In this thesis, intermodal terminal location problem involves determination of number of terminal in such way that customer demand are met at minimum shipping cost. In this regard the problem is addressed as a network flow problem in logistic network with not direct shipping constraint as depicted in Figure 2 below.

The goal is to locate terminals and assign demand nodes to the appropriate terminals.

A simply layout of intermodal terminal insertion is show in Figure 2. The figure depicts the configuration of the network including one seaport representing Abidjan which make our case study in this research work. Sea port is freight generation nodes for the flow in inland destination. Apart from the seaport the network includes inland nodes which serves as final destination point for import freight.

The problem will be formulated in the case of a rail-road network where post-routing is done by road and rail link between terminal.

We present a linear optimization model which is implemented using LINGO Mathematical Modeling Language. The model simultaneously determines the optimal number of terminal to include in the network that result into the minimum container shipping costs to final destination. The model uses Abidjan port, Cote d’Ivoire as a case study for demonstration of a numerical examples.

Here are the different variables used in the model:

Model Parameters:

O: set of freight origin (Abidjan port)

I: set of terminals

J: set of demand nodes

m: Number of demand nodes

n: Number of potential terminals indexed by j, j ∈ J = { 1 , ⋯ , n }

M: constant equal to total quantity (Ton) of freight to be shipped from port to hinterland

p: Number of terminal to be located, 1 ≤ p ≤ n

c o i : The unit transportation cost from port to terminal I (rail link) in Ton/Kilometer

c i j : The unit transport cost from terminal to final demand node in Ton/Km (road link)

d o i : Railway distance from origin to terminal

d i j : Road distance from terminal to final demand node

r o i : Rail mode transport

r i o : Road mode Transport

F i :Fixed terminal installation cost at terminal i.

a j : Demand at node j

Decision Variables: Location variable

y i = 1 if terminal is located at potential terminal i

0 otherwise

Minimize Z:

min = ∑ o ∑ i ∑ j a o i c o i d o i r o i + ∑ o ∑ i ∑ r a i j c i j d i j r r i j + ∑ ∑ F i (1)

Subjects to:

∑ i ∈ I y i = P (2)

∑ j ∈ J y i j = 1 (3)

y j i − a i ≤ 0 (4)

∑ i ∑ j a j = M (5)

a o i ≥ 0 ; a i j ≥ 0 (6)

y i = { 0 ; 1 } (7)

The objective function (1) minimizes the total cost of moving freight import from the port to final destination, being the sum of cost from port to terminal, transportation cost from terminal to hinterland and terminal implementation cost.

The constraint (2) states that P terminals must be located. The constraint (3) requires that each demand node j be assigned to exactly one terminal i. Constraints (4) limit the assignment of demand nodes to open terminal. The constraint (5) ensure that the sum of goods routed via terminal is equal to the demand associated with each origin/ destination pair.

The constrain (6) defines nonnegative parameter. And the (7) is the standard integrity constraints.

The hinterland of a port is basically made up of areas where the port serves and can be served from. To wit, a hinterland is the area over which a port extracts its main clientele base. Port hinterlands can basically be categorized into Captive hinterlands and Contestable hinterlands the captive hinterlands are areas where the port is able to reach and serve its customers and clients at a very competitive price. It can also be described as areas where the port has a well-established clientele base and does not face any form of rivalry from neighboring ports. Because of a lower generalized transportation cost, some ports enjoy a considerable amount of competitive advantage over other ports and so in areas where a port enjoys such competitive advantage, such areas or regions can be referred as its captive hinterlands. So consequently, an immense amount of cargoes to/from this region are handled by the port, which considers those areas as its captive hinterlands. In the specific case of the Abidjan port in Cote d’Ivoire, the four-walls of Cote d’Ivoire could be described as its captive hinterlands because those are the areas that do not receive any competition from any neighboring ports such as Tema, Lome and Cotonou.

