ITS Berkeley

A Theory of Supply Chains

Daganzo, Carlos F.
2003

This work was stimulated by a comment made by a former student (Prof. Alan Erera of Georgia Tech) in connection with an inventory stabil­ ity game he was going to play in one of his logistics classes. This was the well-known "beer-game" that is often played in business schools to illus­ trate the "bullwhip" effect in supply chains. Al had said to me that he did not have to tell his students how to reorder replacement parts from the other members of the supply chain because he knew from experience that the order sizes the players would generate as the game progressed would become chaotic...

A Variational Formulation of Kinematic Wave Theory

Daganzo, Carlos F.
2003

This paper proves that kinematic wave (KW) problems with concave (or convex) equations of state can be formulated as calculus of variations problems. Every well-posed problem of this type, no matter how complicated, is reduced to the determination of a shortest tree in a relevant region of spacetime where cost is predefined. A duality between KW theory and /least cost networks is thus unveiled. In the new formulation space-time curves that constrain flow, such as sets of moving bottlenecks, become space-time shortcuts. These shortcuts become part of the network and affect the nature of the...

A Variational Formulation for a Class of First Order PDE's

Daganzo, Carlos F.
2003

This paper proves that a class of first order partial differential equations, which include scalar conservation laws with concave (or convex) equations of state as special cases, can be formulated as calculus of variations problems. Every well-posed problem of this type, no matter how complicated, even in multi-dimensions, is reduced to the determination of a tree of shortest paths in a relevant region of space-time where "cost" is predefined. Thus, problems of this type can be practically solved with fast network algorithms. The new formulation automatically identifies the unique, single-...

A Network Model of Departure Time Choice with Spillovers and Merging Effects. Part I: Building Block

Lago, Alejandro
Daganzo, Carlos F.
2003

This paper presents a departure-time user equilibrium model that explicitly considers the most important determinants of congestion behavior in cities during the morning commute: different commuter origins, merge interactions and queue spillovers. The proposed model combines three previous works: the departure-time equilibrium theory in Vickrey (1969), the traffic flow model of Newell (1993) and the merge theory in Daganzo (1996). The paper examines the simplest possible network exhibiting the three important features and discusses the ensuing policy implications. The solution algorithm...

Deferred Item and Vehicle Routing within Integrated Networks

Smilowitz, Karen R.
Atamtürk, Alper
Daganzo, Carlos F.
2003

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 solutions for large-scale problem instances with up to 141 consolidation terminals and 17 breakbulk terminals. Allowing deferred items to travel by air...

A Network Model of Departure Time Choice with Spillovers and Merging Effects. Part I: Building Block

Lago, Alejandro
Daganzo, Carlos F.
2003

This paper presents a departure-time user equilibrium model that explicitly considers the most important determinants of congestion behavior in cities during the morning commute: different commuter origins, merge interactions and queue spillovers. The proposed model combines three previous works: the departure-time equilibrium theory in Vickrey (1969), the traffic flow model of Newell (1993) and the merge theory in Daganzo (1996). The paper examines the simplest possible network exhibiting the three important features and discusses the ensuing policy implications. The solution algorithm...

Structure of the Transition Zone Behind Freeway Queues

Munoz, Juan Carlos
Daganzo, Carlos F.
2003

Observations of freeway traffic flow are usually quite scattered about an underlying curve when plotted versus density or occupancy. Although increasing the sampling intervals can reduce the scatter, whenever an experiment encompasses a rush hour with transitions in and out of congestion, some outlying data stubbornly remain beneath the “equilibrium” curve. The existence of these nonequilibrium points is a poorly understood phenomenon that appears to contradict the simple kinematic wave (KW) model of traffic flow. This paper provides a tentative explanation of the phenomenon, based on...

Discretization and Validation of the Continuum Approximation Scheme for Terminal System Design

Ouyang, Yanfeng
Daganzo, Carlos F.
2003

This paper proposes an algorithm that automatically translates the "continuum approximation" (CA) recipes for location problems into discrete designs. It is applied to terminal systems but can also be used for other logistics problems. The study also systematically compares the logistics costs predicted by the CA approach with the actual costs for discrete designs obtained with the automated procedure. Results show that the algorithm systematically finds a practical set of discrete terminal locations with a cost very close to that predicted. The paper also gives conditions under...

A Variable Formulation of Kinematic Waves: Solution Methods

Daganzo, Carlos F.
2003

This paper presents improved solution methods for kinematic wave trafficc problems with concave flow-density relations. As explained in part I of this work, the solution of a kinematic wave problem is a set of continuum least-cost paths in space-time. The least cost to reach a point is the vehicle number. The idea here consists in overlaying a dense but discrete network with appropriate costs in the solution region and then using a shortest-path algorithm to estimate vehicle numbers. With properly designed networks, this procedure is more accurate than existing methods and can be applied...