Text Box: The contents of this report reflect the views of the author, who is responsible for the facts and accuracy of the information presented herein. This document is disseminated under the sponsorship of the Department of Transportation, University Transportation Centers Program, in the interest of information exchange. The U.S. Government assumes no liability for the contents or use thereof.

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



 

 


Final Report

 

 

WebShipCost 每 Quantifying Risk

 

in Intermodal Transportation

 

 

 

Project: MBTC 2035

 

 

 

Submitted to:

 

The Mack-Blackwell Transportation Center

 

 

Date: 08/31/2004

 

 

Contact:

 

Heather Nachtmann, Ph.D.

Assistant Professor

Department of Industrial Engineering

University of Arkansas

4207 Bell Engineering Center

Fayetteville, AR 72701

Phone: (479) 575 - 5857

Fax:   (479) 575 - 8431

Email: hln@uark.edu

Manuel D. Rossetti, Ph.D., P.E.

Associate Professor

Department of Industrial Engineering

University of Arkansas

4207 Bell Engineering Center

Fayetteville, AR 72701

Phone: (479) 575 - 6756

Fax:   (479) 575 - 8431

Email: rossetti@uark.edu

G. Don Taylor, Ph.D.

Professor

Department of Industrial Engineering

University of Louisville

Louisville, KY 40292

Phone: (502) 852-2741

Fax:   (502) 852-5633

Email: don.taylor@louisville.edu

 

 

 

Zhe Li, M.S.

Research Assistant

Department of Industrial Engineering

University of Arkansas

Email: zxl01@uark.edu

 

 


 

1     Problem Statement 3

2     Literature Review.. 6

2.1     Introduction. 6

2.2     Intermodal Railroad 每 Truck Transportation. 9

2.3     Waterway Transportation. 11

2.4     Intermodal Transportation Decision Making. 14

3     Methodology. 16

3.1     Decision Analysis Process Model 16

3.1.1     Uncertain Events. 17

3.1.2     Influence Diagram.. 18

3.2     Problem Formulation. 20

3.2.1     Cost Objective. 21

3.2.2     Time Objective. 23

3.3     Analytic Hierarchy Process. 25

3.3.1     Decision hierarchy construction. 25

3.3.2     Attribute Priority Determination. 26

3.3.3     Alternative Weight determination. 27

3.3.4     Consistency computation. 28

3.3.5     Overall weighted performance determination. 29

3.3.6     Overall Approach. 29

3.4     Data Assumption and Optimal Path Set Evaluation. 30

3.4.1     Data Assumption. 30

3.4.2     Optimal Path Set Evaluation. 31

4     Sensitivity Analysis. 39

4.1     Experiment Design. 39

4.2     Result Analysis. 41

5     WebShipCost 每 Risk Application. 50

5.1     Use Case Models. 50

5.2     Application Design. 51

6     Summary. 53

7     Appendices. 55

7.1     Transportation Network. 55

7.2     Distance Matrix (Units: mile) 56

7.3     Complete Use Case Models. 57

7.3.1     System Level: 57

7.3.2     Subsystem level: 60

7.3.3     Use Case Scenarios for Selected Use Cases: 65

7.4     Application Design. 72

7.4.1     Package wscrisk.graph. 72

7.4.2     Package wscrisk.algorithm.. 74

7.4.3     Package wscrisk.analysis. 76

8     References. 79

1        Problem Statement

This section presents the motivation and description of this project and gives an overview of previously-conducted projects that have laid the groundwork for this research.

 

This project addresses the problem of Arkansas and other states* underutilized waterway transportation networks.  Part of the underutilization of waterway transportation in the U.S. stems from a lack of understanding by shippers of the cost and time trade-offs associated with utilizing waterway transportation as part of an intermodal delivery system.  In particular, users of waterway transportation are faced with uncertain transport times and additional risk associated with meeting intermodal connections.  There exists the need for easy to use and widely available models that can illustrate the advantages and disadvantages of barge transportation within the context of an intermodal transportation network.

 

Prior MBTC research projects (MBTC FR 1036, MBTC FR 1079, MBTC FR 1100-1, and MBTC FR 2024) contributed to the development of WebShipCost, a WWW-based implementation of cost models that describes the costs incurred by all activities (rail, truck, and barge) within an intermodal transportation network.  WebShipCost allows online determination of the ranked shortest paths in terms of cost or time from an origin point to a destination point within the network and enables shippers to understand the trade-offs associated with barge and container-on-barge transportation.  The information below summarizes the cost elements used in WebShipCost.  This analysis is based on data from research at University of Arkansas (Trusty & Malstrom, 1998) and the ShipCost user*s manual (Boardman & Malstrom, 1998).  The information is also derived from a detailed analysis performed for the Defense Logistics Agency (Rossetti et al., 2000).

 

WebShipCost performs its analysis based on a formulation of the total transportation cost and time.  Four cost elements considered in the model are travel cost, transfer cost, dray charges, and inventory carrying costTravel cost is the cost to transport goods by the selected travel mode.  The cost of transferring goods from one mode of travel at the load/unload site to another travel mode is the transfer cost.  Transfer cost includes the cost of labor and equipment at any intermediate points where there is a change in travel mode.  Dray charges are incurred for moving goods to/from a stationary site, such as a warehouse or factory, from/to the loading site for transport.  The fourth element of transportation cost is the in-transit inventory carrying cost.  Inventory carrying cost is a function of the value of the units being shipped and of the total transit time of a shipment.  Typical carrying costs include storage space, insurance, taxes, loss due to spoilage or obsolescence, opportunity cost, etc.

 

Time elements formulated in the model include travel time, transfer time and dray time.  The time of moving goods from loading site to unloading site by selected travel mode is defined as travel time.  Travel time is computed from distance defined in barge, rail, or truck miles divided by the mode average speed.  Transfer time and dray time are defined in a similar way as in the cost scenario.  The time of transferring goods from one mode of travel at the load/unload site to another travel mode is the transfer timeDray time is incurred for moving goods to/from a stationary site from/to the loading site for transport.  Data for transfer time and dray time are from a variety of data sources (Rossetti & Nachtmann, 2003).

 

WebShipCost currently consists of a database, the double-sweep algorithm for solving the K shortest paths problem, and a WWW based user interface.  After the origin, destination, shipment information, and single objective (minimize total cost or total time of the shipment) have been specified by the user, the system creates the network structure, performs the algorithm to derive the resulting paths, and displays the path alternatives in ascending order of cost or time.  Then, the user can evaluate the alternatives considering the associated shipment*s requirements, such as service level or reliability, and choose the best-suited path.  The user is allowed to define other networks to be analyzed by WebShipCost.

 

Currently, WebShipCost assumes that the cost and time elements stored in the database are precisely defined, while in reality the true values of these future costs and times are never certain.  Exploring the effects of this uncertainty on the WebShipCost output is important.  While cost rates might be regarded as stable within a certain short time span, exploring the cost variability can provide an insightful view of cost elements* effect on the mode choice.  A thorough sensitivity analysis will determine how fluctuations in the input data affect selections of the preferable shipping routes.  Often shippers choose shipping options based on the perceived reliability of the service.  The enhancements to WebShipCost will allow for the incorporation of risks associated with intermodal transport.  This enhanced risk and sensitivity analysis will help to better educate shippers in and around the State of Arkansas about the advantages of barge transportation and how these advantages might be put to use for their company.

 

Another limitation is that WebShipCost optimizes a single objective, either minimize time or minimize cost.  A multi-objective optimization approach that incorporates multiple objectives is needed along with methods for improved sensitivity analysis.

 

Due to the current limitations of WebShipCost, this project seeks to enhance it and other prior MTBC research on intermodal transportation by providing a user-friendly, web-based application with the ability to handle uncertain input data, which will allow shippers to analyze risk.  At the same time, it evaluates multiple objectives (minimize cost, minimize time, and maximize reliability) from shipper*s perspective simultaneously and guides them to make trade-offs among these frequently contradicting objectives.  Finally it performs a thorough sensitivity analysis by exploring the variation of input variables and its influence on the intermodal transportation route decision results, especially on the barge modal choice.

 

The outline of this report is as follows:  A literature review on intermodal transportation, decision making models and related topics is presented in Section 2.  Section 3 discusses the solution methodology including problem structure modeling, uncertain elements identification, problem formulation, multi-objective model construction and supporting uncertainty data assumptions.  In Section 4 a thorough sensitivity analysis is performed, and statistical analysis shows the influence of the input factors on the optimal routing decisions.  Section 5 presents some design and implementation issues of the WebShipCost每Risk application and demonstrates the user experience.  Section 6 summarizes with conclusions and potential further research areas.

 

2        Literature Review

 

2.1  Introduction

There are five basic modes of transportation: water, air, highway, rail, and pipeline.  While this research focuses on three of these modes (water, highway, and rail) as these are the primary modes used in the State of Arkansas and surrounding areas, a discussion of all modes is important.  The combination of all possible modal arrangements produces many feasible methods for moving goods (Jennings & Holocomb, 1996).  Each option has its unique advantages and disadvantages for freight movement.  In recent years, there have been developments in transportation methods and linking them with various other modes.  Intermodal transportation can be defined as the movement of goods or services by the coordinated and sequential use of two or more modes of transportation.  Listed below are some examples of vehicles influenced by the medium in which they operate, and thereby constituting modes are listed below (Mahoney, 1985).

 

Ÿ         Water: ocean vessels, coastal vessels, and inland waterway barges;

Ÿ         Air: airplanes;

Ÿ         Land: rail freight trains, highway trucks, and pipelines.

 

The basic elements of the intermodal freight system are shown in Table 2‑1.

 

Table 2‑1  Elements of Intermodal Freight System

(Erickson, Grenzeback, & Schrieber, 1999)

 

Air

Rail

Water

Road

Carriers

Air Cargo Carriers

Railroads

Shipping Lines

Motor Carriers

Conveyance

Airplanes

Trains

Ships and Barges

Trucks

Terminal

Airports

Rail Terminals

Ports

Truck Terminals

Infrastructure

Airways

Railways

Sea and Inland Waterways

Roadways

 

 

There are single mode transfers as well as intermodal transfers of freight between vehicles.  A list of characteristics describing a single mode transfer is given below:

 

         Single mode transfers are typically easier to accomplish than intermodal transfers;

         The vehicles are alike and operating in the same medium;

         Single mode transfers are typically easier to manage than intermodal transfers;

 

Although there are advantages of single modal transportation of goods, intermodal transportation can provide an efficient means of transportation.  In recent times, intermodality has proved to be an invaluable tool for the shipment of goods.  It offers a greater flexibility of routings and costs can be lowered by a precise combination of carriers and vehicles and standardization (Harps, 1995; Mickle & Burns, 1978).

