Dynamic Network Simulation–Assignment Platform for Multiproduct Intermodal Freight Transportation Analysis Hani S. Mahmassani, Kuilin Zhang, Jing Dong, Chung-Cheng Lu, Vishnu Charan Arcot, and Elise Miller-Hooks linked end to end in order to move freight from origin to destination. Transfer points or terminals become particularly critical in this process; their effectiveness ensures that shipments move through multimodal networks efficiently and securely. The assignment of multiple-product intermodal freight flow over a multimodal network has attracted much interest in the past four decades. Various combined shipper–carrier models and spatial price equilibrium models and their variants have been extensively developed and studied (1, 2); the freight network equilibrium model (FNEM) proposed by Friesz et al. is one example (3). In analytical approaches, variational inequality (VI) formulations have been widely used to model freight equilibrium problem in the literature. For example, Fernandez et al. presented a strategic railway freight assignment model to predict equilibrium flows by solving a VI problem on the railway network (4). Agrawal and Ziliaskopoulos applied an iterative VI formulation to model the market equilibrium between shipper and carrier (5). In their model, the cost function is obtained from a carrier submodel, a dynamic multimodal multicommodity network assignment model using a linear programming (LP) formulation. Crainic et al. and Guelat et al. proposed a multimode multiproduct network freight assignment model for strategic planning, implemented in a strategic transportation analysis tool called STAN that solves a system-optimal assignment problem with the objective of minimizing the total delay at arcs and node transfers (6, 7 ). In Crainac et al.’s model, the operation inside a classification yard is modeled as an M/M/1 queue, and the average delay through the yard is estimated by a delay function that relates to product types and traffic flows. Under such assumptions, both the arc traversal times and the node transfer delays could be expressed in closed-form analytic functions. The above analytical freight assignment models are designed for strategic planning purposes and are effective in assigning shipment flows at an aggregated level. However, a wide variety of applications (e.g., service planning and design, market and business case analysis, logistics planning, policy analysis) call for greater level of detail, including the ability to represent individual shipment trajectories, along with experienced link travel times, process times, and transfer delays at terminals. As in passenger demand analysis, freight demand modeling has largely adopted a disaggregated perspective focusing on individual firms’ logistics decisions and shipment-level analysis (8–11). A simulation–assignment approach is then needed to provide a platform in which demand-side decisions are properly interfaced with the supply side representation, allowing considerable analysis flexibility. Similar considerations on the passenger side have led to a new generation of simulation-based dynamic network
This paper develops a dynamic freight network simulation–assignment platform for the analysis of multiproduct intermodal freight transportation systems. At the core of the platform is a model framework for the mode–path assignment problem in multimodal freight transportation networks. The framework consists of three main components: a multimodal freight network simulation component, a multimodal freight assignment component, and a multiple product intermodal shortest path procedure. The freight network simulation component incorporates a bulk queuing model to evaluate transfer delay experienced by shipments at intermodal transfer terminals, classification yards, and ports. The multimodal freight assignment component determines the network flow pattern from a mode–path alternative set calculated by the multiple product intermodal shortest path procedure, based on the link travel costs and node transfer delays from the multimodal freight network simulation component. This model can represent individual shipment mode–path choice behavior, consolidation policy, conveyance link moving, and individual shipment terminal transfer in an iterative solution framework.
