OPTIMIZATION OF CHASSIS REALLOCATION IN DOUBLESTACK
CONTAINER TRANSPORTATION SYSTEMS
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
By
ERNEST DAVID JUSTICE, B.S., M.S.C.S.E
University of Arkansas, 1984
University of Arkansas, 1988
August 1995
University of Arkansas
This dissertation is approved for
recommendation to the
Graduate Council
Dissertation Director:
Hamdy A. Taha
Dissertation Committee:
G. Don Taylor
Ronald W. Skeith
Earnest W. Fant
ACKNOWLEDGEMENTS
This research was supported in part by a grant from the U.S. Department of Transportation, through the Mack-Blackwell National Rural Transportation Study Center. This support is gratefully acknowledged but implies no endorsement of the conclusions stated herein.
I am indebted to my adviser, Dr. Hamdy A. Taha for the opportunity provided in relation to this work. I am even more appreciative of the support and patience displayed by Dr. Taha during the course of this project.
I am thankful to the other members of my dissertation committee, Dr. Don Taylor, Dr. Ron Skeith, and Dr. Earnest Fant for their guidance and helpful suggestions.
I owe a particular debt of gratitude to Dr. Skeith for his guidance and support throughout my graduate level educational experience.
I would also like to acknowledge the support and encouragement of my colleagues in the Agricultural Economics Department.
Most importantly, I appreciate the love, patience, and understanding of my wife, Elizabeth during the long hours required of this work.
TABLE OF CONTENTS
CHAPTER 1 INTRODUCTION............................................... 1
1.0 Brief Overview............................................ 1
1.1 Objectives of the Research................................ 1
1.2 Significance of the Research.............................. 2
1.3 Dissertation Organization....... 3CHAPTER 2 SYSTEM OVERVIEW 4
2.0 Definitions and Descriptions.............................. 4
2.1 COFC Service Review....................................... 5
2.1.1 COFC History....................................... 5
2.1.2 Current COFC Conditions............................ 8
2.1.3 Chassis Management.... 10CHAPTER 3 LITERATURE REVIEW 13
3.0 Introduction............................................. 13
3.1 Empty Equipment Models................................... 14
3.2 Intermodal Models......... 19CHAPTER 4 SOLUTION METHODOLOGY 23
4.0 Introduction............................................. 23
4.1 Problem Statement........................................ 23
4.2 Solution Approach........................................ 24
4.2.1 A Uni-Directional Model........................... 24
4.2.2 A Bi-Directional Model............................ 26
4.2.3 A Bi-Directional Time Based Model................. 28
4.3 Chassis Reallocation Model Elements...................... 32
4.4 Model Nomenclature ...................................... 33
4.5 Solution Model Formulation............................... 35
4.6 Model Complexity......................................... 35
4.7 Model Implementation...... 38CHAPTER 5 SOFTWARE DEVELOPMENT 39 5.0 Introduction............................................. 39
5.1 High Level Design and Operation.......................... 39
5.1.1 Model Scenarios.................................... 41
5.1.2 Computerized System Design......................... 44
5.2 Software Implementation.................................. 46
5.2.1 Development and Operation Environment.............. 46
5.2.2 CHREMAN System Programs............................ 47
5.2.2.1 The CHREMAN Program....................... 49
5.2.2.2 The SCHMAN Program........................ 53
5.2.2.3 The TCTEST Program........................ 53
5.2.2.4 The SUDMID Program........................ 56
5.2.2.5 The CSDVAL Program........................ 58
5.2.2.6 The LTRRA Program ....................... 60
5.3 Software Summary........... 62CHAPTER 6 SOFTWARE EVALUATION 63
6.0 Introduction............................................. 63
6.1 Intermodal System Components............................. 64
6.1.1 Physical Network................................... 64
6.1.2 Train Schedules.................................... 66
6.1.3 Time Estimates..................................... 66
6.1.4 Cost Estimates..................................... 68
6.1.5 Container Loadings................................. 70
6.2 Verification............................................. 74
6.2.1 Verification Results............................... 76
6.2.2 Verification Summary............................... 82
6.3 Characterization.......................................... 82
6.3.1 CHREMAN Memory Requirements........................ 83
6.3.2 CHREMAN Execution Speed............................ 84
6.3.3 Characterization Summary 85CHAPTER 7 RESEARCH APPLICATIONS 87
7.0 Introduction............................................. 87
7.1 Planning Period Experiment. . . . . . . . . . . . . . . . 87
7.1.1 Experimental Design................................ 88
7.1.2 Experimental Results............................... 90
