OPTIMIZATION OF LOGISTIC PROCESSES USING ANT COLONIES * C. A. Silva §,† T.A. Runkler § J.M. Sousa †,§ R. Palm § § Siemens AG † Technical University of Lisbon Corporate Technology Instituto Superior T´ ecnico Information and Communications Dept. Mech. Eng. GCAR-IDMEC 81730 Munich, Germany 1049-001 Lisbon, Portugal KEYWORDS Ant colonies, logistic processes, scheduling. ABSTRACT The scheduling of logistic processes modeled by birth-and- death processes is a combinatorial problem. We consider here the problem of dynamic assignment of components to orders. In this paper, a distributed algorithm based on ant colonies is proposed to optimize this assignment. The ant-agents jointly test several different combinations and choose the solution that is able to deliver more orders at the correct delivery date, while keeping the delay variance small for the orders that are not de- livered at the desired date. A simulation example is presented, comparing this algorithm with three other scheduling methods. Results show the effectiveness of the proposed algorithm. INTRODUCTION In supply chains management, logistics can be defined as the subprocess of the supply chain process that deals with the planning, handling, and control of the storage of goods between the manufacturing point and the consump- tion point. In the past, goods were produced, stored and then delivered on demand. Nowadays, many companies do not work with stocks, using instead cross-docking centers [Jayashankar M. Swaminathan and Sadeh, 1998]. The goods are transported from the suppliers to these cross-docking centers, stored, and then shipped to the costumers. The lack of storage may increase the delivery time, but it considerably reduces the volume of invested capital and increases the flexibility of the supply chain. The key issue is to deliver the goods in time by minimizing the stocks. The goods should be delivered at the correct date (not earlier or later) in order to ensure the costumers satisfaction. The scheduling algorithm has to decide, which goods are delivered to which costumers. If the costumers’ orders are sets of different components, the most common method is to pre-assign the components to the orders. In this strategy, all * This work is supported by the German Ministry of Education and Re- search (BMBF) under Contract no.13N7906 (project NIVELLI) and and by the Portuguese Fundation for Science and Technology (FCT) under Grant no. SFRH/BD/6366/2001. components are assigned to the orders at the moment when the components are ordered from the suppliers. They can therefore not be used by any other order. This static scheduling strategy revealed to be poor. Therefore, a dynamic assignment strategy, allowing to exchange components between the orders is necessary. Dynamic assignment consists of distributing the available components to orders. This can be done with a sorted list of orders. If the first order in the list can be delivered using the available components, the components are taken from the stock and delivery is triggered. Then, the dynamic assignment algorithm proceeds to the next orders in the list, an so on. The easiest way to sort this list is to use a First In First Served (FIFS) principle, where the orders are sorted by order date or a First Desired First Served (FDFS) principle where the orders are sorted by their desired date. Since both principles use a unique orders list, these scheduling methods are called centralized dynamic approaches. This paper proposes a dynamic assignment method using a distributed approach. The idea is to assign individual agents to the orders and let the population of agents interactively find an optimization scheduling solution [Palm and Runkler, 2002]. The interaction between the agents is realized by exchanging information about quantity, desired date and arriving date. In a logistic scheduling problem, the number of agents involved and the quantity of information that has to be ex- changed is very large. Multi-agent algorithms based on social insects can avoid this complexity. Social insects have captured the attention of scientists because of the high structuration level that the colonies can achieve, especially when compared to the relative simplicity of the individuals. Ants are one example of social insects. Even though ants are very simple animals, with no special abilities and almost blind, they are capable of establishing the shortest route paths from their colonies to feeding sources and back to the nests. Here, we propose an ant algorithm for logistic processes. The paper is organized as follows. The next section presents a global description of a logistic process. Then, some of the standard scheduling algorithms are briefly described. Further, the principles of the optimization algorithm using ant colonies are introduced, as well as the new framework for