 

It has been observed that nearly forty major commodities are involved in intermodal transportation.  The listing consists of dry and liquid materials.  The viability of transferring strongly depends on the characteristics of the commodities being transported.  First among the characteristics of transferring commodities is that they all move in large volumes, or are large in physical size in their transported state.  An inherent advantage of barge, rail, or pipeline is carrying capacity; hence it is expected that transfer activities involving these modes would seek to utilize this aspect (Jennings & Holocomb, 1996).

 

The product handling ability is another issue that may determine a preferred commodity characteristic for transfer practices.  Most of the commodities listed are industrial or commercial in nature and thus are to be transported in large volumes and/or sizes.  The products are items used by industry as either raw materials or components for production of other commodities for the consumer or commercial market.  These commodities are listed in Table 2‑2 (Jennings & Holocomb, 1996).

 

Table 2‑2  Commodities Involved in Intermodal Transportation

Dry Flowables

Liquid Flowables

Non-Flowables

Alumina Ore

Asphalt

Aluminum Bars

Ammonium Nitrate

Caustic Soda

Aluminum Ingots

Cements

Chemicals (Misc.)

Bagged Barite

Coal and Coke

Diesel Fuel

Brick

Fertilizers

Gasoline

Coiled Steel

Flour

Methylene Chloride

Lumber

Grain

Motor Oils

Machinery

Grain Products

Processing Oils

Newsprint

Gypsum

 

Pipe

Iron Sulphite

 

Scrap Metal

Plastic Pellets

 

Steel Parts

Polypropylene Powders

 

Steel Wire

Rock

 

Structured Steel

Roofing Granules

 

 

Salt

 

 

Sand

 

 

Zinc Ore

 

 

 

 

The recent growth in intermodal trade has increased public and private interest in the development of intermodal transportation and logistics facilities designed to handle new traffic.  River and canal based cities formed the back bone of the industrial revolution in North America during the eighties.  Advances in multimodal transportation spurred by growing international markets, global outsourcing of materials and production, formation of regional trading blocks, the increasing importance of time-based competition, and rising fuel costs are fostering new potential areas of economic power.  Facilities that integrate large volume air shipments with rail and motor transportation, as well as advanced telecommunications and information systems, production/assembly capabilities, and distribution, are supporting the development of new economic power bases and trade patterns (Stank & Roath, 1998).

 

Future intermodal growth, however, is not fully assured.  There have been a number of improvements in transportation and information technology that have helped to increase the efficiency of intermodalism.  But market pressures and the demand for increased services suggest the need for even greater investment in infrastructure development.  Some constraints to intermodal development are found within the carrier industry.  Due to resource shortages, carriers have had to develop partnerships to meet minimum customer expectations and maintain a competitive edge in intermodal service offerings.  While customers have been relatively satisfied with joint service offerings, the involvement of multiple partners with different goals and objectives has created organizational difficulties (Stank & Roath, 1998).

 

2.2  Intermodal Railroad 每 Truck Transportation

Intermodal railroad-truck (IRT) service is where one or more motor carriers provide the short-haul pick up and delivery service part of the trip and one or more railroads provide the long haul part.  The primary equipment involved is truck trailers/containers as intermodal units, which are carried on railroad cars.  IRT is used for both domestic and international movements (Harper & Evers, 1993).

 

IRT combines the door-to-door convenience of trucks with the high volume, long haul, and economics of railroads.  As compared to alternative services, transit time and rates may be lower, thus serving as a potential advantage for the shipper.  In addition, as IRT represents competition to other modes, it can have the effect of improving service and lowering rates offered by other modes (Harper & Evers, 1993).  In the late 20th century, the number of intermodal units loaded by U.S. railroad increased from 3.0 million units to 6.2 million units, showing growth of 106%.  Accordingly, IRT has become a major source of revenue for railroads; however, despite the rapid growth during the 1980s, IRT still accounts for only 6% of total intercity freight traffic (Harper & Evers, 1993).  For IRT to be a viable alternative, it must be available to shippers and receivers, the quality and cost of the IRT service must be competitive with other modes, and IRT must be accepted and utilized by the shippers (Harper & Evers, 1993).

 

One of the primary disadvantages of IRT is high door-to-door transit time, which can be caused by several factors.  There can be difficulty of making connections between modes in a reasonable amount of time.  Poor train scheduling and excess need to assemble and disassemble trains also adversely affect transit time.  In addition to the mentioned disadvantages, the two mode system often requires that a shipment move not directly from door-to-door, but instead indirectly through railroad terminals at each end.  Furthermore, railroad service sometimes involves more circuitous routing when compared with the Interstate Highway system.  Finally, when more than one railroad is involved, a shipment must be interchanged with another railroad, which is often a time consuming process (Harper & Evers, 1993).

 

Freight damage is another concern about IRT service.  Because of the excessive handling involved in transferring modes, the cars switching impact, and the slack action in train operation, IRT service has had a poor damage record, though it has been reduced considerably in recent times.  Another associated problem is the liability for loss and damage assumed by the carriers.  IRT movements usually involve more than one carrier; hence determining who is liable for the damaged freight can be problem since it depends upon where the loss or damage occurred (Harper & Evers, 1993).

 

While IRT can be a service disadvantage, price often becomes the main selling point in anticipation that the customer will consider it to be more important than service.  The growth forecast for intermodal transportation created new challenges and opportunities for the railroad industry.  Railroads and third-party partners have targeted highway truckload business for future sales gains (Johnston & Marshall, 1993).

 

2.3  Waterway Transportation

Inland water carriers are generally used for long haul bulk movements because their routes are fixed geographically, and their business is mostly bulk commodity (Mahoney, 1985).  In recent past, there have been developments in waterway transportation in the U.S.  The prominent changes occurred in the linking of other modes of transportation to waterway transportation systems (Trusty & Malstrom, 1998).

 

Maritime (water) transport, similar to land and air modes, operates on its own space, which can be at the same time

         Geographical by its physical attributes;

         Strategic by its control;

         Commercial by its usage.

 

There are two major elements of maritime transportation, rivers and oceans.  Although they are connected, each represents a specific domain of maritime circulation.  Maritime traffic has evolved considerably over the last decades especially through growth in transpacific trade.  By establishing commercial linkages between continents, maritime transport supports a considerable traffic that covers 90% of the intercontinental transport demand of freight.  The strength of maritime transport depends upon the capacity and on the continuity of its traffic and not on its speed.  Railway and road transportation are not able to support traffic at such a geographical scale and intensity.  Heavy industrial activities that use bulk raw materials are generally adjacent to port sites, to get the benefits from load breaks.  The average haul length is about 4,200 miles.

 

In the U.S., waterways provide the most economical and environmentally sound mode of moving goods and commodities.  Inland waterways carry approximately 15% of total freight transported in the U.S.  The annual value of goods exchanged between 24 states linked with waterways exceeds $100 billion (Nachtmann, 2002).  The map of the U.S. waterways is shown in Figure 2‑1 and the freight shipments by mode is shown in Table 2‑3 (U.S. Department of Transportation, Federal Highway Administration Online Public Data, 2002).

 

Figure 2‑1       U.S. Inland Waterways

(Navigation Information Connection, http://www.mvr.usace.army.mil/navdata)

 

Table 2‑3  U.S. Freight Shipments by Mode (U.S. Department of Transportation, Federal Highway Administration Online Public Data, 2002)

Mode

Value

Tons

Billions $

%

Millions

%

Truck

7429

83

10859

71

Rail

646

7

2311

15

Water

163

2

1219

8

Air

1083

8

18

0.1

Pipelines & Other

N/A

N/A

864

5.7

Total

9320

100

15271

100

 

The strength of a transportation system lies in its diversity, with each mode having its own specific advantages.  The motor carriers have the ability to provide door to door service, water carriers can handle bulk commodities safely at a very low cost; and rail companies can transport a broad range of commodities over long distances.  Efficient freight transportation systems can play a positive role both in the economic life of industrialized countries and the day-to-day lives of their citizens.  Even though, these transportation systems are essential to a modern society, and there are substantial economic benefits to be realized, there can be also significant negative environmental impacts including preemption of land, disruption of topography, consumption of energy and other resources, and both noise and air pollution.  Waterborne transportation proves a much better option compared with others since it requires significantly less fuel than rail or truck and air pollution resulting from water transportation is almost negligible (U.S. Department of Transportation, Maritime Administration Public Report, 1994).  The cost per ton mile for a barge is only 0.73 cents, compared to 2.28 cents for rail, and 9.15 cents for trucking as shown in the chart Figure 2‑2 (Wilson, 2000).  Additional benefits are listed next (U.S. Department of Transportation, Maritime Administration Public Report, 1994):

 

         An improved natural environment for wildlife, parks and recreational areas,

         Generation of clean and renewable hydroelectric power,

         Reduced soil erosion, and

         Flood reduction.

Because of these advantages, the intermodal traffic across the waterways is increasing.

 

Figure 2‑2       Shipment Cost by Modes

 

2.4  Intermodal Transportation Decision Making

For the last 30 years, research involving modeling the freight transportation choice has been steadily in progress.  There is a substantial literature dealing with such decision problems.  D'Este (1992a) categorized the various freight transportation choice modeling approaches into three broad categories, i.e. input-oriented models, output-oriented models, and process oriented models.

 

Input-oriented models attempt to explain the behaviors of decision makers by investigating various factors that influence freight transportation choice.  Basic statistical techniques are widely used to analyze the factor importance and build relational models (Mentzer & Kahn, 1995).  An example is D'Este (1992b) who identified the relative importance of the various choice factors and their interactions in carrier selection through a survey of companies purchasing shipping services across the Bass Strait.  Drawbacks of input oriented models are that they do not provide insight into the actual decision making process.

