An Ant Colony Algorithm for TimeDependent Vehicle Routing Problem with Time Windows
 Umman Mahir Yildirim,
 Bülent Ç atay
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Summary
In this paper, we address the Vehicle Routing Problem with Time Windows, both timeindependent and dependent cases. In the timeindependent case, our objective is to minimize the total distance. To solve this problem, we propose an Ant Colony Optimization algorithm. Then we implement the algorithm to solve the timedependent case where the objective is to minimize the total tour time. The time dependency is embedded in this model by using a deterministic travel speed function which is a step function of the time of the day. An experimental evaluation of the proposed approach is performed on the wellknown benchmark problems Optimizing a distribution network has been and remains an important challenge both in the literature and in reallife applications and the routing of a eet of vehicles is the most widely addressed problem in a distribution network. The Vehicle Routing Problem (VRP) determines a set of vehicle routes originating and terminating at a single depot such that all customers are visited exactly once and the total demand of the customers assigned to each route does not violate the capacity of the vehicle. The objective is to minimize the total distance traveled. An implicit primary objective is to use the least number of vehicles. The Vehicle Routing Problem with Time Windows (VRPTW) is a variant of VRP in which lower and upper limits are imposed to the delivery time of each customer. The arrival at a customer outside the specified delivery time is either penalized (soft time windows) or strictly forbidden (hard time windows). The interested reader is referred to [1] for more details on VRPTW. In the Stochastic Vehicle Routing Problem, the customer demands and/or the travel times between the customers may vary. Although stochastic travel times and demand distributions have been frequently used in the literature, timevarying travel speeds and timedependent VRPTW (TDVRPTW) have seldom been addressed. In the literature, time dependency is taken into consideration in two ways: stochastic travel times and deterministic travel times. First introduced by [2], stochastic travel times are mainly examined by [4] and [3]. [5] proposeda deterministic travel time based model in which the important nonpassing property is introduced. [6] and [7] also use deterministic travel times in a setting where the day is divided into time intervals.
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 Title
 An Ant Colony Algorithm for TimeDependent Vehicle Routing Problem with Time Windows
 Book Title
 Operations Research Proceedings 2008
 Book Subtitle
 Selected Papers of the Annual International Conference of the German Operations Research Society (GOR) University of Augsburg, September 35, 2008
 Pages
 pp 337342
 Copyright
 2009
 DOI
 10.1007/9783642001420_55
 Print ISBN
 9783642001413
 Online ISBN
 9783642001420
 Series Volume
 2008
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 eBook Packages
 Editors

 Bernhard Fleischmann ^{(ID1)}
 KarlHeinz Borgwardt ^{(ID2)}
 Robert Klein ^{(ID3)}
 Axel Tuma ^{(ID4)}
 Editor Affiliations

 ID1. Fak. Sozial/Wirtschaftswissenschften, Universität Augsburg
 ID2. Inst. Mathematik, Universität Augsburg
 ID3. LS für Mathematische Methoden der, Universität Augsburg
 ID4. Fak. Wirtschaftsund Sozialwiss., Universität Augsburg
 Authors

 Umman Mahir Yildirim ^{(1)}
 Bülent Ç atay ^{(1)}
 Author Affiliations

 1. Orhanli, Tuzla, Sabanci University, Istanbul, 34956, Turkey
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