This thesis introduces design strategies and operational planning techniques for multimode, multiservice networks for package delivery carriers where service levels are defined by the guaranteed delivery items of 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, multiservice networks. This thesis discusses two principal design and routing approaches employed in the literature, and shows how the two approaches can be integrated. One approach utilizes detailed mixed-integer programming formulations and numerical methods. The other employs less detailed models based on continuous approximations. While the first approach provides a much higher level of detail, the second is more revealing of “the big picture”. Therefore, numerical methods are well suited for operational control, while continuous approximation methods are particularly effective for strategic planning and design, especially under uncertainty. An approach based on the complementary use of analytical approximation models and numerical optimization is developed to design, test and evaluate integrated strategies. This is the first application of hybrid continuous approximation/numerical optimization models to large-scale integrated networks with shipment choice. As such, advancements in both continuous approximation and numerical optimization, and the integration of the two, are required. Continuous approximation cost functions are shown to be capable of realistically modeling complex distribution systems with multiple trans-shipments and peddling tours. This research also demonstrates the application of solution techniques to reduce complex cost models to a series of subproblems that can be solved with common spreadsheet technology. Cost components are shown to accurately model costs using independent cost validation. A variety of integration scenarios are analyzed and the advantages of integrated operations are presented. Qualitative conclusions suggest that benefits of integration are greater when deferred demand exceeds express demand. This insight helps to explain the different business strategies of package delivery firms in industry today. This research demonstrates how hybrid modeling approaches can be used to better understand and better plan operating strategies for distribution companies.

Traffic data from a 4-mile long congested rural road in Orinda, California, are used to show that traffic delays and vehicle accumulations between any two generic observers located inside a road section can be predicted from the traffic counts measured at the extremes of the section. The traffic model does not require "recalibration" on the day of the experiment, and works well despite what appears to be location-specific driver behavior.

Network optimization problems with a "scalable" structure are examined in this report. Scalable networks are embedded in a normed space and must belong to a closed family under certain transformations of size (number of nodes) and scale (dimension of the norm). The transportation problem of linear programming (TLP) with randomly distributed points and random demands, the earthwork minimization problem of highway design, and the distribution of currents in an electric grid are examples of scalable network problems. Asymptotic formulas for the optimum cost are developed for the case where one holds the scale parameter constant while increasing the size parameter, N.

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 of linear problems depends on the dimensionality of the space. In the linear case, we find that the cost per node is bounded from above in 3+ dimensions (3+-D), but not in 1- and 2-D. Curiously, zone shape has no effect (asymptotically) 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). A simple formula for the 2-D, Euclidean TLP is given. Asymptotic results are also developed for a class of non-linear network problems with link costs that are a concave power function of flow. It is found that if these functions are strictly concave than the solution in 2+-D is bounded.

Network optimization problems with a "scalable" structure are examined in this report. Scalable networks are embedded in a normed space and must belong to a closed family under certain transformations of size (number of nodes) and scale (dimension of the norm.) The transportation problem of linear programming (TLP) with randomly distributed points and random demands, the earthwork minimization problem of highway design, and the distribution of currents in an electric grid are examples of scalable network problems. Asymptotic formulas for the optimum cost are developed for the case where one holds the scale parameter constant while increasing the size parameter, N. 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 of linear problems depends on the dimensionality of the space. In the linear case, we find that the cost per node is bounded from above in 3+-dimensions (3+-D), but not in 1- and 2-D. Curiously, zone shape has no effect (asymptotically) 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). A simple formula for the 2-D, Euclidean TLP is given. Asymptotic results are also developed for a class of non-linear network problems. It is found that when the objective function is quadratic (as occurs in electric circuits), then the solution is always unbounded.

This paper studies the possible integration of long-haul operations by transportation mode and service level (defined by guaranteed delivery time) for package delivery carriers. Specifically, we consider the allocation of deferred items to excess capacity on alternative modes in ways that allow all transportation modes to be utilized better. Model formulation and solution techniques are discussed. The solution techniques presented produce efficient solutions for large-scale problem instances. Allowing deferred items to travel by air reduces long-haul transportation costs. These savings increase with the amount of excess air capacity.

The arrival times of vehicles traveling southbound along a two-lane, bi-directional highway were recorded at eight neighboring locations upstream of a bottleneck caused by an oversaturated traffic signal. Cumulative curves constructed from these observations describe completely and in great detail the evolution of the resulting long queues. These queues formed directly upstream of the signal when the signal's service rate fell below the southbound arrival rates, and never formed away from the bottleneck. The predictability of bottlenecks like the one studied here can be exploited to manage traffic more effectively. The behavior of vehicles within the queue, however, was rather interesting. While the flow oscillations generated by the traffic signal were damped-out within one-half mile of the bottleneck, it was found that other oscillations arose within the queue farther upstream, at varied locations, and then grew in amplitude as they propagated in the upstream direction. Thus, the queue appeared to be stable close to the bottleneck and unstable far away. Oscillations never propagated beyond the upstream end of the queue, however; i.e., the unusual phenomena always arose after the onset of queuing and remained confined within the queue. Some of these findings run contrary to current theories of traffic flow. As the data set collected in this study is unprecedented in scope and detail, and so that it may be of use to other researchers, it has been posted on the internet and is fully described here. KEY WORDS Bottleneck Observation; Car Following; Jam Development; Queueing; Traffic Instability