mixed integer non-linear model for the green vessel scheduling problem in a liner shipping route, which minimizes the total route service cost and accounts for the costs, associated with CO2 production in sea and at ports due to container handling. The original mathematical formulation is linearized, and then solved using CPLEX. A number of computational experiments are conducted for the Asia-North America AZX route, served by the Nippon Yusen Kaisha (NYK) liner shipping company, to demonstrate applicability of the proposed methodology and reveal some important managerial insights. Unlike the published to date studies on vessel scheduling, which either completely ignore emissions produced by vessels or do model emissions without accounting for the associated costs, this study presents a holistic approach for modeling the CO2 emissions, produced by oceangoing vessels in sea and at ports of call, and accounting for the associated costs. The developed mathematical model will serve as effective planning tool for liner shipping companies and facilitate construction of green vessel schedules. The remainder of the manuscript is structured in the following manner. The second section presents an overview of the relevant literature with the main focus on the vessel scheduling models and environmental aspects. The third section provides a detailed description of the problem studied herein, while the fourth section presents a mixed integer non-linear model for the problem. The fifth section discusses the adopted solution methodology, while the sixth section describes the numerical experiments, performed in this study. The last section summarizes findings and outlines potential future research extensions. Literature review Decisions that have to be made by liner shipping companies can be categorized into three groups (Meng et al., 2014): 1) strategic decisions (e.g., fleet size and mix, alliance strategy, network design); 2) tactical decisions (e.g., frequency determination, fleet deployment, speed optimization, schedule construction); and 3) operational decisions (e.g., cargo booking, cargo routing, vessel rescheduling, potential reject of cargo). The literature review presented herein primarily focuses on a tactical level vessel scheduling problem. A critical review of the relevant studies is provided next. Related work All of the collected studies on vessel scheduling were divided in two groups. The first group of studies focuses on various operational aspects in vessel scheduling without explicitly capturing the environmental issues and emissions produced by vessels, while the second group of studies accounts for both operational and environmental aspects in vessel scheduling (i.e., ‘‘green vessel scheduling”). Vessel scheduling in liner shipping Fagerholt (2001) studied a vessel scheduling problem in a liner shipping route, where port arrival time windows (TWs) could be violated. An additional cost was introduced to penalize violation of port arrival TWs. The objective minimized the total transportation and inconvenience costs. A set partitioning algorithm was developed to solve the problem. Numerical experiments demonstrated that the algorithmic performance was substantially affected with the problem size. Dulebenets (2015a) presented a Memetic Algorithm for the vessel scheduling problem, minimizing the total route service cost. The proposed solution algorithm was compared against the static secant approximation. Computational experiments showed that the developed Memetic Algorithm outperformed the static secant approximation in terms of solution quality and computational time. Wang et al. (2015) presented a methodology for assessing the perceived value of container transit time. The objective minimized the fuel consumption and container transit time costs. A number of computational examples demonstrated that the proposed approach could assist liner shipping companies with design of the optimal transit times and vessel sailing speeds between consecutive ports. Certain studies modeled uncertainty in liner shipping scheduling operations. Chuang et al. (2010) formulated the vessel routing and scheduling problem with uncertain market conditions, port handling times, and vessel sailing times, maximizing the total profit. The problem was solved using a Fuzzy Evolutionary Algorithm. Qi and Song (2012) focused on the vessel scheduling problem, modeling the port handling time uncertainty. The objective minimized the total expected fuel conPlease cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003

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sumption cost and penalties due to vessel delays. Numerical experiments indicated that degree of the port handling time uncertainty could substantially influence the fuel consumption. Wang and Meng (2012a) studied the vessel scheduling problem, capturing uncertainty in port handling and vessel sailing times and aiming to minimize the total transportation cost. The authors developed a cutting-plane based solution algorithm to solve the problem. Computational experiments underlined that uncertainty in port handling and vessel sailing times could affect the quantity of vessels required for service of the given liner shipping route. Wang and Meng (2012c) formulated the vessel scheduling problem with uncertain port waiting and container handling times, minimizing the total transportation cost. The Sample Average Approximation method was used to capture uncertainty. It was found that increasing quantity of vessels to be deployed at the given liner shipping route could improve reliability of the vessel schedule. A number of studies under the first group focused on evaluation of various collaborative agreements between liner shipping companies and marine container terminal operators. Wang et al. (2014) and Alhrabi et al. (2015) proposed a collaborative agreement, according to which the liner shipping company could negotiate arrival TWs with marine container terminal operators at each port of call. Both studies aimed to minimize the total transportation cost. Results from numerical experiments showed that availability of multiple TWs could affect the quantity of vessels to be deployed at the given liner shipping route, vessel sailing speed selection, and the total transportation cost. Dulebenets (2015b) presented a collaborative agreement, according to which the liner shipping company could negotiate the vessel handling rate with the marine container terminal operator at each port of call. The objective of a mixed integer non-linear model minimized the total route service cost. The original model was linearized and solved using CPLEX. It was found that the proposed agreement could yield up to 14.4% savings in terms of the total route service cost. Green vessel scheduling in liner shipping Only a very limited number of studies developed vessel scheduling models that captured environmental issues (Mansouri et al., 2015). Kontovas (2014) presented a generalized formulation for the green vessel routing and scheduling problem, minimizing the total transportation cost. A number of alternatives for modeling vessel emissions were discussed in the paper, including the following: (a) emission cost as the objective function; (b) emission cost as component of the objective function; (c) emissions produced as constraint set, and (d) emission cost as one of the objective functions. Dulebenets et al. (2015) developed a mathematical model for the green vessel schedule design problem, minimizing the total route service cost and imposing constraints on the quantity of emissions produced at voyage legs of the liner shipping route. CPLEX was used to solve the linearized version of the model. Computational experiments indicated that introduction of emission constraints could substantially increase the total route service cost. Fagerholt and Psaraftis (2015) and Fagerholt et al. (2015) studied the problem of sailing speed optimization and vessel routing within ‘‘Emission Control Areas” (ECAs), but did not explicitly model the vessel service at ports of call. Dulebenets (2016) compared the existing IMO regulation with an alternative environmental policy, where along with the requirements on the sulphur content in fuel liner shipping companies had to meet the emission restrictions within ECAs. Two mathematical models were presented for both polices, where the objective aimed to minimize the total route service cost. An iterative optimization algorithm was developed to solve the models. Computational experiments indicated that additional emission restrictions within ECAs reduced the amount of emissions produced, but caused an increase in the operational, fuel consumption, and inventory costs. Song et al. (2015) proposed a mathematical formulation for the stochastic multi-objective vessel scheduling problem with uncertain port times. The model minimized three objectives: (a) the annual vessel operational costs; (b) the average schedule unreliability; (c) the annual total CO2 emissions. A Genetic Algorithm was designed to solve the problem. Numerical experiments demonstrated that the least CO2 emissions could be achieved either with the least annual vessel operational costs or with the least average schedule unreliability. Dulebenets (2017) assessed the effects of introducing the transit time requirements on certain cargo types in green vessel scheduling, where emission restrictions were imposed within ECAs. The problem was formulated as a mixed integer non-linear mathematical programming model, aiming to minimize the total route service cost. The problem was solved using an iterative optimization algorithm. Numerical experiments demonstrated changes in vessel schedules from introducing both emission restrictions and transit time requirements. Literature summary The literature review findings are summarized in Table 1, including the following information for each one of the reviewed papers: (1) author(s); (2) year; (3) objective; (4) solution approach, and (5) environmental considerations (if any). We observe that the majority of the collected studies proposed models, minimizing the total cost (e.g., vessel weekly operational cost, port handling cost, container inventory cost, etc.). However, only Song et al. (2015) developed a multiobjective model, where one of the objectives aimed to minimize the total CO2 emissions, produced by oceangoing vessels. Contributions Based on review of the vessel scheduling literature, it can be concluded that the green vessel scheduling receives a growing attention. Researchers and practitioners are seeking for new mathematical models that may assist liner shipping companies with the design of green vessel schedules and novel environmental policies that may reduce emissions produced by vessels and alleviate pollution levels. The contributions of this study to the state of the art can be summarized as follows: Please cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003