7.1.3 Further Analysis................................... 92
7.1.4 Experimental Conclusions........................... 94
7.2 Predicted Loading Experiment............................. 94
7.2.1 Experimental Design................................ 95
7.2.2 Experimental Results............................... 96
7.2.3 Experimental Conclusions 98CHAPTER 8 CONCLUSIONS AND FUTURE RESEARCH 100
8.0 Introduction............................................. 100
8.1 Conclusions.............................................. 100
8.2 Future Research.......................................... 101
REFERENCES.......................................................... 103
APPENDIX A.......................................................... 105
APPENDIX B.......................................................... 122
CHAPTER 1
INTRODUCTION
1.0 Brief Overview
This dissertation addresses the issue of chassis logistics associated with containerized freight movements in the intermodal transportation industry. The focus of the associated research effort is the development of a model that provides solutions to chassis logistic problems that typically occur in industry. Subsequent to model development is the incorporation of the model into a software system that provides decision support for chassis fleet management on a continuing basis. Requirements for such a system include the ability to provide solutions in a reasonable time frame while featuring a favorable operating environment for the user. Chassis logistics problems are similar in structure to other problems in the transportation industry. Thus the knowledge gained in this effort may prove useful in other transportation applications.
1.1 Objectives of the Research
There are four objectives of this research:
1. Construct a model that provides minimum cost solutions to chassis allocation problems and characterize the complexity of the model in order to demonstrate its practical significance.
2. Develop a software system that incorporates the model as a basis for
decision support in chassis fleet management issues.
3. Evaluate the effectiveness of the solution software in scenarios supported by data collected from industry.
4. Propose and assess strategies for integrating the software into operational environments.
Achievement of these objectives requires knowledge and skill from two distinct fields:
1. Development and analysis of models to solve large decision problems requires skill in the field of operations research.
2. The incorporation of these models into functionally practical software systems requires development skills associated with the field of computer science.
1.2 Significance of the Research
The significance of this work is rooted in the issue of equipment utilization in the intermodal transportation industry. Effective equipment management translates into lower capital equipment investment and fewer equipment shortages that can be costly and disruptive in daily business operations. Ineffective management of equipment assets is generally agreed upon as universal problem in the intermodal industry. This is evidenced by the fact that turn-around times for intermodal containers average 1.7 times per month versus 4 times per month for over-the-road trailers [Sparkman, 1994]. Recent industry resolutions to equipment utilization problems involved additional investment in equipment to offset shortages (see for example Richardson [1994], or MacDonald [1994]). At present, intermodal equipment shortage problems have been relieved due to the recent equipment investments. However an acknowledged lack of control of asset utilization, most particularly with respect to chassis, is among the most important challenges facing the intermodal industry (see Anonymous, Traffic World [1994] or Sparkman [1995]). Improved use of information available through computerized information systems is an alternative that can assist in addressing these problems.
Certainly intermodal equipment utilization problems involve more than reduction of equipment and operating cost in chassis fleet management. However it is likely that success in resolving chassis logistics problems could result in better understanding of supply and demand structures in addition to improved planning and forecasting in the industry.
1.3 Dissertation Organization
The remainder of this dissertation begins with a description of the current system in Chapter 2 that is initiated by a review of the historical development of container based intermodal freight transportation. Chapter 3 is a review of the related literature that illustrates the absence of information that effectively addresses chassis reallocation issues. A detailed solution model for chassis reallocation is presented in chapter 4 and is followed by the discussion of a software implementation of the model in chapter 5. An exploration of computational issues and related software experience is in chapter 6. This is followed by a study of research applications in chapter 7. Conclusions and directions for further research are addressed in chapter 8.