 

Output-oriented models are concerned with predicting the outcome of a particular decision situation.  They tend to be predictive rather than explanatory models according to D'Este (1992a).  For example, Rossetti & Nachtmann (2003) formulated the intermodal transportation routing problem as a K-shortest path network model with time and cost values on each arc.  Decision trees, conjoint analysis, and the Analytic Hierarchy Process (Saaty, 1980) have also been used to formulate and solve the problem (Mangan, Lalwani, & Gardner, 2001).  Output-oriented models focus on the mathematical formulation aspect of the problem rather than the interactive behavior of the decision system.  Therefore, like input-oriented models, they do not provide understanding of the actual decision making process.

 

Unlike the previous two models, process oriented models focus on identifying the interactive relations among pertinent decision factors.  D*Este (1992c) constructed a framework to represent the stages of the decision process and the interaction of factors that influence the shipping managers in the context of RO/RO ferry trade.  This model was built based on a survey of the shippers.  Clemen & Reilly (2001) present influence diagrams to structure and illustrate the decision making process.  Many outcome oriented techniques, such as decision trees, shortest path, AHP, etc., could also be applied to such structural models, assuming the requisite data were available to yield a quantitative solution (Mangan, Lalwani, & Gardner, 2001).

 

 

3        Methodology

In this section, we first describe the problem using a decision analysis process model.  Then we illustrate the uncertainty formulation.  We also present the application of the Analytic Hierarchy Process (AHP) to build the multi-objective decision model and incorporate the uncertainty factors into this model.  Finally we discuss our uncertainty data assumptions and optimal path set evaluation.

3.1  Decision Analysis Process Model

As previously stated, the intermodal transportation problem deals with the situation where multiple modes 每 e.g. truck, rail, and barge 每 are used to move cargo from an origin to a destination.  In an intermodal transportation system, individual transportation modes are connected from origin to destination in such a way that meets the needs of the shippers efficiently and effectively.  The chosen modes affect the overall performance measures of the transportation system such as the total cost and the total delivery time.  Therefore the key issue is how to select the most appropriate transit mode and route in the intermodal transportation network so as to optimize the chosen performance measures.

 

Like many other complex decision making problems, a variety of elements cause the intermodal transportation decision to be difficult to make.  The most pertinent are as follows:

 

Ÿ         Complexity 每 There are many factors involved in the intermodal decision analysis process.  Some factors are user specified input data such as shipment size while others include external uncertainty factors and constraints of the transportation network.  It is difficult for the decision maker to handle the complex interactions between a large number of factors.

Ÿ         Uncertain events 每 Uncertainty brings risk into the decision process.  In this scenario, there are many uncertain events that may occur within the transportation network, e.g. transfer time may not be estimated accurately, additional cost may incurred for delays, a portion of the route may be closed for the inclement weather, etc.

Ÿ         Multi-objectives 每 When multiple objectives are involved in the decision making process, decision makers must trade off benefits in one area against costs in others.  The goal in this problem is multi-objective where it is necessary to evaluate the decision within a multi-objective decision model to optimize the performance measures.

 

Multi-objective optimization and decision analysis provide the tools and effective methods to deal with such elements.  The first step for the decision maker is to identify the decision situation and understand what their objectives are.  Based on the previous MBTC research projects (MBTC FR 1036, MBTC FR 1079, MBTC FR 1100-1, and MBTC FR 2024) and literature review (Tsamboulas & Kapros, 2002, LOGIQ, 1999, and Wood & Johnson, 1995), the basic decision elements are presented in the following subsections.

3.1.1  Uncertain Events

There are many uncertain elements that exist in an intermodal transportation network and are involved in the decision making process.  Based on our previous research and literature review, we have grouped these into four categories: cost rates, traffic speed, network route and node availability, and transport safety.  Each of these uncertainties may be caused by specific uncertain events.

 

         Cost rates 每 Cost is incurred during the transport and transfer processes.  In realistic transportation planning scenarios, rates may fluctuate around the average value due to multiple economic and industrial environments, such as competition and fuel price during a given planning horizon.

         Traffic speed 每 Transport speed also may fluctuate around an average value for each of the primary modes 每 rail, truck, and barge.  For example, weather conditions, traffic congestion, and road condition may directly affect the time it takes to transport cargo.  Weather does affect all modes, (i.e. truck, rail, and barge).  Water transportation in the colder regions of the U.S. shuts down completely during winter months.  A bad snowstorm can bring air, truck, and rail traffic to a halt.  Flooding is another weather phenomenon that interferes with transport operations.

         Network route and node availability 每 Sometimes a particular network arc may not be available for reasons such as inclement weather, accidents, lock closures, road maintenance, and river dredging, etc.  Terminal capacity, as some terminals may not have enough capacity to handle goods with large order size, may cause a node not to be available for goods transfer.

         Transport safety 每 This is related to the reliability of the goods transit service associated with a route.

 

3.1.2  Influence Diagram

An influence diagram is particularly insightful for bringing out the transformation of the system in terms of the structural and causal relationships between system components.  In this section, the decision analysis process is depicted by an influence diagram.  The diagram shows the decisions, uncertain events, outcomes, consequences and existing inter-relationships in an intermodal transportation system.  The overall goal is to achieve the cost objective, to achieve the time objective, and to achieve the reliability objective, i.e. to minimize lost and damage probability of goods.  These three objectives are influenced by uncertain events, user input variables (see below), and route and node choice.  As identified before, four uncertain elements are cost rate, traffic speed (time), network route & node availability, and transport safety.  All these basic uncertain events are influenced by variety of other specific uncertain elements. 

 

Inputs variables are controllable parameters within the decision system.  For each transportation task, the input variables must be specified by the decision maker.  The following input variables for the intermodal shipping decision were identified.  These are the same input variables as in the WebShipCost application:

         Origin city 每 the location where the shipment is originating;

         Destination city 每 the location where the shipment is terminating;

         Order size 每 the number of units to be shipped;

         Container capacity 每 the number of units each container can hold;

         Item cost 每 the value of the units ordered, based on the cost of each unit to the producer and order size;

         Holding cost rate 每 annual cost rate of carrying one unit in inventory

When the decision maker schedules a transport task, input variables must be specified.

 


Figure 3‑1 Influence Diagram for Intermodal Transportation Decision Analysis Process


As previously discussed, cost rate is one basic uncertain element.  The user estimates the cost according to the cost rate and input variables such as origin city, destination city, and order size before choosing the appropriate routes and modes.  Network route and node availability should also be considered in order to get a viable route.  Many uncertain events affect this availability.  Depicted in the diagram are terminal capacity, weather, re-establish works, accident, and deterioration of the route.  For example, water transportation in the colder regions of the U.S. shuts down completely during winter months.  These uncertainties affect the dray cost, transfer cost, transport cost, and inventory holding cost, which are each components of the overall transportation cost.  Transport speed is another significant uncertain element.  The user estimates the transport time and the probability that the goods will reach the destination on time based on the expected speed.  The input variables, such as order size, origin and destination, are all influential elements in this estimate.  The overall transit time includes transfer time, transport time, and dray time.  Network route and node availability is also a basic uncertain element.  Transport safety affects the shipper*s choice in such a way that the shipper wants to minimize the lost and damage of goods (referred to as reliability) during the whole transportation process.

 

In our project, we did not model all these system components.  For example, network route and node availability is hard to model because representative data are scarce.  Typically decision makers have cost and time as their primary concerns; therefore we will focus on these two objectives in the next section.

3.2  Problem Formulation

In the previous section, the intermodal decision was depicted as an influence diagram.  This section presents the illustrated mathematical formulation of the uncertain elements and decision objectives in order to provide the basis for our analysis.

 

In the intermodal transportation network of WebShipCost, the arc lengths separately represent the time or cost values associated with the corresponding transportation activities such as transfer, transport, etc.  Because all the data are assumed to be precise and known, there is no uncertainty to deal with.  Therefore, the problem can be formulated as a deterministic shortest path problem.  Single shortest path problem is a special case of k-shortest paths problem: Given a directed network, where is the node set, and is the arc set, with arc lengthsassociated with each arc .  The network has a distinguished source node s and a destination node t.  The length of a directed path is the sum of the lengths of the arcs in that path.  The shortest path problem is to determine a directed path from node s to node t with the shortest total length.  The k-shortest paths problem considered in WebShipCost can be described as follows: Given a directed network, a distinguished source node s and a destination node t, and a set of arc lengths , find the first, second,.., kth shortest paths from s to t, for any user-specified value of .

 

As previously mentioned, there are many uncertain elements in transportation route planning.  These uncertain elements should be taken into account when the transportation decision makers plan and schedule the optimal shipment route.  Uncertainty and associated risk are critical characteristics in such decision scenarios.  Three primary objectives have been identified in the influence diagram, i.e. cost, time, and reliability.  Since the reliability objective is not as significant in containerized transportation, we will focus on the cost and time related uncertain elements and objectives here.

3.2.1  Cost Objective

In the previous section, the elements that may influence the transit cost are identified in the influence diagram.  In a realistic intermodal transportation network that takes into account uncertainty, each arc should have an uncertain cost element.  The cost of the arcs may be modeled as random variables.  The distribution of the random variable may have a theoretical basis or may be empirically derived from historical data.

 

The notation used in the formulation is listed as follows:

 

G         每    Define the directed network, where is the node set, and is the arc set;

s           每    Let s denote the distinguished source node in the network G;

t           每    Let t denote the distinguished destination node in the network G;

P          每    For a given pair of source s and destination t nodes, let  be the set of arcs that define the path where , ;

           For the cost objective, let  be the random variable that represents the cost associated with arc ; For a given path P, suppose ,  are independent random variables;

      每    Let denote the total cost of the path P, i.e.;

每    Let  be the expected value of cost for path P;

每 Let  be the standard deviation of cost for path P;

p*        每    Let p* denote the path which the decision maker prefers;

       每    Let be an upper cost threshold specified by the user for this decision problem.  The upper cost threshold represents the highest cost for the path that the decision maker is willing to accept.

 

For the cost objective, the decision maker would like to find the path that minimizes the expected total cost .  In addition, decision makers will quite naturally want to control the risk associated with the problem.  As such it could be natural to find the path that minimizes the standard deviation of the cost and/or to find the path that minimizes the chance of exceeding an upper cost threshold .  Therefore three subobjectives are taken into consideration: the mean value of the total cost, the standard deviation of the total cost, and the probability that the total cost associated with the selected route is within the decision makers* acceptable threshold. 