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M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

Table 1 Vessel scheduling literature summary. a/ a

Author(s)

Year

Objective

Solution Approach

Environmental Considerations

1 2 3 4 5

Fagerholt Chuang et al. Qi & Song Wang & Meng Wang & Meng

2001 2010 2012 2012a 2012c

Minimize the total cost Maximize the total profit Minimize the total cost Minimize the total cost Minimize the total cost

N/A N/A N/A N/A N/A

6

Kontovas

2014

Minimize the total cost

Heuristic Heuristic Stochastic approximation A cutting-plane algorithm Sample average approximation N/A

7

Wang et al.

2014

Minimize the total cost

8

Alhrabi et al.

2015

Minimize the total cost

9 10 11 12

2015a 2015b 2015 2015

Minimize the total cost Minimize the total cost Minimize the total cost Maximize the total profit

13 14

Dulebenets Dulebenets Dulebenets et al. Fagerholt & Psaraftis Fagerholt et al. Song et al.

2015 2015

15

Wang et al.

2015

Minimize the total cost Minimize the annual vessel operating cost; Minimize the schedule unreliability; Minimize the total CO2 emissions Minimize the total cost

16

Dulebenets

2016

Minimize the total cost

17

Dulebenets

2017

Minimize the total cost

18

This paper

–

Minimize the total cost

Iterative optimization algorithm Iterative optimization algorithm Heuristic CPLEX CPLEX Analytical method

Discussion of emission modeling alternatives N/A N/A N/A N/A Constraints on CO2, SO2, and NOx Use of low sulphur fuel within ECAs

Xpress-MP Heuristic

Use of low sulphur fuel within ECAs CO2 minimization – one of the objectives

Iterative optimization algorithm Iterative optimization algorithm Iterative optimization algorithm CPLEX

N/A Use of low sulphur fuel within ECAs Use of low sulphur fuel within ECAs; Transit time requirements CO2 costs in sea and at ports are included in the objective function

Note: N/A – not applicable; ECA – ‘‘Emission Control Area”.

1) A novel mathematical model is presented for the green vessel scheduling problem, which extends the work, conducted by Song et al. (2015), and directly accounts not only for the cost of CO2 emissions produced by vessels throughout the voyage, but also for the cost of CO2 emissions produced during container handling at ports of call; 2) An exact solution approach is proposed for solving the developed mathematical model, unlike Song et al. (2015) who applied an Evolutionary Algorithm to solve the problem that did not guarantee optimality of vessel schedules; 3) A detailed analysis is conducted to determine how changes in the CO2 tax may affect the design of vessel schedules; 4) Important managerial insights are drawn using the developed mathematical model, which will be of interest to liner shipping companies.

Problem description This study models a liner shipping route, which includes P ¼ f1; . . . ; ng ports of call. The sequence of ports to be visited (a. k.a., port rotation) is assumed to be known. Generally, the liner shipping company decides on the port rotation at the strategic level (Meng et al., 2014). An example of the liner shipping route is presented in Fig. 1, where ports ‘‘1”, ‘‘2”, ‘‘4”, ‘‘5”, and ‘‘6” are visited once, while port ‘‘3” is visited twice. Multiple visits to the same port of call are modeled by introducing a dummy node in the port rotation graph for every additional visit to the same port. The port rotation graph for the considered liner shipping route is presented in Fig. 2, where dummy node ‘‘3⁄” is introduced after the node for port ‘‘6” to model the second visit to port ‘‘3”. Two consecutive ports p and p þ 1 are connected with voyage leg p. It is assumed that the liner shipping company has to provide service with a certain frequency at each port of call of the port rotation. Weekly or bi-weekly service frequencies are the most common in liner shipping scheduling (Meng et al., 2014; NYK, 2017). A weekly port service frequency will be adopted for the considered liner shipping route. The marine container terminal operator at each port of call establishes a specific arrival time window (TW) for a vessel. The arrival TW at each port is determined based on the following two attributes: (a) twsp ; p 2 P – start of TW at port p; and (b) twep ; p 2 P – end of TW at port p. Duration of a TW varies from port to port and can be up to three days (OOCL, 2017). Once a vessel arrives at the port, it is towed by push boats to the assigned berth, where quay cranes start (un)loading containers. It is assumed that an additional penalty (cLT p ; p 2 P), measured in USD/hour, Please cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003

M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

5

2 3

4

1 6

5

Fig. 1. A liner shipping route example.

1

2

3

4

5

6

3*

1

Fig. 2. The port rotation graph example.

will be imposed to the liner shipping company for arriving after the end of TW at port p. If a vessel arrives before the start of TW at port p, it will be waiting for service at a dedicated area, located close to the terminal. Service of vessels at ports of call The container demand CDp (measured in TEUs) at each port of the port rotation is assumed to be known (Meng et al., 2014). The liner shipping company is able to request one of the available handling rates at each port of call. Each handling rate has a corresponding handling productivity hpph ; p 2 P; h 2 H (measured in TEUs/hour). The marine container terminal operator will impose higher vessel handling cost cVH ph ; p 2 P; h 2 H (measured in USD) for a handling rate with a higher productivity. The vessel handling time HT ph ; p 2 P; h 2 H (measured in hours) is estimated based on the container demand at a CD

given port and handling productivity requested: HT ph ¼ hp p 8p 2 P; h 2 H. Multiple handling rates at ports will provide the ph

liner shipping company more flexibility in terms of selection of sailing and port handling times. For instance, if the liner shipping company chooses a handling rate with a higher productivity, the port handling time at a given port of call will be reduced, which will allow sailing at a lower speed to the next port of the port rotation. Fuel consumption This study assumes that a given liner shipping route is served with a string of vessels, which have the same/similar technical characteristics (i.e., the vessel fleet is ‘‘homogeneous”). Such practice is widely used in published to date vessel scheduling studies (Wang and Meng, 2012a–c; Wang et al., 2013, 2014; Dulebenets et al., 2015). The fuel consumption increases with the vessel sailing speed and can be estimated using the following equation (Du et al., 2011; Wang and Meng, 2012b):

DFCðv Þ ¼ DFCðv  Þ




v v

a

¼ cðv Þa

ð1Þ

where:  Þ – average daily vessel fuel consumption (tons of fuel per day); DFCðv – average daily vessel sailing speed (knots); DFCðv  Þ – average daily vessel fuel consumption when sailing at the designed speed (tons of fuel per day); v  – design vessel sailing speed (knots); a; c – coefficients of the fuel consumption function.

v

The fuel consumption FC p at voyage leg p can be computed per nautical mile using the following equation:

FC p ¼ DFCðv p Þ


 ST p 1 lp 1 cðv p Þa1 ¼ cðv p Þa ¼ 8p 2 P 24 lp 24v p lp 24

ð2Þ

where: v p – vessel sailing speed at voyage leg p, which connects ports p and p þ 1 (knots); lp – length of voyage leg p (nmi); ST p – sailing time between consecutive ports p and p þ 1 (hours).