CHAPTER 2
SYSTEM OVERVIEW
2.0 Definitions and Descriptions
The term "intermodal" as applied in the transportation industry refers to the involvement of more than one form of carrier during the movement of freight from source (the shipper) to destination (the consignee). The form of a carrier refers to the mode of transportation employed by the carrier, with typical examples being railcar, highway truck, aircraft, or ocean vessel transport. Most intermodal cargo must be reloaded in the transition from one mode to another. The dominant forms of intermodal transportation in practice today involve mixes of rail-truck, ocean-rail, and ocean-truck transport. The two most common forms of intermodal rail transport services are TOFC (trailer on flatcar) and COFC (container on flatcar). TOFC involves the transport of an entire highway trailer containing freight on a railcar. COFC services require the loading of containers of freight from either a ship or a truck for the rail portion of the journey.
A typical example involves a truck hauling a load from a shipper to an intermodal terminal. At the terminal the load is secured on a flatcar (COFC or TOFC) and hauled some distance by rail to another intermodal terminal in the vicinity of the consignee. The final segment of the journey is the haul from the second terminal to the consignee. In industry terminology a haul by truck to or from the terminal is a "short haul" and the longer trip by rail is the "line haul". Note that the rail portion of COFC services involves transport of containers only. This allows containers to be stacked in specially designed doublestack cars for vertical space efficiency. Containers that are to be hauled by truck must be attached to highway chassis designed to mate with containers. Individual chassis configuration requirements are tied to container size which is commonly 20 and 40 feet in length for international containers and 45, 48, and 53 feet for domestic containers. Extendable chassis exist that are capable of accommodating domestic containers sizes of 48 or 53 feet. COFC movements and the inherent logistics problem of satisfactorily mating containers and chassis is the primary focus of this paper.
2.1 COFC Service Review
2.1.1 COFC History
The origins of modern container based intermodal transportation go as far back as the late eighteenth century in England. In this instance coal was hauled in iron crates by horse drawn trams to a nearby canal and loaded by crane onto ships [McKenzie et al., 1989]. Experiments continued on a relatively small scale throughout the nineteenth century in both England and North America, with American examples involving both ship and rail transport. Sustained ventures into containerization did not occur until after World War I when transfer delays, high operating costs, and disproportionate damage claim ratios associated with less-than-carload (LCL) shipments troubled U.S. rail companies who were required to offer the service [Mahoney, 1985]. Benjamin Fitch developed a system for LCL intermodal transfer using trucks with demountable bodies that was first demonstrated in Cincinnati in 1917. He formed the Motor Terminals Company to service LCL rail traffic in the Cincinnati area after the war. This service, however, was short-lived due to the poor financial condition of the local interurban railroads [McKenzie et al., 1989]. Fitch later developed an intermodal system employing flatbed trailers, flatcars, sliding transfer equipment, and special insulated tanks for carrying milk from dairy sources to markets in urban areas. He formed the National Fitch Corporation and implemented his system successfully beginning in 1940 until the early 1950s [McKenzie et al., 1989].
New York Central Railroad also experimented with containerization in the 1920s in response to LCL shipment problems. The New York Central initially used 2800 pound steel containers placed in gondola cars to carry department store merchandise from New York to Chicago and later contracted with the U.S. postal service to transport mail in the containers [McKenzie et al., 1989].
The Pennslyvania Railroad, a chief competitor with the New York Central, operated a container service in the late 1920s that transported containers on flatcars fitted with mounting brackets. However this was more of a boxcar service since the containers were usually loaded and unloaded while still on the flatcars [McKenzie et al., 1989].
Although the aforementioned services employed containers largely in a combination of rail-truck services, they were never a significant business and were practically non-existent by the early 1950s [McKenzie et al., 1989]. A major reason for the lack of successful COFC or TOFC services during this period were restrictive regulatory policies enforced by the Interstate Commerce Commission (ICC) from 1931 through 1980. The ICC ruled in 1931 that commodities shipped in containers by rail must move at traditional high rail class (commodity-based) rates, rather than at lower flatcar rates [Mahoney, 1985]. This ruling effectively prevented railroads from competing with truckers in the merchandise freight market, allowing the truckers to dominate the market through the 1970s. Other reasons cited for the lack of intermodal freight industry development during the mid-twentieth century include government restrictions on establishing multi-modal companies to coordinate services, lack of commitment on behalf of railroad management, and railroad resolve against rail-truck cooperation [McKenzie et al., 1989; Mahoney, 1985].