 

Since we assume each arc is associated with a random variable representing uncertain cost, we obtain values for the three subobjectives through Monte Carlo simulation.  After we have obtained deterministically optimal path candidates,  the Monte Carlo simulation method is used to simulate the uncertainty and provide three subobjective values for each path, i.e. the mean value of the total cost, the standard deviation of cost, and .  The procedure of this method is listed as follows:

 

1.      Specify the number of iterations n;

let k represent the current iteration, set k = 1;

let m represent the number of iterations during which the cost threshold goal is met, set m = 0;

 

2.      Generate a random variate for each arc of the route from the distribution defined by historical

      data;

compute the total cost of current route ;

      compare  and , if m = m + 1;

      k = k + 1;

 

3.      If k = n, stop;

Otherwise, return to Step 2;

4.   Compute mean value of total cost ;

      the standard deviation of total cost ; and

      the probability .

3.2.2  Time Objective

The time objective includes three subobjectives similar to the cost subobjectives, i.e. the mean total time, the standard deviation of total time, and the probability of being within a time threshold.  In addition, another subobjective that we want to consider is the probability of being within a particular time span.  There are many realistic situations where this subobjective applies.  For example, suppose the decision maker is a supervisor of a parts plant where Just In Time (JIT) is implemented.  Therefore he wants his material resources from suppliers to arrive just in time, no sooner and no later,  and he can only afford a certain amount of deviation from this expected time point.  In this situation, this decision maker is primarily interested in the time span subobjective. 

 

Time related notation is given below:

     

       For the time objective, let  represent the transportation time associated with the transportation activities with arc .  For a given path P, suppose ,  are independent random variables;

             每 Let denote the total time associated with the transportation activities of the path P, i.e.;

   每 Let  be the expected value of cost for path P;

每 Let  be the standard deviation of cost for path P;

             每 Let  be an upper time threshold specified by the user for this decision problem.  The upper time threshold represents the longest time for the path that the decision maker is willing to accept;

        每 Let  be the lower bound of the time span;

             每 Let  be the upper bound of the time span;

 

In this situation, we want to minimize the mean value  and standard deviation of the total transportation time , while at the same time, maximizing the probability that total transportation time is within time threshold  and the probability that goods arrive within a preferred time span .

 

Monte Carlo simulation is also performed here to evaluate these performance metrics of a predetermined route.  The computation procedure is similar to that of the cost objective.

 

3.3  Analytic Hierarchy Process

Now that the problem has been formulated, the next issue is how to handle the multiple performance measures.  The Analytic Hierarchy Process (Saaty, 1980) is widely used to solve multi-objective decision problems.  The power of AHP lies in its ability to structure a complex, multi-attribute, and multi-period problem hierarchically.  Applying the AHP to solve the path alternative decision problem consists of five stages (Canada et al., 1996).

         Decision hierarchy construction;

         Attribute priority determination;

         Alternative weight determination;

         Consistency computation, and

         Overall weighted performance determination.

 

In the remainder of this section, we will show the detailed procedure of applying AHP methodology to this decision problem.

3.3.1  Decision Hierarchy Construction

The first step is to construct the decision hierarchy.  The hierarchy structure is presented in Figure 3‑2.  The top level of the hierarchy diagram refers to the overall goal of choosing the best path from the alternative path set.  We will discuss how to generate the alternative path set in Section 3.3.6.  The second level contains the three objectives for path evaluation: cost, time, and reliability.  Each of these can be decomposed into subobjectives as shown in the third level of the decision hierarchy.  At the bottom are the k path alternatives from which the decision maker must choose the most preferred.

 

 

 

Figure 3‑2 Decision Hierarchy

 

3.3.2  Attribute Priority Determination

Once the hierarchy is established, priorities should be established for each set of elements at every level of the hierarchy.  The user of WebShipCost-Risk must be asked to evaluate a set of elements at one hierarchy level in a pairwise fashion regarding the relative importance with respect to each of the elements at the next higher level of the hierarchy.  For example, the priority weights of the cost objective, time objective, and reliability objective in Table 3‑1 were set to be equally important.  Actual priority weight are set by the decision maker.

Table 3‑1        Priority Weight

 

Objective (2nd level)

Priority Weight

Objective (3rd level)

Priority Weight

Cost objective

(A)

0.33

Mean of total cost

(A1)

0.33

Std Dev of total cost (A2)

0.33

Probability of within cost threshold

(A3)

0.33

Time objective

(B)

0.33

Mean of total time

(B1)

0.25

Std Dev of total time (B2)

0.25

Probability of within time threshold

(B3)

0.25

Probability of JIT

(B4)

0.25

Reliability objective

(C)

0.33

N/A

 

3.3.3  Alternative Weight Determination

The next step is to determine the priority of each of the alternatives with respect to each of the attributes, i.e. the objective and subobjectives identified in the decision hierarchy.  Typically, these priorities are also set using a pairwise comparison process.  However because all of our performance data are quantifiable, we can directly convert our performance data to priority weight as described next.

 

When higher values of an alternative*s performance on a particular attribute are ※better§, e.g. the probability of being within the cost threshold, the following single step normalization process is utilized. 

 

where

 =  the normalized priority weight of attribute j of path i

              =  the performance data value of attribute j of path i

            k       =  the number of alternative paths

 

Conversely, when lower values are preferred such as total cost and total time, the following normalization process is used.

 

           

where

             =  the minimal value of performance data for attribute j of all k alternatives

 

3.3.4  Consistency Computation

One of the strengths of AHP is its ability to measure the degree of consistency present in the subjective judgments made by the decision maker (Canada et al., 1996).  Judgmental consistency is concerned with the transitivity of preference in the pairwise comparison matrices.  It includes a local measure of consistency and global measure consistency.  The local consistency ratio (C.R.) is an approximate mathematical indicator of the consistency of pairwise comparisons.  Priority weights constructed directly from performance data always have perfect consistency.

 

3.3.5  Overall Weighted Performance Determination

The last step is the weighted performance determination for each alternative which is obtained by multiplying the matrix of evaluation ratings by the vector of priority weights and summing across all attributes. i.e.,

 

      Weighted performance for alternative k =

 

The alternative with the highest weighted performance is the preferred alternative.

3.3.6  Overall Approach

The methodology for choosing the most desirable route in the intermodal transportation network is summarized as follows (notation is defined in Section 3.2):

 

Step 1. Construct the intermodal transportation network according to the specific decision scenario.  In other words, abstract the real network into nodes and arcs;

Step 2. Decorate each arc with expected cost value .  Sinceare independent with each other, for path P, the expected value of total cost equals the summation of the expected cost value of each arc in path P, i.e. ;

Step 3. Run the double sweep algorithm to get first k least cost path set = ;

Step 4. Decorate each arc with the expected time value .  Also because of the independence among , for path P, the expected value of total time equals the summation of the expected time value of each arc in path p, i.e. ;

Step 5. Run the double sweep algorithm to get first k least time path set  = ;

Step 6. Combine the path set  and  into a candidate path set = ;

Step 7. Run Monte Carlo simulation on each path of path set , compute the performance matrices;

Step 8. Use the AHP method to determine the final optimal path set ranked in the descending order of the overall weighted evaluation.

 

Figure 3‑3 presents a diagram of this approach.

 

 

Figure 3‑3 Methodology Diagram

 

 

3.4  Data Assumption and Optimal Path Set Evaluation

As stated in the problem formulation and AHP sections, the uncertain elements in the intermodal transportation decision model are represented by random variables.  In general, there are two ways to obtain the distribution information for these variables.  The first way is to empirically fit the data to random variables.  The second is to assume reasonable theorized distributions to these variables.  In this case, it is extremely difficult to obtain accurate historical data for the entire network.  Therefore we make reasonable assumptions about these random variable distributions first.  Then Monte Carlo simulation is used to evaluate the results of the optimal path set.

 

3.4.1  Data Assumption

The time and cost related uncertain elements are listed in Table 3-2, the random variables associated with these elements are assumed to be triangularly distributed, where the mode parameter equals the mean value identified by WebShipCost-Risk, the minimal boundary value equals 70% of the mode and the maximal boundary value is set as 130% of the mode.

 

Table 3‑2  Time and Cost Related Uncertain Elements

Transportation Rates

Barge transportation rate 每 Inland barge transportation rate

Rail transportation rate - Rail transportation rate per container-mile

Long haul truck transportation rate per container-mile of each truck arc in the network

Drayage Costs

Truck-to-Barge drayage cost

Truck-to-Rail drayage cost

Mode Speeds

Barge transportation speed

Rail transportation speed

Long haul truck transportation speed

Transfer Times and Costs

Barge/Rail transfer time and cost 每 The amount of time and associated cost of transferring containers from barge to rail or from rail to barge

Barge/Truck transfer time and cost - The amount of time and associated cost of transferring containers from barge to truck or from truck to barge

Truck/Rail transfer time and cost - The amount of time and associated cost of transferring containers from truck to rail or rail to truck

 

3.4.2  Optimal Path Set Evaluation

Since input data assumptions have been made, the network is ready for evaluation according to single objective.  In this section, a thorough Monte Carlo simulation was performed based on the minimal cost objective and minimal time objective in order to evaluate the optimal path generated by the methodology described in the previous section.  The procedure can be described as follows:

 

Step 1. Set the low level and high level of user input variables including order size, container capacity, item cost, holding cost rate, and the distance between origin and destination cities;

 

Step 2. Combine these user input variables; for distance, randomly pick up a pair of cities as origin and destination cities in the corresponding distance level;

 

Step 3. At each combination point, run the Monte Carlo simulation, get the shortest cost path and shortest time path;

 

Step 4. If maximum iteration number is reached, stop; otherwise return to Step 3.

 

In this problem, taking the simulation run time into consideration, the maximum iteration number is set to be 100.  In each iteration, there are 32 experimental design points.  The factor levels of user input variables are set based on general transportation knowledge as shown in Table 3‑3.  In regards to the distance between origin and destination cities variable, 665 miles is the median of the distance matrix for the network as shown in Appendix 7-2.