Please cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003

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The fuel consumption coefficients a; c are generally calculated based on the regression analysis using the data collected from vessels. Due to lack of the data, this study selects the fuel consumption coefficients based on the available liner shipping literature (Psaraftis and Kontovas, 2013; Wang and Meng, 2012b): a ¼ 3 and c = 0.012. Once a sailing speed is chosen at a given voyage leg of the liner shipping route, it is assumed to remain constant. Uncertainty in the sailing time between consecutive ports of call due to inclement weather, height of waves, speed of wind, and other factors is not modeled in this study. Since the fuel consumption by auxiliary engines typically does not change significantly throughout the voyage, the cost associated with fuel consumption by auxiliary engines will be included in the weekly vessel operational cost. Container inventory cost Throughout the design of vessel schedules the liner shipping company must account for the container inventory cost, which is primarily dependent on the total container transit time at voyage legs of the liner shipping route and can be computed based on the following relationship (Wang et al., 2014):

IC ¼ cIC

X ST p NC p

ð3Þ

p2P

where: IC – total container inventory cost (USD); cIC – unit container inventory cost (USD per TEU per hour); NC p – number of containers transported at voyage leg p (TEUs). Service frequency at ports of call Denote q as the number of vessels, which is required for service of ports, belonging to the given liner shipping route. Let WT p be the waiting time of a vessel at port p. Let xph be the vessel handling rate decision variable at port p (=1 if handling rate h is selected at port p; =0 otherwise). The following relationship is used by the liner shipping company to determine the required number of vessels to be deployed at the given liner shipping route in order to provide the weekly port service frequency (Wang et al., 2014; Alhrabi et al., 2015):

168q P

X XX X ST p þ ðHT ph xph Þ þ WT p p2P

p2P h2H

ð4Þ

p2P

The left-hand side of inequality (4) represents a product of the number of vessels, required for service of the given liner shipping route, and a numerical value ‘‘168”, which corresponds to the total amount of hours in a one week (as the liner shipping company is required to provide a weekly service at ports). The right-hand side of inequality (4) is the total vessel turnaround time, which essentially represents the total time that will be spent by a given vessel to visit all ports of call, belonging to the given liner shipping route, and return to the first port of call. The total vessel turnaround time consists of the following three components: (i) the total vessel sailing time; (ii) the total vessel handling time at ports of call; and (iii) the total vessel waiting time at ports of call. Based on inequality (4), in case of increasing total vessel turnaround time (e.g., as a result of slow steaming and increase in the total vessel sailing time) the liner shipping company will have to allocate more vessels for service of the given liner shipping route in order guarantee the weekly port service frequency. Vessel waiting time estimation at ports of call In some instances a given vessel may arrive at a given port of call before the start of the arrival TW, negotiated with the marine container terminal operator. For example, if the vessel leaves port p at time t dp (where notation t dp will be further used for the vessel departure time from port p, hours) and arrives at port p þ 1 at time t apþ1 ¼ t dp þ ST p < twspþ1 (where notation t ap will be further used for the vessel arrival time at port p, hours), it will be required to wait before the service begins at port p þ 1. The port waiting time can be estimated using the following relationships:

WT pþ1 P twspþ1  tap 

X ðHT ph xph Þ  ST p 8p 2 P; p < jPj

ð5Þ

h2H

WT 1 P tws1  t ap 

X ðHT ph xph Þ  ST p þ 168q8p 2 P; p ¼ jPj

ð6Þ

h2H

Note that for a vessel, returning from the last port to the first port, the waiting time equation includes the total turnaround time component – 168q (along with the start of TW at the first port, arrival time at the last port, handling time at the last port, and sailing time between the last and the first ports) to account for a round trip journey. Fig. 3 provides an illustrative example of how vessel schedules are generated in this study. The port rotation includes 4 ports of call. Based on the established schedule, the vessel arrives at port ‘‘1” at ta1 ¼ 0 h and is being served under handling rate ‘‘1” (based on the agreement with the marine container terminal operator at port ‘‘1”) for Please cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003

M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

HT11=48 hrs. ta1=0 hrs. WT1=0 hrs. 1

ST4=148 hrs. l4=2,590 nmi

ST1=110 hrs. l1=2,475 nmi

2 HT21=24 hrs. ta2=158 hrs. WT2=10 hrs.

7

HT41=20 hrs. ta4=504 hrs. WT4=0 hrs. 4

ST3=126 hrs. l3=2,457 nmi

ST2=144 hrs. l2=2,592 nmi

3 HT31=42 hrs. ta3=336 hrs. WT3=0 hrs.

Fig. 3. A vessel schedule example.

HT 11 ¼ 48 h. The vessel leaves port ‘‘1” at time t d1 ¼ 0 þ 48 ¼ 48 h and sails to port ‘‘2” at sailing speed

v 1 ¼ 22:5 knots for

¼ 110 h. The vessel arrives at port ‘‘2” at ta2 ¼ 48 þ 110 ¼ 158 h and has to wait for WT 2 ¼ 10 h before the service ST 1 ¼ 2;475 22:5 begins, as the start of TW at port ‘‘2” is tws2 ¼ 168 h. The vessel is being served at port ‘‘2” for HT 21 ¼ 24 h and leaves port ‘‘2” ¼ 144 h at td2 ¼ 158 þ 10 þ 24 ¼ 192 h. After that, the vessel sails to port ‘‘3” at sailing speed v 2 ¼ 18:0 knots for ST 2 ¼ 2;592 18:0 and arrives at port ‘‘3” at t a3 ¼ 192 þ 144 ¼ 336 h. The vessel is being served at port ‘‘3” for HT 31 ¼ 42 h and leaves port ‘‘3” at

¼ 126 h and arrives at t d3 ¼ 336 þ 42 ¼ 378 h. Then, the vessel sails to port ‘‘4” at sailing speed v 3 ¼ 19:5 knots for ST 3 ¼ 2;457 19:5 port ‘‘4” at t a4 ¼ 378 þ 126 ¼ 504 h. The vessel is being served at port ‘‘4” for HT 41 ¼ 20 h and leaves port ‘‘4” at