Contestable hinterland where no port has a continual cost advantage over other neighboring ports, port competition becomes fiercest, and these areas can be referred to as Contestable hinterlands. To wit, the contestable hinterlands of a port are those areas that the port serves and can be served from but are also up for competition from other ports. Depending on the efficiency of a port, it can lose or maintain or even expand its contestable hinterlands. Taking the West Africa region countries under consideration in this study, their contestable hinterlands are the Sahel regions of West, Africa. These are regions, which are basically land-locked and need the services of these ports to serve as a gateway for maritime transport (Niger, Burkina Faso and Mali) (Figure 3).

Corridors Abidjan-Ouagadougou and Abidjan-Bamako overlaps partially, connecting Ivory Coast in Burkina Faso to a lesser extent in Niger and in Mali. The corridor Abidjan-Ouagadougou is at the same time a railroad. The corridor Abidjan-Bamako follows the same road of Abidjan to Ouangolodougou, then branches out to Bamako , whereas the road/railroad borrows the railroad connecting Abidjan with Ferkéssédougou and continues by the road to Bamako.

The goal is to describe a method that helps determine the best potential locations. The basic idea is to use commodity flows and their geographic dispersion as input to determine a set of potential locations for rail-road container terminals

Terminal localization problems require a set of potential locations, as well as the matrices of flows and costs between these locations. In the case of a large network, the number of potential locations becomes too large for this location problem to be resolved by an exact method. The methodology used to determine the potential locations in our case study will be one of the approaches presented by [14] : potential locations are nodes connected to railways and roads (Table 1).

The main cities on railway link are considered as potential sites for the terminals.

When these potential locations are determined, the possible container flows between them are evaluated by taking into account the demands related to the market areas. Then, transportation costs between these potential locations are evaluated by multiplying the distances obtained by the unit cost, road or rail depending on the mode of transport envisaged.

Spatial aggregation of demand nodes is a very common technique used to solve location problems. It was like reducing the size of these problems to make their solution possible. The aggregation of the nodes of demand is frequently made by a technique of classification. The classification makes it possible to group data (in the problem which concerns us: demand nodes) in several classes so that the data of the same class are as similar as possible and that the classes are as different as possible. Then each class is represented by a single demand node, usually the centroid of the class.

Indeed port statistics only indicate final destination of freight in the country without any indication of the region, district, city or town. Due to this deficient, we adopted approach base on population and Gross Domestic Production correlation to determine the quantity on freight (tons) at each demand point.

Demand nodes in Abidjan port hinterland in Cote d’Ivoire were established based on economic and demographic factors. It was assumed that the demand for freight was directly correlated to population of given region and their purchasing power measured in term of GDP per capita. Since socio-economic factor such as per-capita income and population are useful in determining freight production and attraction [15] . The same were used in determining freight destination in Ivorian market. Cote d’Ivoire is subdivided into 12 administrative region and 2 autonomous districts (Table 2). These region and districts were used to define the consumption market for freight imports. The capital of each region is designated as the final cargo center used for analysis in this study.

For the transit countries of Mali, Burkina Faso and Niger the capital city of each country was designated as the cargo center for that country as follows Bamako (Mali), Ouagadougou (Burkina Faso), and Niamey (Niger).

Now, the flow matrices and costs between each pair of potential locations are estimated and can serve as inputs to terminal location problem.

The problem of market areas has been addressed by many authors, for example Hotelling H. (1929) [16] or Berry B. J. L. (1967) [17] , Niérat (1997) [18] studied

the market area of a rail-road terminal by taking a carrier’s point of view and comparing the cost of transportation solutions (Table 3).

The market area is determined by all M points for which intermodal transport is cheaper than road transport (see Figure 4).

In this section, the problem of the p-median will be formulated with Lingo Mathematical Language (Appendix 1) in the case of a rail-road network where post-routing is done by road and rail link between terminal.

The problem define above is a linear optimization formulation for minimum cost network flow. In modeling the problem several assumptions and considerations were made, namely:

• There is only one source node (Abidjan port) and five potentials terminal

• The number and location of proposed intermodal terminal are known (exogenous model), hence the model evaluates the optimality of location, number of terminal to be included in the network and optimal for attaining the minimum cost for freight flows through the port.

• The installation and fixed cost of terminals are not considered.

• The capacity (annual throughput) of terminals is unlimited.

• Not direct shipping constraint