The situation began to change in the 1950s when the ICC ruled in 1953 that hauling trailers by rail on flatcar was considered a rail transport and thus did not require a motor carrier certificate. Shortly afterward steamships carrying cargos of container freight began operating in the maritime shipping industry. These "containerships" originated with Malcom McLean and the Pan Atlantic Steamship Company in 1956 [Mahoney, 1985]. The "container revolution' caught on very quickly and replaced traditional breakbulk shipping as the dominant form of ocean goods transport over the next two decades. In the 1960s marine containers began to appear on railroads. They became common in the 1970s as so called "landbridge" intermodal services developed for the shipping of goods from overseas to inland or overseas destinations.
Landbridge refers to transfers of containers from ship to rail at a port on one coast followed by a rail haul to the other coast where the containers are loaded on another ship for transport overseas. Landbridge services came about with the growth of Pacific Rim export countries and their transport of goods to destinations in Europe and America. These routes are known to save significant time over all-water routes through the Panama Canal [McKenzie et al, 1989]. Services related to landbridge include minibridge and microbridge transport. Minibridge refers to enterprises that serve a second port by land transport from a single port call. In other words, the containers are destined for a second inland port instead of an overseas port as in landbridge services. Microbridge refers to services that connect inland origins or destinations with ocean container traffic [Mahoney, 1985].
Growth in the container based intermodal industry accelerated in the early 1980s as a result of deregulation, continued rapid growth of containerized imports, and advancing railway technology [U.S. Dept. of Transportation, 1990]. The Staggers Act of 1980 relaxed regulation of railroad rate determination policies and effectively prevented the ICC from challenging minimum rates as long as they covered variable costs. The ICC followed up in 1981 by exempting intermodal rates on rail service from the regulatory process. By 1984 all COFC/TOFC traffic rate regulation had been eliminated and the Shipping Act of 1984 facilitated intermodal billing consolidation. Doublestack railcar technology introduced in the late 1970s and early 1980s provided a means for improved cost efficiency and service quality. Doublestack cars are lighter than conventional flatcars and permit containers to be stacked, resulting in a more efficient use of vertical space, improved aerodynamics, and considerable fuel savings. Since these cars are articulated, ride quality is improved and freight damage is reduced [U.S. Dept. of Transportation, 1990].
2.1.2 Current COFC Conditions
Traffic switching from highway to intermodal exceeded traffic switching from intermodal to highway across the board in 1993 and is most significant in companies with revenues exceeding one billion dollars [Spizziri, 1994]. Unfortunately, data depicting the breakdown between TOFC and COFC intermodal traffic is scarce, but recent data published by the Association of American Railroads indicates that COFC traffic loading comprises the majority of intermodal traffic and that the COFC share is growing with respect to TOFC (See Table 2.1 below).
Table 2.1 Cumulative Traffic Originated, 1st 51 Weeks of Years Shown *
|
Traffic |
1994 |
1993 |
% Change |
|
Trailers |
3,821,244 |
3,458,406 |
10.5 |
|
Containers |
4,345,922 |
3,692,051 |
17.7 |
|
Total |
8,167,166 |
7,150,457 |
14.2 |
* Source: Association of American Railroads 1/25/95
Present concerns in the intermodal industry center on asset utilization with respect to intermodal equipment. Although recent equipment investments have resolved earlier equipment shortage problems, there is also concern that existing equipment is not being utilized efficiently and that improved management of assets is needed. Suggested means of improvement include better use of information systems, rail scheduling, and interchange management.
2.1.3 Chassis Management
The nature of COFC service in rail-truck environments requires maintenance of a separate chassis fleet for highway transport. Containers arriving at intermodal terminals must be loaded on an available highway chassis in order to be moved by truck. Conversely, containers must be detached from truck and chassis to be loaded on departing trains. This situation raises logistical questions concerning where, when, and how chassis should be positioned in order to insure the proper matching of chassis to containers.
