Fleet Management

Fleet management addresses the problem of managing fleets of trailers, containers, boxcars, taxicabs, locomotives and business jets. In many applications, requests to be moved from one location to another arrive randomly over time. Since it may take days to move from one location to the next, it is often useful (even necessary) to reposition equipment before a customer demand is known. We use the techniques of stochastic optimization to solve two-stage and multistage fleet management problems, using the problem of rail car distribution as the motivating application. Rail car distribution is characterized by a high degree of randomness: in the orders being placed by the customers, in the empty cars becoming available, and in the transit times between locations. Car distribution problems also introduce other issues that are not typically addressed in the classical stochastic programming literature, such as lagged information processes, the need for discrete solutions, and the challenges posed when the relevant attributes of a car are allowed to grow (a common progression when solving real problems). This chapter is intended to introduce the reader to a real problem, providing a bridge between the classical literature of stochastic programming and the modeling and algorithmic challenges that would arise while solving a real problem.

[1]  F. Downton.  Stochastic Approximation , 1969, Nature.

[2]  Warren B. Powell,et al.  An Adaptive Dynamic Programming Algorithm for the Heterogeneous Resource Allocation Problem , 2002, Transp. Sci..

[3]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[4]  H. Robbins.  A Stochastic Approximation Method , 1951 .

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

[6]  Warrren B Powell,et al.  A discrete on-line monotone estimation algorithm , 2003 .

[7]  J. Birge,et al.  A separable piecewise linear upper bound for stochastic linear programs , 1988 .

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

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

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

[11]  S C Misra.  LINEAR PROGRAMMING OF EMPTY WAGON DISPOSITION , 1972 .

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

[13]  H Herren.  THE DISTRIBUTION OF EMPTY WAGONS BY MEANS OF COMPUTER. AN ANALYTICAL MODEL OF THE SWISS FEDERAL RAILWAYS , 1974 .

[14]  George B. Dantzig,et al.  Linear Programming Under Uncertainty , 2004, Manag. Sci..

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

[16]  T G Crainic,et al.  A DYNAMIC STOCHASTIC MODEL FOR THE ALLOCATION OF EMPTY CONTAINERS , 1991 .

[17]  J. Blum.  Multidimensional Stochastic Approximation Methods , 1954 .

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

[19]  John N. Tsitsiklis,et al.  Neuro-Dynamic Programming , 1996, Encyclopedia of Machine Learning.

[20]  U. Rieder,et al.  Markov Decision Processes , 2010 .

[21]  Ali E. Haghani,et al.  Formulation and solution of a combined train routing and makeup, and empty car distribution model , 1989 .

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

[23]  Yuri Ermoliev,et al.  Stochastic quasigradient methods. Numerical techniques for stochastic optimization , 1988 .

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

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

[26]  R. Wets,et al.  Stochastic programming , 1989 .

[27]  G. Infanger,et al.  Planning under uncertainty solving large-scale stochastic linear programs , 1992 .

[28]  Warren B. Powell,et al.  Dynamic-Programming Approximations for Stochastic Time-Staged Integer Multicommodity-Flow Problems , 2006, INFORMS J. Comput..

[29]  Peter Stone,et al.  Reinforcement learning , 2019, Scholarpedia.

[30]  Martin Joborn.  Optimization of empty freight car distribution in scheduled railways , 2001 .

[31]  Yu. M. Ermol'ev,et al.  Planning of shipping empty seaborne containers , 1976 .

[32]  Stein W. Wallace.  A piecewise linear upper bound on the network recourse function , 1987, Math. Program..

[33]  Stein W. Wallace,et al.  Solving stochastic programs with network recourse , 1986, Networks.