Stochastic Programming in Transportation and Logistics

Abstract

Freight transportation is characterized by highly dynamic information processes: customers call in orders over time to move freight; the movement of freight over long distances is subject to random delays; equipment failures require last minute changes; and decisions are not always executed in the field according to plan. The high-dimensionality of the decisions involved has made transportation a natural application for the techniques of mathematical programming, but the challenge of modeling dynamic information processes has limited their success. In this chapter, we explore the use of concepts from stochastic programming in the context of resource allocation problems that arise in freight transportation. Since transportation problems are often quite large, we focus on the degree to which some techniques exploit the natural structure of these problems. Experimental work in the context of these applications is quite limited, so we highlight the techniques that appear to be the most promising.

Multi-period stochastic optimization problems in transportation management

“…Many papers investigate stochastic optimization models for fleet management, see [Crainic, 2003], [Frantzeskakis & Powell, 1990], [Powell & Topaloglu, 2003], and [Powell, 2011]. Here, the uncertainty is mostly due again to customer demands that arise randomly over time, and the models emphasize issues related to the repositioning of empty vehicles and to the acceptance or rejection of incoming orders.…”

SMART: A Stochastic Multiscale Model for the Analysis of Energy Resources, Technology, and Policy

“…This contrasts with the use in Pereira & Pinto (1991) of multidimensional cuts based on Benders decomposition, which carries with it provable convergence properties (Higle & Sen (1991), Ruszczyński (1993)). We have compared both of these strategies and found that the separable approximations produced much faster convergence than approximations based on Benders cuts (see for an analysis in the context of two-stage problems) and very accurate solutions for complex multistage problems that arise in transportation (see Powell & Topaloglu (2003, Topaloglu & Powell (2006)). However, both strategies use the same basic idea of forming piecewise linear approximations based on dual information.…”

An Approximate Dynamic Programming Approach to Urban Freight Distribution with Batch Arrivals

“…Furthermore, a distinction can be made between myopic policies and policies that explicitly take into account information regarding future demand, the latter vastly increasing complexity [5,8]. The use of information regarding future events in transportation is recognized as an important aspect of optimization, yet its incorporation in solution methods is still an ongoing development [9,5,12].…”

“…Mathematical programming has traditionally been applied to handle high-dimensional problems in transportation. However, this method generally does not cope well with stochastic information revealed over time [9]. Topaloglu and Powell [13] present a generic framework for solving dynamic resource-allocation problems.…”

“…Provided that the value functions of the defined problem can be accurately approximated, ADP is a powerful approach to solve realistic transportation problems. Following frameworks such as [9,13,8], we develop an ADP approach to solve our dispatch problem. We aim to contribute to existing literature with (i) the formulation of a Markov model for DDPs with time windows, and (ii) an ADP approach to provide high-quality solutions for realistic-sized DDPs.…”