A genetic algorithm for the stochastic mixed-model U-line balancing and sequencing problem

Mixed-model assembly lines are widely used to improve the flexibility to adapt to the changes in market demand, and U-lines have become popular in recent years as an important component of just-in-time production systems. As a consequence of adaptation of just-in-time production principles into the manufacturing environment, mixed-model production is performed on U-lines. This type of a production line is called a mixed-model U-line. In mixed-model U-lines, there are two interrelated problems called line balancing and model sequencing. In real life applications, especially in manual assembly lines, the tasks may have varying execution times defined as a probability distribution. In this paper, the mixed-model U-line balancing and sequencing problem with stochastic task times is considered. For this purpose, a genetic algorithm is developed to solve the problem. To assess the effectiveness of the proposed algorithm, a computational study is conducted for both deterministic and stochastic versions of the problem.     

Line balancing in a just-in-time production environment: balancing multiple U-lines

The introduction of multiple, independent production lines has helped many firms to increase their production flexibility, provide for redundancy when equipment breaks down, reduce idle time and labor costs, and achieve many other benefits. This paper introduces and formalizes the multiple U-line balancing problem. Optimal solution methodologies are provided for Type I (minimize the number of stations for a given cycle time), Type II (minimize the cycle time for a given number of stations), and cost-minimization line-balancing problems. A branch-and-bound algorithm is also developed for the situation in which equipment requirements are dependent on the line configuration and the task assignment to stations. Computational results indicate that the greatest benefit of exploiting multiple lines occurs for smaller cycle-time problems that require higher output.     

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.     

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.     

Balancing manual mixed-model assembly lines using overtime work in a demand variation environment

This study deals with the balancing problem of a manual mixed-model assembly line, where the production volume or the product mix changes from shift to shift during the planning horizon. The unstable demand can be characterised by several representative scenarios, and the line uses overtime work to meet the demand variation. The balancing problem concerns how to assign assembly tasks to stations and determine the amount of overtime in each possible demand scenario. The objective is to satisfy the demand in each possible scenario with the minimum labour costs paid for both normal shifts and overtime work. A lower bound on the labour costs is proposed, and a heuristic algorithm is developed to quickly find a feasible solution. A branch, bound and remember (BB&;R) algorithm is then proposed to find better solutions. These solution methods are tested on 765 instances. The BB&;R algorithm obtains optimal solutions for 510 instances and gives high-quality solutions for the remaining 255 instances within 60?s. The experimental results show that the use of overtime work and adjustable cycle times significantly reduces the labour costs, especially when the demand or task processing time variations are large.     

考虑工人行走的作业时间随机分布的U型线平衡

针对工人作业时间随机分布并与工人行走路径时间相互独立的U型线平衡问题,运用遗传算法与仿真建模分析相结合的方法求解。在给定的节拍与完工率下,以最小化工作站数目为目标,设计遗传算法求解作业元素分配序列。基于作业序列建立U型线布局仿真模型,模拟工人行走路径以及工人作业时间的随机分布,仿真结果得到各个工作站实际完工率达到给定的完工率下的最小工作站数,并得出工人行走时间不可忽略。最后结合实例验证方法是有效的。     

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.     

Flexible assembly line design problem with fixed number of workstations

In the paper, we study a flexible assembly line design problem with equipment decisions. We assume the task times and equipment costs are correlated in the sense that for all tasks the cheaper equipment gives no smaller task time. Given the cycle time and number of workstations we aim to find the assignment of tasks and equipment to the workstations so as to minimise the total equipment cost. We develop a branch and bound algorithm that uses powerful lower bounds and reduction mechanisms. Our computational experiments have revealed that our algorithm can solve large-sized problem instances in reasonable solution times.     

Improved imperialist competitive algorithms for rebalancing multi-objective two-sided assembly lines with space and resource constraints

In this paper, a mathematical model and an improved imperial competition algorithm (IICA) are proposed to solve the multi-objective two-sided assembly line rebalancing problem with space and resource restrictions (MTALRBP-SR). The aim is to find lines’ rebalance with the trade-off between efficiency, rebalancing cost and smoothing after reconfiguration. IICA utilises a new initialisation heuristic procedure based on classic heuristic rules to generate feasible initial solutions. A novel heuristic assimilation method is developed to vigorously conduct local search. In addition, a group-based decoding heuristic procedure is developed to fulfil the final task reassignment with the additional restrictions. To investigate the performance of the proposed algorithm, it is first tested on MTALRBP of benchmark problems and compared with some existing algorithms such as genetic algorithm, variable neighbourhood search algorithm, discrete artificial bee colony algorithm, and two iterated greedy algorithms. Next, the efficiency of the proposed IICA for solving MTALRBP-SR is revealed by comparison with a non-dominated sorting genetic algorithm (NSGA-II) and two versions of original ICA. Computational results and comparisons show the efficiency and effectiveness of IICA. Furthermore, a real-world case study is conducted to validate the proposed algorithm.     

The type-II assembly line rebalancing problem considering stochastic task learning

Assembly lines with non-constant task time attribute are widely studied in the literature. For the SALBP-II assembly line balancing problem, we take account of stochastic task time changes, which is more practical than the deterministic times often assumed in industrial application. An algorithm – ENCORE, which leverages the traditional algorithm SALOME2, is proposed to address the assembly line balancing problem with stochastic task time attribute. Computational and statistical experiments are conducted to show the efficiency of proposed algorithms over traditional methods with regards to the improvement of total production times.     

