multimodal freight transport network design for developing countries

Journal of the Eastern Asia Society for Transportation Studies, Vol. 7, 2007

MULTIMODAL FREIGHT TRANSPORT NETWORK DESIGN FOR DEVELOPING COUNTRIES Jun T. Castro Associate Professor School of Urban and Regional Planning University of the Philippines E. Jacinto St., Diliman Quezon City 1101, Philippines E-mail: jtcastro@upd.edu.ph

Tadashi Yamada Associate Professor Department of Urban Management Kyoto University Yoshida-Honmachi, Sakyo-ku Kyoto 606-8501, Japan E-mail:t.yamada@kiban.kuciv.kyoto-u.ac.jp

Bona Frazila Russ Lecturer Bandung Institute of Technology Jl. Ganesha 10, Bandung Indonesia E-mail: frazila@yahoo.com

Makoto Iida Graduate Student Graduate School of Engineering Hiroshima University 1-4-1 Kagamiyama Higashi-Hiroshima 739-8527, Japan

Abstract: This paper focuses on strategic planning in developing countries, particularly in freight transport network design and terminal development. An optimal set of transport projects is determined using a transport network design model with some objective function, which can be a single objective function or a multi-objective function. The model involves bilevel modelling approach, where multimodal multi-user assignment is incorporated in the lower level problem and the combination of transport interventions or projects is optimized in the upper level problem. Application of the model is undertaken using data from the two archipelagic countries of Indonesia and the Philippines - both countries that would definitely benefit from a multimodal transport design. Key Words: Multimodal transport, Network design, Genetic algorithm

1. INTRODUCTION Both Indonesia and the Philippines are composed of more than 7,000 islands. Because of their archipelagic nature, the various modes play a vital role in the efficient transport of passengers and goods. A majority of flows is carried by road and water, while air and rail have nominal shares due to the inherent characteristics of the transport network, which is designed primarily for road and water transport. Nonetheless, a lot is to be desired when it comes to land and water transport infrastructure in terms of quality, and to a certain extent, in quantity. This lack of infrastructure support is one of the major causes why a large percentage of harvested produce annually are wasted before, during, and after the transportation process. A multimodal transport system which will minimize goods handling, and to a large degree waiting and conveyance time could reduce these unwanted losses. At present, the existing multimodal facilities consisting of roads, rail and ports in both countries can be generally described as still undeveloped. The capacities of the roads especially outside urban areas are still inadequate, and there are several road segments where the conditions of the roads are very poor. In addition, most of the port terminals provide low

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service levels with lack of berths and supporting equipment. Hence, transport infrastructures have not been optimally developed to suit the needs for a well-coordinated and efficient multimodal operation. To address the problem of multimodal transport planning, particularly the prioritization of transport infrastructure projects, this paper will highlight the optimal planning of multimodal freight transport network in developing countries using the model developed for the optimal design of multimodal freight transport network (Russ et al. (2005), Yamada et al. (2007)). The model incorporates bi-level modelling, in which multimodal multi-user assignment is applied in the lower level problem and the combination of transport initiatives is optimized in the upper level problem. Application of the model is undertaken for the two archipelagic countries of Indonesia and the Philippines.

2. MODEL Several concerns are needed to be addressed to make a more effective and efficient multimodal freight transport system in developing countries. One of these concerns is the need for a decision support analysis for multimodal freight network planning. The analysis tool should be able to incorporate development projects proposed by the government. Furthermore, the design should be application-oriented or that it should comply with data publicly available in developing countries. This section describes the model used in this research. A general mathematical formulation is first presented based on bi-level programming followed by a discussion of Genetic Algorithm (GA) which will be adopted as the solution technique to optimize the best combination of transport projects. The relevant objective functions for the lower and upper level problems are then explained. 2.1 Bi-level Approach In the design of the transport network, the problem may be divided into two levels of analysis: 1) network design at the upper level of analysis, and 2) network operation at the lower level of analysis. The interaction between the two levels is cyclical, where the upper level determines the design specification and the lower level determines the network performance which then feeds into the improved design specification at the upper level of analysis. Thus, a bi-level programming approach can be employed in formulating the problems. As discussed by Russ et al. (2005), the lower level can be formulated as a variational inequality problem, while the upper level can be formulated as a combinatorial optimization problem. The problem can be defined by two conditions. The first is the initial condition or the condition without any infrastructure improvement, also called the “do-nothing scheme”, and the second is the condition with infrastructure improvement, or the “do-something scheme”. For both conditions, sets of equilibrium flows x0* at the “do-nothing scheme” and x* at the “do-something scheme” exist. The model can be formulated as follows (Yamada et al. (2007)):

