A Branch, Bound, and Remember Algorithm for the Simple Assembly Line Balancing Problem

Sewell, Edward C.; Jacobson, Sheldon H.

doi:10.1287/ijoc.1110.0462

Cited by 104 publications

(35 citation statements)

References 30 publications

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“…The BB&R algorithm is a hybrid of a branch and bound (B&B) procedure and a dynamic programming (DP) procedure that memorises each subproblem created in the B&B framework (Sewell and Jacobson 2012). Before branching on a subproblem, the algorithm cheques the memory to examine whether the subproblem is dominated by a previously encountered subproblem.…”

Section: Solution Methodsmentioning

confidence: 99%

“…This is because some variants of the tasks in pack V B k have to be allocated to station k + 1, and pack V A k may fill station k as compactly as pack V B k when the workload of pack V B k is greater than σ k . The BB&R algorithm adopts the cyclic-best-first-search (CBFS) strategy as in Sewell and Jacobson (2012). The CBFS is a hybrid of the depth-first search and best-first search strategies.…”

Section: Branching Dominance Rules and Search Strategymentioning

confidence: 99%

“…After a complete solution is built, the CBFS cycles back to the top level. For details of the BB&R algorithm and the CBFS strategy, refer to Sewell and Jacobson (2012). After the optimal task assignment solution Y * is found by the BB&R algorithm, a feasible variant allocation solution can be obtained using the GTA procedure.…”

Section: Branching Dominance Rules and Search Strategymentioning

confidence: 99%

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Balancing mixed-model assembly lines with adjacent task duplication

Yang

Gao

2014

International Journal of Production Research

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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...

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Section: Solution Methodsmentioning

confidence: 99%

Section: Branching Dominance Rules and Search Strategymentioning

confidence: 99%

Section: Branching Dominance Rules and Search Strategymentioning

confidence: 99%

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Balancing mixed-model assembly lines with adjacent task duplication

Yang

Gao

2014

International Journal of Production Research

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“…The literature covers multiple approaches to solve the SALBP, including both heuristic, see Bautista and Pereira (2009);Pape (2015), and exact, see Sewell and Jacobson (2012); Vilà and Pereira (2013); Morrison, Sewell and Jacobson (2014), methods. For the SALBP-1, exact methods are based on enumeration, with branch-and-bound-based techniques being the preferred approach.…”

Section: Literature Reviewmentioning

confidence: 99%

A new model for supply chain network design with integrated assembly line balancing decisions

Pereira

Vilà

2015

International Journal of Production Research

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Supply chain network design aims at the integration of the different actors of a supply chain within a single framework in order to optimize the total profit of the system. In this paper, we consider the integration of line balancing issues within the tactical decisions of the supply chain, and we offer a novel model and a solution approach for the problem. The new approach decomposes the problem into multiple line balancing problems and a mixed-integer linear model, which is easier to solve than the previously available nonlinear mixed-integer formulation. The results show that the new method is able to solve previously studied models within a fraction of the previously reported running times, and also allows us to solve larger instances than those reported by previous works. Finally, we also provide some analysis on the influence of the cost structure, the demand, and the structure of the assembly process on the final configuration of the assemblies and the distribution network.

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“…This problem is known to be NP-hard. Even if it was introduced in the literature almost 60 years ago [10], many recent studies still address it [2,3,7,9,11].…”

Section: Introduction and Related Literaturementioning

confidence: 99%

An Exact Method for the Assembly Line Re-balancing Problem

Makssoud

Battaïa

Dolgui

2013

IFIP Advances in Information and Communication Technology

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Abstract. In this paper, we propose a mathematical optimisation model to solve the simple assembly line rebalancing problem. This problem arises when an existing assembly line has to be rebalanced in order to meet new production requirements. In this paper, a Mixed Integer Program is proposed for solving this problem with the objective to minimize the number of changes in the initial line. The computational experiments show the efficacy of the proposed method.

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A Branch, Bound, and Remember Algorithm for the Simple Assembly Line Balancing Problem

Cited by 104 publications

References 30 publications

Balancing mixed-model assembly lines with adjacent task duplication

Balancing mixed-model assembly lines with adjacent task duplication

A new model for supply chain network design with integrated assembly line balancing decisions

An Exact Method for the Assembly Line Re-balancing Problem

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