Incorporating Pricing Decisions into the Stochastic Dynamic Fleet Management Problem

This paper shows how to coordinate the decisions on pricing and fleet management of a freight carrier. We consider a setting where the carrier announces its prices at the beginning of a certain time horizon and the load arrivals over this horizon depend on the announced prices. Assuming that the vehicle fleet is managed according to a particular class of fleet management models, we present a tractable method to obtain sample path-based directional derivatives of the objective function with respect to the prices. We use this information to search for a good set of prices. Numerical experiments show that our approach yields high-quality solutions.

[1]  Warren B. Powell,et al.  Sensitivity Analysis of a Dynamic Fleet Management Model Using Approximate Dynamic Programming , 2007, Oper. Res..

[2]  W. Lieberman The Theory and Practice of Revenue Management , 2005 .

[3]  Garrett J. van Ryzin,et al.  Simulation-Based Optimization of Virtual Nesting Controls for Network Revenue Management , 2008, Oper. Res..

[4]  Yuri Ermoliev,et al.  Numerical techniques for stochastic optimization , 1988 .

[5]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[6]  Warren B. Powell Marginal cost pricing of truckload services: A comparison of two approaches , 1985 .

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

[8]  J. A. Rose Artifical Intelligence Through Prolog by Neils Rowe Prentice-Hall, Englewood Cliffs, New Jersey, U.S.A., 1988 (£15.95) , 1988, Robotica.

[9]  Warren B. Powell,et al.  A Review of Sensitivity Results for Linear Networks and a New Approximation to Reduce the Effects of Degeneracy , 1989, Transp. Sci..

[10]  Bernard Delyon,et al.  Accelerated Stochastic Approximation , 1993, SIAM J. Optim..

[11]  Dimitris Bertsimas,et al.  Simulation-Based Booking Limits for Airline Revenue Management , 2005, Oper. Res..

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

[13]  Michael C. Fu,et al.  Sample Path Derivatives for (s, S) Inventory Systems , 1994, Oper. Res..

[14]  D. R. Fulkerson,et al.  MINIMIZING THE NUMBER OF CARRIERS TO MEET A FIXED SCHEDULE , 1954 .

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

[16]  Garrett J. van Ryzin,et al.  Stocking Retail Assortments Under Dynamic Consumer Substitution , 2001, Oper. Res..

[17]  Martin W. P. Savelsbergh,et al.  The Stochastic Inventory Routing Problem with Direct Deliveries , 2002, Transp. Sci..

[18]  George B. Dantzig,et al.  The Problem of Routing Aircraft--A Mathematical Solution. , 1954 .

[19]  Itir Z. Karaesmen,et al.  Overbooking with Substitutable Inventory Classes , 2004, Oper. Res..

[20]  Paul Glasserman,et al.  Sensitivity Analysis for Base-Stock Levels in Multiechelon Production-Inventory Systems , 1995 .

[21]  Warren B. Powell,et al.  An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, I: Single Period Travel Times , 2002, Transp. Sci..

[22]  Kenneth S. Nickerson,et al.  Maximizing Profits for North American Van Lines' Truckload Division: A New Framework for Pricing and Operations , 1988 .

[23]  Warren B. Powell,et al.  Learning Algorithms for Separable Approximations of Discrete Stochastic Optimization Problems , 2004, Math. Oper. Res..

[24]  Michel Gendreau,et al.  Dynamic and Stochastic Models for the Allocation of Empty Containers , 1993, Oper. Res..

[25]  Yuri M. Ermoliev Stochastic Quasigradient Methods , 2009, Encyclopedia of Optimization.

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

[27]  Daniel Adelman,et al.  Price-Directed Control of a Closed Logistics Queueing Network , 2007, Oper. Res..

[28]  Julia L. Higle,et al.  Adaptive and nonadaptive samples in solving stochastic linear programs , 2005 .

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

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

[31]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

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

[33]  Huseyin Topaloglu,et al.  Incorporating the pricing decisions into the dynamic fleet management problem , 2007, J. Oper. Res. Soc..

[34]  Kellen Petersen August Real Analysis , 2009 .

[35]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

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

[37]  Paul Glasserman,et al.  Gradient Estimation Via Perturbation Analysis , 1990 .

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

[39]  Michael F. Gorman Intermodal Pricing Model Creates a Network Pricing Perspective at BNSF , 2001, Interfaces.