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(

max f y , b, x * , x 0* y

)

(1)

subject to

where x x* x0 x0* y b c K1,K0

c ( x * ), x − x * ≥ 0 ∀x ∈ Κ 1

(2)

c( x0* ), x 0 − x 0* ≥ 0 ∀x 0 ∈ Κ 0

(3)

: vector of link flows : vector of equilibrium link flows : vector of link flows in the initial condition : vector of equilibrium link flows in the initial condition : set of multimodal transport projects : vector of investment/operation costs : vector of link user costs : feasible constraint set

Generally, the decisive objective function is to find a set of transport projects with the maximum improvement as compared to the initial condition by considering the investment and operational costs for that set of projects. However, additional objective functions can also be considered and incorporated, such as the impact of the projects to the environment. Equations (2) and (3) are variational inequality equations for user equilibrium flows in the network. 2.2 Genetic Algorithm Genetic Algorithm (GA) is a metaheuristic method based on the mechanism of natural selection and genetics. The possible solution is constructed into individuals known as chromosomes or strings. The process starts with a population of random strings representing possible solutions to the problem and the population of string members is evaluated using a defined fitness function and the new set of population is generated by genetic operators, i.e. selection, reproduction and mutation. Several applications of GAs in optimization problems, such as in the transport field have been discussed by Goldberg (1989), Xiong and Schneider (1993), and Yamada et al. (1999) among others. 2.3 Overall Procedure The general modelling procedure is shown in Figure 1. Given a short list of transport projects, the combination of projects is selected and the network is updated based on the implemented projects, i.e. “do-something scheme”. The traffic flows are then predicted on the network by modal split and assignment procedures. The lower level problem is an aggregated-type freight network model developed from existing approaches (such as in Guelat et al., (1990) and Friesz et al. (1983)) and influenced by data availability. The main output of the lower level problem is the flow on the network, which is used for the calculation of the objective function. The objective function in the upper level problem is based on the comparison of freight costs between the upgraded network under the “do-something scheme” and the initial network or the “do-nothing scheme”.

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Optimal Projects

Upper Level

Fitness of Combination

Objective Function Network Performances

Modal Split and Assignment

Lower Level

Generation of Combinations (Sets of Projects) List of Transport Projects

Figure 1 General modelling procedure The above model allows freight and passengers to be treated as multi-class users, with modal split and route choice carried out simultaneously by converting the multimodal network into a unimodal abstract mode network. The user equilibrium conditions can be stated with a nonseparable and asymmetric Jacobian matrix cost function among user types using variational inequality (Dafermos, 1980). The model incorporates the diagonalization method (Florian and Spiess (1982); Sheffi (1985)) as a solution procedure. The next step involves the assessment of the fitness of the combination of projects. This is basically a selection process in which the combination of projects that has the highest fitness value will be selected as the solution. Other combinations will be generated and the process is repeated until the combination of projects with highest fitness values is found. The mechanism for generating the combination and selecting the best combination of projects is based on GA. 2.4 Generalized Link Cost Function The generalized link cost function as shown in Equation (4) is composed of a fare component and a time cost component which is the product of the time spent on the link and time value for each user type. The fare component is fixed and does not depend on volume, while the time cost component is a function of volume and differs by link type. c a ( x ai , y a ) = ρ ai + α i d ai ( x ai , y a )

where cai(xai,ya) : generalized freight cost on link a for user type i ρia : fare on link a for user type i i α : time value for user type i i i d a(xa ,ya) : time spent on link a for user type i

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(4)


However, this function has an asymptotic behaviour, which can lead to a complex objective function, and thus, the time spent on the link function is converted to a continuous function in the form of polynomial approximation as proposed by Crainic et al. (1990) to keep the link cost function monotonically increasing: ⎡ ⎛ xT d ( x ) = t 0 ⎢1 + φ 1 x aT + φ 2 ⎜⎜ Ta ⎢⎣ ⎝ ra i a

