A general system theory approach to rail freight car fleet sizing

Abstract The transportation of goods from shippers to consignees is a railroad's major activity. Rail freight cars are enormously expensive and a rail vehicle fleet represents one of the largest capital resources of most railroads. Resource allocation to rail freight cars is an extraordinary complex managerial problem. This paper describes the determination of an optimal number of rail freight cars so as to satisfy the demand, on one hand, and minimize the total cost, on the other. A new mathematical model relying on optimal control theory is developed. The problem is formulated as the problem of finding an optimal regulator for a linear system, excited by Gaussian white noise, a quadratic performance index, and random initial conditions. The model has been tested on numerical examples.

[1]  R. Hall,et al.  Fleet sizing and empty equipment redistribution for center-terminal transportation networks , 1997 .

[2]  Yen-Shwin Shan.  A dynamic multicommodity network flow model for real time optimal rail freight car management , 1985 .

[3]  Mark A. Turnquist,et al.  MODEL FOR MANAGEMENT OF EMPTY FREIGHT CARS , 1982 .

[4]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[5]  Warren B. Powell,et al.  A Multiplier Adjustment Method for Dynamic Resource Allocation Problems , 2000, Transp. Sci..

[6]  Linos F. Frantzeskakis,et al.  A Successive Linear Approximation Procedure for Stochastic, Dynamic Vehicle Allocation Problems , 1990, Transp. Sci..

[7]  Mark S. Daskin,et al.  Logistics: An overview of the state of the art and perspectives on future research , 1985 .

[8]  Veena B. Mendiratta.  A dynamic optimization model of the empty car distribution process , 1981 .

[9]  Joseph M. Sussman,et al.  INVENTORY MODEL OF THE RAILROAD EMPTY-CAR DISTRIBUTION PROCESS , 1977 .

[10]  Warren B. Powell,et al.  Dynamic Control of Logistics Queueing Networks for Large-Scale Fleet Management , 1998, Transp. Sci..

[11]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[12]  William C. Jordan,et al.  A STOCHASTIC, DYNAMIC NETWORK MODEL FOR RAILROAD CAR DISTRIBUTION , 1983 .

[13]  Warren B. Powell,et al.  An Algorithm for Multistage Dynamic Networks with Random Arc Capacities, with an Application to Dynamic Fleet Management , 1996, Oper. Res..

[14]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[15]  Hanif D. Sherali,et al.  Static and dynamic time-space strategic models and algorithms for multilevel rail-car fleet management , 1997 .

[16]  Warren B. Powell,et al.  A Stochastic Formulation of the Dynamic Assignment Problem, with an Application to Truckload Motor Carriers , 1996, Transp. Sci..

[17]  William C. Jordan,et al.  Fleet Sizing under Production Cycles and Uncertain Travel Times , 1986, Transp. Sci..

[18]  S. Sethi,et al.  The Dynamic Transportation Problem: A Survey , 1980 .

[19]  Warren B. Powell,et al.  Real-Time Optimization of Containers and Flatcars for Intermodal Operations , 1998, Transp. Sci..

[20]  Benita M. Beamon,et al.  Performability-based fleet sizing in a material handling system , 1998 .

[21]  Chelliah Sriskandarajah,et al.  Design and operational issues in AGV-served manufacturing systems , 1998, Ann. Oper. Res..

[22]  William R. Lesyna.  Sizing industrial rail car fleets using discrete-event simulation , 1999, WSC '99.

[23]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[24]  Warren B. Powell,et al.  Dynamic fleet management as a logistics queueing network , 1995, Ann. Oper. Res..

[25]  M. Mesarovic,et al.  Theory of Hierarchical, Multilevel, Systems , 1970 .

[26]  H. Stern,et al.  DEFICIT FUNCTION BUS SCHEDULING WITH DEADHEADING TRIP INSERTIONS FOR FLEET SIZE REDUCTION , 1981 .

[27]  Paolo Toth,et al.  A Survey of Optimization Models for Train Routing and Scheduling , 1998, Transp. Sci..