This paper presents a network modeling and analysis platform for evaluating the effectiveness of alternative configurations and operational strategies for multiple-product intermodal freight transportation systems. Trends toward outsourcing, the globalization of manufacturing, and the use of complex virtual supply chains and associated logistics processes place growing demands quantitatively and qualitatively on the freight transportation system. Shippers’ demands for exacting service, and their need to have products delivered reliably at a cost that is low enough to enable them to remain viable in a world economy that seeks to exploit competitive locational advantage wherever it may be, call for a continual process of improving mobility and productivity of freight transportation systems. Third-party logistics providers increasingly rely on intermodal transport options to optimize cost and meet shipper demand, leveraging the comparative advantages and access characteristics of the various modes. Shipping plans routinely involve moving different types of products using intermodal transportation options in which two or more transportation modes are
Department of Civil and Environmental Engineering, University of Maryland, 3128 Jeong H. Kim Engineering Building, College Park, MD 20742. Corresponding author: H. S. Mahmassani,
[email protected]. Transportation Research Record: Journal of the Transportation Research Board, No. 2032, Transportation Research Board of the National Academies, Washington, D.C., 2007, pp. 9–16. DOI: 10.3141/2032-02
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traffic assignment tools that enable the microassignment of trips in a way that is directly compatible with activity/trip chaining models of individual and household behavior (12, 13). Following a similar modeling philosophy, an evaluation platform based on simulation– assignment for intermodal freight transportation analysis is introduced in this paper. The platform is designed to evaluate terminal delays and consolidation policies at classification yards, intermodal transfer terminals, and ports, as well as at train and ferry service networks. Unlike urban road traffic, freight usually spends considerable time at terminals because of the required processing steps and associated waiting in queues. For example, in the U.S. railway system, 77% of overall delay occurs inside classification yards, according to Reebie Associates (14 ). Therefore understanding and modeling operations at terminals is of fundamental importance for proper representation of freight transportation systems. Numerous studies have focused on this topic. Queuing models in particular are widely applied to the analysis of freight terminals, especially rail classification yards, consolidation (break–bulk) terminals in trucking, and container port terminal operations. Beckmann et al. defined classification policy as a set of rules that completely specifies the manner in which incoming traffic is reconstituted into outbound trains (15). Petersen modeled the classification and train assembly operations as M / G / s queues and the connection delay as an M/Ek /1 bulk queue, where railcars arrive according to a Poisson process and are periodically pulled out and assembled into outbound trains (16, 17 ). In contrast, Turnquist and Daskin proposed a batch arrival queuing model for the classification operation and analyzed the “best” and “worst” case situations with regard to train length and service time distributions (18). All of the above queuing models eventually come to some analytical function with respect to inbound and outbound train flows, which is applicable for an aggregated network or yard operations without depicting the individual characteristics or activity logs of each railcar for each yard. To capture important features of real-world yard operations at a tactical level, the batch (bulk) nature of arrival, service, and departure processes at classification yards needs to be considered. In this regard, Simao and Powell introduced a queuing network model to simulate stochastic, transient networks of bulk queues that occur in consolidation networks, which can be used in less-than-truckload (LTL) railroad, subway, and air networks (19). The unloading queue of inbound vehicles is modeled as a bulk arrival, x individual service queue (ΣGl /M/1) with a first-come-first-served (FCFS) policy; the departure queue for outbound vehicles is modeled as an individual arrival, general dependent bulk service queue (G/GD y /1). Extensive numerical experiments conducted by Simao and Powell confirmed the efficiency and accuracy of the approximation procedure (20). A similar bulk queuing model is applied in this study to represent operations at the classification yards, ports, and intermodal terminals. This paper is structured as follows. First, the problem context, elements, and assumptions are presented in the next section. Second, the simulation–assignment solution framework for multiple product multimodal freight assignment problems is proposed. Third, the structure of the freight traffic simulator is elaborated with respect to the bulk queuing model for terminal transfers. Finally, discussion on applications of the model and future research is given.
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
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horizon) is discretized into a set of small time intervals, T = {t0, t0 + σ, t0 + 2σ, . . . , t0 + Hσ}, where t0 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 t0 to t0 + Hσ cover the planning horizon T. Each node v ∈V is associated with either an intersection in the road (or vehicular) subnetwork or a terminal in a rail or marine subnetworks. A terminal could be a classification yard, port, station, or 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: 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 notations and variables are used in this paper: • O = set of origin zones; • D = set of destination zones; • P = set of product types; • M = set of modes; • o = origin zone index, o ∈O; • d = destination zone index, d ∈D; • p = product type index, p ∈P; • m = travel mode index, m ∈M; • τ = departure time interval index, τ ∈T; • K mo,d,τ,p = set of feasible paths for product p departing from origin o to destination d during time interval τ and using mode m; • k = path index, k ∈ Kmo,d,τ,p; • ro,d,τ,p = number of shipments of product p from origin o to destination d during the departure time interval τ; • r m,k o,d,τ,p = number of shipments of product p from origin o to destination d departing during time interval τ using mode m and route k; m,k • [r o,d,τ,p ]n = mode–path flow solution at iteration n; m,k • [y o,d,τ,p]n = auxiliary mode–path flow solution at iteration n; • 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(s,i) = systematic utility of joint mode and route alternative i to individual shipment s; • ASCi = alternative specific attributes for alternative i; • Xs = attributes of individual shipment s; • Xi = attributes of mode–route alternative I; and • αs, αi = coefficients of utility function. 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 ro,d,τ,p over the planning horizon are assumed to be known a priori. A feasible mode m is defined as a sequence of conveyances (a least one) with the use of two consecutive conveyances being allowed 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 of 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
Mahmassani, Zhang, Dong, Lu, Arcot, and Miller-Hooks
joint mode and route choice set, a shipper will choose an (intermodal) path k that 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.
