Chapter 3 Stochastic and dynamic networks and routing

Powell, Warren B.; Jaillet, Patrick; Odoni, Amedeo R.

doi:10.1016/s0927-0507(05)80107-0

Cited by 226 publications

(126 citation statements)

References 192 publications

Supporting

Mentioning

121

Contrasting

Unclassified

Order By: Relevance

“…Research on solving vehicle routing problems is common. Extensive reviews of the basic vehicle routing problem, time constrained routing and scheduling and dynamic and stochastic routing and scheduling can be found in Fisher (1995), Desrosiers et al (1995) and Powell, Jaillet and Odoni (1995), respectively.…”

Section: Gdp (Bts 1997)mentioning

confidence: 99%

Approximation algorithms for the bid construction problem in combinatorial auctions for the procurement of freight transportation contracts

Song

Regan

2005

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

The bid valuation and construction problem for carriers facing combinatorial auctions for the procurement of freight transportation contracts is very difficult and involves the computation of a number of NP-hard sub problems. In this paper we examine computationally tractable approximation methods for estimating these values and constructing bids. The benefit of our approximation method is that it provides a way for carriers to construct optimal or near optimal bids by solving a single NP-hard problem. This represents a significant improvement in efficiency. In addition, this method can be extended to many other applications.

show abstract

Section: Gdp (Bts 1997)mentioning

confidence: 99%

Approximation algorithms for the bid construction problem in combinatorial auctions for the procurement of freight transportation contracts

Song

Regan

2005

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

show abstract

“…Early survey papers by Assad (1978) and Kennington (1978) describe various solution approaches to the linear version. The integer version has seen increased attention due to its wide applicability to fields such as airline fleet assignment (Hane et al 1995), car and container distribution in the railroad and maritime industries (Jordan and Turnquist 1983, Shan 1985, Chih 1986, Crainic et al 1993, Holmberg et al 1998, and dynamic fleet management (Powell et al 1995). All of these problem instances involve solving the min-cost integer multicommodity flow problem on a state-time network, where the state is typically the location of the physical resource being managed.…”

Section: Introductionmentioning

confidence: 99%

Dynamic-Programming Approximations for Stochastic Time-Staged Integer Multicommodity-Flow Problems

Topaloğlu

Powell

2006

INFORMS Journal on Computing

Self Cite

168

142

View full text Add to dashboard Cite

In this paper, we consider a stochastic and time dependent version of the min-cost integer multicommodity flow problem that arises in the dynamic resource allocation context. In this problem class, tasks arriving over time have to be covered by a set of indivisible and reusable resources of different types. The assignment of a resource to a task removes the task from the system, modifies the resource, and generates a profit. When serving a task, resources of different types can serve as substitutes of each other, possibly yielding different revenues. We propose an iterative, adaptive dynamic programming-based methodology that makes use of linear and/or nonlinear approximations of the value function. Our numerical work shows that the proposed method provides high quality solutions and is computationally attractive for large problems.

show abstract

“…Examples of such models from three different industries are Dantzig and Fulkerson (1954), Hane et al (1995), andHolmberg et al (1998), and we refer the reader to Dejax and Crainic (1987) and Powell et al (1995) for detailed surveys. For these types of models, sensitivity information is readily obtained by using the dual solution.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Analysis of a Dynamic Fleet Management Model Using Approximate Dynamic Programming

Topaloğlu

Powell

2007

Operations Research

Self Cite

View full text Add to dashboard Cite

We present tractable algorithms to assess the sensitivity of a stochastic dynamic fleet management model to fleet size and load availability. In particular, we show how to compute the change in the objective function value in response to an additional vehicle or an additional load introduced into the system. The novel aspect of our approach is that it does not require multiple simulations with different values of the model parameters, and in this respect it differs from trial-anderror-based "what-if" analyses. Numerical experiments show that the proposed methods are accurate and computationally attractive. IntroductionGiven a vehicle fleet and a stochastic process characterizing the load arrivals in a transportation network, the primary objective of fleet management models is to make the vehicle repositioning and vehicle-to-load assignment decisions so that some performance measure (profit, cost, deadhead miles, number of served loads, etc.) is optimized. However, besides making these vehicle repositioning and assignment decisions, an important question that is commonly overlooked by many fleet management models is how the performance measures would change in response to a change in certain model parameters. For example, freight carriers are interested in how much their profits would increase if they introduced an additional vehicle into the system or if they served an additional load on a certain traffic lane. Railroad companies want to estimate the minimum number of railcars that is necessary to cover the random shipper demands. The Airlift Mobility Command is interested in the impact of limited airbase capacities on the delayed shipments. Answering such questions, in one way or another, requires sensitivity analysis of the underlying fleet management model responsible for making the vehicle allocation decisions.In this paper, we develop efficient sensitivity analysis methods for a stochastic fleet management model previously developed in Godfrey and Powell (2002a, b). This model formulates the problem as a dynamic program, decomposing it into time-staged subproblems, and replaces the value functions with specially structured approximations that are obtained through an iterative improvement scheme. Two aspects of this model are crucial to our work: (1) Due to the special structure of the value function approximations, the subproblem that needs to be solved for each time period is a min-cost network flow problem. This enables us to use the well-known relationships between the sensitivity analyses of min-cost network flow problems and min-cost flow augmenting trees. In particular, we can use the fact that the change in the optimal solution of a mincost network flow problem in response to a unit change in the supply of a node or a unit change in the upper bound of an arc is characterized by a min-cost flow augmenting path.(2) Letting be the set of time periods in the planning horizon, just as the value functions V t · t ∈ describe an optimal vehicle allocation policy through the so-called optimality equation (se...

show abstract

Chapter 3 Stochastic and dynamic networks and routing

Cited by 226 publications

References 192 publications

Approximation algorithms for the bid construction problem in combinatorial auctions for the procurement of freight transportation contracts

Approximation algorithms for the bid construction problem in combinatorial auctions for the procurement of freight transportation contracts

Dynamic-Programming Approximations for Stochastic Time-Staged Integer Multicommodity-Flow Problems

Sensitivity Analysis of a Dynamic Fleet Management Model Using Approximate Dynamic Programming

Contact Info

Product

Resources

About