Chassis management issues originated with the growth of marine-rail container transport in the 1960s. During that period neutral chassis pools were developed by leasing companies to relieve carriers of the burden of chassis management. The leasing services owned and maintained pools of chassis that would mate with stardard size containers, charging daily rates for chassis rental. However, the proliferation of leasing companies led to space problems at terminals that forced chassis lessors to move to off-terminal locations. As a result leasing costs continued to rise and many carriers chose to invest in the acquisition and management of their own chassis fleets [Braun, 1987]. In the late 1980s the neutral pool concept surged again with the advent of doublestack intermodal services [McKenzie et al., 1989]. This time fewer leasing companies set up operations at larger terminals, often contracting with a single rail or marine carrier at specific terminals.
In the 1990s the deregulated market has tempted new carriers into the intermodal market [Raper, 1994]. The concept of neutral chassis pools operated on a national level continues to be discussed as a solution to chassis management problems [Sparkman, 1995]. However, new carriers and established carriers alike continue to choose to own and manage their own COFC highway chassis fleet. In some cases carriers have opted for non-standard chassis-container combinations that limit the possiblity of their inclusion in neutral pools [Anonymous, Traffic World 1992].
Historically, chassis management practices have consisted of investing in large and under-utilized chassis fleets. Automated equipment tracking systems and advancing computer technology may provide means for improvement.
CHAPTER 3
LITERATURE REVIEW
3.0 Introduction
A review of literature focusing on transportation, computer, and operations research journals reveals no published work presenting solution procedures for chassis fleet management under central control in intermodal operations. The chassis fleet problem investigated in this work is similar in structure to a number of other problems addressed in the literature. Proposed solutions to these problems may be classified as operational level models in that they impact short term decisions made in daily business operations. Other models that address medium or long term decisions are classified as tactical or strategic models.
Examples of operational problems in the transportation industry include vehicle routing and scheduling problems as well as driver/crew assignment and scheduling problems [Powell, 1991]. More closely related to the subject of this work are fleet management problems and the various models in the literature that address them. Fleet management models generally involve the positioning of a fleet of vehicles or other similar equipment over a given period of time in response to given or forecasted demands. The types of fleets considered by transportation models include trucks, railcars, aircraft, and containers. Of particular interest to this work are those fleet management models that focus on empty vehicle or container positioning problems. Also of interest are a small set of models in the literature that address problems specific to intermodal operations.
The remainder of this review consists of a discussion of empty equipment allocation models in the next section followed by a review of the intermodal models of interest to this work.
3.1 Empty Equipment Models
White and Bomberault [1969] developed a model for empty freight car allocation in railroad systems. The authors formulate the problem as a space-time network flow problem that can be solved using linear programming techniques applicable to minimum cost flow network problems. The model incorporates four rules of flow for cars in the network as follows:
1. Cars become available at nodes in the network representing
specific points in time. They are either available at the
beginning or become available at locations as time progresses.
2. Cars are either required at nodes in the network during the
period of solution or they remain available at the end of the
time span.
3. For any node at any given time the number of cars arriving plus
the number of cars that become available is equal to the
number of cars leaving plus the number of cars required there.
4. The flow of cars is positive in time, cars cannot go backward in
time.
The formulation for the problem has a minimum cost objective with constraints that represent the rules of flow described above. An solution algorithm is described that uses an inductive method of solving successive subnetworks of the problem until the overall network solution is reached. White [1972] subsequently applied the solution principles of the empty freight car problem to the distribution of empty containers.
Misra [1972] also formulated a model of solution for the empty freight car allocation problem. This model represents the problem as a linear program with an objective of minimizing the total empty hours of the freight car fleet. Total empty hours are defined as the sum of waiting times at origin and destination stations plus the travel times between the stations. The constraints of the model represent route capacities and congestion definitions as well as supply and demand specifications.