SIMULATION–ASSIGNMENT FRAMEWORK To solve the dynamic freight assignment problem in intermodal transportation networks, this paper seeks 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: (a) freight traffic simulation (or supply), (b) shippers’ behavior model, and (c) 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.
Simulation–Assignment Solution Framework Details of several components are provided after the framework description. Figure 1 presents a heuristic iterative procedure for solving the intermodal dynamic freight assignment problem with joint mode and route choice. The main steps of the solution algorithm are as follows.
OD shipment demand and historical paths
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Step 0. Initialization Let iteration number n = 1. On the basis of 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–destination (O-D) pair o-d, for each departure time interval τ, and for each product type p, this procedure results in a set of mode–path flow solutions: ∀ m ∈ M, k ∈ K mo,d,τ,p
m,k [ro,d,τ,p ]n
Step 1. Freight Network Simulation Perform freight network simulation for the mode–path flow solution ∀ m ∈ M, k ∈ K mo,d,τ,p
m,k ]n [r 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 modetransfer delays obtained by the multimodal freight network simulator or determined by train and ferry timetable, a time-dependent multiple product intermodal least-cost path algorithm finds the leastcost paths for each O-D 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 the multinomial logit choice model. Doing so generates a set of auxiliary mode–path flow solutions: ∀ m ∈ M, k ∈ K mo,d,τ,p
m,k [y o,d,τ,p ]n
Multimodal Freight Network Simulator
Step 4. Update of Mode and Path Assignment Time-dependent intermodal least-cost paths for multiple products
n=n+1
Mode-path choice and network flow assignment
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: ⎡⎣rom,d,k,τ , p ⎤⎦
n +1
n
= ⎡⎣rom,d,k,τ , p ⎤⎦ +
1 n
i
{⎡⎣ y
m ,k o ,d , τ , p
n
⎤⎦ − ⎡⎣rom,d,k,τ , p ⎤⎦
n
}
(1)
Step 5. Convergence Criterion Check the number of cases N(δ) for which
No
Convergence checking
Yes Stop
FIGURE 1
Simulation–assignment solution framework.
⎡⎣rom,d,k,τ , p ⎤⎦
n +1
n
− ⎡⎣rom,d,k,τ , p ⎤⎦ ≤ δ
If N(δ) < Ω, convergence is achieved, where δ and Ω are prespecified parameters. If convergence is attained, stop. Otherwise, set n = n + 1 and go to Step 1.
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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 terminals, classification yards, sidings, ports, borders, and so forth), and links, such as road links, rail links, and marine links. The service network 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; it 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 or 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 as 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., 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 (21). For each product and each mode, this algorithm calculates the time-dependent intermodal least-cost path tree. Although 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.
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.
MULTIMODAL FREIGHT NETWORK SIMULATOR The problem addressed by the freight network simulation platform (the multimodal freight network simulator) can be stated as follows: given a multimodal network with known service supply attributes and time-dependent O-D demands for multiple commodity classes for the network of interest for each mode, the network simulation model determines the resulting flow of shipments on the road, rail, and sea network for the various time intervals of interest, and the associated service levels and network performance experienced by the shipments. Freight Simulator The simulation platform is shown in Figure 2. The network simulator consists of two main components: link moving and node/mode transfer, which process, respectively, flow propagation along links and through nodes/transfer points. A third component, demand generation and loading, prepares the shipments to be loaded and actually
Inputs: OD flow; Path split; Mode share.
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 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 (10, 11, 22). Current trends in modern manufacturing and logistics, especially in high-value-added industries, favor a more flexible and dynamic approach oriented toward shorter horizons than are 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 being equal to a 20-ft. equivalent unit (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 ) = ASCi + α s X s + α i Xi
Demand loading: Shipments generation; Shipments consolidation; Conveyances loading.