T a

⎞ ⎟ ⎟ ⎠

γ

⎤ ⎥ ⎥⎦

(5)

where xTa : total flow on link a (veh) T r ,a : total capacity of link a (veh) φ1, φ2,γ : parameters to be calibrated By applying this equation to all the links, the multimodal network is converted to a single abstract mode network. Example of parameter calibration results can be found in Russ, et al. (2004). 2.5 Benefit-Cost Ratio The combination of projects is optimized on the basis of the ratio of reduced total generalized freight cost and the required investment and operational costs. This can be simplified using benefit-cost ratio (BCR), which is an indicator of economic efficiency. The single-objective function is to maximize the following: ⎛

max f ( y ) =

∑ ⎜⎜ ∑ i∈F

⎝ a∈ A1 ∪ A2

x 0i*a c ai ( x 0i*a ) −

∑x

a∈ A1

∑b

a∈ A2

c ( x ai* ) −

i* i a a

a

∑x

a∈ A2

⎞ c ( x ai* , y a ) ⎟⎟ ⎠

i* i a a

(6)

ya

where y : set of possible projects F : set of user types xi*oa: flow on link a for user type i (i.e. solution in the do-nothing scheme) xai* : flow on link a for user type i (i.e. solution in the do-something scheme) cai(xai*,ya): generalized freight cost on link a for user type i ba: investment/operation cost for link a ya : project implementation indicator (i.e. 1 if implemented, and 0 if otherwise) A GA-based procedure is used to solve the problem, where the combination of projects is randomly generated and the chromosomes are created. Although GA cannot ensure obtaining exact optimal solutions, it can provide reasonable and practical solutions for problems wherein exact optimal solutions are hard to determine. Therefore, GA has been widely used to obtain approximate optimal solutions to large-scale applications.

3. MODEL APPLICATION The applicability of the model is tested using Indonesian and Philippine data. The transport network of Indonesia is modelled into 51 zones, comprising 761 nodes and 3,466 links. On the other hand, the modelled transport network for the Philippines is composed of 424 nodes,

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and 1871 links comprising the national, provincial and toll roads, railways, and port-to-port sea routes. The zoning for the Philippines is aggregated into 24 zones following the zoning system used in the JICA funded “The Inter-Regional Passenger and Freight Flow Surveys in the Republic of the Philippines (SIRPAFF)” study in 2004. Geographic Information System (GIS) was utilized to facilitate modelling of the transport network. A base map was first established by registering it to real-world coordinates. Additional layers of features were then digitized and created separately for the zonal areas, zone centroids, road links, sea links, railway links, railway terminals, ports, and related transport facilities. A database of the attributes of each feature was then prepared based on existing data gathered from both the government and the private sectors.

50000

7500

5000

model flow (ton/day)

10000

Model flow (ton/day)

75000


100000




3.1 Validation of Flows Prior to full computation, the modal split-assignment model was first validated to confirm the flows resulting from the model and actual flow data and to make adjustments to model parameters. 20000

15000

10000

2500

25000

5000

0

0 0

25000

50000

75000

0 0

100000

2500

5000

7500

10000

0

5000

10000

Data flow (ton/day)

Road R2 = 0.60

15000

20000

data flow (ton/day) Data flow (ton/day)

data flow (ton/day) Data flow (ton/day)

data flow (ton/day)

Sea R2 = 0.64

Rail R2 = 0.80

300

200

100

400

300

200

Model Flow (Thousand Ton/Day)

Model Flow (Thousand Ton/Day)

400

Model flow (thousand ton/day)


Model Flo w (Tho usand To n/Da y)


Figure 2 Validation of flows for the Philippines 200

150

100

100

0 0

100

200

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Flow (Thousand Ton/Day) DataData flow (thousand ton/day)

Road R2 = 0.70

50

0

0 0

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Flow(thousand (Thousand Ton/Day) DataData flow ton/day)

Rail R2 = 0.72

0

50

100

150

200

Flow (Thousand Ton/Day) DataData flow (thousand ton/day)

Sea R2 = 0.85

Figure 3 Validation of flows for Indonesia The results shown in Figures 2 and 3 indicate that the assignment model performed well enough and can be used for the next step of computation. Though it is not a perfect fit, estimated values from the model have a strong correlation with the actual values from the available data set as indicated by the correlation coefficients ranging from 0.60-0.80 for the Philippines and 0.70-0.85 for Indonesia.