¼ 148 h and t d4 ¼ 504 þ 20 ¼ 524 h. After that, the vessel sails to port ‘‘1” at sailing speed v 4 ¼ 17:5 knots for ST 4 ¼ 2;590 17:5 arrives at port ‘‘1” at t a1 ¼ 524 þ 148 ¼ 672 h. The total vessel turnaround time (VTT) for the example route will be VTT ¼ 48 þ 110 þ 10 þ 24 þ 144 þ 42 þ 126 þ 20 þ 148 ¼ 672 h. The liner shipping company will be required to deploy VTT ¼ 672 ¼ 4 vessels. Moreover, the returning time at port ‘‘1” should be adjusted from ta1 ¼ 672 h to ta1 ¼ 0 h as follows: q ¼ 168 168 t a1 ¼ t d4 þ ST 4  168q ¼ 524 þ 148  168  4 ¼ 0 h. The latter adjustment is required, as variable ta1 can be assigned only one value in the mathematical model (i.e., t a1 ¼ 0 hours not t a1 ¼ 672 h). Therefore, term ‘‘168q” is introduced in inequality (6) to account for a round trip journey. CO2 emissions and associated costs This study models CO2 production in sea and at ports of call. The quantity of CO2 emissions (in tons) at voyage leg p can be calculated based on the total fuel consumption at that voyage leg and the CO2 emission factor in sea EF SEA (Psaraftis and Kontovas, 2013; Kontovas, 2014, 2014): SEA COSEA FC p lp 8p 2 P 2p ¼ EF

ð7Þ

The quantity of CO2 emissions produced from container handling at port p is proportional to the container demand at that port and the CO2 emission factor at ports EF PORT ph ; p 2 P; h 2 H (Tran et al., 2016). The type of equipment used at ports for container handling may vary, which will cause differences in the quantity of emissions produced per TEU for the same handling productivity requested (captured by index p in the EF PORT parameter). Furthermore, since marine container terminal operaph tors provide multiple handling rate options to the liner shipping company at ports of call, the CO2 emission factor will vary parameter). For example, if a handling rate with a higher productivity is requested, the (captured by index h in the EF PORT ph marine container terminal operator will have to allocate more resources for service of a given vessel (e.g., deploy more quay cranes for loading and unloading containers, assign more internal transport vehicles for transfer of containers between the seaside and the marshaling yard, allocate more gantry cranes for handling containers in the marshaling yard, etc.), which will increase the quantity of CO2 emissions produced. The quantity of CO2 emissions (in tons) produced from container handling at port can be estimated using the following equation.

COPORT ¼ CDp 2p

X

ðEF PORT ph xph Þ8p 2 P

ð8Þ

h2H

Unlike published to date papers on vessel scheduling in liner shipping, this study takes into account costs associated with CO2 production in sea and at ports of call that can be calculated using the following equation: Please cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003

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M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

CDC ¼ cCO2

X SEA X PORT CO2p þ CO2p p2P

! ð9Þ

p2P

where: CDC – total CO2 emission cost (USD); cCO2 – unit CO2 emission cost (USD per ton of CO2). The CO2 emission factor in sea is assumed to be EF SEA ¼ 3:082 tons of CO2 per ton of fuel (Psaraftis and Kontovas, 2013, ¼ 0:01729 tons of CO2 per TEU han2014; IMO, 2014; Kontovas, 2014), while the CO2 emission factor at ports is set to EF PORT ph dled for the base handling productivity of 180 TEUs/hour (Tran et al., 2016). The value of CO2 emission factor is assumed to increase proportionally with the handling rate requested. Based on the available literature (Schroten et al., 2011; Tran et al., 2016) the unit CO2 emission cost (i.e., CO2 tax) is adopted to be cCO2 ¼ 32 USD per ton of CO2. Vessel sailing speed selection A number of factors have to be considered by liner shipping companies in order to select the appropriate sailing speed at a given voyage leg. The lower bound on vessel sailing speed v min is typically set to decrease wear of the vessel’s engine (Wang et al., 2013). The upper bound on vessel sailing speed v max is determined by capacity of the vessel’s engine (Psaraftis and Kontovas, 2013). Lower vessel sailing speeds will allow the liner shipping company reducing the fuel consumption at voyage legs of the given liner shipping route, associated fuel consumption costs, and CO2 emissions produced in sea. However, decrease in the vessel sailing speed will also increase the total transit time of containers and increase the associated container inventory costs. The latter will increase the total turnaround time of vessels and in turn will require deployment of more vessels at the given liner shipping route to guarantee the agreed service frequency at ports of call. In the meantime, the liner shipping company should consider the limit on the number of vessels (q 6 qmax ), allocated for service of the given liner shipping route. Mathematical model This section presents notations that will be used throughout the manuscript and a mixed integer non-linear mathematical model for the green vessel scheduling problem with CO2 emission minimization – GVSPCD. Nomenclature Sets P ¼ f1; . . . ; ng H ¼ f1; . . . ; mg Decision variables v p; p 2 P xph ; p 2 P; h 2 H

vessel sailing speed at voyage leg p (knots) =1 if handling rate h is selected at port p (=0 otherwise)

Auxiliary variables q tap ; p 2 P tdp ; p 2 P ST p ; p 2 P FC p ; p 2 P WT p ; p 2 P LT p ; p 2 P

number of vessels deployed at the given route (vessels) arrival time at port p (hours) departure time from port p (hours) vessel sailing time at voyage leg p (hours) fuel consumption at voyage leg p when sailing at speed waiting time of a vessel at port p (hours) vessel late arrival at port p (hours)

COSEA 2p ; p 2 P

quantity of CO2 emissions produced by a vessel at voyage leg p (tons)

COPORT ;p 2p

quantity of CO2 emissions produced due to container handling at port p (tons)

2P

Parameters n m a,c cF cOC cVH ph ; p 2 P; h 2 H

set of ports to be visited set of available handling rates

vp

(tons of fuel per nmi)

number of ports to be visited (ports) number of available handling rates (handling rates) fuel consumption function coefficients unit fuel cost (USD/ton) vessel weekly operational cost (USD/week) handling cost at port p under handling rate h (USD)

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M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

cLT p ;p 2 P

delayed arrival penalty at port p (USD/hour)

IC

c cCO2 lp ; p 2 P CDp ; p 2 P NC p ; p 2 P HT ph ; p 2 P; h 2 H

qmax twsp ; p 2 P

unit container inventory cost (USD per TEU per hour) unit CO2 emission cost, i.e. CO2 tax (USD per ton of CO2) length of voyage leg p (nmi) container demand at port p (TEUs) number of containers transported at voyage leg p (TEUs) vessel handling time at port p under handling rate h (hours) minimum vessel sailing speed (knots) maximum vessel sailing speed (knots) maximum number of vessels allocated to serve a given route (vessels) the start of TW at port p (hours)

twep ; p 2 P

the end of TW at port p (hours)

EF SEA EF PORT ph ; p 2 P; h 2 H

CO2 emission factor in sea (tons of CO2 per ton of fuel) CO2 emission factor at port p under handling rate h (tons of CO2 per TEU)

v min v max

GVSPCD:

9

"

min cOC q þ cF

# XX X X SEA X PORT X X LT IC CO2 lp FC p þ cVH x þ c LT þ c ST NC þ c ð CO þ CO Þ p p p ph ph p 2p 2p p2P

p2P h2H

p2P

p2P

p2P

ð10Þ

p2P

Subject to:

X xph ¼ 18p 2 P

ð11Þ

h2H

ST p ¼

FC p ¼

lp

8p 2 P

vp

cðv p Þa1 24

ð12Þ

8p 2 P

WT pþ1 P twspþ1  t ap 

ð13Þ X ðHT ph xph Þ  ST p 8p 2 P; p < jPj

ð14Þ

h2H

WT 1 P tws1  t ap 

X ðHT ph xph Þ  ST p þ 168q8p 2 P; p ¼ jPj

ð15Þ

h2H

tdp ¼ t ap þ

X ðHT ph xph Þ þ WT p 8p 2 P

ð16Þ

h2H

LT p P tap  twep 8p 2 P

ð17Þ

tapþ1 ¼ t dp þ ST p 8p 2 P; p < jPj

ð18Þ

ta1 ¼ t dp þ ST p  168q8p 2 P; p ¼ jPj

ð19Þ

168q P

XX X X ST p þ ðHT ph xph Þ þ WT p p2P

p2P h2H

SEA FC p lp 8p 2 P COSEA 2p ¼ EF

¼ CDp COPORT 2p

X

ðEF PORT ph xph Þ8p 2 P

ð20Þ

p2P

ð21Þ ð22Þ

h2H

q 6 qmax

ð23Þ

v min 6 v p 6 v max 8p 2 P

ð24Þ

xph 2 f0; 1g8p 2 P; h 2 H

ð25Þ

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M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

q; qmax ; n; m; CDp ; NC p 2 N8p 2 P

ð26Þ

PORT LT IC CO v p ; tap ; tdp ; ST p ; FC p ; WT p ; LT p ; COSEA ; a; c; cF ; cOC ; cVH ph ; c p ; c ; c 2 ; CO2

2

p

p

; lp ; HT ph ; v min ; v max ; twsp ; twep ; EF SEA ; EF PORT ph

2 Rþ 8p 2 P; h 2 H

ð27Þ

In the GVSPCD mathematical model the objective of the liner shipping company is to minimize the total route service cost (10), which includes 6 components: (i) total vessel weekly operational cost; (ii) total fuel consumption cost; (iii) total port handling cost; (iv) total late arrival penalty; (v) total container inventory cost; and (vi) total CO2 emission cost. Constraint set (11) ensures that the liner shipping company negotiates only one handling rate with the marine container terminal operator at each port of call. Constraint set (12) estimates the vessel sailing time at each voyage leg. Constraint set (13) calculates the fuel consumption by vessels at each voyage leg. Constraint sets (14) and (15) compute the vessel waiting time at each port of call. Constraint set (16) estimates the vessel departure time from each port of call. Constraint set (17) calculates the vessel late arrival hours at each port of call. Constraint sets (18) and (19) compute the vessel arrival time at the consecutive port of call. Constraint set (20) guarantees the weekly service frequency at each port of call. Constraint set (21) estimates the quantity of CO2 emissions produced at each voyage leg. Constraint set (22) calculates the quantity of CO2 emissions produced due to container handling at each port of call. Constraint set (23) guarantees that the number of deployed vessels will not exceed the number of vessels allocated for service of the given liner shipping route. Constraint set (24) ensures that the vessel sailing speed will be within the established bounds at each voyage leg. Constraint sets (25)–(27) define ranges of parameters and variables of the GVSPCD mathematical model. Solution approach GVSPCD is a non-linear mathematical model due to: 1) objective function (fuel consumption cost component); and 2) constraint sets (12) and (13). Replacing of vessel sailing speed v p with its reciprocal yp ¼ v1p will linearize constraint set (12). Denote RFðyp Þ as the fuel consumption function, estimated based on vessel sailing speed reciprocal yp . The nonlinear fuel consumption function RFðyp Þ can be linearized using its piecewise linear approximation RF w ðyp Þ, where w is the number of linear segments (Wang et al., 2013). Examples of the fuel consumption function linear approximations are presented in Appendix A. Let S ¼ f1; . . . ; wg be the set of linear segments in the piecewise function RF w ðyp Þ. Let bps ¼ 1 if linear segment s is chosen to approximate the fuel consumption function at voyage leg p (=0 otherwise). Denote st s ; eds ; s 2 S as the speed reciprocal values at the start and the end of linear segment s; SLs ; IN s ; s 2 S as the slope and the intercept of linear segment s used to approximate the fuel consumption function; and M 1 ; M 2 as sufficiently large positive numbers. Then GVSPCD can be reformulated as a linear problem (GVSPCDL) as follows. GVSPCDL

"

XX X XX X X SEA X PORT IC min c q þ c RF ps lp þ cVH cLT ST p NC p þ cCO2 CO2p þ CO2p ph xph þ p LT p þ c OC

F

p2P s2S

p2P h2H

p2P

p2P

p2P

!#

ð28Þ

p2P

Subject to: Constraint sets (11), (14)-(20), (22), (23), (25)-(27

ST p ¼ lp yp 8p 2 P

ð29Þ

X bps ¼ 18p 2 P

ð30Þ

s2S

sts bps 6 yp 8p 2 P; s 2 S

ð31Þ

eds þ M 1 ð1  bps Þ P yp 8p 2 P; s 2 S

ð32Þ

RF ps P SLs yp þ IN s  M 2 ð1  bps Þ8p 2 P; s 2 S

ð33Þ

SEA lp COSEA 2p ¼ EF

X

RF ps 8p 2 P

ð34Þ

s2S

1=v max 6 yp 6 1=v min 8p 2 P

ð35Þ

In the GVSPCDL mathematical model the objective function (28) minimizes the total route service cost. Constraint set (29) calculates the vessel sailing time at each voyage leg. Constraint set (30) guarantees that only one linear segment will be selected for approximating the fuel consumption function at each voyage leg. Constraint sets (31) and (32) define the range Please cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003

