Problem definition and assumptions

4.2 Methodology

4.2.1 Problem definition and assumptions The MIMTLP can be stated as follows:

“Given the distribution of containerised cargo and candidate terminal locations on the transport network, what are the best places to locate p intermodal terminals to best serve the metropolitan containerised market?”

What is best depends on the objective function and in this study, the objective to be optimised is the entropy, which is a function of the modal decision variables. The motivation for maximising entropy was discussed in Chapter 3, and in this chapter, it will be shown that maximising entropy is equivalent to maximising shippers expected utility or welfare.

In formulating the problem, it was assumed that the study area (e.g., the metropolitan region) is segmented into freight analysis zones where cargo can be seen as originating from one zone and destined to another zone. The zones are connected to both the rail and highway networks so that cargo can be transported from one zone to another using at least one mode of transport. Two main modes of transport are assumed to be available to each user or shipper;

road alone transport and intermodal transport. Road alone transport mainly involves the use of trucks to transport containers to and from the port. Intermodal transport, on the other hand, combines the use of trucks and a high carrying capacity mode such as rail for the movement of

IMT

Warehouses in the Metropolitan region Seaport

Main leg by Final delivery/Local pickup

Figure 4.1: Modal options: Import market (Export market is the reverse) IMT

containers to and from the port, where the rail is used for the main leg and the trucks for local pickups and/or local deliveries as shown in Figure 4.1. In addition to the above assumptions, following information are assumed to be available or can readily be deduced:

1. Fixed origin-destination movement of cargo (in TEUs) in the study area.

2. The transport budget (known or assumed). Here, the analyst has the opportunity to investigate the implications of different transport budgets on IMT location and usage.

Plausible ways of deriving this budget are discussed below.

3. The generalised cost of using each mode of transport between each origin-destination pair.

The construction of these costs variables is discussed in below.

4. Candidate IMT sites (plausible places where IMTs can be located), the number of IMTs to locate and handling capacity of each candidate IMT location.

The intermodal transport cost 𝑐_𝑖𝑡𝑗 is a very important policy variable and comprises three main components:

𝑐_𝑖𝑡𝑗 = 𝑐_𝑖𝑡+ 𝑐_𝑡+ 𝑐_𝑡𝑗 (4.1)

where for import cargo movements, 𝑐_𝑖𝑡 is the unit cost of transporting cargo from the port to IMT 𝑡 by rail ($ per TEU); 𝑐_𝑡𝑗 is the unit road cost from IMT 𝑡 ∈ 𝒯 to cargo destination 𝑗 ∈ 𝒟 ($ per TEU). For export cargo movements, 𝑐_𝑖𝑡 is the unit truck cost of transporting cargo from origin 𝑖 to IMT 𝑡 ($ per TEU); 𝑐_𝑡𝑗 is the unit rail cost from IMT 𝑡 ∈ 𝒯 to the port (cargo destination 𝑗 ∈ 𝒟). The parameter 𝑐_𝑡 is the terminal usage cost or rental ($ per TEU) passed on to the shipper, who then decides whether or not to use the terminal and comprised the fixed installation costs and terminal operation costs. The transport network cost (road or rail) between any two zones 𝑖 ≠ 𝑗 is generally assumed to consist of two cost components:

𝑐_𝑖𝑗 = 𝜑̃ + 𝜃𝐺𝑇_𝑖𝑗 (4.2)

where 𝜑̃ is the fixed transport cost ($ per TEU), 𝜃 is the cost sensitivity parameter of generalised travel time, 𝐺𝑇_𝑖𝑗 between two locations on the network with the combined term 𝜃𝐺𝑇_𝑖𝑗 representing the variable cost component. The generalised time 𝐺𝑇_𝑖𝑗 can be a function

of distance or time as may be the case for rail or a linear combination of distance and time as expressed below:

𝐺𝑇_𝑖𝑗 = 𝑡𝑖𝑚𝑒_𝑖𝑗+ 𝑣𝑜𝑐

𝑣𝑜𝑡 𝑑𝑖𝑠𝑡_𝑖𝑗 (4.3)

𝑡𝑖𝑚𝑒_𝑡𝑗 and 𝑑𝑖𝑠𝑡_𝑡𝑗 are the travel time (minutes) and distance between location 𝑖 and location 𝑗 respectively, 𝑣𝑜𝑐 is the vehicle operating cost ($ per km) and 𝑣𝑜𝑡 is driver’s value of time savings ($ per minutes). It can further be assumed that the truck travel times and distances will come from an existing suitable transport model of the study area and that the model contains assignment models that adequately capture the non-linearity between flows and travel times on the transport network.

The transport budget is also very important variable in the model and provides the analyst or location planner some degree of flexibility in locating IMTs to achieve certain economic, environmental or social policy targets. The budget 𝑐 can be derived using 𝑐 = 𝑐̅𝑍, where 𝑐̅ is the average transport cost within the study area and 𝑍 is the total cargo in the system.

The average cost can be derived from a sample of origin-destination cargo flows with associated costs. Alternatively, it seems reasonable to assume that shippers individually would not choose to increase their transport costs because a new IMT becomes available, so they would not do so collectively. Thus, collectively shippers can be assumed to behave in such a way that the average transport costs over all origin-destination cargo movements after the addition of IMT(s) are no higher than before. The average transport cost can therefore be computed using equation (4.4), which is the average cost of using road alone transport. Once the average transport is known, the budget can be derived using 𝑐 = 𝑐̅𝑍.

𝑐̅ = ∑_𝑖∈𝒪∑_𝑗∈𝒟𝑐_𝑖𝑗𝑞_𝑖𝑗

∑_𝑖∈𝒪∑_𝑗∈𝒟𝑞_𝑖𝑗

(4.4)

where 𝑞_𝑖𝑗 is the quantity of cargo to be transported between the sampled origin-destination cargo movements and 𝑐_𝑖𝑗 is the associated road alone transport cost. The transport budget can more generally be computed using:

𝑐 =𝜅𝑐̅𝑍; 𝜅> 0 (4.5)

Equation (4.5) allows the budget to be specified such that the location of the terminals can be used to improve the average existing cost of transport in addition to the environmental and other benefits associated with intermodal transport.

Decision variables

The key decision variables are 𝑌_𝑡 with 𝑌_𝑡= 1 indicating that candidate location 𝑡 ∈ 𝒯 must be developed as an intermodal terminal. The values of the variable 𝑉_𝑖𝑡𝑗 represent the demand for terminal 𝑡 ∈ 𝒯 in the movement of cargo between zones 𝑖 ∈ 𝒪 and 𝑗 ∈ 𝒟 hence determines the demand for intermodal transport, whilst 𝑋_𝑖𝑗 outputs the demand for road alone transport.