21 st International Conference on Production Research An Exact Solution Algorithm for Balancing Simple U-Type Assembly Öncü Hazır, Alexandre Dolgui ROGI, LSTI Henri Fayol Institute École des Mines de Saint-Étienne 158, cours Fauriel, 42023 Saint-Étienne cedex, France Abstract In this research, we address U-type assembly line balancing and aim to solve large scale instances to optimality. Specifically, we consider simple line balancing problem with minimizing the number of workstations (UALBP-1) and cycle time objectives (UALBP-2). Optimal solution of UALBP-1 is important, since each additional station requires additional workers and equipment. On the other hand, for UALBP-2, a slight improvement in cycle time increases the production capacity. To be able solve large scale instances to optimality, a decomposition based algorithm is proposed and enhancement strategies are integrated. We perform computational experiments to test the efficiency of the algorithm and present the results. The main contribution of this paper is the proposed decomposition strategy and integrated acceleration mechanisms. Keywords: Assembly line balancing, U-type lines, Combinatorial optimization 1 INTRODUCTION Assembly lines are flow-oriented production systems that perform various operations continuously in serially located workstations. Since they enable mass production of standardized products, they have been commonly used in many industries. These industries require support tools to solve large scale line balancing problems. These problems are classified regarding the number of product models produced: simple (SALBP), mixed (MALBP) and multi- model (Scholl [6]). Simple lines produce one homogeneous product, whereas several versions of the same product are assembled in the mixed-model lines. These lines require similar production processes for all the models. However in multi-model lines, the production processes differ significantly and set-ups are needed. We refer to the surveys of Rekiek et al. [10] for the classification and review of line balancing problems. Recently, many companies have adapted just-in-time (JIT) manufacturing in order to improve their efficiency and minimize work-in process inventory. JIT philosophy has lead to using U-type lines since they are advantageous to traditional straight line assembly designs in terms of efficiency and flexibility. They offer more alternatives for grouping tasks since the same worker could work in different stations which are located at entrance and exit sides of the lines. As a result, U-type lines could be balanced by using less work stations. In addition to efficiency, they also have the flexibility to adapt to changes more easily than straight lines. For instance, reallocation of the workers to machines is easier in cases when demand changes. In this paper, we will address the single U-type assembly line balancing problem, both UALBP-1 and UALBP-2, and our aim is to solve large scale instances to optimality. Specifically, UALBP-1 addresses assigning the operations to minimum number of work stations so that a product is assembled within a given cycle time C, which is the maximum of the station times (the sum of processing times of all operations assigned to it). In addition, precedence relations, that define the processing order of the operations, should be satisfied. A graph G = (N,A), where N is the set of nodes and A ⊆ N ×N is the set of arcs, models these temporal relations. Having two sides; entrance and exit, U-lines allow both forward and backward assignments to the stations. For instance, it is possible to assign the first and the last operation in the precedence diagram to the same station. To facilitate this, two-sided allocations, [5] introduced an auxiliary network called as ”Phantom network”. In order to examine further the characteristics and application areas of U-lines, we refer the readers to the survey paper of [9]. Up to now, small and moderate-size instances of UALBP have been solved to optimality by using branch and bound algorithms ([2], [5], [7] and [11]). For large size instances, approximate algorithms have been proposed ([8] and [16]). All these methods have been proposed for the deterministic problems. However, in real life, production systems are subject to various sources of uncertainty, such as variability in operation times, resource uses and availabilities, etc. Stochastic modeling is a widely applied optimization approach that uses probabilistic models to describe the uncertain data in terms of probability distributions. It has also been used for U-line balancing problems (see [12], [14]). We note that majority of U-line balancing studies addressed minimizing the number of stations (UALBP-1) and research on cycle time minimization (UALBP-2) is scarce. Therefore, we will concentrate on the computational results for UALBP-2. First, we present mixed integer programming (MIP) models of the problems. Then, we will propose a decomposition algorithm to solve U-line balancing problems in Section 3.2. We aim to solve large scale instances to optimality. To accomplish this, enhancement strategies are integrated. Later, in Section 4, we will present experimental analysis and computational results. Finally, conclusions and directions for future research are given in Section 5. 2 PROBLEM FORMULATION UALBP-1 could be stated as follows [6]: Min = + ∑ k 1 z UB k LB (1)