STOCHASTIC ALGORITHMS FOR THE LINE BALANCING PROBLEM IN AUTOMOTIVE INDUSTRY Corinne Boutevin, Michel Gourgand, Sylvie Norre Université Blaise Pascal – Clermont-Ferrand II LIMOS CNRS FRE 2239 Campus Scientifique des Cézeaux F - 63177 Aubière Cedex, boutevin@iris.univ-bpclermont.fr, gourgand@isima.fr, norre@moniut.univ-bpclermont.fr Abstract: This paper deals with the study of a line balancing problem. The considered problem is issued from the automotive industry. It consists in gradually assembling vehicles which go through a line. Assembly operations are made by workstations placed along the line. The goal is to assign operations to these workstations in order to minimize different criteria while satisfying several constraints. To solve this problem, stochastic algorithms are applied, namely stochastic descent and simulated annealing, for which two neighboring systems are proposed. They are applied on generated data and industrial data and provide interesting results. Copyright © 2002 IFAC Keywords: automotive industry, decision-making, mathematical models, operations research, optimization problems. 1. INTRODUCTION The line balancing problem is a very well-known problem in the automotive industry. This kind of industry uses assembly lines for manufacturing vehicles. The density (number of considered vehicles) and the diversity (number of types of vehicle) of the production require an optimization. The literature lists four classical models: the “single- model” (only one type of vehicle is considered), the “mixed-model” (several types of vehicle are considered), the “multi-model” (vehicles issued from the same type are manufactured in fixed batches) and the “batch-model” (a multi-model where the dimensions of batches must be computed). All these models have been studied, for instance, in (Bhattacharjee and Sahu, 1987; Van Zante-de Forkkert, 1997; Scholl, 1999; Rekiek, 2001). The line balancing problem consists in searching a good assignment of operations to workstations. This optimization is difficult due to the combinatory (number of workstations, operations and types of vehicle) of this industrial problem and the number of constraints. The problem is NP-complete (Scholl, 1999) even if there is one type of vehicle and no precedence constraints. It is solved, in the literature, with exact methods for small instances (Van Zante-de Forkkert, 1997) and with heuristics (Bhattacharjee and Sahu, 1987; Palekar, 1998; Scholl, 1999) for large instances (more than 50 operations). To solve the line balancing problem, stochastic algorithms have been used: stochastic descent and simulated annealing. In this paper, two kinds of neighboring system are presented, used in the stochastic algorithms. Different objective functions have been tested, such as economical criteria. In the first part, the industrial problem is presented. In the second part, a formalization of this problem is proposed. In the third part, two neighboring systems for stochastic algorithms are given. In the fourth part, computational results are presented, based on generated data and on two industrial cases. 2.PROBLEM PRESENTATION The line is divided into several sections (figure 1), which contain several workstations (at most, 5 workstations); a workstation is assimilated to one operator. An operator realizes a set of operations on the vehicles; these operations depend on the type of the vehicle. Vehicles go through a line, with a constant speed, to be assembled. So the vehicle is available on each section during a same duration, all operations assigned to operators placed on the Copyright © 2002 IFAC 15th Triennial World Congress, Barcelona, Spain