Optimizing Door Assignment in LTL-Terminals by Evolutionary Multiobjective Algorithms Thomas Bartz-Beielstein, Annette Chmielewski, Michael Janas, Boris Naujoks and Robert Scheffermann Abstract— In less-than-truckload terminals arriving trucks have to be allocated to a gate and to a time slot for unloading. The allocation to a specific gate results in different transporta- tion volumes for the forklift trucks inside of the terminal, depending on the destinations of the truck’s loads. While minimizing these transports the time for trucks waiting to be ordered to a gate also has to be minimized. For the first time this problem has been tackled as a 2-objective optimization problem and was solved by an (1+1)-evolution strategy. We developed a model which is derived from real freight forwarder’s data and represents a small company’s terminal on an average workday. I. I NTRODUCTION In logistical terminals it is to be decided at which gate and at what time a truck should be unloaded. The goods have different destinations inside of the terminal and the distance from the gates to these destinations is different for each gate as illustrated in Fig. 1. It is important to minimize the waiting time for trucks and keep the transportation volume inside of the terminal low. Goods with a total weight under three tonnes, which are often placed on a pallet for further transport activities, are called less-than-truckload (LTL) consignments. Bermudez & Cole (2001) were one of the first tackling this kind of problem. They used a genetic algorithm to min In their model they assume that a single gate does serve only a single truck, which means just the allocation of trucks to gates is considered and no time constraints exist. Another approach by Stickel & Furmans (2005) on crossdocking terminals concentrates on the time-scheduling aspect and also takes the vehicle routing for inbound and outbound routes into account. The associated mathematical model is very complex. It was possible to solve the mixed integer linear program (MILP) with CPlex for very small problem instances. The processes inside of terminals were solved by Li & Rodrigues (2004) using an hybrid evolutionary algorithm. Chmielewski & Clausen (2005, 2006) developed an enhanced mathematical model for optimizing less-than- truckload terminals that is based on a time discrete multicom- modity flow and supplemented by necessary side constraints. The resulting MILP was programmed with the optimization solver CPlex 4.1 and different test scenarios were applied to Thomas Bartz-Beielstein, Michael Janas, and Boris Naujoks are with the Chair of Algorithm Engineering and Systems Analysis, University of Dortmund, 44221 Dortmund, Germany (email: {thomas.bartz-beielstein, michael.janas, boris.naujoks}@udo.edu) Annette Chmielewski and Robert Scheffermann are with the Chair for Transportation Science, University of Dortmund, 44221 Dortmund, Ger- many (email: {scheffermann, chmielewski}@uni-dortmund.de) the Branch-and-Cut algorithm implemented in CPlex. On the one hand the test scenarios show that for small and middle sized problem instances good solutions can still be found. But on the other hand—especially for the case of medium sized problems—finding optimal solutions takes up to 30 minutes or more. Obviously, this time span is prohibitive for on-line optimization problems. So, exact solution methods are not relevant for the dynamic allocation of trucks to gates in logistical terminals. Also the two objectives have so far only been considered by including a penalty for late docking into the monocriterial objective function. In our paper we present an approach that allows to allocate multiple trucks to the same gate on different timeslots, so extending the model Bermudez & Cole (2001) used for their genetic algorithm. Compared to Stickel & Furmans (2005) we were able to find good solutions for much larger prob- lem instances, but the underlying model of crossdocking- terminals is different in many aspects from LTL-terminals. Therefore, the results are not directly comparable. The un- derlying model is similar to the one used by Chmielewski & Clausen (2005), but in our new approach the problem was tackled as a multiobjective problem for the first time. We solved the two criteria decision problem of minimizing the transportation volume inside of LTL terminals and the waiting time for trucks between arrival at the terminal and being assigned to a gate. This problem will be referred to as the LTL-problem in the remainder of this article. The next section will give a more detailed definition of the corresponding model, which is very similar to the model used in Chmielewski & Clausen (2005). Section 3 will introduce the algorithm we used to solve the problem: a 1+1 evolution strategy. The experiments are then described in Sect. 4. Next the experiment’s results are discussed in Sect. 5 and different variants are being compared. Finally we give a summary in Sect. 6. II. PROBLEM The transport of LTL goods within a country or a region is organized via a transportation network. The transportation request of one customer (normally between 1 and 10 pallets) usually does not suffice to fill the load area of a whole truck (up to 33 pallets). The network structure allows companies to use bundling effects by consolidating all consignments with the same long distance destination on one truck. Therefore, a transportation network consists of several logistical sites, which will be referred to as freight forwarding terminals.