M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

11

of vessel sailing speed reciprocal values, when a given linear segment is selected for approximating the fuel consumption function at each voyage leg. Constraint set (33) computes the approximated fuel consumption at each voyage leg. Constraint set (34) estimates the quantity of CO2 emissions produced each voyage leg. Constraint set (35) ensures that the vessel sailing speed reciprocal will be within the established bounds at each voyage leg. Strict lower bounds for M 1 and M 2 can be defined 1 1 , M 2 ¼ SLs v max þ IN s . Note that M 1 and M 2 can be substituted in constraint sets (32) and (33) by M = max as follows: M 1 ¼ v min {M1; M2}. GVSPCDL can be solved efficiently using CPLEX even for large size instances. However, the increasing number of segments in the fuel consumption piecewise approximating function may increase the computational time. A tradeoff between the solution accuracy and the computational time will be analyzed in the numerical experiments section. Numerical experiments This section presents numerical experiments that were performed to showcase applicability of the proposed mathematical model for a real-life liner shipping route and reveal managerial insights that can be of importance to liner shipping companies. Input data description The study focuses on vessel scheduling at the Asia-North America AZX route (see Fig. 4), served by the Nippon Yusen Kaisha (NYK) liner shipping company (NYK, 2017). This liner shipping route connects Asia, Red Sea, Africa, Europe, and United States East Coast. The port rotation for the Asia-North America AZX route includes 14 ports of call that have to be visited by vessels on a weekly basis (the distances between consecutive ports, measured in nautical miles, are presented in parenthesis and were retrieved from the world seaports catalogue1): 1. Port of Laem Chabang, Thailand (850) ? 2. Port of Singapore, Singapore (1,695) ? 3. Port of Colombo, Sri Lanka (3,871) ? 4. Port of Damietta, Egypt (1,459) ? 5. Port of Cagliari, Italy (3,968) ? 6. Port of Halifax, Canada (636) ? 7. Port of New York, United States (871) ? 8. Port of Savannah, United States (570) ? 9. Port of Norfolk, United States (1,422) ? 10. Port of Halifax, Canada (3,968) ? 11. Port of Cagliari, Italy (1,459) ? 12. Port of Damietta, Egypt (3,227) ? 13. Port of Jebel Ali, United Arab Emirates (3,971) ? 14. Port of Singapore, Singapore (850) ? 1. Port of Laem Chabang, Thailand. The numerical data, required for computational experiments, were generated using the available liner shipping literature (Wang and Meng, 2012a–c; Wang et al., 2013; Zampelli et al., 2014; OOCL, 2017; World Bank, 2017; World Shipping Council, 2017, etc.) and are presented in Table 2. The end of TW at each port of the port rotation was computed based on the end of TW at preceding port, bounds of the vessel sailing speed, and length of a voyage leg between consecutive ports using the l

following relationship: twepþ1 ¼ twep þ U½v minp;v max  8p 2 P, where U – is a notation that was adopted to represent the uniformly distributed pseudorandom numbers. The quantity of containers to be transported at voyage leg p was generated as follows: NC p ¼ U½5; 000; 8; 0008p 2 P TEUs. The weekly container demand at large ports of the port rotation was set as follows: CDp ¼ U½500; 2; 0008p 2 P TEUs. This study defined a given port of call as a ‘‘large port” if it was included in the list of the top 20 world container ports based on the total throughput (World Shipping Council, 2017). The weekly container demand at the other ports was assigned as follows: CDp ¼ U½200; 1; 0008p 2 P TEUs. It was assumed that the liner shipping company was able to request four handling rates at each port of call. Marine container terminal operators offered the following handling productivities (dph ) at large ports: [125; 100; 75; 50] TEUs/hour. Marine container terminal operators were able to provide either [100; 75; 60; 50] TEUs/hour or [75; 70; 60; 50] TEUs/hour at smaller ports for the four handling rates respectively. The latter assumption can be supported by the fact that marine container terminal operators at smaller ports generally have less handling equipment available for service of the arriving vessels, therefore, they are able to offer handling rates with lower handling productivities than marine container terminal operators at large ports. The vessel handling cost per TEU cTEU at port p under handling rate h was calculated as follows: ph cTEU ph ¼ mhc  U½0; 508p 2 P; h 2 H USD/TEU, where mhc – is the mean handling cost. The total port handling cost was estiTEU mated as follows: cVH ph ¼ c ph  CDp 8p 2 P; h 2 H USD. The mean handling cost (mhc) was assumed to be equal to [700; 625;

550; 475] USD/TEU for the four available handling rates respectively (World Bank, 2017; The Port Authority of New York and New Jersey, 2017). Marine container terminal operators were assumed to perceive the handling cost differently (i.e., different vessel handling costs would be applied for exactly the same handling rate at different ports of call), which is captured by the random term in the equation. ðd 180Þ

The CO2 emission factor at ports was generated as follows: EF PORT ¼ 0:01729 þ U½1:0; 1:2  ph180  0:017298p 2 P; h 2 H ph (Tran et al., 2016). As mentioned in the problem description section of the paper, the type of equipment used at ports for container handling may vary, which will cause differences in the quantity of emissions produced per TEU for the same handling productivity requested. The latter aspect is captured by the second (and random) of the EF PORT equation. All computaph tional experiments on were conducted on a Dell T1500 Intel(T) Core i5 Processor with 2.00 GB of RAM. The piecewise linear 1

http://ports.com/sea-route/.

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M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

Fig. 4. The Asia-North America AZX route.

Table 2 Numerical data. Parameter

Value

Source (s)

Fuel consumption coefficients: a, c

a = 3, c = 0.012

Unit fuel cost: cF (USD/ton) Weekly vessel operational cost: cOC (USD/week) Delayed arrival penalty: cLT p (USD/hour) Unit inventory cost: cIC (USD per TEU per hour) CO2 tax: cCO2 (USD per ton of CO2) Duration of TW: [twep  twsp ] (hours) Minimum vessel sailing speed: vmin (knots) Maximum vessel sailing speed: vmax (knots) Maximum quantity of deployed vessels: qmax CO2 emission factor in sea: EFSEA (tons of CO2 per ton of fuel) CO2 emission factor at ports: EF PORT (tons of CO2 per TEU ph handled)

500 300,000 U[5,000; 10,000] 1 32 U½24; 72 15 25 15 3.082 0.01729 for h ¼ 180

Du et al. (2011), Wang and Meng (2012b), Psaraftis and Kontovas (2013) Fagerholt and Psaraftis (2015) Wang and Meng, 2012a–c; Dulebenets (2015a,b); Zampelli et al. (2014) Wang et al. (2014), Dulebenets et al. (2015) Tran et al. (2016) OOCL (2017) Wang and Meng, 2012a–c; Wang and Meng, 2012a–c Wang and Meng, 2012a–c Psaraftis and Kontovas (2013), Kontovas (2014) Tran et al. (2016)

approximations for the fuel consumption function were developed using MATLAB 2016a (Mathworks, 2016). The GVSPCDL mathematical model was coded in General Algebraic Modeling System (GAMS, 2017) and solved using CPLEX. Piecewise approximating function selection As discussed in the solution approach section of the paper, increasing number of liner segments in the piecewise function will improve accuracy of the fuel consumption approximating function, but in the meantime will negatively affect the computational time. A set of numerical experiments were performed for analysis of the latter tradeoff. A total of 14 candidate approximations were considered with number of segments, varying from 2 to 100. The GVSPCDL mathematical model was solved using each one of those approximations. Results from the computational experiments are presented in Table 3, including the following information: (1) approximation ID; (2) number of segments used; (3) objective function value – Z; 

(4) value of the non-linear objective function at the solution provided by GVSPCDL – Z⁄; (5) objective gap D ¼ j ðZ ZZÞ j and (6)  CPU time (average over 10 replications). We observe that the GVSPCDL computational time starts significantly increasing when more than 20 segments are used in the piecewise approximating function without substantial changes in the objective gap. Hence, a piecewise function with 20 linear segments will be further used in this study for approximation of the fuel consumption function. Managerial insights A total of 20 problem instances were generated based on the data, described in the beginning of the numerical experiCO2 2 2  U½1:01; 2:00, where cCO – is ments section and shown in Table 2, by increasing the CO2 tax value as follows: cCO iþ1 ¼ c i i the CO2 tax value for problem instance i. The generated CO2 tax values are presented in Table 4. Note that the unit CO2 tax values were assigned randomly (using the uniform distribution) primarily due to lack of data, i.e. the accurate future pro-