Link moving: Trucks moving; Shuttle trains moving; Trains moving; Ferries moving. t=t+1 Node/mode transfer: Truck transfers at road intersections; Train transfers at intermediate stations; Mode transfers at intermodal transfer terminals, classification yards, and ports.
No Have all shipments reached their respective destinations? Or Is simulation time at end of planning horizon?
Yes
(2)
Stop
Dynamic network loading of shipment demand is based on the choice outcome of the logit model. Note that although the detailed
FIGURE 2
Multimodal freight network simulator.
Mahmassani, Zhang, Dong, Lu, Arcot, and Miller-Hooks
loads them onto the network. The three components are described in the following subsections.
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Node Transfer
Terminal Processes Demand Generation, Consolidation, and Loading Demand is generated during each demand generation interval in economic regions, represented in the network model as nodes corresponding to centroids of their respective economic regions. Shipments are loaded onto links specified as “generation links.” The inputs to the simulator are time-dependent multiple-product O-D shipment flows with corresponding mode shares and path splits that can be obtained from the intermodal shortest paths stored after the load-up period, or from any paths externally specified in the data or freight assignment component. At the time of generation, each shipment is assigned a product type: either container unit or bulk unit, based on the specified fraction of each product type. Due to the capacity of different conveyances, the number of shipments whose product type is nonbulk unit in different conveyances is different. This gives rise to a consolidation policy that is used to load several shipments in one conveyance (with the number of shipments being subject to the capacity of that conveyance) at generation links, intermodal transfer terminals, and ports, where shipments could be loaded in conveyances. The consolidation policy for nonbulk units requires that • All shipments be of the same product type; • All shipments have the same next (intermediate or final) destination, which can be an intermodal transfer terminal, port, or destination zone centroid; • All shipments have the same mode between the current position and the next destination; • All shipments have the same path node sequence between the current position and the next destination; and • The probability distribution of the number of shipments in one conveyance is based on the product type and location. After consolidation, conveyances are generated, and their paths are based on those of the shipments they carry. Then conveyances are loaded into the network based on the actual departure time of the loaded shipments. Note that it is possible to load with exogenously determined characteristics directly, instead of generating them based on the given fractions. However, the latter approach corresponds to input likely to be available in a given application. Link Moving During this procedure, the conveyances on the links are moved according to the speeds of the respective modes. Trucks are moved on the links according to the prevailing speeds. Shuttle trains are moved according to a preset constant speed. Trains and ferries are moved along their respective links according to the given timetables. Delays incurred by shipments on rail links caused by meets and overtakes are assumed to be reflected in the given train timetables. This assumption is reasonable for international intermodal freight transportation, where the majority of delays occur at the terminals rather than on the links. For example, in 1996, on average, only 14% of the time taken for a shipment to go from its shipper to its consignee was spent on a moving train; the remainder was spent at classification yards (23).
Node (or terminal) processes such as sorting in classification yards and loading and unloading in intermodal terminals and ports contribute a significant portion of total delays, as discussed earlier. In the present platform, these processes are simulated to estimate the delays that are eventually used in the intermodal shortest path calculations. Classification yards are used to sort and group railcars and to dismantle and assemble trains. Trains arriving at yards are inspected by yard crew and are then queued on the receiving tracks until they are classified or sorted onto the marshaling or classification track where similarly bound railcars are combined. The classification operation is performed by pushing a train over the hump in a hump yard or by the switching engines in a flat yard. After classification, the sorted railcars (blocks) wait for dispatch on an appropriate outbound train. The schedule of the outbound train determines the start of the assembly operation for the blocks assigned to that train. After the cutoff time for a departing train occurs, the outbound train is assembled or marshaled on the departure track. Trains then depart to the next yard or to the nearest intermodal terminal or port if shipments are to be transferred to other modes. Transfers of shipments among rail, road, and sea modes are carried out at ports and intermodal terminals. Ports have access to different transport modes: deep sea vessels, barges, trains, and trucks. Transshipment processes (loading and unloading) at a port, well elaborated in Vis and de Koster, generally consist of a three-piece operation: ship to quay with gantry crane; quay to stack with MAFI trailer and reach-stacker; and stack to rail wagon or truck with reachstacker (24). Direct transfer of shipments is possible if an appropriate outbound vehicle is available during the unloading time, in which case shipments need not be stacked in storage areas. Intermodal terminals transfer containers and trailers between trains and trucks. These terminals have no direct link to the water mode. Facilities and operations of intermodal terminals are similar to those of ports. Shipments are unloaded from trains onto ramps and then are stacked or transferred directly if a designated truck is available. Shipments that are transferred from trucks to railcars are transported to the nearest classification yard by a local shuttle train.
