Measuring the Impact of the Internet on the Trucking Industry.
Final report
Carlos Daganzo
Dept. of Civil & Environmental Engineering
University of California
Berkeley, CA 94720-1720
University of California Transportation Center Year 12 (1999-2000)
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The contents of this report reflect the views of the authors, who are responsible
for the facts and the accuracy of the information presented herein. This document
is disseminated under the sponsorship of the Department of Transportation, University
Transportation Centers Program, in the interest of information exchange. The
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Acknowledgements
The research on which this report is based was carried out for the University of California Transportation Center (UCTC). Funding for the Center comes in equal parts from the US Dept. of Transportation and the California Department of Transportation (Caltrans.) The University of California also provides support though reduction of overhead charges and the donated time of many faculty, students, and administrative staff. The researchers of the UCTC are grateful for all of this support.
The objective of this project was to explore the effect of the Internet on transportation networks, and an overarching goal was to do so in an educational context that would allow students to investigate aspects of the problem of particular interest to them.
The core of our research was a PhD thesis (K. Smilowitz's, [1]) that deals with the optimal structure of multi-commodity multi-service transportation networks such as those of integrated carriers (e.g., UPS). One paper [5], summarizing the main aspects of the thesis has been produced.
This work introduced design strategies and operational planning techniques for multi-mode, multi-service networks for package delivery carriers where service levels are defined by the guaranteed delivery times for packages (e.g., overnight, two-day delivery, etc…) Large scale transportation network design problems are typically challenging, due to the large number of interdependent decision variables and constraints. These problems are even more complex with multiple service levels. Conventional network design and routing models cannot sufficiently capture the complexity of multimode, multi-service networks. These publications discuss two principal design and routing approaches: detailed (mixed-integer programming) and approximate (continuous approximations). While the first approach provides a much higher level of detail, the second is more revealing of the “big picture.” An approach based on the complementary use of analytical approximation models and numerical optimization is developed to design, test and evaluate integrated strategies. This constitutes the first application of hybrid optimization methods to design and operate large-scale integrated networks with shipment choices. The methodology allowed us to decompose the very complex problem to a series of sub-problems that could be solved with spreadsheets. A variety of scenarios are analyzed and the advantages of integration are presented. It is found that the percentage savings achieved by integrating a land-based carrier with an express (air) carrier, relative to the costs of the express carrier, grow with the size of the land carrier. This result helps explain the different strategies that firms like FedEx and UPS are pursuing today. The research also shows that very large systems can be studied systematically.
As part of this project, we also developed asymptotic formulae for very large, scalable transportation linear programs (TLP’s) [2, 3, 4]. The formulas developed in these papers were used in the applied portion of the project [1, 5].
A scalable problem is one where the nodes of the network are embedded in a normed space and the demand data are such that problem instances belong to a closed family under certain transformations of size (number of nodes, N) and scale (dimension of the norm.) The TLP with homogeneously but randomly distributed points and demands in a region of arbitrary shape is a problem in this class. As occurs in some applied probability problems such as the Ising model of statistical mechanics, and the first passage of time of a random walk, the nature of the solution depends on the dimensionality of the space. It is shown in these papers that the cost per item is bounded from above in 3+ dimensions (3+-D), but not in 1-D and 2-D.
A simple formula for the 2-D, Euclidean TLP is also given. Curiously, zone shape has no effect asymptotically as N ® ¥ on the optimum cost per point in 2+-D, but it has an effect in 1-D. Therefore, the 2-D case can be viewed as a transition case that shares some of the properties of 1-D (unbounded cost) and some of the properties of 3-D (shape-independence).
The results are extended to general network problems with link costs that are a concave power function of flow. It is found that if these functions are strictly concave, as is common in some logistics applications, then the solution in 2+-D is bounded.
Publications:
1. Smilowitz, Karen, “Design and Operation of Multimode Multiservice Logistics systems” PhD Thesis, Dept. of Civil and Environmental Engineering, U. C. Berkeley, 2001.
2. Daganzo, Carlos and Karen Smilowitz, “Asymptotic Approximations for the Transportation LP and Other Scalable Network Problems”, ITS WP 2000-2, November 2000. (Submitted for publication)
3. Daganzo, Carlos and Karen Smilowitz, “Bounds and approximations for the Transportation LP” (submitted for publication.)
4. Daganzo, Carlos and Karen Smilowitz, “Asymptotic Formulae for Some One Dimensional Network Flow Problems.” Presented at TRISTAN, Acores, Portugal, June 2001.
5. Smilowitz, K.and Daganzo, C. F. “Cost modeling and design techniques for complex transportation systems” (submitted for publications.)
One PhD thesis (K. Smilowitz's, [1]) that deals with the optimal structure of multi-commodity multi-service transportation networks such as those of integrated carriers (e.g., UPS) was produced. One paper [5], summarizing the main aspects of the thesis was also produced. It is now under review. In addition, two papers addressing methodological/technical aspects of the thesis, were finished [2, 3]. These are too under review.
A more specialized paper, exploring in depth the statistical properties of the one-dimensional version of the problem addressed in [2 and 3] was presented at the TRISTAN conference [5]. This is also being considered for journal publication