Problem Context and Assumptions
3.2 Problem Context and Assumptions
Consider a multimodal freight transportation network G(V, A), where V is a finite set of nodes, indexed by v, and A is a finite set of directed arcs, indexed by a. The time period of interest (planning horizon) is discretized into a set of small time intervals, T = {t 0 , t 0 +σ, t 0
+2σ,…, t 0 +Hσ}, where t 0 is the earliest possible departure time from any origin node, σ is a small time interval during which no perceptible changes in traffic conditions and/or travel cost occur, and H is a large number such that the intervals from t 0 to t 0 +Hσ cover the planning horizon T. Each node v∈V is associated with either an intersection in the road (or vehicular) sub-network or a terminal in rail or marine sub-networks. A terminal could be any of the following types: classification yard, port, station, and intermodal transfer terminal. Specific definitions are given later. Each arc a∈A is serviced by only one type of conveyance. In this study, three types of conveyance are considered, that is, truck, train, and ferry. The timetables detailing itineraries of trains and ferries are also given. Information on the itinerary of any train or ferry includes its service route and stop locations, scheduled departure (and/or arrival) times at terminals, and the applicable fares (rates or tariffs).
The following notation and variables are used in this chapter.
O = the set of origin zones.
D = the set of destination zones. P = the set of product types. M = the set of modes. o
= origin zone index, o∈O.
d = destination zone index, d∈D.
European Commission UMD and UOB Sixth Framework Programme
Organization Code:
p = product type index, p∈P. m
= travel mode index, m∈M. τ
= departure time interval index, τ ∈T. K m
o , d , τ , p = the set of feasible paths for product p departing from origin o to destination d during time interval τ and using mode m.
k m = path index, k ∈ K
r o , d , τ , p = number of shipments of product p from origin o to destination d during the departure time interval τ.
= number of shipments of product p from origin o to destination d departing during time interval τ using mode m and route k.
[ n r o , d , τ , p ] = mode-path flow solution at iteration n.
⎡ n y m , k
⎤ = auxiliary mode-path flow solution at iteration n.
⎢⎣ o , d , τ , p ⎥⎦
δ = convergence threshold. N(δ) = total number of violations. Ω
= maximum number of violations. s
= shipment index. i
= alternative index for joint mode and route choice.
V (i s , ) = systematic utility of joint mode and route alternative i to individual shipment s. ASC i = alternative specific attributes for alternative i.
X s = attributes of individual shipment s.
X i = attributes of mode-route alternative i. α s , α i = coefficients of utility function.
Organization Code:
UMD and UOB
European Commission
Classification:
Unclassidied
Sixth Framework Programme
A shipment is the smallest unit of cargo (in container or in bulk) that a given shipper wants to transport from a firm (origin) to a market (destination). The time-dependent zonal
demands r o , d , τ , p over the planning horizon are assumed known a priori.
A feasible mode m is defined as a sequence of (a least one) conveyances allowing the use of two consecutive conveyances if there is a feasible transfer between them. A feasible joint mode and path alternative is defined as a sequence of arcs that are serviced by available modes with feasible intermodal transfers. Alternative costs are assumed to be additive in link travel times and costs, as well as node (i.e. terminal or intersection) transfer delays and costs. The behavioral assumption made in this study is the following: facing a joint mode and route choice set, a shipper will choose a (intermodal) path k which minimizes that shipper’s
generalized cost of transporting a given type of shipment from origin o at time τ to destination d. The generalized cost may include random components in a random utility perspective on shipper’s choice, resulting in a probabilistic choice function for the selection of a mode-path combination. The specification of the mode choice function used in the REORIENT platform was developed under Work Package 6, and is described in detail in the final report of WP 6.1.