From Single Commodity to Multiattribute Models for Locomotive Optimization: A Comparison of Optimal Integer Programming and Approximate Dynamic Programming

Abstract

We present a general optimization framework for locomotive models that captures different levels of detail, ranging from single and multicommodity flow models that can be solved using commercial integer programming solvers, to a much more detailed multiattribute model that we solve using approximate dynamic programming (ADP). Both models have been successfully implemented at Norfolk Southern for different planning applications. We use these models, presented using a common notational framework, to demonstrate the scope of different modeling and algorithmic strategies, all of which add value to the locomotive planning problem. We demonstrate how ADP can be used for both deterministic and stochastic models that capture locomotives and trains at a very high level of detail.

A comparison of two exact methods for passenger railway rolling stock (re)scheduling

“…Cordeau et al [10], Cordeau et al [11], Lingaya et al [18], and Brucker et al [6]), but also to freight trains (see e.g. Ahuja et al [1], Rouillon et al [21], Vaidyanathan et al [22], and Bouzaiene-Ayari et al [5]). The problem of (re)scheduling self-propelled units is also considered in multiple publications (see e.g.…”

Approximate Dynamic Programming for a Class of Long-Horizon Maritime Inventory Routing Problems

“…However, their value function approximation requires hours of off-line training to construct; all of our computations are performed on-line. Bouzaiene-Ayari et al [5] tackle locomotive planning problems arising at Norfolk Southern. One of their models involves much more detail than the one presented here and ADP is successfully employed to generate high-quality solutions.…”

“…When the subproblem is a MIP, it is not clear whether similar dual information can be obtained. Bouzaiene-Ayari et al [5] solve MIP subproblems and report good results from updating the slopes of their VFAs using the duals of the LP relaxation. In all of our attempts, however, using the values of the dual variables π j,u,t from the LP relaxation was not productive.…”

“…The key difference between our problem and the DFMP is the presence of an inventory management component. A second reason is the success ADP has enjoyed when solving large-scale dynamic problems in road-based and rail-based applications found in industry [32,5]. A third motive is that ADP has the ability to accommodate stochasticity without drastic changes to the framework or implementation.…”

Clearing the Jungle of Stochastic Optimization

“…Even I concluded this in the 1980s while looking for methods to solve stochastic fleet management problems. But 20 years later, I finally cracked these problems with successful systems that are planning driver fleets for one of the largest truckload carriers in the country (Simão et al [59]) and planning locomotives at one of the largest railroads in the country (Bouzaiene-Ayari et al [13]). The same algorithmic strategy was used to solve a stochastic energy investment problem in hourly increments over 20 years with 175,000 time periods (see Powell et al [45]).…”