M. Abareshi, M. Zaferanieh,
Volume 15, Issue 1 (4-2018)
Abstract
Transportation problems are usually considered in large-scale networks, where finding the optimal solution of these problems is so time-consuming and costly. Therefore, a useful method to solve the large-scale network problems is dividing them into some smaller sub-problems. In this paper, for the first time, the origin-destination (o-d) matrix estimation problem is considered through a mixed planar approach wherein the travel demands between o-d pairs are estimated in a large-scale network. A decomposition method is proposed in three phases. In each phase, the solution of some smaller problems in compared with the original one, are estimated. In the first phase, the travel demands between main nodes are estimated while in the second one, the flow pattern in all inner networks corresponding to main nodes is determined. In last phase, the travel demands between primary o-d pairs are estimated by using the obtained information from steps one and two.
S. Safari, M. Zaferanieh, M. Abareshi, E. L. Rahimi,
Volume 16, Issue 2 (7-2019)
Abstract
In this paper, a constrained shortest path problem (CSP) in a network is investigated, in which some special plans for each link with corresponding pre-determined costs as well as reduction values in the link travel time are considered. The purpose is to find a path and selecting the best plans on its links, to improve the travel time as most as possible, while the costs of conducting plans do not exceed the available budget. Using the Lagrangian relaxation approach, some constraints of the problem are relaxed and the Lagrangian dual problem is decomposed into two smaller sub-problems. Then, by applying the sub-gradient algorithm, a near optimal solution is determined for the original problem. Finally, by considering the proposed model on a small-sized network and on Khorasan state network, solutions for different origin-destination pairs with different parameters are determined.