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M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx Table 3 Piecewise approximation selection. Approximation ID

Segments, w

Z, 106 USD

Z  , 106 USD

Gap, %

CPU time, sec

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14

2 3 4 5 6 7 8 9 10 20 40 60 80 100

19.381 19.540 19.418 19.414 19.414 19.417 19.416 19.415 19.427 19.494 19.464 19.520 19.530 19.445

19.490 19.602 19.450 19.441 19.434 19.430 19.426 19.423 19.433 19.497 19.465 19.521 19.530 19.445

0.56 0.32 0.17 0.14 0.10 0.07 0.05 0.04 0.03 0.01 0.00 0.00 0.00 0.00

0.4 0.3 0.3 0.4 0.6 0.6 0.6 0.7 1.0 1.5 3.5 7.7 14.8 52.6

Table 4 Generated CO2 tax values. Instance

cCO2 , USD/ton

Instance

cCO2 , USD/ton

Instance

cCO2 , USD/ton

Instance

cCO2 , USD/ton

1 2 3 4 5

32.0 37.5 43.1 48.4 59.9

6 7 8 9 10

69.6 82.5 139.6 163.9 183.5

11 12 13 14 15

216.5 320.8 342.9 433.5 538.8

16 17 18 19 20

634.7 752.1 893.3 902.5 1060.4

jections for CO2 tax values were not available. Technically, a comprehensive socio-economic analysis should be conducted for each segment of a given liner shipping route to accurately determine the unit CO2 emission cost and its future projections based on the economic assessment of negative externalities the given pollutant may cause on living organisms and environment. The latter analysis will be one of the future research directions for this study. GVSPCDL was solved for each one of the considered instances. Discussion of managerial insights from increasing the CO2 tax value is presented next, including: (1) vessel sailing speed and sailing time selection; (2) handling rate selection at ports of call; (3) vessel late arrivals; (4) CO2 emission production; and (5) total route service cost and its components. Vessel sailing speed and sailing time selection The average vessel sailing speed and the total vessel sailing time were retrieved for each one of the considered problem instances using the GVSPCDL mathematical model, and results are presented in Fig. 5. We observe that increasing CO2 tax reduces the average vessel sailing speed at voyage legs of the given liner shipping route and in turn increases the total vessel sailing time. Lower vessel sailing speeds allow the liner shipping company reducing the fuel consumption, the quantity of CO2 emissions produced in sea, and the associated CO2 cost. A substantial decrease (7.5%) in the vessel sailing speed is observed for instance 12, where the CO2 tax increased from 216.5 USD/ton to 320.8 USD/ton. Handling rate selection at ports of call To assess the effect from increasing CO2 tax value on the marine container terminal operations the average vessel handling rates over all ports of call were estimated for each once of the generated problem instances, and results are presented. It can be noticed that increasing CO2 tax value does not affect the handling rates, selected by the liner shipping company at ports of call. The lowest handling rate was chosen at each port for each problem instance. The latter can be explained by the fact that the quantity of CO2 emissions produced at ports is significantly smaller as compared to the quantity of CO2 emissions produced in sea (more details are presented in later in the CO2 emission production section). Hence, increasing value of the CO2 tax will have limited effects on the port operations. Selection of handling rates with higher handling productivities at ports of call can be expected, only if marine container terminal operators would reduce the associated handling charges. Vessel late arrivals The vessel late arrivals may substantially affect the liner shipping and marine container terminal operations. The total hours of vessel late arrivals at ports of call were computed for each one of the considered problem instances, and results are illustrated in Fig. 6. We observe that increasing CO2 tax may substantially increase the hours of vessel late arrivals at ports of call. The latter can be explained by increasing vessel sailing time at voyage legs of the liner shipping route. Increase in the sailing time between consecutive ports of call will reduce the quantity of CO2 emissions produced in sea and associated CO2 emission costs, but in the meantime may cause violation of port arrival TWs, negotiated with marine container terminal operators. Please cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003

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M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

Fig. 5. The average vessel sailing speed and total sailing time values.

CO2 emission production The total quantities of CO2 emissions produced in sea (CO2 – Sea) and at ports of call (CO2 – Ports) were calculated for each one of the generated problem instances, and results are shown in Fig. 7. It can be noticed that increasing CO2 tax reduces the quantity of CO2 produced in sea, but does not affect the quantity of CO2 produced at ports of call. Such finding can be justified by the fact that the quantity of CO2 emissions produced at ports (which comprises on average 108 tons over the considered problem instances) is significantly smaller as compared to the quantity of CO2 emissions produced in sea (which comprises on average 21,887 tons over all the considered problem instances). Furthermore, the GVSPCDL mathematical model demonstrates a significant decrease (14.3%) in the quantity of CO2 produced in sea for instance 12, where the CO2 tax increased from 216.5 USD/ton to 320.8 USD/ton. Results from computational experiments also suggest that the CO2 taxation can be an efficient mean of reducing CO2 emissions and, hence, improving the environmental sustainability. The quantity of CO2 emissions produced in sea decreased by 64.3% by increasing the CO2 tax from 32.0 USD to 1060.4 USD. Total route service cost and its components The objective function value and its components were estimated for all the considered problem instances and are presented in Table 5 and Fig. 8, including the following cost components: 1) the total route service cost – Z; 2) the total weekly vessel operational cost – TOC; 3) the total fuel consumption cost – TFC; 4) the total port handling cost – TPC; 5) the total late

Fig. 6. Total vessel late arrival hours.

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M.A. Dulebenets / International Journal of Transportation Science and Technology xxx (2017) xxx–xxx

Fig. 7. Total CO2 production in sea and at ports.

Table 5 Objective function component values vs. CO2 tax. Instance

cCO2 , SD/ton

Z, 106 USD

TOC, 106 USD

TFC, 106 USD

TPC, 106 USD

TLP, 106 USD

TIC, 106 USD

TCCS, 106 USD

TCCP, 106 USD

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

32.0 37.5 43.1 48.4 59.9 69.6 82.5 139.6 163.9 183.5 216.5 320.8 342.9 433.5 538.8 634.7 752.1 893.3 902.5 1060.4

19.49 19.62 19.76 19.87 20.15 20.39 20.71 22.01 22.65 23.05 23.92 26.32 26.78 28.29 30.50 32.34 34.64 36.91 37.02 39.23

2.40 2.40 2.40 2.40 2.40 2.40 2.40 2.40 2.40 2.40 2.40 2.70 2.70 2.70 2.70 2.70 3.00 3.00 3.00 3.00

4.21 4.14 4.13 4.05 4.03 4.02 4.01 3.84 3.86 3.83 3.86 3.38 3.37 3.13 3.09 3.08 2.87 2.78 2.77 2.57