Mendiratta and Turnquist [1982] developed a model for empty freight car distribution consisting of two interacting submodels. A network submodel maximizes profits over the entire network as constrained by empty freight car supply and demand. A terminal submodel incorporates inventory control principles for stochastic demands and lead times in empty freight car delivery. The models interact by iteratively exchanging shadow prices for cars in the network until the results of the submodels are consistent. At any given iteration the shadow prices for empty cars in the network represent the marginal value of the cars at their current location. The network model is a linear program that maximizes revenues less cost associated with moving empty cars between terminals subject to gross supply and demand at each terminal. Each solution of the network model generates a new set of shadow prices for cars in the network which are used by the terminal submodels representing each terminal in the network. The terminal submodels combine the generated shadow prices with shortage costs and order/release costs to determine the desired inventory of empty cars for particular terminals. This information is then transmitted back to the network submodel to solve for the next set of shadow prices. The network submodel solution effectively reduces the prices of resources in excess supply and increases the prices of resources for which there is excess demand. The exchange of information between the submodels continues until the results for the submodels match and the solution is considered optimal.
Kikuchi [1985] developed a model for dispatching empty railcars from freight car pools to demand points at minimum cost. The model is represented as a linear program with an objective of minimizing the sum of car shipment costs, car storage costs, holding costs for cars held at the end of the period, and penalty costs for car shortages. The constraint equations of the model are defined as follows:
1. Cars becoming available at unloading points throughout a day
must be dispatched to loading points or held for the remainder
of the planning horizon.
2. Daily demand for cars at loading points must be satisfied by
cars in the system and by cars dispatched in response to
shortages.
The solution procedure presented involves the formulation of the model as a transshipment problem that is solved as a linear programming problem.
Crainic et. al [1993] proposed models for the allocation of empty containers in land distribution and transportation systems in the context of international maritime shipping. The basic model discussed is a deterministic single commodity model, where single commodity means that container size substitutions are not allowed. The transportation system as defined consists of port depots, nonport depots, supply customers, and demand customers. Port depots are sources of containers at harbors where containers enter and exit the system. Nonport depots are inland depots where containers may be held before being transported to meet demand at other depots and customer locations. Supply customers refer to customers that have containers available after unloading them. Demand customers require empty containers for the loading function.
The objective of the model is to minimize the sum of costs during a given time period from the following sources:
1. The transportation of empty containers from depots to demand
customers.
2. The transportation of empty containers from supply customers to
depots.
3. The transportation of empty containers between depots.
4. The holding costs of empty containers at depots.
5. Costs of bringing in containers from outside the system.
6. Penalty costs for not satisfying demand for empty containers at
ports.
The constraints of the model are defined as follows:
1. The volume of empty containers allocated in a period for each
customer is equal to the customer demand minus the volume of
containers whose shipment to the customer was initiated prior
to the start of the period.
2. The volume of empty containers picked up during a period at each
customer is equal to the supply of empty containers that
become available at each customer location.
3. The stock of empty containers available at each nonport depot at
the end of a time period is equal to the stock at the
beginning of the period plus the flow of empty containers
arriving during the period minus the empty containers
departing during the period. Arriving empty containers are
defined to be those en route at the beginning of the period
plus those arriving from external sources and other depots and
supply customers. Departing containers are those sent to
other depots and demand customers during the period.
4. The stock of empty containers available at each port depot at
the end of a time period is defined similarly to that of
nonport depots except that export demand at each port depot
must be subtracted and import supply must be added. Export
demand represents external empty container demands that are
shipped on departing containerships. Import supply is empty
containers that come from external sources on arriving
containerships.
5. Balancing movements (i.e. flows between depots) are carried out
according to exogeneous bounds defined by policies and
agreements with carriers.
The suggested method of solution for the model described above involves its transformation into a dynamic network model applied in a rolling horizon framework. However specific algorithms for model solution are not presented.
Gao [1994] presented an approach for operational control in maritime shipping that includes the positioning of empty containers to correct imbalances during a planning period. A two stage process is defined with the initial stage concerned with identifying imbalances between supply and demand for empty containers given that cargo flows, containership schedules, and average unloading times are known. The second stage of the modelling process involves correcting the imbalances in the first stage with a minimum cost linear programming formulation whose objective function cost trems are defined as follows:
1. Storage costs of empty containers between voyages at each port.
2. Costs of positioning empty containers between ports during
voyages.
3. Costs of leasing/letting containers during consecutive voyages
at each port.
4. Capital costs of owning containers during consecutive voyages at
each port.
The constraints of the linear program are given as:
1. The number of empty containers available at a port after a
voyage equals the number available after the previous voyage
plus the net of leased/let containers and the net of
positioned containers minus the given imbalance.