 

Table 3‑3        Level Setting of User Input Variables

User Input Variables

Low Level

High Level

Distance between origin and destination cities

Less than 665 miles

More than 665 miles

Order size

1,000

5,000

Container capacity

100

500

Item cost

10

50

Holding cost rate

0.05

0.25

 

 

The simulation results for the minimal cost scenario are depicted in Table 3‑4.  From these results it is clear that barge transportation dominates the optimal path set when the objective is to minimize cost.  This mode also comes with a longer total transport time span and a larger percentage of transport time.  An interesting observation is that more than 40% of the total cost is attributed to the transfer activities.

 

 

 

Table 3‑4        Descriptive Statistics of Shortest Cost Path Set (Minimal Cost)

Characteristic of Shortest Path Set

Mean

Standard Error

Percentage of dray cost

0.192

0.001

Percentage of transport cost

0.364

0.002

Percentage of transfer cost

0.402

0.002

Percentage of inventory holding cost

0.042

0.001

Percentage of transport time

0.948

0.001

Percentage of transfer time

0.052

0.001

Percentage of barge arcs

0.769

0.005

Percentage of truck arcs

0.040

0.002

Percentage of rail arcs

0.191

0.005

Percentage of barge distance

0.769

0.005

Percentage of truck distance

0.040

0.002

Percentage of rail distance

0.191

0.005

Total number of arcs

3.034

0.012

Total distance

1205.264

8.218

Number of barge arcs

2.496

0.020

Distance of barge arcs

1078.405

9.909

Total cost ($)

8121.836

107.981

Total time (hour)

192.570

1.690

 

 

Figures 3-4 through 3-6 are used to depict the relationships among the modes and cost activities.

Figure 3‑4       Percentage of Activity Cost (Minimal Cost)

 

As shown in Figure 3-4, transfer cost accounts for more than 40% of the total cost.  There are two reasons for this dominance.  First, as we can see in Figure 3-5 and 3-6, barge is the dominant mode in the optimal path considering the minimal cost objective.  However drayage is performed by truck which caused more transfer activity.  Second, transfer cost rate is higher for barge with other modes than the transfer rate between truck and rail.  This further increases the transfer cost percentage.

 

Figure 3‑5       Percentage of Mode Arcs (Minimal Cost)

 

Figure 3‑6       Percentage of Mode Distance (Minimal Cost)

 

The simulation results for the minimize time objective scenario are shown in Table 3‑5. 

 

Table 3‑5 Descriptive Statistics of Shortest Cost Path Set (Minimal Time)

Characteristic of Shortest Path Set

Mean

Standard Error

Percentage of dray cost

0.023

0.001

Percentage of transport cost

0.934

0.002

Percentage of transfer cost

0.040

0.001

Percentage of inventory holding cost

0.003

0.000

Percentage of transport time

0.986

0.001

Percentage of transfer time

0.014

0.001

Percentage of barge arcs

0.000

0.000

Percentage of truck arcs

0.872

0.004

Percentage of rail arcs

0.128

0.004

Percentage of barge distance

0.000

0.000

Percentage of truck distance

0.879

0.004

Percentage of rail distance

0.121

0.004

Total number of arcs

2.773

0.010

Total distance

912.326

7.034

Number of barge arcs

0.000

0.000

Distance of barge arcs

0.000

0.000

Total cost ($)

22140.850

396.837

Total time (hour)

22.220

0.176

 

As shown in Table 3‑5,  when minimizing time is the objective, the truck mode dominates the shortest path set while the barge mode was never included in the optimal path.  This is an expected result considering barge*s significantly lower transport speed.  Also, observed in Figure 3‑7, more than 90% of total cost is attributed to transport activities since the transfer and dray cost are significantly reduced.

 

 

Figure 3‑7       Percentage of Activity Cost (Minimal Time)

 

Figure 3‑8       Percentage of Mode Arcs (Minimal Time)

 

Figure 3‑9       Percentage of Mode Distance (Minimal Time)

 

This section described the intermodal k shortest path problem as a multi-criteria decision problem under uncertainty.  Uncertainty formulation and the application of the AHP to build the multi-objective decision model were discussed.  The uncertain data assumptions were also discussed.  Finally the optimal path sets were evaluated through Monte Carlo simulation.  In the next section a thorough sensitivity analysis is performed to evaluate the effects of the experimental factors on the optimal path set.

4        Sensitivity Analysis

In the previous section we formulated the uncertain elements, multi-objective model and a methodology to guide shippers in choosing the most desirable transportation route.  In the current model, there are many factors that might affect the rankings of preferable routes: What  influence do these factors have on the decision results?  Under what conditions could the barge mode demonstrate superiority over the other modes?  These questions can be addressed with a thorough sensitivity analysis using experimental design methods.  In this section, we will discuss the design of experiments and the sensitivity analysis for the intermodal transportation decision problem.

4.1  Experiment Design

In our experimental design, several basic issues have to be examined initially 每 input variables (factors), their corresponding level identification, and response identification.  Based on the analysis presented in the previous section, nine factors were identified and listed in Table 4-1.  The experiment was conducted using a two level full factorial design investigating nine factors which are based on the general transportation knowledge.  Table 4-1 also shows the setting of the factors in one scenario of the experiments.

 

Table 4‑1  Factors of DOE

Factor

Low

High

A

Weight of the cost, time, reliability objective

0.2, 0.4, 0.4

0.6, 0.2, 0.2

B

Cost threshold,

threshold = (1 + B) * optimal value

0.5

1.0

C

Time threshold,

threshold = (1 + C) * optimal value

0.5

1.0

D

Time lower & upper bound,

Time lower bound = (1-D) * optimal value;

Time upper bound = (1+D) * optimal value

0.2

0.5

E

Distance between origin and destination cities

<= 665 miles

> 665 miles

F

Order size

1,000

5,000

G

Container capacity

100

500

H

Item cost

$10

$50

I

Holding cost rate

0.05

0.25

 

 

As shown in Table 4-1, the weights of the cost/ time/ reliability objectives are defined as one single factor.  Since the summation of these three parameters must equal 1, they are not independent.  Suppose the shipper is primarily interested in one of the three objectives, three separate scenarios (cost, time, and reliability) can be defined where the weight of corresponding objective is specified and the weight of the other two are assumed to be equal.  For example, in the cost scenario as shown in Table 4-1, shippers view the cost as the most important factor, the low and high value of weight of cost is set as 0.2 and 0.6.  Then the weights of time and reliability are equally specified as  and  correspondingly;

 

The value or range of the preferred thresholds are also identified as factors.  There are four such values: cost threshold, time threshold, time lower bound and time upper bound.  We choose these values as the percentage of the corresponding value of the optimal path in the candidate path set.  In other words, the optimal value for each objective in the candidate path is set to be the reference value.  Based on this value, the decision maker set the preferred threshold value, expressed in percentage form.

 

Distance between origin and destination cities is the next factor.  According to the distance matrix of the network (see Appendix 7.2), the distances are grouped into two categories: under 665 miles and beyond 665 miles where 665 is the median of truck distances among all network cities.  The origin-destination pair among the category is randomly chosen based on a generated random number when the path selection scenario is specified.

 

Other user input variables, such as order size, container capacity, item cost, and holding cost rate are also identified as factors.

 

In order to evaluate the influence of the model factors on the decision results, the following three responses were specified:

         Percentage of each cost and time element in the resulting most preferable path;

         Number of arcs of each mode type in the resulting most preferable path;

         Distance percentage of each mode type in the resulting most preferable path.


 

4.2  Result Analysis

In this section, we discuss the evaluation results and conclusions, perform further experiments, and explore under which circumstances does the barge mode demonstrate advantages.

 

Considering the cost scenario of the experiment shown in Table 4-1, the shipper is primarily interested in the cost objective.  The variation of cost weight, which is from 0.2 to 0.6, is higher than that of the time and reliability weights.  The main effects plot for barge arcs in this case is shown in Figure 4-1.

 

A main effects plot is a plot of means at each level of a factor.  It can be used to compare the magnitudes of the various main effects.  A main effect occurs when the mean response changes across the levels of a factor.  As shown in Figure 4-1, the X-axis gives the name of nine factors (from A to I as defined in Table 4-1).  Each factor changes from the low value to the high value as shown on the top of the figure.  The Y-axis marks the value of the response variable, which is, in this example, the number of barge arcs in the optimal path.  As we can see, the weight of cost has the largest effect on the number of barge arcs.  The detailed discussion of the effect of each factor on the response variable is shown in Table 4-2. 

Figure 4‑1       Main Effect Plot for Barge Arcs (Cost Scenario)

 

Table 4‑2        Main Effect Plot Interpretation

Factor

Interpretation

A

Weight of the cost

The weight of cost has a large impact on the number of barge arcs.  When the weight of cost increases, the barge mode becomes the dominant mode in the optimal path because of its much lower shipping rate compared with truck and rail.

B

Cost threshold,

threshold = (1 + B) * optimal value

This factor is insignificant.  This might be caused by the cost factor which is so significant.

C

Time threshold,

threshold = (1 + C) * optimal value

When the time threshold becomes more relaxed, more barge arcs enter the optimal path.  This seems reasonable because the transport time for barge is longer and has larger variations within the total transport time.

D

Time lower & upper bound,

Time lower bound = (1-D) * optimal value;

Time upper bound = (1+D) * optimal value

Like the time threshold, time lower & upper bound is another time constraint.  When this constraint relaxes, more barge arcs enter the optimal path set.

E

Distance between origin and destination cities

When the distance between origin and destination increases, barge arcs in the optimal path increase.  This indicates that because of the much lower transport cost, the gain of the barge mode becomes significant when the goods need to be shipped through a long path.

F

Order size

Order size is insignificant.

G

Container capacity

When container capacity increases, the same amount of goods can be handled by fewer containers.  Thus the percentage incurred by the transport component of the total cost decreases which causes the benefit of barge mode to be not as significant as before.

H

Item cost

When more valuable items are shipped, the inventory holding cost became a significant part of the total transport cost.  Since barge is much slower than truck and rail which comes with a much high inventory holding cost, the barge mode becomes less attractive and the number of barge arcs in the optimal path decreases. 