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3.2 Multimodal Transport Projects Sixteen multimodal transport projects are considered for each country, which includes development of new roads, rails, ports, and upgrading or improvement of existing infrastructure. The projects are mainly situated along the major multimodal corridors in Indonesia and the Philippines (Figures 4 and 5).

No. No. 1 2 3 3* 4 4* 5 6 7 7* 8 8* 9 9* 10 11 12 12* 13 14 15 16

Type of Actions Project

Location

Sea Port Improvement

Jakarta (Tanjung Priok)


Banten (Ciwandan)


South Sulawesi (Makasar)


Irian (Sorong)


North Sulawesi (Bitung)

New Sea Sea Port Port Rail Terminal Improvement Impt Rail

Jambi (Muara Sabak)

Rail Impt Rail Terminal Improvement Rail Terminal Improvement Impt Rail New Bridge

Central Java (Cilacap) Java-Sumatera Bridge

New Bridge

Java-Madura Bridge

Road Widening Widening

Lampung-South Sumatera

Road Widening Widening New Expressway Express Way

Central-South Kalimantan

New Expressway Express Way

Cirebon-Semarang

New Expressway Express Way

West Java (Bandung) Lampung (Bandar

Semarang-Surabaya Bandung-Cirebon * Hypothetical action

Figure 4 Location of transport projects for Indonesia

10

6

7

8

9 3 2

4 14

1 5 11 13

16 No. Project type Location 1 New expressway Lipa – Batangas 2 New expressway Subic – San Fernando 3 Newof expressway Tarlac – Subic N o. T ype A ction Locati on 1 4 N ew Road E xpress W ay C al am ba-B –atangas widening Manila Batangas S ubic-S an F ernando, P am panga 2 5 N ew Road E xpress W ay widening San Isidro – Tacloban 3 N ew E xpress W ay T arlac-S ubic 6 Road widening San Fernando – Ilagan 4 R oad W idening P asig-B atangas widening Caloocan–Sn Fernando A llen/S an Isidro-T acl oban 5 7 R oadRoad W ideni ng railway Manila - os Angeles 6 8 R oadNew W ideni ng Ilagan-M alol S n F ern, L aU nion-C 7 9 R oadNew W ideni ng railway Angeles – Snaloocan Fernando 810 N ew New R ail Wrailway ay M ani la-A ngel es Tarlac - Tuguegarao A ngeles-S n F ern LaU nion 9 N ew R ail W ay 11 Sea port improv’t Calapan 10 N ew R ail W ay T arlac-T uguegarao improv’t Dapitan ort port Im provem ent C alapan 1112 S ea PSea improv’t ort port Im provem ent D apiLiloan tan 1213 S ea PSea S ea P ort I m provem ent 1314 Sea port improv’t Liloan Matnog ort port Im provem ent M atnog 1415 S ea PSea improv’t Pulupandan ort Im provem ent P ulupandan 1516 S ea PSea port improv’t Roxas

15

12

16 S ea P ort Im provem ent R oxas

Figure 5 Location of transport projects for the Philippines

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3.3 Model Results For Indonesia, the optimal solution contains project no. 6, which is a new seaport development in Sumatra Island. This solution improves the non-road mode share and reduces some overloaded road links resulting in a transport benefit of 513 billion rupiah. However, the project requires a corresponding investment cost of 500 billion rupiah (Table 1). The optimal solution obtained indicates that it is necessary to develop a new seaport in Sumatra Island to provide better access and to improve other-than-road mode for freight movements. For the Philippines, the optimal solution obtained from the simplified benefit-cost ratio model contains a single project, project no. 4, which is a road widening project from Manila to Batangas with a BCR value of 1.86. The benefit of this project with respect to transport is estimated to be 3.6 billion pesos per year, while the related cost for construction and operation per year is estimated to be 1.9 billion pesos (Table 2). The result obtained from the model is fairly sensible because a cursory investigation of the existing conditions in the Philippines will reveal that this road link is already heavily loaded. A majority of the whole stretch of this arterial road only has two lanes, one for each direction. Increasing the capacity of this road link would obviously improve traffic conditions in the area. At present, increasing attention has been given on the construction and rehabilitation of expressway connections between Manila and Batangas. For example, there have been plans to widen the existing South Luzon Expressway (SLEX) from Manila to Calamba and to construct a SLEX extension linking Calamba and Santo Tomas which will connect with the existing Southern Tagalog Arterial Road (STAR) Tollway that stretches from Santo Tomas to Lipa City. A new STAR tollway extension is also planned from Lipa City to Batangas Port. However, these projects would still require several years of planning, implementation and construction. Table 1 Benefit-Cost Ratio of the best solution for Indonesia Project No. Transport Benefit Improvement Cost BCR (billion rupiah) (billion rupiah) 6 513 500 1.03 Table 2 Benefit-Cost Ratio of the two best solutions for the Philippines Project No. Transport Benefit Improvement Cost BCR (million peso) (million peso) 4 3635 1959 1.86 15 2363 2110 1.12