2. The number of positioned empty containers arriving at a port i
from another port h on a voyage equals the number of
positioned empty containers leaving port h for port i on the
voyage.
3. Arriving empty containers take up space that is not greater than
space reserved at the receiving ports.
4. Departing empty containers take up space that is not greater
than space reserved at the destination ports.
5. The net of leased/let containers are not greater than the number
of containers available for leasing/letting.
Solutions to the hypothetical cases discussed were reached with the use of commercial linear programming software packages.
3.2 Intermodal Models
The work of Sinclair and Dyk [1987] addresses movements of containers by truck as a result of import and export activity at a maritime intermodal terminal. The described model considers the movement of containers between clients and between clients and the container depot at the intermodal terminal. All movements resulting from client supply and demand are considered, including truck movements with empty containers, full containers, and no containers. Chassis/container mating issues are not considered except in the context of containerless truck movements with or without chassis - both are unproductive. The objective of the model is the minimization of time spent on unproductive movements and waiting time between movements. The constraints discussed include client time window restrictions, driver shift restrictions, linking of related movements, client storage capacity, and company priorities for movements. A heuristic for model solution is presented since a mixed-integer linear programming formulation of the problem is too large for practical implementation.
The heuristic consists of two phases relating to preprocessing and scheduling. The preprocessing phase involves examining expected movements and determining feasible starting and ending time windows for the movements. Lists of movements and lists of clients with common characteristics, as well as a priority list of movements, are also constructed during the preprocessing phase. The scheduling phase implements a repeated selection of unscheduled movements from the priority list and adds movements before or after the priority movement according to the minimum sum of unproductive movements and waiting time added to the trip. When a complete route is formed, a vehicle is assigned to the route and the priority list is updated for selecting the next unscheduled movement.
In practice, the schedules developed using the heuristic often require adjustment as a result of scheduling conflicts.
Chih, Bidden, Hornung, and Kornhauser [1990] present a model for management of intermodal doublestack trains and discuss the implementation of the model in software. The model addresses marine-rail intermodal operations - specifically container loading and route selection aspects of COFC service. Highway chassis logistics are not included in this model.
The problem is presented as a cost minimization problem in a time-space network. Constraints on the system consist of fleet size constraints, car capacity constraints, container size constraints, and minimum car load constraints. The heuristic solution procedure is sequenced as follows:
1. Generate a time-space network based on train schedules and
physical characteristics of the network.
2. Account for the flow of cars in route in the network.
3. Route containers through the network that have been preassigned
to specific trains.
4. Route non-preassigned containers through the network based on
least initial cost.
5. Reroute the containers in step 4 based on updated costs from
estimated train length.
6. Use a network transhipment problem to match container flows with
available cars.
Spasovic [1990] developed a model concerned with the minimization of costs associated with the short haul highway portion of rail-truck intermodal transport. The model targets TOFC services exclusively and so does not address COFC operations or chassis logistics. The constraints in the model are time window constraints and fleet capacity constraints. The model accounts for various drop off and pick up policies in order to determine solutions that satisfy demands within a given level of service.
Two heuristic procedures are presented for model solution. First a two-stage solution procedure is presented that solves two sub-problems formulated as linear programs in order to obtain integer solutions. The second procedure is a multi-stage process that obtains improved integer solutions by exploiting the structure of the model.
Nozick [1992] presented a model of integrated rail-truck intermodal operations that provides solutions for activities within a basic time period of one day. Activities consist of load movements between shipper and consignee, movements of empty cars between terminals, and movements of empty trailers and containers between terminals. The basic model applies to TOFC operations and possible incorporation of containers in the model is only discussed with respect to the load assignment and conservation of flow constraints. Chassis fleet considerations are not included in the model, effecting the assumption that COFC operations are equivalent to TOFC operations.
The model is formulated as a large integer program with a minimum cost objective. Cost components consist of costs associated with satisfying load demands, repositioning empty trailers, and repositioning empty flatcars. Constraints are formulated for level of service (i.e. time window) requirements, trailer fleet conservation, and flat car conservation. The method of solution is a heuristic procedure based on the LP relaxed solution.