I

Holding cost rate

Same as the factor item cost, when the holding cost rate increases, the mode barge becomes less attractive because of its much longer total transport time which causes a higher inventory holding cost.

 

After repeating the analysis for barge arc percentage and barge distance percentage,  they are found to be similar to the results shown in Figure 4.1.  In other words, these nine factors have similar effects on these two response variables 每 barge arc percentage and barge distance percentage.

 

In a similar way, experiments based on different cost, time, and reliability setting were also performed, the settings are listed in Table 4‑3.

 

Table 4‑3        Experiment Settings

Experiment

Weight of cost/ time/ reliability

Level 1

Level 2

1

0.2, 0.4, 0.4

0.6, 0.2, 0.2

2

0.4, 0.2, 0.4

0.2, 0.6, 0.2

3

0.2, 0.4, 0.4

0.8, 0.1, 0.1

4

0.4, 0.2, 0.4

0.1, 0.8, 0.1

 

In  the AHP model presented previously, the time and cost weight are set by the user.  The setting of weight has a direct influence on the resulting most preferable path.  Here we study the effect of choosing the time and cost weight on the responses such as arc and distance percentage of each mode type in the resulting path, percentage of each cost and time element in the resulting path, etc. as defined in Section 4.1.

 

In Figures 4-2 and 4-3, mode arc percentage are plotted versus time and cost weights respectively.  In these two figures, the X-axis denotes the time and cost weight while Y-axis is the mode arc percentage value.   As we can see, the weight of time and cost have large effects on the mode choice.  According to Figure 4-2, as the weight associated with the time objective increases (cost weight decreases),  the truck mode becomes so dominant that it drives the other two modes out.  The same thing happens when the time weight is at lowest point (cost weight at highest point), the barge mode is the dominant mode.  Interestingly, the mode truck plays a part even when the weight of time or cost are not highly important considerations.

 

Figure 4‑2       Mode Arc Percentage VS Time Weight

 

Figure 4‑3       Mode Arc Percentage VS Cost Weight

 

Figure 4‑4 and 4-5 show the relationships of total mean cost and mean time with time weight.  In Figure 4‑4, as time becomes a more important consideration, total mean cost increases.  In Figure 4-5, as the time weight increases, the total mean time decreases.  These two figures can easily be interpreted since as time weight increases, the barge mode is less prevalent in the optimal path set gradually while the more expensive but less-time-consuming truck mode increasingly appears in the path set.

Figure 4‑4       Mean Cost VS Time Weight

 

Figure 4‑5       Mean Time VS Time Weight

 

In a similar way we plot the relationships of total mean cost and mean time with cost weight in Figure 4-6 and 4-7.  In Figure 4-6, as cost becomes more important, total mean cost decreases.  In Figure 4-5, as the cost weight increases, the total mean time increases.  These two figures can be interpreted in a similar way as well.  Since as cost weight increases, the barge mode is more prevalent in the optimal path set gradually while truck mode gradually disappears in the path set.

Figure 4‑6       Mean Cost VS Cost Weight

 

Figure 4‑7       Mean Time VS Cost Weight

 

The relationships of cost and cost percentage for each transportation activities to the time and cost weights is the next consideration.  As shown in Figures 4-8, 4-9, 4-10, and 4-11, cost and cost percentage have similar patterns.  As the time weight increases, the transport cost becomes the dominant part of the total transportation cost while the other activity costs become insignificant.  Another interesting thing is that at the point where time weight is 0.1, transfer cost is almost as much as transport cost.  The sum of transfer cost and dray cost at this point is even greater than transport cost.  This is caused by the high drayage and transfer cost rate.  As shown in Figures 4-10 and 4-11, as cost weight increases, more intermodal activities emerge such as intermodal drayage, transferring, etc. which caused the percentage of transport cost to decrease significantly. 

Figure 4‑8       Cost Percentage VS Time Weight

 

Figure 4‑9       Cost VS Time Weight

 

Figure 4‑10     Cost Percentage VS Cost Weight

 

Figure 4‑11     Cost VS Cost Weight

 

This section performed a thorough sensitivity analysis based on the experimental results.  The mode barge plays a significant role in the current intermodal transportation network.  In some cases, such as when the shipper considers minimum cost to be important, the barge becomes dominant in the most preferable route.  The results also show that high drayage and transfer cost could be obstacles for barge to gain more superiority over truck and rail modes.

 

The WebShipCost 每 Risk application design and implementation issues are discussed in Section 5.

5        WebShipCost 每 Risk Application

In this section, we discuss the results of the software analysis, design, and implementation phases of the project.  We first present a description of the use cases identified for the application.

 

5.1  Use Case Models

A use case is a statement of high-level functional system requirements in narrative text.  Use cases serve as the basis for the software requirements and for setting the stage for the early identification of objects within the system.  In addition, use cases serve as a basis for system test development.  Use cases should emphasize top-level functions and interfaces based on the viewpoint of an actor.  An actor is a well-defined role for a user or group of users.  Actors can be people or they may be other systems with which the system interacts.  Use cases begin at a high level and can be refined by subsystem all the way down to the object level.  A use case model is the statement of use, use case diagram, use case description, and actor description.

 

The following presents the major actors of the WebShipCost - Risk system.

 

 

Actor Name:   User

Description:    A human user uses the WebShipCost 每 Risk system to compute the shortest paths between cities in a network and evaluate the associated risk elements.  The user can also make changes to the user-related data in the database.

 

Actor Name:   Database Manager

Description:    A human user who takes the collected data and places it into the database.  The database manager must have knowledge of the data set validation process and the database.  The database manager can make changes to all of the data in the database.

 

Actor Name:   Administrator

Description:    A human user who has full control of the system 每 compute the shortest paths, evaluate the risks, perform sensitivity analysis and update the database.  The administrator must have in-depth knowledge about the decision context and methodologies including the Analytic Hierarchy Process and design of experiments.

 

 

The following use case diagram identifies the ※Shortest Paths Risk Evaluation§ use case.  A complete set of use cases and some important use case scenarios are listed in Appendix 7.3.

Table 5‑1 ※Shortest Paths Risk Evaluation§ Use Case

 

Use case:

Shortest Paths Risk Evaluation

Section:

System level

Purpose:

To calculate the shortest paths and perform risk evaluation

Description:

User/administrator enters transportation information into the program and specifies the necessary parameters in order to get the shortest paths and the evaluation of risk performed by the program

Actors:

User, Administrator

 

5.2  Application Design

In order to reach the development goal of flexibility, reliability and efficiency, WebShipCost-Risk takes a strong object 每 orientation view of data structures and algorithms.  The architecture of WebShipCost每Risk currently consists of five Java packages.  Each package contains a set of interfaces and/or classes.  They are grouped by related purpose and functionality.  The current packages of the program are the following:

 

         wscrisk.graph:              Package of graph building related interface and classes.

         wscrisk.algorithm:         Package of  shortest path algorithm related interface and classes.

         wscrisk.analysis:           Package of interfaces and classes used for performing risk analysis and sensitivity analysis.

         wscrisk.comparator:     Package of a variety of comparators used for sorting algorithms.  The program handles the shortest path algorithm and these comparators sort the path list automatically according to different rules such as mean cost, mean time, and total weight (AHP), etc.

         wscrisk.util:                   This package contains some auxiliary classes providing functions such as database connection management, debugging output, etc.

 

For detailed information, readers can refer to Appendix 7.4.

 

 

 

6        Summary

Prior MBTC WebShipCost research has been enhanced and has resulted in the development of WebShipCost-Risk, a risk-based multi-objective decision model for intermodal transportation networks which can help shippers make trade-offs among a variety of objectives and incorporate the uncertainty into the decision making process.  In particular, the following results have been achieved:

 

Ÿ         A review of the relevant literature in this area has been conducted.

Ÿ         Key uncertain elements and risk-based performance measures associated with intermodal transportation have been identified;

Ÿ         A multi-objective decision model has been built;

Ÿ         A thorough sensitivity analysis based on experimental design methodology was performed to evaluate the influence of the model factors on the decision results;

Ÿ         A user interaction model has been developed and implemented using a flexible web services approach.

 

Given the current architecture, WebShipCost-Risk is capable of performing risk analysis and multi-objective decision making. 

 

For users of industry, analysis results are only as good as the data behind it.  End users depend on current, accurate data to make correct decisions.  Currently this analysis is based on data from research at University of Arkansas (Trusty and Malstrom, 1998) and the ShipCost user*s manual (Boardman and Malstrom, 1998).  The information is also derived from a detailed analysis performed for the Defense Logistics Agency [TLI-AR00-2].  The network is predefined.  However, real, living, changing, evolving network information over time needs to be considered.  How to keep data continuously updated is a challenging task for the current system.

 

A geographic information system (GIS) is computer software/system that links geographic information (where things are) with descriptive information (what things are).  A GIS can present many layers of different information.  All the transportation information〞 infrastructure information such as roadways, railroads, waterways, bridges and tunnels, transit place, and decision related information such as cost, transport speed, reliability, etc. 〞is stored as layers in digital format in the computer.  The integration of WebShipCost with a GIS will provide the end user with more convenient and efficient data management methods to support the decision making in terms of route planning.

 

Future work will seek to:

Ÿ         Expand WebShipCost to interactively accept user input transportation network data,

Ÿ         Integrate WebShipCost with a Geographical Information System (GIS),

Ÿ         Provide intermodal shippers with graphical and user-friendly information to improve decision making, and

Ÿ         Test models and algorithms on problems associated with Arkansas waterway utilization.

Additional funding has been secured from the Mack Blackwell Transportation Center (MBTC 2047) to complete the future work discussed in this section.

7        Appendices

7.1  Transportation Network

 

 

Figure 7‑1       Transportation Network (13 cities)

 

Table 7‑1        City Location

City Name
Abbreviation
Location
River

Brownsville

Bro

Gulf Coast

Gulf Coast

Chicago

Chi

Midwest

Illinois

Cincinnati

Cin

Northeast

Ohio

Houston

Hou

Gulf Coast

Gulf Coast

Little Rock

LR

South

Arkansas

Memphis

Mem

Midwest

Mississippi

Mobile

Mob

Southeast

Alabama

New Orleans

NO

South

Mississippi

Omaha

Oma

Midwest

Missouri

Pittsburgh

Pit

Northeast

Ohio

St. Louis

SL

Midwest

Mississippi

St. Paul

SP

Midwest

Mississippi

Veracruz

Ver

Mexico/Central America

Ocean

 

 

7.2  Distance Matrix (Units: mile)

The distance matrix table shows the ground direct distances between each pair of cities.  The length unit is miles.

