A mixed integer linear programming formulation for optimal balancing of mixed-model U-lines

2014

When a mixed-model assembly line (MAL) is balanced, it is generally assumed that the variants of a task over different models should be assigned to an identical station. In this study, this restriction is relaxed and the variants of a task over different models can be duplicated on two adjacent stations (referred to as adjacent task duplication) to improve the MAL's efficiency. The adjacent task duplication incurs few additional training and tool duplication costs as each task is duplicated on at most two stations. Moreover, for each task, the assembly part storage is not duplicated as it can be shared by the two adjacent stations. The mathematical model of this problem is formulated and some important properties are characterised. A branch, bound and remember algorithm is then developed to solve the problem. The performance of the proposed algorithm is tested on 900 representative instances, of which 889 instances are optimally solved. The experimental results show that the use of the adjacent task duplication policy effectively reduces the number of stations, especially when the WEST ratios are small. IntroductionAssembly lines are flow-oriented production systems that are typical in the industrial production of high-quantity standardised commodities (Becker and Scholl 2006). The labour productivity of assembly lines is largely driven by how the tasks (indivisible elements of work) are assigned to stations subject to technological constraints, commonly referred to as assembly line balancing (ALB) (Battaïa and Dolgui 2013). The simple assembly line balancing problem (SALBP) aims to minimise the number of stations given the cycle time (type I) or the cycle time given the number of stations (type II) (Baybars 1986).The mixed-model assembly line (MAL) is a more complex environment in which several product models are assembled simultaneously in intermixed sequences (Thomopoulos 1967). MALs are widely used in many industries such as automobiles, white goods and consumer electronics, where demand is characterised by high variability and relatively small volume for each model (Becker and Scholl 2006). A MAL generally assembles different versions of one basic product rather than completely different items. Hence, many studies assume that a single precedence diagram can be drawn to resume the precedence relationships among different tasks over each model (Merengo, Nava, and Pozzetti 1999). However, the processing time of a task may differ over the various models, and each variant of the task over these models should be regarded as a separate work element (Boysen, Fliedner, and Scholl 2008). The MAL balancing problem (MALBP) involves assigning all the task variants to stations.A straightforward approach for modelling and solving MALBPs is to restrict all the variants of a task over different models to an identical station. This restriction is reasonable, considering that these task variants may require the same skills, tools or assembly parts (Thomopoulos 1967). With this restriction, MALBPs are reduced to some version of...

Section: Literature Reviewmentioning

confidence: 97%

Balancing mixed-model assembly lines with adjacent task duplication

Yang

2014

“…They suggested a simulated annealing algorithm for this problem. Kara and Tekin (2009) presented a mixed integer programming formulation for optimal balancing of MMUL and proposed a new heuristic solution procedure to handle large-scale MMUL balancing problems. Hwang and Katayama (2009) proposed a multidecision genetic approach for workload balancing of MMULs.…”

Section: Literature Reviewmentioning

confidence: 99%

A modified colonial competitive algorithm for the mixed-model U-line balancing and sequencing problem

Lian

Zhang

et al. 2012

Implementation of mixed-model U-shaped assembly lines (MMUL) is emerging and thriving in modern manufacturing systems owing to adaptation to changes in market demand and application of just-in-time production principles. In this study, the line balancing and model sequencing (MS) problems in MMUL are considered simultaneously, which results in the NP-hard mixed-model U-line balancing and sequencing (MMUL/BS) problem. A colonial competitive algorithm (CCA) is developed and modified to solve the MMUL/BS problem. The modified CCA (MCCA) improves performance of original CCA by introducing a third type of country, independent country, to the population of countries maintained by CCA. Implementation details of the proposed CCA and MCCA are elaborated using an illustrative example. Performance of the proposed algorithms is tested on a set of test-bed problems and compared with that of existing algorithms such as co-evolutionary algorithm, endosymbiotic evolutionary algorithm, simulated annealing, and genetic algorithm. Computational results and comparisons show that the proposed algorithms can improve the results obtained by existing algorithms developed for MMUL/BS.

“…the model sequence. Kara and Tekin (2009) addressed the balancing problem on a MMUL, for which a model sequence is given. The proposed approach minimises the number of stations under the constraint that the workload of any station in any cycle cannot exceed the cycle time.…”

Section: Introductionmentioning

confidence: 99%

Sequencing minimum product sets on mixed-model U-lines to minimise work overload

Sun

2012

In a mixed-model assembly line (MMAL), varying models of the same basic product are produced in a facultative sequence. This gives rise to the short-term model sequencing problem, which has to decide on the production sequence of a given number of model copies so that work overload is minimised. Recently, many MMALs have been arranged in 'U-lines', where one operator supervises both the entrance and the exit. This paper addresses the model sequencing problem on a paced mixed-model U-line in a cyclic production environment. Some useful properties of the problem are characterised, and the problem is formulated to minimise the steady-state work overload. A branch-and-bound algorithm is proposed to solve small-sized problems, and a heuristic is proposed for practical-sized problems. Numerical experiments on 540 randomly generated instances show that the proposed heuristic can find near-optimal solutions efficiently.