Balancing and sequencing of stochastic mixed-model assembly U-lines to minimise the expectation of work overload time

A mixed-model assembly U-line is a flexible production system capable of manufacturing a variety of similar models, and it has become popular as an important component of the just-in-time production system. However, it poses new challenges for the optimal design of assembly lines because both the task assignment and the production sequence affect the workload variance among workstations. As a consequence, this paper addresses the line balancing problem and the model sequencing problem jointly and proposes a 0–1 stochastic programming model. In this model, task times are assumed to be stochastic variables independently distributed with normal distributions and the objective is to minimise the expectation of work overload time for a given combination of cycle time and number of workstations. To solve the problem, a simulated annealing-based algorithm is developed, which can also be used to minimise the absolute deviation of workloads in a deterministic environment. The experimental results for a set of benchmark problems show that the proposed algorithm outperforms the existing algorithms in terms of solution quality and running time.     

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

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.     

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

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.     

A new approach for rebalancing of U-lines with stochastic task times using ant colony optimisation algorithm

In real world, line balancing involves existing lines in existing factories and the line typically needs to be rebalanced rather than balanced. Rebalancing of a U-line can be defined as a changeover process from its initial configuration to a new configuration for a while due to the reasons such as demand variations, changes in product design and changes in task times, etc. This study defines U-line rebalancing problem with stochastic task times and proposes a solution procedure based on ant colony optimisation. The objective of the proposed algorithm is to minimise total cost of rebalancing which is the sum of task transposition costs, workstation opening/closing costs and operating costs of workstations for a particular planning horizon. A comprehensive experiment is conducted to generate problem instances and to compare rebalancing costs of U-lines by means of several factors. A total of 6600 rebalancing solutions are obtained and several comparisons are performed.     

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

The mixed-model U-line balancing problem was first studied by Sparling and Miltenburg (Sparling, D. and Miltenburg, J., 1998. The mixed-model U-line balancing problem. International Journal of Production Research, 36(2), 485–501) but has not been mathematically formulated to date. This paper presents a mixed integer programming formulation for optimal balancing of mixed-model U-lines. The proposed approach minimises the number of workstations required on the line for a given model sequence. The proposed formulation is illustrated and tested on an example problem and compared with an existing approach. This paper also proposes a new heuristic solution procedure to handle large scale mixed-model U-line balancing problems. A comprehensive experimental analysis is also conducted to evaluate the performance of the proposed heuristic. The results show the validity and usefulness of the proposed integer formulation and effectiveness of the proposed heuristic procedure.     

Heuristic approaches for mixed-model sequencing problem with stochastic processing times

Despite many pioneering efforts and works over the past decades, stochastic events have not been studied extensively in mixed-model assembly lines thus far. For a mixed-model sequencing problem with stochastic processing times, this paper aims to minimise expected total work overload. It also focuses on the most critical workstation of the line. In practice, this assumption is useful when the whole or a big portion of the assembly line is considered as a single station. In order to tackle the problem, a dynamic programming (DP) algorithm as well as two greedy heuristics from the literature is employed. However, it is realised that the DP cannot guarantee the optimal sequence neither for stochastic nor deterministic problems. It is because the calculation of work overload is involved in a recursive procedure that affects the states’ value functions. Therefore, by the use of network representation, the problem is modelled as a shortest path problem and a new heuristic, inspired by Dijkstra’s algorithm is developed to deal with it. Numerical results show that the proposed method outperforms other algorithms strongly. Finally, some discussion is provided about why one should consider stochastic parameters and why the proposed heuristic performs well in this regard.     

Analysis of the type II robotic mixed-model assembly line balancing problem

In recent years, there has been an increasing trend towards using robots in production systems. Robots are used in different areas such as packaging, transportation, loading/unloading and especially assembly lines. One important step in taking advantage of robots on the assembly line is considering them while balancing the line. On the other hand, market conditions have increased the importance of mixed-model assembly lines. Therefore, in this article, the robotic mixed-model assembly line balancing problem is studied. The aim of this study is to develop a new efficient heuristic algorithm based on beam search in order to minimize the sum of cycle times over all models. In addition, mathematical models of the problem are presented for comparison. The proposed heuristic is tested on benchmark problems and compared with the optimal solutions. The results show that the algorithm is very competitive and is a promising tool for further research.     

Balancing of mixed-model parallel U-shaped assembly lines considering model sequences

As a consequence of increasing interests in customised products, mixed-model lines have become the most significant components of today’s manufacturing systems to meet surging consumer demand. Also, U-shaped assembly lines have been shown as the intelligent way of producing homogeneous products in large quantities by reducing the workforce need thanks to the crossover workstations. As an innovative idea, we address the mixed-model parallel U-shaped assembly line design which combines the flexibility of mixed-model lines with the efficiency of U-shaped lines and parallel lines. The multi-line stations utilised in between two adjacent lines provide extra efficiency with the opportunity of assigning tasks into workstations in different combinations. The new line configuration is defined and characterised in details and its advantages are explained. A heuristic solution approach is proposed for solving the problem. The proposed approach considers the model sequences on the lines and seeks efficient balancing solutions for their different combinations. An explanatory example is also provided to show the sophisticated structure of the studied problem and explain the running mechanism of the proposed approach. The results of the experimental tests and their statistical analysis indicated that the proposed line design requires fewer number of workstations in comparison with independently balanced mixed-model U-lines.     

