Simulation-Assignment Framework
3.3 Simulation-Assignment Framework
To solve the dynamic freight assignment problem in intermodal transportation networks, we seek to determine the number of shipments for each alternative and the resulting temporal-spatial loading of shipments and conveyances. To this end, the simulation assignment-based solution framework features the following three main components: (1)
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freight traffic simulation (or supply), (2) shippers behavior model, and (3) path processing and shipment assignment. The freight traffic simulator depicts freight flow propagation in the multimodal network, and thus evaluates network performance under a given set of intermodal and route decisions made by the individual shippers. Given shipper behavior parameters, the shipper behavior component describes shipments’ mode and route selection decisions in a stochastic utility maximization framework with multiple evaluation criteria. The third component is intended to generate realistic route choice sets and perform stochastic network loading for solving the shipment assignment problem.
3.3.1 Simulation-assignment solution framework
Details of several components given in italics are provided after the framework description. Figure 3-1 presents an iterative heuristic for solving the intermodal dynamic freight assignment problem with joint mode and route choice. The main steps of the solution algorithm are as follows:
Step 0: Initialization
Let iteration number n=1. Based on a set of initial link travel times and node transfer delays, find an initial feasible shortest path set for each mode in the multimodal network. Perform stochastic network mode-path assignment using this path set. For each origin and destination pair o-d, for each departure time interval τ, and product type p, this procedure results in a set
of mode-path flow solution m [
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Step 1: Freight network simulation
Perform freight network simulation, for the mode-path flow solution n ⎡
⎢⎣ o , d , τ , p ⎥⎦
m m ∈ M , k ∈ K o , d , τ , p , given in Step 1, using the Multimodal Freight Network Simulator.
Step 2: Computing time-dependent multiple product intermodal least-cost paths
Given time-dependent link travel times, travel costs and mode-transfer delays obtained by the Multimodal Freight Network Simulator or determined by train and ferry timetable, time- dependent multiple product intermodal least-cost path algorithm finds the least cost paths for each OD pair, each departure time interval, each product type, and each mode.
Step 3: Auxiliary mode-path alternative flow assignment
Compute the utility of choice alternatives and determine the corresponding probability of choosing each mode-path alternative based on multinomial logit choice model. This generates
a set of auxiliary mode-path flow solution m ⎡
⎢⎣ o , d , ,
o , d , τ τ , p p ⎥⎦
Step 4: Update of mode and path assignment
Find the new mode-path flow pattern using a predetermined move size by the method of successive averages (MSA) given in Equation (1):
⎡ n r m , k ⎤ = ⎡ r m , k
(1) ⎢⎣ o , d , τ , p ⎥⎦
⎢⎣ o , d , τ , p ⎥⎦ n ⎢⎣ o , d , τ , p ⎥⎦ ⎢⎣ o , d , τ , p ⎩ ⎬ ⎥⎦ ⎭
Step 5: Convergence criterion
n + 1 Check the number of cases N(δ) for which n ⎡
⎢⎣ o d τ , p ⎥⎦
⎢⎣ o , d , τ , p
If N(δ) < Ω convergence is achieved, where δ and Ω are pre-specified parameters. If convergence is attained, stop. Otherwise, set n=n+1 and go to Step1.
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OD shipment demand and historical paths
Multimodal Freight Network Simulator
Time-dependent intermodal least-cost paths
for multiple products
Mode-path choice and network flow n=n+1
assignment
Update of mode and path assignment
No
Convergence checking
Yes Stop
Figure 3-1. Simulation-assignment solution framework.
3.3.2 Multimodal network representation and intermodal shortest path
The multimodal freight transportation network includes two kinds of networks: the physical network and the carriers’ service network. The physical network consists of nodes, such as road intersections and terminals (e.g. intermodal transfer terminal, classification yard, siding, port, or border), and links, such as road, rail, and marine links. The service network
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consists of service routes, such as train routes and ferry routes operating according to train and ferry timetables, providing all carriers’ services (supply) for intermodal freight transportation.
Road intersections and road links are modeled in the same manner as in the DYNASMART simulation-assignment methodology (12). An intermodal transfer terminal is modeled as a transfer node between the road and rail networks, and also permits storage and generation of shipments. A classification yard is modeled as a transfer node, where inbound trains consisting of railcars intended for many destinations are sorted/classified to depart in appropriate outbound trains. A port is modeled as a transfer node between land transportation (truck and rail) and waterway (ferry) and also a place for shipment storage and generation.
With link travel costs and terminal transfer delays for multiple products obtained from the freight traffic simulation component, a time-dependent intermodal least-cost path approach, introduced by Zhou et al. (2005), is extended to a time-dependent multiple product intermodal least-cost path algorithm and is used to generate the joint mode and route alternative set. For each product and each mode, this algorithm calculates the time-dependent intermodal least-cost path tree. Note that while the freight simulation is performed on the physical network, computations of least cost paths are based on both the physical network and the carriers’ service network.
3.3.3 Joint mode and route choice model and network loading
Shippers (or their agents) are the decision-makers who determine the transport choice for their respective shipments based on available service supply. Several studies (Samuelson,
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1977, Chiang, 1980, Mahmassani, 2001) have pointed to the relation between shipment size and freight mode selection, particularly for manufacturing enterprises following a classical inventory-theoretic logistics process under stationary conditions. Current trends in modern manufacturing and logistics, especially in high-value added industries, favor a more flexible and dynamic approach oriented towards shorter horizons than typically considered in the inventory-theoretic literature. The modeling platform allows considerable flexibility in terms of representing individual shipper decision processes. In this study, the aggregated demands from shippers are compiled into shipment units that can be carried in containers (with shipment size equal to a TEU) or railcars (i.e. bulk commodities). This study uses a logit- based discrete choice model for joint mode and route choices made by shippers with regard to each shipment (i.e. shippers’ choices are reflected in shipments’ choices). Each alternative (a mode-route combination) can be serviced by one or more carriers, with the costs of switching carriers included in the utility function. For a shipment i, a general formulation of the systematic disutility function can be expressed as:
V ( s , i ) = ASC i + α s X s + α i X i (2) Dynamic network loading of shipment demand is based on the choice outcome
of the logit model. Note that although the detailed shipper-carrier relationship is not explicitly presented in the paper, the freight platform can integrate a richer model of individual shipper and shipper-carrier decision-making; unfortunately, many applications lack the necessary data to develop such models.
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