 

Table 7‑2        Distance Matrix

 

 

Bro

Chi

Cin

Hou

LR

Mem

Mob

NO

Oma

Pit

SL

SP

Ver

Bro

0

1240

1180

295

685

680

660

530

1060

1420

980

1340

470

Chi

1240

0

250

945

550

490

780

840

430

410

260

340

1650

Cin

1180

250

0

890

530

405

615

700

615

260

310

590

1530

Hou

295

945

890

0

390

490

440

315

800

1150

690

1060

730

LR

685

550

530

390

0

130

380

360

490

790

300

710

1100

Mem

680

490

405

490

130

0

330

360

530

670

240

695

1160

Mob

660

780

615

440

380

330

0

140

350

810

560

1020

950

NO

530

840

700

315

360

360

140

0

850

920

600

1050

840

Oma

1060

430

615

800

490

530

350

850

0

840

355

300

1520

Pit

1420

410

260

1150

790

670

810

920

840

0

560

730

1750

SL

980

260

310

690

300

240

560

600

355

560

0

465

1380

SP

1340

340

590

1060

710

695

1020

1050

300

730

465

0

1790

Ver

470

1650

1530

730

1100

1160

950

840

1520

1750

1380

1790

0

 

 

 

Table 7‑3 Descriptive Statistics of Distances

 

Distances

Mean

718.2051282

Median

665

Mode

530

Range

1660

Minimum

130

Maximum

1790

Count

78

 

7.3  Complete Use Case Models

7.3.1  System Level:

 

※Calculate the Shortest Paths§ Use Case

 

Use case:

Calculate the Shortest Paths

Section:

System level

Purpose:

To get the shortest paths between cities in a network

Description:

User/administrator enters transportation information such as shipping size, item cost, etc. into the program in order to get the shortest paths computed by the program

Actors:

User, Administrator

 

※Shortest Paths Risk Evaluation§ Use Case

 

Use case:

Shortest Paths Risk Evaluation

Section:

System level

Purpose:

To calculate the shortest paths and perform risk evaluation

Description:

User/administrator enters transportation information into the program and specify the necessary parameters in order to get the shortest paths and the evaluation of risk performed by the program

Actors:

User, Administrator

 

 

※Sensitivity Analysis§ Use Case

 

Use case:

Sensitivity Analysis

Section:

System level

Purpose:

To study the influence of transportation factors such as time and cost weight, cost threshold, etc. on the mode choice and explore the advantages of the barge mode

Description:

Administrator setups the experiment factors. The program performs the full experiment and presents the results

Actors:

Administrator

 

 ※Update Database§ Use Case

 

Use case:

Update Database

Section:

System level

Purpose:

To keep the data in the database updated

Description:

User can change user related information in the database.  Database manager and administrator have the privilege to update the data stored in all the tables.  The database and tables are also created by database manager or administrator.

Actors:

User, Database Manager, Administrator

 

7.3.2  Subsystem Level:

 

※Input Transportation Information§ Sub Use Case

Use case

Input Transportation Information

Upper level

Calculate the Shortest Paths

Purpose:

Input necessary transportation information into system in order to compute the shortest paths

Description:

Necessary information includes origin city, destination city, number of units to be shipped, number of units per container, unit price, percentage of the unit cost to be used in the carrying cost, objective (minimize time or cost) and the number of paths to be found

 

※View the Shortest Paths Results§ Sub Use Case

Use case

View the Calculation Results

Upper level

Calculate the Shortest Paths

Purpose:

Show the computation results

Description:

User is provided with the computation results including all of the nodes of each path and mode information between each pair of nodes

 

※Specify Risk Evaluation Related Parameters§ Sub Use Case

Use case

Specify Risk Evaluation Related Parameters

Upper level

Shortest Paths Risk Evaluation

Purpose:

Input transportation information and specify the risk evaluation related parameters into system

Description:

Transportation information includes origin city, destination city, number of units to be shipped, number of units per container, unit price, percentage of the unit cost to be used in the carrying cost and the number of paths to be found. 

Risk related parameters include priority weight of cost goal, priority weight of time goal, priority weight of reliability goal, upper bound of acceptable cost threshold, upper bound of acceptable time threshold, acceptable delivery time span

 

※View the Risk Evaluation Results§ Sub Use Case

Use case

View the Risk Evaluation Results

Upper level

Shortest Paths Risk Evaluation

Purpose:

Show the evaluation results

Description:

User is provided with the computation results including all of the nodes of each path and mode of transportation between each pair of nodes and the risk evaluation, i.e. the overall priority weight of each path

 

 

※Setup Experiment Factors§ Sub Use Case

Use case

Setup Experiment Factors

Upper level

Sensitivity Analysis

Purpose:

To setup the experiment factor levels

Description:

Administrator determines the factor levels in order to perform the sensitivity analysis.  The factors include: priority weight of cost, acceptable cost threshold, acceptable time threshold, time lower & upper bound (i.e. acceptable delivery time span) , cost lower & upper bound, distance between origin and destination cities (divided in two groups: less than or equal to 665 miles and more than 665 miles), order size, container capacity, item cost and holding cost rate

 

※View the Experiment Results§ Sub Use Case

Use case

View the Experiment Results

Upper level

Sensitivity Analysis

Purpose:

Show the sensitivity analysis results

Description:

The results include percentage of arcs of each mode in the resulting best path and distance percentage of each mode in the resulting best path

 

※Update the User Information§ Sub Use Case

Use case

Update the User Information

 

 

Upper level

Update Database

Purpose:

To update information related to system user

 

Description:

User information includes user name, email address and user description.

 

 

※Update the Problem Information§ Sub Use Case

Use case

Update the Problem Information

 

 

Upper level

Update Database

Purpose:

To update information related to problem

 

Description:

Problem information includes title, create date and description

 

 

※Update the Input Scenario Information§ Sub Use Case

Use case

Update the Input Scenario Information

 

 

Upper level

Update Database

Purpose:

To update information related to input scenario

 

Description:

Input scenario information includes title and description

 

 

※Update the Network Information§ Sub Use Case

Use case

Update the Network Information

 

 

Upper level

Update Database

Purpose:

To update information related to network

 

Description:

Network information includes network name, currency units, distance units and time units

 

 

※Update the Node Information§ Sub Use Case

Use case

Update the Node Information

 

 

Upper level

Update Database

Purpose:

To update information related to node

 

Description:

Node information includes node name

 

 

※Update the City Information§ Sub Use Case

Use case

Update the City Information

 

 

Upper level

Update Database

Purpose:

To update information related to city

 

Description:

City information includes city name

 

 

 

 

 

※Update the Specific Transfer Information§ Sub Use Case

Use case

Update the Specific Transfer Information

 

 

Upper level

Update Database

Purpose:

To update information related to specific transfer time and rate

 

Description:

Specific Transfer information includes transfer cost rate and transfer time

 

 

※Update the Mode Information§ Sub Use Case


Use case

Update the Mode Information

 

 

Upper level

Update Database

Purpose:

To update information related to mode

 

Description:

Mode information includes mode name, average mode transport speed, average cost rate, average dray cost rate and average carrying cost

 

 

※Update the Dray Cost Information§ Sub Use Case

Use case

Update the Dray Cost Information

 

 

Upper level

Update Database

Purpose:

To update information related to dray cost information

 

Description:

Dray cost information includes cost rate

 

 

※Update the Transport Information§ Sub Use Case

Use case

Update the Transport Information

 

 

Upper level

Update Database

Purpose:

To update information related to transport

 

Description:

Transport information includes transport cost rate, speed and distance between all pairs of origin and destination cities

 

 

※Update the Average Transfer Information§ Sub Use Case

Use case

Update the Average Transfer Information

 

 

Upper level

Update Database

Purpose:

To update information related to average transfer

 

Description:

Average transfer information includes average transfer cost rate and average transfer time

 

 

 

 

7.3.3  Use Case Scenarios for Selected Use Cases:

 

This section includes detailed use case scenarios for a select group of use cases that are important and representative of the system.

 

Use Case: Input Transportation Information

 

Use Case Scenario for ※Input Transportation Information§

 

Actor Action

System Response

1

The use case begins when the actor clicks the ※Shortest Path§ tag on the homepage

 

2

 

Displays the following items:

  1. Source City(Dropdown menu)
  2. Destination City(Dropdown menu)
  3. Number of Units to be shipped(Textbox)
  4. Number of Units per container( Textbox)
  5. Cost of each unit to the producer(Textbox)
  6. Percentage of the unit cost used n calculating Carrying Cost(Textbox)
  7. Objective(Radio button)
  8. Number of paths to be found(Textbox)
  9. Options for ※Calculate the Shortest Paths§(Button), ※Reset§(Button) and ※Home§(Link) are provided

 

3

User can enter values and click on ※Calculate the Shortest Paths§ button

 

4

 

System checks the validation of the input information

5

 

If all values are valid, system should take user to the ※Shortest Path List§ page; otherwise ask the user to reenter the invalid values

6

User can click ※Reset§ button

 

7

 

All values entered should be cleared

8

User can choose ※Home§ link

 

9

 

System should display the homepage

 

Use Case: View the Shortest Paths Results

 

Use Case Scenario for ※View the Shortest Paths Results§

 

Actor Action

System Response

1

The use case begins when the actor clicks on ※Calculate the Shortest Paths§ button on the page ※Shortest Path§

 

2

 

Displays the following item:

  1. Problem Scenario(Text)
  2. Shortest paths list(Text)
  3. Options for ※Detail§(Button) and ※Return§(Button) are provided

 

3

User can click ※Detail§ button

 

4

 

System should display the path details such as all of the nodes of that path and mode information between each pair of them

5

User can click ※Return§ button

 

6

 

System returns to the ※Shortest Path§ page

 

 

Use Case: Specify Risk Evaluation Related Parameters

 

Use Case Scenario for ※Specify Risk Evaluation Related Parameters§

 

Actor Action

System Response

1

The use case begins when the actor clicks the ※Risk Evaluation§ tag on the homepage

