The traffic assignment problem with elastic demands can be formulated as an optimization problem, whose objective is sum of a congestion function and a disutility function. We propose to use a variant of the Analytic Center Cutting Plane Method to solve this problem. We test the method on instances with different congestion functions (linear with … Read more
We consider the vehicle routing problem where one can choose among vehicles with different costs and capacities to serve the trips. We develop six different formulations: the first four based on Miller-Tucker-Zemlin constraints and the last two based on flows. We compare the linear programming bounds of these formulations. We derive valid inequalities and lift … Read more
We study the route-guidance system proposed by Jahn, Möhring, Schulz and Stier-Moses (2004) from a theoretical perspective. This approach computes a traffic pattern that minimizes the total travel time subject to user constraints, which ensure that routes suggested to users are not much longer than shortest paths. We show that when distances are measured with … Read more
In this paper we present a methodology to decide capacity expansions for a transit network that finds a robust solution with respect to the uncertainty in demands and travel times. We show that solving for a robust solution is a computationally tractable problem under conditions that are reasonable for a transportation system. For example, the … Read more
In this paper, we propose to solve the linear multicommodity flow problem using a partial Lagrangian relaxation. The relaxation is restricted to the set of arcs that are likely to be saturated at the optimum. This set is itself approximated by an active set strategy. The partial Lagrangian dual is solved with Proximal-ACCPM, a variant … Read more
We present the optimization component of a decision support system developed for a sedan service provider. The system assists supervisors and dispatchers in scheduling driver shifts and routing the fleet throughout the day to satisfy customer demands within tight time windows. We periodically take a snapshot of the dynamic data and formulate an integer program, … Read more
This problem deals with the uncapacitated multiple allocation hub location problem. The dual problem of a four-indexed formulation is considered and a heuristic method, based on a dual-ascent technique, is designed. This heuristic, which is reinforced with several specifical subroutines and does not require any external linear problem solver, is the core tool embedded in … Read more
Classical facility location models like the P-median problem (PMP) and the uncapacitated fixed-charge location problem (UFLP) implicitly assume that once constructed, the facilities chosen will always operate as planned. In reality, however, facilities “fail” from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to … Read more
The Facility Location Model with Risk Pooling (LMRP) extends the uncapacitated fixed charge model to incorporate inventory decisions at the distribution centers (DCs). In this paper, we introduce a capacitated version of the LMRP that handles inventory management at the DCs such that the capacity limitations at the DCs are not exceeded. We consider a … Read more
We consider the rail car management at industrial in-plant railroads. Demands for materials or empty cars are characterized by a track, a car type, and the desired quantity. If available, we assign cars from the stock, possibly substituting types, otherwise we rent additional cars. Transportation requests are fulfilled as a short sequence of pieces of … Read more