Browsing by Subject "Valid Inequalities"

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Open Access
An exact algorithm for the vehicle routing problem with backhauls
(2001) Geloğulları, Cumhur Alper
We consider the Vehicle Routing Problem with Backhauls, in which a eet of vehicles located at a central depot is to be used to serve a set of customers partitioned into two subsets of linehaul and backhaul customers. The ob jective of the problem is to minimize the total distance traveled by the entire eet. The problem is known to be N P-hard in the strongest sense and nds many practical applications in distribution planning. We present an exact algorithm for the Asymmetric Vehicle Routing Problem with Backhauls based on solving a relaxation of the problem. In a cutting plane fashion, the algorithm iteratively solves the relaxation while at each iteration, infeasible solutions are identi ed and seperated from the feasible set of the relaxation. The procedures to identify infeasible solutions are presented, and a set of cuts to eliminate these solutions is proposed. Local search procedures are incorporated to improve the algorithm. Computational tests on randomly generated instances, involving up to 90 customers, are given. The results show the e ectiveness of the proposed approach.
Open Access
Release Time Scheduling and Hub Location for Next-Day Delivery
(INFORMS, 2012-02-01) Yaman, H.; Karasan, O. E.; Kara, B. Y.
Inspired by a real-life problem faced by one of the largest ground-based cargo companies of Turkey, the current study introduces a new facet to the hub location literature. The release time scheduling and hub location problem aims to select a specified number of hubs from a fixed set of demand centers, to allocate each demand center to a hub, and to decide on the release times of trucks from each demand center in such a way that the total amount of cargo guaranteed to be delivered to every potential destination by the next day is not below a threshold and the total routing cost is minimized. The paper introduces integer programming models to solve this problem in the special cases when the cargo uniformly arrives to each demand center during the day and the more realistic pattern of when the cargo arrivals exhibit a piecewise linear form. Several classes of valid inequalities are proposed to strengthen the formulations. Extensions with multiple service levels and discrete sets for release times are also discussed. Computational results show the computational viability of the models under realistic scenarios as well as the validity of the proposed problems in answering several interesting questions from the cargo sector’s perspective.