Agent-based simulation of dispatching rules dynamic pickup and delivery problems Andreas Beham ∗ , Monika Kofler † , Stefan Wagner ‡ , Michael Affenzeller § School of Informatics, Communications and Media Upper Austria University of Applied Sciences Softwarepark 11 4232 Hagenberg Austria ∗ andreas.beham@heuristiclab.com † monika.kofler@heuristiclab.com ‡ stefan.wagner@heuristiclab.com § michael.affenzeller@heuristiclab.com Abstract—This work treats the topic of solving dynamic pickup and delivery problems, also known as dial-a-ride problems. A simulation model is introduced that describes how an agent is able to satisfy the transportation requests. The agent behavior is given in form of a complex dispatching rule, which is optimized by metaheuristic approaches. For this purpose, a fitness function is described which is used to evaluate the quality of a solution. The rule to be optimized is a weighted sum of several primitive dispatching rules whereeach describes a smallpart of the information available in the system at a given time. Given a good configuration of the weights, we willshow that the agents are able to serve the transportation requests. The optimization of the weights was conducted with the generic, open, and extensible optimization framework HeuristicLab. Index Terms—simulation, pickup and delivery, dispatching, optimization I. INTRODUCTION The pickup and delivery problem is a popular subclass of the vehicle routing problem (VRP) in which a set of customers not only has to be served from a depot, but served from other customers as well. There are two variants, one where a pickup phase has to be completed before the delivery can be started and another variantwhere both phases are interleaved. The dial-a-ride problem [1] is a popular example for the interleaved problem variant. Practical applications include an advanced taxi system, respectively a public transport for elderly and disabled people. In the dial-a-ride problem customers can requesta ride,and thetaxi company tries to satisfy the requests such that the taxi can be utilized to a greater degree. Through sharing the costs can be lowered, butconstraints, such as delivery dates, should also be met. Public transport however is not the only problem situation where such a system is ofgreatinterest. Similarproblem situations arise for example in hospitals where drugs and patients have to be transported between departments. Also, the logistics and The work described in this paper was done within the Josef Ressel Centre for heuristic optimization sponsored by the Austrian Research Promotion Agency (FFG) production industries have an interest in solving such probl situations, especially in very dynamic production environme or in warehouses. One way to solve these problems is by calculating a sched ule that consists of a number of routes that would consider the requests, and their constraints. However when the situa is very dynamic and requests arrive on the fly, planning ahe is difficult and possibly not worth the effort. In such a case i feasible to make decisions as they come up, reacting to a ne order situation very quickly. Existing approaches often follo the first way and provide quick dispatching methods to avoi reoptimization of the whole schedule and invent fast heurist to calculate a plan given a longer scheduling horizon. In this work we will focus on the second way and introduce a purel dynamic approach where no a priori planning occurs. Throu simulation and optimization we will show how this approach is able to tackle the problem. The restof the paper is organized as follows: In the next section we give a short review on existing literature and rel approaches. Then,in Section II we introduce the simulation modeland describe the basic dispatching rules that we have created. In Section III we introduce the optimization approa and discuss its application on the simulation model. The res of this optimization and an analysis are given in Section IV afterwhich conclusions are drawn and directions for future work identified. A. Literature review A number of related articles have been published that trea pickup and delivery problems with simultaneous pickup and delivery already, but to the best knowledge of the authors n has yet evaluated the possibility to combine simple dispatch information in custom dispatching rules. Some ofthe more closely related publications are briefly described: The closest related approach that is based on dispatching rules is described in [2]. The problem situation is described a dynamic pickup and delivery problem, but vehicles only ha 978-1-4244-3958-4/09/$25.00 ©2009 IEEE