4. MULTI-OBJECTIVE CASE In recent years, single-objective optimization to multi-objective optimization has been desired in many actual decision making situations due to the increasing diversity and complexity of decision making procedures and approaches. For example, in strategic infrastructure planning, decision makers have to consider not only the maximization of economic benefits but also the minimization of environmental impacts. Therefore, the selection of the most favorable projects in infrastructure planning usually deals with several criteria or conflicting objectives.

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For instance, the objective function concerning economic benefits can be assessed using the Benefit-Cost Ratio (BCR) while the objective function regarding environmental impact can be evaluated using NOx reduction, which is generally considered to be the most significant component of freight vehicle emissions. Multiple Criterion Decision Making (MCDM) is the terminology used in reference to the problems in which two or more non-commensurable and conflicting criteria exist. MCDM has been comprehensively studied in the literature and Pareto optimality, for example, is the basis of the solutions of the MCDM problems. A perfect optimal solution which minimizes all objective functions simultaneously does not always exist in a multi-objective optimization problem. Therefore, Pareto optimal solution is introduced, implying that any improvement of one objective function can be achieved only at the expense of at least one of the other objective functions. Since there are, in general, many Pareto optimal solutions, it has been revealed by past studies that genetic algorithms (GA), which is one of the most efficient search methods, are useful in enumerating them. One of the GA-based algorithms for solving such multi-objective transportation infrastructure planning problem is the Vector Evaluated Genetic Algorithm (VEGA) (Yamada et al., 1999). This algorithm treats objective functions separately in order to find multiple non-dominated solutions in a single run of the algorithm. In VEGA, subpopulations are formed in each generation from the existing population by using proportional selection according to each of the objectives. The local search and reproduction are performed on each subgroup. These subpopulations are then mixed together, forming a new population on which ordinary operators such as crossover and mutation can be carried out. By this method, the offspring produced from parents of different subpopulations is expected to have good fitness on both the objectives, and the population may be expected to evolve towards the set of solution which is considered as Pareto-optimal. 4.1 Multi-Objective Function Formulation Multi-objective functions that can be used are those that consider, for example, economic and environmental aspects. The objective function concerning economic aspect may be the same as that used in the previous discussion, i.e. Benefit-Cost Ratio. The other objective function regarding the environmental aspect may be concerned with the benefit obtained from the reduction of emissions. This paper will only tackle NOx emission because it is the most significant component of vehicle emission. The first objective function (f1), which is the Benefit-Cost Ratio, is given by Equation (7), and the second objective function (f2) relating to NOx reduction is formulated as Equation (8): ⎛ ⎞ ⎜ x0i*acai ( x0i*a ) − xai*cai ( xai*) − xai*cai ( xai*, ya ) ⎟ ⎜ ⎟ i∈F ⎝ a∈A1 ∪ A2 a∈A1 a∈A2 ⎠ max f1( y) = ba ya

∑ ∑

∑

∑

∑

(7)

a∈A2

⎞ ⎛ ⎜ EFai ( x 0i*a ) − EFai ( x ai* ) − EFai ( x ai* , y a ) ⎟ ⎟ ⎜ i∈F ⎝ a∈A1 ∪ A2 a∈A1 a∈A2 ⎠ max f 2 ( y ) = ba y a

∑ ∑

∑

∑

a∈A2

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∑

(8)


where EFai(xai*,ya)

: NOx emission on link a by user type i that depends on the equilibrium flow and whether the projects are implemented or not (action implementation indicator ya) (grams)