Line balancing and model sequencing to reduce work overload in mixed-model U-line production environments

Mixed-model U-lines (MMULs) are important elements of just-in-time production systems. For successful implementation of MMULs, a smoothed workload distribution among workstations is important. This requires that line balancing and model sequencing problems are solved simultaneously. This article presents a mixed, zero–one, nonlinear mathematical programming formulation for balancing and sequencing MMULs simultaneously with the objective of reducing work overload. Since the problem is NP-hard, an effective simulated annealing approach is also presented and its performance compared with existing approaches. The results show that the proposed simulated annealing algorithm outperforms existing approaches.     

遗传禁忌搜索算法在混流装配线排序中的应用

针对混流装配线排序问题，提出了一种混合遗传禁忌搜索算法，在每一代遗传演化之后，按一定比例随机选择部分解进行禁总搜索，以提高算法的全局搜索能力和收敛性。通过一个混流装配线排序实验，分别利用遗传算法和遗传禁忌搜索算法进行求解，结果表明遗传禁忌搜索算法具有更好的全局搜索能力和收敛性能。     

Non-dominated ranked genetic algorithm for a multi-objective mixed-model assembly line sequencing problem

The increasing market demand for product variety forces manufacturers to design mixed-model assembly lines (MMAL) on which a variety of product models similar to product characteristics are assembled. This paper presents a method combining the new ranked based roulette wheel selection algorithm with Pareto-based population ranking algorithm, named non-dominated ranking genetic algorithm (NRGA) to a just-in-time (JIT) sequencing problem when two objectives are considered simultaneously. The two objectives are minimisation the number of setups and variation of production rates. This type of problem is NP-hard. Various operators and parameters of the proposed algorithm are reviewed to calibrate the algorithm by means of the Taguchi method. The solutions obtained via NRGA are compared against solutions obtained via total enumeration (TE) scheme in small problems and also against four other search heuristics in small, medium and large problems. Experimental results show that the proposed algorithm is competitive with these other algorithms in terms of quality and diversity of solutions.     

A multi-decision genetic approach for workload balancing of mixed-model U-shaped assembly line systems

A mixed-model assembly line is a type of production line where a variety of product models similar in product characteristics are produced. As a consequence of introducing the just-in-time (JIT) production principle, it has been recognised that a U-shaped assembly line system offers several benefits over the traditional straight line system. This paper proposes a new evolutionary approach to deal with workload balancing problems in mixed-model U-shaped lines. The proposed method is based on the multi-decision of an amelioration structure to improve a variation of the workload. This paper considers both the traditional straight line system and the U-shaped assembly line, and is thus an unbiased examination of line efficiency. The performance criteria considered are the number of workstations (the line efficiency) and the variation of workload, simultaneously. The results of experiments enhanced the decision process during multi-model assembly line system production; thus, it is therefore suitable for the augmentation of line efficiency in workstation integration and simultaneously enhancement of the variation of the workload. A case study is examined as a validity check in collaboration with a manufacturing company.     

A note on ‘A bit-wise mutation algorithm for mixed-model sequencing in JIT production systems’ (Nazar & Pillai, 2015, IJPR, 53:19, 5931-5947)

This note discusses three points about the problem of sequencing units on a mixed-model assembly line in ‘A bit-wise mutation algorithm for mixed-model sequencing in JIT production systems’ (Nazar & Pillai, 2015, IJPR, 53:19, 5931-5947). Specifically, the mixed-integer quadratic model, the bit-wise mutation algorithm and the bi-objective problem to optimise both product rate variation and makespan. The conclusion of the discussion is that the three alleged contributions are not valid or are outperformed by those presented in some previously published papers.     

Balancing mixed-model assembly lines: a computational evaluation of objectives to smoothen workload

Mixed-model assembly lines are widely used in a range of production settings, such as the final assembly of the automotive and electronics industries, where they are applied to mass-produce standardised commodities. One of the greatest challenges when installing and reconfiguring these lines is the vast product variety modern mixed-model assembly lines have to cope with. Traditionally, product variety is bypassed during mid-term assembly line balancing by applying a joint precedence graph, which represents an (artificial) average model and serves as the input data for a single model assembly line balancing procedure. However, this procedure might lead to considerable variations in the station times, so that serious sequencing problems emerge and work overload threatens. To avoid these difficulties, different extensions of assembly line balancing for workload smoothing, i.e. horizontal balancing, have been introduced in the literature. This paper presents a multitude of known and yet unknown objectives for workload smoothing and systematically tests these measures in a comprehensive computational study. The results suggest that workload smoothing is an essential task in mixed-model assembly lines and that some (of the newly introduced) objectives are superior to others.     