Bulk Queuing Model As discussed above, real-world operations at all kinds of terminals are complicated and differ from one terminal to another. To capture the main characteristics of each terminal while maintaining generality that is applicable to all terminals, a bulk queuing model is developed to represent terminal transfer processes and evaluate terminal delay. Each terminal is associated with a queuing server with known service (time) distributions. A generalized bulk queuing model is used to model terminal transfer processes as shown in Figure 3. This model is similar to the one presented by Simao and Powell (19, 20). There are two kinds of queuing elements in this study: railcars for classification yards, and shipments for intermodal terminal and ports. The bulk queuing model consists of two kinds of queues in a queuing network: arrival queues and departure queues. Arrival Queue ( l G x / G x / 1)
Because trains, ferries, and trucks carry several shipments as they arrive at the terminals, the arrival of elements at the terminals is assumed to follow a bulk-arrival process
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Bulk departure
Bulk arrival Bulk arrival 1 ... ...
Arrival queue
... ...
Bulk departure
Departure queue n
Bulk departure
Generalized bulk queuing model.
(Gx). Elements queue on the inbound links and are assumed to be served by a single superserver. Type of service, service time, and cost for the elements depends on the terminal type. For classification yards, the bulk service process (G x ) is assumed as railcars belonging to a train are processed one at a time. Service times at classification yards reflect the time required for inspection, classification, and assembly of the railcars into trains, as shown in Figure 4. The bulk service process is sensitive to the facilities available at the yards, including the number of switch engines and the number of tracks. Service times can also vary, with product type reflecting the operating conditions. For ports and intermodal terminals, shipments are assumed to be served individually. The service times reflect unloading, loading, and transport time within the terminal, as shown in Figure 5. The service times are sensitive to the facilities that are available in the terminals (e.g., the number of cranes and the loading and unloading rates for ferries, trains, and trucks). Elements (railcars or shipments) in the arrival queue are processed to estimate the earliest possible departure time (EPDT) for each element. ⎧ ATi + Wi + ∑ Si ⎪ x EPDTi = ⎨ ⎪⎩ ATi + Wi + Si
Bulk departure
Server
Bulk arrival m
FIGURE 3
Departure queue 1
for classification yards (3)
Departure Queue (G x/GD y/1) At the scheduled departure time of trains, ferries, or trucks, processed elements on inbound queues are assigned to corresponding outbound queues and sorted based on destination, EPDT, and priority of the elements, respectively, to generate a departure queue for the particular outbound link. The capacity of the outbound vehicle determines the number of elements that depart (bulk departure, GD y) from the departure queue at the scheduled time. The model also considers delays experienced by elements waiting for scheduled connections at classification yards or storage areas in terminals, referred to as “scheduled delay.” The scheduled delay of an element i is calculated as follows:
SDi = ADTi − EPDTi
(4)
where SDi = scheduled delay for element i; ADTi = actual departure time for element i based on bulk departure time (e.g., timetable); G x = general bulk arrival process; GD y = general dependent service process based on bulk departure time (e.g., timetable); x = arrival bulk size; and y = departure bulk size.
for terminals and ports CONCLUDING REMARKS
where = = = =
element; bulk size; EPDT for element i (same for all elements in same bulk); arrival time for element i (same for all elements in same bulk); Wi = waiting time for element i (same for all elements in a same bulk) in arrival queue; and Si = service time for element i (stochastic) on process.
i x EPDTi ATi
Receiving yard
Classification yard
Inbound inspection
Classification & assembly operation
Trains from other yards
Trains queue for service
Shuttle trains from terminals
FIGURE 4
A dynamic network simulation–assignment framework was presented in this paper to address the multiple product multimodal freight assignment problem in multimodal freight transportation networks. The framework consists of three components: a multimodal freight network simulation component, a multimodal freight assignment component, and a multiple product intermodal shortest path procedure. The multimodal freight network simulation component uses a bulk queuing model to simulate transfer delay experienced by each
Processes at a classification yard.