 

2

 

Displays the following item:

  1. Source City(Dropdown menu)
  2. Destination City(Dropdown menu)
  3. Number of Units to be shipped(Textbox)
  4. Number of Units per container        (Textbox)
  5. Cost of each unit to the producer(Textbox)
  6. Percentage of the unit cost used n calculating Carrying Cost(Textbox)
  7. Number of paths to be found(Textbox)
  8. Priority weight of cost goal(Textbox)
  9. Priority weight of time goal(Textbox)
  10. Priority weight of reliability goal(Textbox)
  11. Options for ※Value Bound§ and ※Percentage Bound§(Optional box)
  12. Cost upper bound(Textbox)
  13. Time upper bound(Textbox)
  14. Delivery time span(Textbox)

Options for ※Run Evaluation§(Button), ※Reset§ (Button) and ※Home§ (Link) are provided

 

3

User can enter values and click on ※Run Evaluation§

 

4

 

System check the validation of the input information

5

 

If all values are valid, system should take user to the ※Risk Evaluation Results§ page; otherwise ask the user to reenter the invalid values

6

User can click ※Reset§ button

 

7

 

All values entered should be cleared

8

User can choose ※Home§ link

 

9

 

System should display the homepage

 

Use Case: View the Risk Evaluation Results

 

Use Case Scenario for ※View the Risk Evaluation Results§

 

Actor Action

System Response

1

The use case begins when the actor clicks on ※Run Evaluation§ button on the page ※Risk Evaluation§

 

2

 

Displays the following item:

  1. Problem Scenario(Text)
  2. Shortest paths list(Text)
  3. Overall priority weight of each path(Text)
  4. Options for ※Detail§(Button) and ※Return§(Button) are provided

 

3

User can click ※Detail§ button

 

4

 

System should display the path details such as all of the nodes of that path and mode information between each pair of them

5

User can click ※Return§ button

 

6

 

System returns to the ※Risk Evaluation§ page

 

Use Case: Setup Experiment Factors

 

Use Case Scenario for ※Setup Experiment Factors§

 

Actor Action

System Response

1

The use case begins when the actor clicks the ※Sensitivity Analysis§ tag on the homepage

 

2

 

Displays the following items:

  1. Options for scenario selection: ※Cost§, ※Time§ and ※Reliability§(Optional box)
  2. Weight, corresponding to the scenario selection(Textbox)
  3. Cost threshold(Textbox)
  4. Time threshold(Textbox)
  5. Time lower & upper bound(Textbox)
  6. Cost lower & upper bound(Textbox)
  7. Distance between origin and destination cities: ※less than 500 miles§, ※between 500 and 1000 miles§ and ※more than 1000 miles§ (Optional box)
  8. Order size(Textbox)
  9. Container capacity(Textbox)
  10. Item cost(Textbox)
  11. Holding cost rate(Textbox)
  12. Options for ※Run Sensitivity Analysis§, ※Reset§ and ※Home§ are provided

 

3

User can enter values and click on ※Run Sensitivity Analysis§

 

4

 

System checks the validity of the input information

5

 

If all values are valid, the system performs the analysis and takes the user to the ※Experiment Results§ page; otherwise asks the user to reenter the invalid values

6

User can click ※Reset§ button

 

7

 

All values entered should be cleared

8

User can choose ※Home§ link

 

9

 

System should display the homepage

 

Use Case: View the Experiment Results

 

Use Case Scenario for ※View the Experiment Results§

 

Actor Action

System Response

1

The use case begins when the actor clicks the ※Run Sensitivity Analysis§ button on the page ※Sensitivity Analysis§

 

2

 

Displays the following item:

  1. Experiment Factors(Text)
  2. Analysis results(Text)
  3. ※Return§(Button)

 

3

User can click ※Return§ button

 

4

 

System returns to the ※Sensitivity Analysis§ page

 

 

Use Case: Update the Specific Transfer Information

 

Use Case Scenario for ※Update the Specific Transfer Information§

 

Actor Action

System Response

1

The use case begins when the user choses to update the Specific Transfer Information

 

2

 

Displays the input boxes such as ※Choose the city§, ※Choose the From Mode§, ※Choose the To Mode§, ※Cost data§ and ※Setup time data§

3

The user inputs the new data into these input boxes

 

4

The user clicks the submit button

 

5

 

System checks the validity of the input data

6

 

If all values are valid, the system updates the database with the new data; otherwise  asks the user to reenter the data

7

User can click ※Cancel§ button

 

 

 

 

7.4  Application Design

As mentioned in Section 5, the architecture of WebShipCost每Risk consists of five Java packages.  Each package contains a set of interfaces and/or classes. 

         wscrisk.graph:                Package of graph building related interface and classes.

         wscrisk.algorithm:           Package of  shortest path algorithm related interface and classes.

         wscrisk.analysis:             Package of interfaces and classes used for performing risk analysis and sensitivity analysis.

         wscrisk.comparator:       Package of a variety of comparators used for sorting algorithm.

         wscrisk.util:                    This package contains some auxiliary classes providing functions such as database connection management, debugging output, etc.

 

As the first three packages are the most important, we discuss them in detail.

7.4.1  Package wscrisk.graph

The purpose of the graph building package is to extract the information that is stored in the database and to build a proper intermodal graph representation for the shortest path algorithm.  A graph is a set of vertices and arcs.  Arcs are used to represent a linkage between two vertices.  For the details of graph representation, please refer Rossetti & Nachtmann (2003).  The package diagram is the following:

 

 

Figure 7‑2 Class Diagram of Graph Package

 

 

In Interface GraphBubilder defines the behaviors of the classes responsible for graph construction.  The four methods shown in Table 7-4 are the most important.

 

Table 7‑4 Interface GraphBuilder Method Summary

 

Method Summary

public void

buildGraph()

build the graph, has to be implemented by sub class

public Graph

getMyGraph()

return the graph, implemented by the abstract class

public Object

getMyGraphProperty(Object objKey)

return a specific property object of the graph, the meaning of the properties are defined by the user; if the objKey is not defined, return null.

public Object

putMyGraphProperty(Object objKey, Object objValue)

save the specific graph property into GraphBuilder's property map structure

 

 

For our specific problem, WSCGraphBuilder knows the WebShipCost 每 Risk database structure and is responsible for the intermodal transportation network construction.  It extends from the abstract class AbstractGraphBuilder which implements the GraphBuilder interface. 

 

Class VertexKey has two purposes.  The first purpose is to hold the information associated with a specific vertex in the network.  This is very useful during the graph construction process.  The second function is to store all of the information about the vertex used to retrieve the path information at a later time.  For example, in package analysis, class WSCProblemSolver uses this information to build the path representation.  In addition to that, the vertex information is used during the AHP analysis.

 

There is one difference between the current program*s graph and the graph used in the WebShipCost project.  Since we incorporate the uncertain elements these elements must be stored in the graph.  Class EdgeElement is used to hold the time and cost distribution for the arcs.

 

7.4.2  Package wscrisk.algorithm

This package contains the interfaces and classes that handle the shortest path solving problem.  The following is the diagram:

 

Figure 7‑3 Class Diagram of Algorithm Package

 

Two main methods are defined by the interface ShortestPathAlgorithm, i.e. doGetMyShortestPathes() and evaluateShortestPathes().  All of the shortest path algorithms should implement this interface.  In this project, we implemented the double sweep algorithm developed by (Shier, 1974) in the class DoubleSweep to solve the k shortest path problem.  The double sweep algorithm is an iterative process. Thus, another interface IterativeProcess is defined and class DoubleSweep also implements this interface.  In fact, DoubleSweep extends the abstract class AbstractIterativeProcess since it implements some methods for progrommer convenience.  Class DoubleSweep handles the general Graph object generated by the GraphBuilder.  All of the specific problem related issues such as path representation and path evaluation are separated from the general algorithm.  The method summary of these two interfaces and package diagram is given in Table 7-5.

 

Table 7‑5 Interface ShortestPathAlgorithm Method Summary

Method Summary

public List

doGetMyShortestPathes()

return shortest paths

public void

evaluateShortestPathes()

compute the shortest paths

 

 

7.4.3  Package wscrisk.analysis

This package contains key classes and interfaces for risk and sensitivity analysis.  Figure 7-4 presents the class diagram:

Figure 7‑4 Class Diagram of Analysis Package

 

Interface SPProblemSolver takes GraphBuilder and ShortestPathAlgorithm as its input parameters.  We encapsulate problem specific tasks into classes implemented this interface.  For example, class WSCProblemSolver knows the WebShipCost每Risk problem context and does a series of tasks such as build the path description which is related to our specific transportation network.  Here is the interface definition.

Table 7‑6 Interface SPProblemSolver Method Summary

Method Summary

public void

evaluateShortestPathes()

construct the List of path objects

public List

getMyShortestPaths()

return the list of path objects

 

Class WSCPath denotes the path object which is a fundamental element in this problem.  One important method is doMonteCarloSimulation().  In this method the Monte Carlo simulation is implemented to evaluate the variability of cost and time attributes of the path. 

 

Another key class is WSCAHP which accepts a list of path objects and does AHP analysis on them.  Most of the methods are self 每 explanatory and are listed in Table 7-7:

Table 7‑7 Class WSCAHP Method Summary

Method Summary

private List

computeTotalWeight()

public List

evaluate()

implement the AHP methodology here

private void

setMyCostThreshold()

specify from the optimal path set

public void

setMyCostThresholdFactor(double myCostThresholdFactor)

public void

setMyCostWeight(double myCostWeight)

public void

setMyLUBoundThresholdFactor(double myLUBoundThresholdFactor)

public void

setMyReliabilityWeight(double myReliabilityWeight)

private void

setMyTimeThreshold()

specify from the optimal path set

public void

setMyTimeThresholdFactor(double myTimeThresholdFactor)

public void

setMyTimeWeight(double myTimeWeight)

 

Finally,  in order to perform the sensitivity analysis we implement the experiment design methodology.  Class Factor denotes the experiment factor and holds the information such as factor name, factor levels, etc.  Interface Experiment defines the general behavior of an experiment.  The key method is doExperiment() and doAnalysis() which are necessary for the subclasses to override and put the specific tasks here.

 

 

8        References

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