4.2 Modelling Results The models are again applied to Indonesia and the Philippines. The transport network and projects are assumed to be similar with those described in the previous sections. For Indonesia, three optimal solutions are identified as shown in Figure 6 and Table 3. The marked points in Figure 6 are the non-dominated solutions and thus are the optimal solutions. The solutions are all single-project solutions with positive values for both f1 (i.e. BCR) and f2 (i.e. NOx reduction). Project no. 6 corresponds to a new sea port project, while project nos. 7 and 9 are both rail terminal improvement initiatives. For multi-objective design maximizing BCR and NOx reduction in Indonesia, the optimal strategy would be to improve non-road transport facilities, most specifically sea port and rail terminal improvements. For the Philippines, the Pareto optimal is given by Figure 7 and Table 4. However, although solution nos. 1, 2 and 3 have the highest values for f1 (i.e. BCR), all have negative values of f2 (i.e. NOx reduction) implying that the proposed projects for implementation would have negative impacts to the environment. Solution no. 4 consisting of project nos. 12, 13, 15 and 16 has positive f1 and f2, and so is solution no. 5 consisting of project nos. 12, 13 and 15. However, their BCR values are less than 1.0, which implies that they are not economically feasible.

Figure 6 Pareto optimal for Indonesia

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Solution No. 1 2 3

Table 3 Pareto optimal solution for Indonesia Project f1 (BCR) f2 (NOx No. reduction) 6 1.03 0.00065 7 0.97 0.00168 9 0.78 0.00423

Figure 7 Pareto optimal for the Philippines

Solution No. 1 2 3 4 5

Table 4 Pareto optimal solution for the Philippines f2 (NOx Project f1 (BCR) No. reduction) 4 1.86 -0.2510 15 1.12 -0.1454 15, 16 0.95 -0.0975 12, 13, 15, 16 0.43 0.0269 12, 13, 15 0.76 0.0226

4.3 Policy Implications for Transportation Project Evaluation The two criteria of maximizing economic benefits and minimizing environmental impacts have a trade-off relationship such that if one solution scores highly in the first objective function, then it will score lowly in the second objective function. For both Indonesia and Philippines, the best solution for the multi-objective function is different from the result obtained from the single objective function using BCR analysis. This is because the solution with the best BCR value in the single objective function might have a negative value for the NOx objective function, implying increased NOx emission than the donothing scheme. The Pareto-set identifies several optimal solutions depending on the values of each objective function. The extreme case of maximizing the BCR function tends to select fewer infrastructure projects, while the extreme case of minimizing the NOx function tends to select several projects. This difference is due to their inherent characteristics where the first function of maximizing economic benefits considers investment and operational costs associated with implementing the projects while the second function of minimizing environmental impacts 1028


does not consider these costs. For transportation project evaluation in developing countries, it might still be more appropriate to prioritize economic benefits than environmental benefits. This is because of the limited financial resources which oftentimes characterize transportation infrastructure development in developing countries. 5. CONCLUSION An overall framework of designing optimal freight transport network was described in this paper. The model used in this paper is aimed at the strategic level of planning, particularly in the development of freight transport network and terminals. The model incorporates computation techniques based on genetic algorithms for solving discrete network design problems. The best combination of transport development projects are selected among the set of projects that includes improvement of existing infrastructure and development of new roads, sea links and freight terminals. The model is initially applied to a single-objective problem based on benefit-cost ratio (BCR) and then further extended to a multi-objective problem. The other objective function developed is based on environmental aspect, particularly in maximizing NOx reductions. This function is mostly influenced only by the link flows making it less sensitive than the objective function of maximizing BCR, which is also influenced by the time spent on the link. The two objective functions have a trade-off relationship such that if one solution has a relatively high value for the first objective function, then it will have a relatively low value for the second objective function. The results show that the model can be applied in a wide range of planning purposes using actual data for Indonesia and the Philippines. The case of the single objective function indicates that it is necessary to develop a new seaport in Sumatra Island to provide better access, and that it is necessary to develop the road connection from Manila to Batangas to have immediate impacts in terms of improving transport efficiency. The Pareto-set in the multi-objective case then identifies that the best solution for the multi-objective function might be different from the result obtained from the single objective function. Although the model cannot ensure obtaining exact optimal solutions, it can provide reasonable and practical solutions. However, to strengthen the accuracy of model results and scope of analysis, there are further explorations that should be done. For example, although some approximation on cost functions was done, the accuracy of the functions have not been tested and verified in detail. Some cost function types might be evaluated and validated to obtain more realistic freight costs. Likewise, for better model application result, more accurate network data especially regarding rail link, sea link and terminal is required. Finally, the application is limited to regional movements, and thus further application incorporating international movements will provide a more comprehensive model performance.

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