Departure yard Scheduled delay
Outbound inspection Trains to other yards
Shuttle trains to terminals
Mahmassani, Zhang, Dong, Lu, Arcot, and Miller-Hooks
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Unloading time
Scheduled delay
Truck unloading
Storage Area
Loading time
Truck loading
Indirect transfer Transport time within terminal
Direct Transfer Train unloading
Train loading Ferry unloading
FIGURE 5
Ferry loading
Processes at a port.
shipment and the operations at the intermodal transfer terminal, classification yard, and port. The multimodal freight assignment component determines the network flow pattern from a mode–path alternative set calculated by the multiple product intermodal shortest path procedure based on the link travel cost and node transfer delay from the multimodal freight network simulation component. Compared with existing models in the literature, this model can represent individual shipment mode–path choice behavior, consolidation policy, con-
FIGURE 6
Reorient network.
veyance link moving, and individual shipment terminal transfer in an iterative solution framework. This model is being applied to an ongoing European community coordinated action project (Reorient) as a network modeling tool used to support planning and policy evaluations and market analysis for international intermodal freight transport in a trans-European corridor linking the Nordic region and southeastern Europe (25). The Reorient network is shown in Figure 6. To capture the interactions
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between shippers and carriers in real-world freight transportation more realistically, this model can also be integrated with external (collaborative or noncollaborative decision making) carrier models that determine optimal service networks (e.g., train routes, timetables, and fare structures) instead of using an internally generated mode–path choice set. REFERENCES 1. Harker, P. T., and T. L. Friesz. Prediction of Intercity Flows, I: Theory. Transportation Research 20B, Vol. 2, 1986, pp. 139–153. 2. Harker, P. T., and T. L. Friesz. Prediction of Intercity Flows, II: Mathematical Formulation. Transportation Research 20B, Vol. 2, 1986, pp. 155–174. 3. Friesz, T. L., J. A. Gottfried, and E. K. Morlok. A Sequential Shipper– Carrier Network Model for Prediction Freight Flows. Transportation Science, Vol. 20, No. 2, 1986, pp. 80–91. 4. Fernández, J. E, J. De Cea, and R. Giesen. A Strategic Model of Freight Operations for Rail Transportation Systems. Transportation Planning and Technology, Vol. 27, No. 4, 2004, pp. 231–260. 5. Agrawal, B. B., and A. Ziliaskopoulos. Shipper–Carrier Dynamic Freight Assignment Model Using a Variational Inequality Approach. In Transportation Research Record: Journal of the Transportation Research Board, No. 1966, Transportation Research Board of the National Academies, Washington, D.C., 2006, pp. 60–70. 6. Crainic, T. G., J. A. Ferland, and J. M. Rousseau. A Tactical Planning Model for Rail Freight Transportation. Transportation Science, Vol. 18, 1984, pp. 165–184. 7. Guelat, M., M. Florian, and T. G. Crainic. A Multimode Multiproduct Network Assignment Model for Strategic Planning of Freight Flows. Transportation Science, Vol. 24, 1990, pp. 25–39. 8. Holguín-Veras, J. A Framework for an Integrative Freight Market Simulation. Proc., IEEE 3rd Annual Intelligent Transportation Systems Conference ITSC-2000, Dearborn, Mich., 2000, pp. 476–481. 9. Holguín-Veras, J. Revealed Preference Analysis of the Commercial Vehicle Choice Process. Journal of Transportation Engineering, American Society of Civil Engineers, Vol. 128, No. 4, 2002, pp. 336–346. 10. Chiang, Y., P. O. Roberts, and M. Ben-Akiva. Development of a PolicySensitive Model for Forecasting Freight Demand. Center for Transportation Studies, Massachusetts Institute of Technology, Cambridge, 1980. 11. Mahmassani, H. S. Freight and Commercial Vehicle Applications Workshop Report. In Travel Behavior Research: The Leading Edge (D. A. Henscher, ed.), Pergamon, London, 2001.
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