Barnhart and Ratliff [1993] present a methodology for determining minimum cost intermodal routing in a rail-truck context with no distinction made between TOFC and COFC routings, which means that chassis logistics are ignored. Routing problems with rail transport cost expressed per trailer are shown to be solvable using simple shortest path procedures. Routing problems with rail cost expressed per flatcar are shown to be solvable when allowing at most two units per flat car. The solution procedure in this case requires the establishment of link costs on a pairs network. Such a network is shown to be solvable by weighted matching algorithms.
In summary, the results of the literature review indicate that no work has been published on solution models supporting chassis distribution decisions in centrally controlled intermodal operations. Published intermodal models have not addressed the problem of interest, although papers addressing similar problems are a source of ideas in solution approaches.
CHAPTER 4
SOLUTION METHODOLOGY
4.0 Introduction
A feasible approach to chassis management logistic problems is to develop a planning model that may be implemented periodically to suggest an allocation of highway chassis (timing, number, location) that will assure a successful and efficient mating of chassis to containers. Such a model would require inputs defining the state of the system at the start of a period along with the flow of containers planned during the period. Results from the model would define a cost efficient flow of chassis corresponding to the given container flow.
4.1 Problem Statement
Assume at a point in time that a certain number of centrally controlled intermodal terminals (ramps) are doing COFC business. These terminals have the technology required to separate containers from highway chassis and load them onto rail cars. This technology permits containers to be unloaded from rail cars and placed on available chassis. Trucks pulling loaded containers on chassis arrive at ramps throughout the day. The containers are loaded on rail cars and the chassis may remain in storage at the ramp. At scheduled times the trains depart the origination ramps and make the journey to destination ramps, arriving at scheduled times. At destination ramps the containers are unloaded from the rail cars and placed on available chassis before being driven to consignees by truck.
Chassis may be pooled at the ramps from previous supplying operations or they may be loaded on rail cars and shipped from one ramp to another. In cases where ramps are located within reasonably close physical proximities, chassis can be driven by truck from one ramp to another.
When containers arrive by rail at a destination ramp, it is necessary to mate them with available chassis. The nature of normal business activity does not guarantee that a sufficient pool of chassis will remain at all ramps since container loads vary depending on the day of the week and the season. Ramps that have more arrivals than departures over time could deplete a supply of chassis unless some action is taken to redistribute the chassis on a timely basis. A method is needed to determine when, where, how many, and by what means (truck, rail) chassis are to be moved from one location to another.
4.2 Solution Approach
4.2.1 A Uni-Directional Model
A solution approach to the chassis reallocation problem can be considered in terms of the classic transportation problem. Consider the transportation network shown in Figure 4.1 where the defined ramps exist in the Chicago and Los Angeles metropolitan areas. The numbers in parentheses in Figure 4.1 represent the unit cost of transporting a chassis between the connecting ramps. In this network, all chassis moved between the Chicago and Los Angeles areas are shipped by rail from the Illinois ramp or the California ramp at a cost of $40. Chassis moved between ramps within the metropolitan areas are moved by truck at a cost of $20. The transportation problem illustrated in Table 4-1a is one of shipping chassis from supply ramps in the Chicago area to demand ramps in
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the Chicago Ramp to the Illinois Ramp, a $40 move from the Illinois Ramp to the California Ramp, and a $20 move from the California Ramp to the West Coast Ramp. The supplies are counts of chassis existing at the given ramps in the Chicago metropolitan area. The demands represent the number of chassis required at the given ramps in the Los Angeles area.
TABLE 4-1a
WC CA Supply
CH 80 60 2
IL 60 40 4
NC 80 60 6
Demand 5 7
The application of transportation model solution techniques to the example of Table 4-1a gives the solution shown in Table 4-1b. The largest cost in the solution is shown in the third entry in Table 4-1b, interpreted as the shipment of 5 chassis from the North Chicago Ramp to the West Coast Ramp at a cost of $400.
TABLE 4-1b
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From |
To |
Amount |
Cost/Unit |
Total Cost |
|
CH |
CA |
2 |
60 |
120 |
|
IL |
CA |
4 |
40 |
160 |
|
NC |
WC |
5 |
80 |
400 |
|
NC |
CA |
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