Worker allocation in lean U-shaped production lines

U-shaped lines are widely used in lean systems. In U-shaped production lines, each worker handles one or more machines on the line: the worker allocation problem is to establish which machines are handled by which worker. This differs from the widely-investigated U-line assembly line balancing problem in that the assignment of tasks to line locations is fixed. This paper address the worker allocation problem for lean U-shaped production lines where the objectives are to minimize the quantity of workers and maximize full work: such allocations provide the opportunity to eliminate the least-utilized worker by improving processes accordingly. A mathematical model is developed: the model allows for any allocation of machines to workers so long as workers do not cross paths. Walking times are considered, where workers follow circular paths and walk around other worker(s) on the line if necessary. A heuristic algorithm for tackling the problem is developed, along with a procedure representing the ‘traditional’ approach of constructing standard operations routines. Computational experiments considering three line sizes (up to 20 machines) and three takt time levels are performed. The results show that the proposed algorithm both improves upon the traditional approach and is more likely to provide optimal solutions.     

Level scheduling of mixed-model assembly lines under storage constraints

In a mixed-model assembly line, different models of a common base product can be manufactured in intermixed production sequences. A famous solution approach for the resulting short-term sequencing problem is the so-called level scheduling problem, which aims at evenly smoothing the material requirements over time in order to facilitate a just-in-time supply. However, if materials are delivered in discrete quantities, the resulting spread of material usages implies that issued cargo carriers of a respective material remain at a station for a longer period of time. In practical applications with many materials required per station, this procedure might lead to bottlenecks with respect to the scarce storage space at stations. This paper investigates level scheduling under the constraint that the induced part usage patterns may not violate given storage constraints. The resulting sequencing problem is formalised and solved by suitable exact and heuristic solution approaches.     

Sequencing problem for a mixed-model assembly line in the Toyota production system

The paper discusses a sequencing problem of a mixed-model assembly line in the Toyota Motor Corporation production system, which is well known as the Just-in-Time production system. Whenever a worker in the assembly line finds that he might fail to complete his operations within the work zone, he pushes a button to call an auxiliary worker who assists him in the operations. If he can complete the operations within his work zone with the help of the auxiliary worker, the line does not stop. Otherwise, the line stops. In the Toyota production system, it is very important to keep a constant rate of usage of every part used by the assembly line. Hence, there are two goals for the sequencing problem in the Toyota production system. The paper provides a new formulation for the sequencing problem with two goals. It considers the goal of keeping the constant rate of part usage as a constraint of the sequencing problem, and it formulates a sequencing problem of minimizing the total line stoppage time with auxiliary workers and the constraints for keeping the constant rate of part usage. Since this problem is NP-hard and the size of the practical problems at Toyota are huge, a two-phase approximation algorithm is proposed. Numerical examples show that the proposed algorithm is efficient and can find a good suboptimal solution.     

Integrated procedure of balancing and sequencing for mixed-model assembly lines: a multi-objective evolutionary approach

A mixed-model assembly line is a type of production line which is used to assemble a variety of product models with a certain level of similarity in operational characteristics. This variety causes workload variance among other problems resulting in low efficiency and line stops. To cope with these problems, a hierarchical design procedure for line balancing and model sequencing is proposed. It is structured in terms of an amelioration procedure. On the basis of our evolutionary algorithm, a genetic encoding procedure entitled priority-based multi-chromosome (PMC) is proposed. It features a multi-functional chromosome and provides efficient representation of task assignment to workstations and model sequencing. The lean production perspective recognises the U-shape assembly line system as more advanced and beneficial compared to the traditional straight line system. To assure the effectiveness of the proposed procedure, both straight and U-shape assembly lines are examined under two major performance criteria, i.e., number of workstations (or line efficiency) as static criterion and variance of workload (line and models) as dynamic criterion. The results of simulation experiments suggest that the proposed procedure is an effective management tool of a mixed-model assembly line system.     

Sequencing mixed-model assembly lines to level parts usage and minimize line length

The problem of sequencing units on a mixed-model assembly line can be viewed with several objectives in mind. Past research has focused mainly on two separate performance measures: (1) minimizing the length of the line (which is equivalent to minimizing the risk of stopping the conveyor when system variability is present and the station lengths are fixed); or (2) maintaining a rate of assembly equal to the demand rate for each model type in the production schedule. The latter is the more appropriate in a just-in-time environment. We present a bicriteria formulation of the problem that can be used to examine the tradeoffs between line length and parts usage. The resultant model takes the form of a mixed integer nonlinear program and is solved with a combination of heuristics and branch and bound. Results are reported for a wide range of problem sizes, as defined by the number of stations on the line, the number of different model types, and the total number of units to be assembled. In almost all cases, at least one of the heuristics found either the optimum or the best available solution. Computation times were quite reasonable for the heuristics, but grew exponentially for branch and bound. In general, it was only possible to verify optimality on problems with 20 units.