[28]  Joseph G. Monks,et al.  Operations Management: Theory and Problems , 1977 .

[29]  Mark A. Turnquist,et al.  A Model for Fleet Sizing and Vehicle Allocation , 1991, Transp. Sci..

[30]  M. Liou.  A novel method of evaluating transient response , 1966 .

[31]  P. Kleindorfer,et al.  Quadratic performance criteria with linear terms in discrete-time control , 1967, IEEE Transactions on Automatic Control.

[32]  Martin Joborn,et al.  Improved Empty Freight Car Distribution , 1998, Transp. Sci..

[33]  Michael L. McGinnis,et al.  A heuristic methodology for sizing a large-scale system of constrained, reusable resources , 1997, J. Heuristics.

[34]  Radivoj Petrovic,et al.  Hierarchical Spare Parts Inventory Systems , 1986 .

[35]  Mark A. Turnquist,et al.  Research opportunities in transportation system characteristics and operations , 1985 .

[36]  B. Vinod,et al.  Optimal prepositioning of empty freight cars , 1984 .

[37]  William W. White,et al.  Dynamic transshipment networks: An algorithm and its application to the distribution of empty containers , 1972, Networks.

[38]  D. Joseph,et al.  On linear control theory , 1961, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[39]  Bruce L. Golden,et al.  VEHICLE ROUTING: METHODS AND STUDIES , 1988 .

[40]  S. H. Sim,et al.  Queue-dependent vehicle dispatching with options and optimal fleet size , 1982 .

[41]  Michael Athans,et al.  Optimal Control , 1966 .

[42]  Warren B. Powell,et al.  Stochastic and dynamic networks and routing , 1995 .

[43]  William W. White,et al.  A Network Algorithm for Empty Freight Car Allocation , 1969, IBM Syst. J..

[44]  S. C. Parikh.  On a Fleet Sizing and Allocation Problem , 1977 .

[45]  Gene F. Franklin,et al.  A General Solution for Linear, Sampled-Data Control , 1963 .

[46]  Denos C. Gazis,et al.  On-Line Estimation of Traffic Densities from Time-Series of Flow and Speed Data , 1971 .

[47]  Richard C. Grinold,et al.  Model Building Techniques for the Correction of End Effects in Multistage Convex Programs , 1983, Oper. Res..

[48]  J. P. Saksena,et al.  An optimal fleet utilisation problem , 1986 .

[49]  Warren B. Powell,et al.  Mitigating end effects in the dynamic vehicle allocation model , 1988 .

[50]  Warren B. Powell,et al.  A Stochastic Model of the Dynamic Vehicle Allocation Problem , 1986, Transp. Sci..

[51]  Warren B. Powell,et al.  A COMPARATIVE REVIEW OF ALTERNATIVE ALGORITHMS FOR THE DYNAMIC VEHICLE ALLOCATION PROBLEM , 1988 .

[52]  Warren B. Powell,et al.  THE DYNAMIC VEHICLE ALLOCATION PROBLEM WITH UNCERTAIN DEMANDS , 1987 .

[53]  I. Gertsbach,et al.  Constructing an Optimal Fleet for a Transportation Schedule , 1977 .

[54]  John E. Beasley,et al.  Vehicle Fleet Composition , 1983 .

[55]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[56]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[57]  Teodor Gabriel Crainic,et al.  Survey Paper - A Review of Empty Flows and Fleet Management Models in Freight Transportation , 1987, Transp. Sci..

[58]  Hanif D. Sherali,et al.  LARGE-SCALE NETWORK DISTRIBUTION OF POOLED EMPTY FREIGHT CARS OVER TIME, WITH LIMITED SUBSTITUTION AND EQUITABLE BENEFITS , 1985 .

[59]  Russell L. Ackoff,et al.  Introduction to operations research , 1957 .

[60]  Charles S. Tapiero.  TRANSPORTATION‐LOCATION‐ALLOCATION PROBLEMS OVER TIME* , 1971 .

[61]  Hanif D. Sherali,et al.  A Tactical Decision Support System for Empty Railcar Management , 1998, Transp. Sci..