4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85 4.85

0.00 0.00 0.00 0.02 0.03 0.03 0.04 0.02 0.05 0.04 0.05 0.42 0.44 0.63 0.95 0.98 1.51 1.70 1.71 2.43

7.20 7.27 7.28 7.34 7.36 7.36 7.37 7.58 7.59 7.58 7.58 8.25 8.27 8.59 8.61 8.61 9.01 9.19 9.21 9.51

0.83 0.96 1.10 1.21 1.49 1.73 2.04 3.31 3.90 4.33 5.16 6.69 7.12 8.35 10.25 12.06 13.31 15.29 15.39 16.77

0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.10 0.10 0.11

arrival penalty – TLP; 6) the total container inventory cost – TIC; 7) the total CO2 emission cost in sea – TCCS, and 8) the total CO2 emission cost at ports – TCCP. Results from numerical experiments indicate that the increasing CO2 tax decreases the vessel sailing speed between consecutive ports of call, the total fuel consumption, and in turn reduces the total fuel cost. In the meantime, decrease in the vessel sailing speed increases the transit time of containers at voyage legs of the given liner shipping route and associated container inventory costs. Moreover, increasing transit time of containers increases the total turnaround time of vessels, which requires the liner shipping company to deploy more vessels at the given liner shipping route to provide the weekly service frequency at each port of the port rotation. The latter incurs increasing weekly vessel operational costs. Increasing CO2 tax also increases the hours of vessel late arrivals at ports of call (see the vessel late arrivals section for more details) and associated vessel late arrival penalties. Furthermore, increase in CO2 tax does not cause significant changes in the port operations (see the handling rate selection at ports of call section for more details) and associated port handling costs. Results also demonstrate that the CO2 taxation may substantially change the total route service cost and costs due to production of CO2 in sea and at ports.

Please cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003

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Fig. 8. Objective function and its components.

Discussion This study presents a novel mathematical model for the green vessel scheduling problem, which directly accounts not only for the cost of CO2 emissions produced by vessels throughout the voyage, but also for the cost of CO2 emissions produced during container handling at ports of call. Computational experiments, performed for the Asia-North America AZX liner shipping route, indicate that the CO2 tax value significantly affects the design of vessel schedules. Findings suggest that increasing CO2 tax will require liner shipping companies to decrease sailing speed of vessels at voyage legs of the given liner shipping route. The latter will reduce the fuel consumption, associated CO2 produced by vessels in sea, and improve the environmental suitability. However, decrease in vessel sailing speeds will increase the transit time of containers, associated inventory costs, and may result in violation of port arrival TWs. Furthermore, increasing CO2 tax will cause increase in the total vessel turnaround time, which will require deployment of more vessels to provide the agreed service frequency at ports of call. The developed mathematical model suggests that the CO2 taxation can be an efficient mean of reducing CO2 emissions. Results also demonstrate that changes in the CO2 tax will have limited effects on the port operations, as the quantity of CO2 emissions produced at ports is significantly smaller as compared to the quantity of CO2 emissions produced in sea. However, the CO2 emissions produced at ports cannot be disregarded. The proposed GVSPCD mathematical model may become more sensitive in terms of the CO2 emissions produced at ports to changes in the CO2 tax under certain scenarios, including

Please cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003

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the following: (a) decrease in the vessel handling costs at ports of call (i.e., the liner shipping company may be willing to request vessel handling rates with higher handling productivities, which will further increase the amount of CO2 emissions produced at ports); (b) congestion at the ports of the given liner shipping route (i.e., port congestion may further delay vessel service and significantly increase the quantity of CO2 emissions produced at ports); (c) introduction of the alternative types of fuels, changes in the configuration of the main and auxiliary vessel changes, structural design of vessels, and other strategies for reducing the CO2 emissions produced in sea (which will make those emissions more comparable to the CO2 emissions produced at ports); and others. Conclusions and future research Taking into consideration increasing volumes of the international seaborne trade and substantial changes in the global climate due to carbon dioxide emissions, liner shipping companies should enhance efficiency of their operations and in the meantime account for environmental concerns in the design of their vessel schedules. To address the latter objective this paper proposed a novel mixed integer non-linear mathematical model for the green vessel scheduling problem, accounting for the carbon dioxide emission costs in sea and at ports of call. The original mathematical model was linearized and then solved using CPLEX. A set of numerical experiments were performed for the Asia-North America AZX route, served by the Nippon Yusen Kaisha (NYK) liner shipping company, to demonstrate applicability of the proposed methodology and reveal some important managerial insights. Results demonstrated that the carbon dioxide tax value might cause significant changes in the design of vessel schedules. Specifically, increasing carbon tax required the liner shipping company decreasing the vessel sailing speed to reduce fuel consumption and carbon dioxide emissions, produced by vessels in sea. Reduction in vessel sailing speed increased the transit time of containers, associated inventory costs, and resulted in violation of port arrival time windows, negotiated with the marine container terminal operators. The latter also caused increase in the total vessel turnaround time and required deployment of more vessels at the given liner shipping route to provide the agreed service frequency, which incurred increasing weekly vessel operational costs. In the meantime, limited effects on the port operations were observed from changing the carbon dioxide tax. It was found that the carbon dioxide could be an efficient mean of reducing the carbon dioxide emissions and improving the environmental sustainability. Increasing the carbon dioxide tax from 32.0 USD to 1060.4 USD reduced the quantity of carbon dioxide emissions produced in sea by 64.3%. Hence, the developed mathematical model can serve as an efficient plan-

Fig. A1. Fuel consumption function linear approximations.

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ning tool for liner shipping companies and assist with the design of vessel schedules, enhancing energy efficiency, and evaluation of various carbon dioxide taxation schemes. The future research may focus on the following extensions: (1) apply the developed mathematical model for various liner shipping routes; (2) model production of non-greenhouse gas emissions; (3) account for emission regulations for liner shipping routes, passing through ‘‘Emission Control Areas”; (4) consider deployment of a ‘‘heterogeneous” vessel fleet (i.e., vessels, serving a given liner shipping route, have different technical characteristics); (5) model uncertainty in vessel sailing speeds and port handling times (i.e., account for increasing production of emissions due to port congestion); and (6) conduct a comprehensive socio-economic analysis to quantify the negative externalities from the carbon dioxide emissions, produced by oceangoing vessels. Appendix A1 Fuel consumption function linear approximations Fig. A1 and provides examples of linear approximations with different number of linear segments (w ¼ 1; 3; 5; 10) for a non-linear fuel consumption function RFðyÞ ¼ 0:012ðyÞ . The vessel sailing speed was assumed to vary from v min ¼ 15 knots 24 to v max ¼ 25 knots, i.e. 0:040 6 y 6 0:067 (Wang and Meng, 2012a–c). It can be noticed that increasing number of linear segments improves accuracy of the approximation for RFðyÞ function. 2

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Please cite this article in press as: Dulebenets, M.A. Green vessel scheduling in liner shipping: Modeling carbon dioxide emission costs in sea and at ports of call. International Journal of Transportation Science and Technology (2017), https://doi.org/10.1016/j.ijtst.2017.09.003