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.     

A new distribution-free model for disassembly line balancing problem with stochastic task processing times

Effective conduct with End of Life (EOL) products is a hot research topic in green and smart manufacturing. For EOL product recycling and remanufacturing, a fundamental problem is to design an efficient disassembly line under consideration of stochastic task processing times. This problem focuses on selecting alternative task processes, determining the number of opened workstations, and assigning operational tasks to the workstations. The goal is to minimise the total cost consisting of workstation operational cost and hazardous component processing cost. Most existing works assume that the probability distribution of task processing times can be estimated, however, it is often not likely to access the complete probability distribution due to various difficulties. Therefore, this study investigates disassembly line design with the assumption that only the mean, standard deviation and an upper bound of task processing times are known. Our main contributions include: (i) a new decomposition color graph is proposed to intuitively describe all possible processes, (ii) a new distribution-free model is proposed, and (iii) some problem properties are established to solve the model. Experimental results show that the distribution-free model can effectively deal with stochastic task processing times without given probability distributions.     

Profit-oriented partial disassembly line design: dealing with hazardous parts and task processing times uncertainty

This paper addresses the problem of profit-oriented disassembly line design and balancing considering partial disassembly, presence of hazardous parts and uncertainty of task processing times. Few papers have studied the stochastic disassembly line balancing problem and existing approaches have focused on heuristic and metaheuristic methods. Most existing work has concentrated on complete disassembly where task times are assumed to be normal random variables and where AND/OR graphs are not considered. The objective of this paper is the design of a serial line that obtains the maximum revenue and then balances the workload under uncertainty. The processing time of a disassembly task is assumed to be a random variable with any known probability distribution. An AND/OR graph is used to model the precedence relationships among tasks. Stochastic programming models and exact-based solution approaches combining the L-shaped algorithm and Monte Carlo sampling techniques are proposed. The relevance and applicability of the proposed models and solution methods are shown by solving efficiently a set of disassembly problem instances from the literature.     

Design of stochastic assembly lines considering line balancing and part feeding with supermarkets

This article aims to address the assembly line balancing problem (ALBP) and supermarket location problem (SLP) as two long-term interrelated decision problems considering the stochastic nature of the task times and demands. These problems arise in real-world assembly lines during the strategic decision-making phase of configuring new assembly lines from both line balancing and part-feeding (PF) aspects. A hierarchical mathematical programming model is developed, in which the first level resolves the stochastic ALBP by minimizing the workstation numbers and the second level deals with the stochastic SLP while optimizing the PF shipment, inventory and installation costs. The results of case data from an automotive parts manufacturer and a set of standard test problems verified that the proposed model can optimize the configuration of assembly lines considering both ALBP and SLP performance measures. This study also validates the effect of the stochastic ALBP on the resulting SLP solutions.     

An integrated model for the production-inventory-distribution problem in the Physical Internet

In contrast to traditional supply chain networks, Physical Internet (PI) is an interconnected open global logistics network based on open PI hubs and standard PI-containers that has the potential to achieve ground-breaking improvements in integrated production-inventory-distribution management. In this paper, to quantify the advantages of PI from a cost performance perspective, we propose a mixed-integer linear programming (MILP) formulation for addressing the problem that combines an integrated production-inventory-distribution decision with PI, which has been addressed separately in the existing literature. The results of computational experiments show that while achieving a comparable or better service level, PI can achieve significant cost savings compared to a traditional supply chain network with a dynamic configuration and a hybrid configuration. Moreover, we investigate the impact of several problem parameter changes on the total costs under each network setting, and managerial insights are derived.     

企业设备布局方式的仿真

针对设备布局问题研究的不足,分析了3种常用设备布局方式(传统直线形布局、U形布局和单元式布局)的特性,利用仿真工具对一电子制造企业做了个案研究.仿真结果表明当产品品种单一或需求量较少时,U形布局的单产品生产周期相对其他两种布局方式要短一些;当品种较多或需求量较大时,单元式布局能获得最佳效益.     

A weighted approach for assembly line design with station paralleling and equipment selection

This paper studies the problem of assembly line design, focusing on station paralleling and equipment selection. Two problem formulations, minimizing the number of stations, and minimizing the total cost, are discussed. The latter formulation is demonstrated by several examples, for different assembly system conditions: labor intensive or equipment intensive, and with task times that may exceed the required cycle time. It is shown that the problem of assembly system design with parallel stations can be treated as a special case of the problem of equipment selection for an assembly line. A branch and bound optimal algorithm developed for the equipment selection problem is adapted to solve the parallel station problem. Experiments are designed to investigate and demonstrate the influence of system parameters, such as assembly sequence flexibility and cycle time, on the balancing improvement due to station paralleling. An ILP formulation is developed for the combined problem of station paralleling with equipment selection, and an optimal solution of an example problem is presented.     

A multi-objective distribution-free model and method for stochastic disassembly line balancing problem

End-of-life product recycling is a hot research topic in recent years, which can reduce the waste and protect the environment. To disassemble products, the disassembly line balancing is a principal problem that selects tasks and assigns them to a number of workstations under stochastic task processing times. In existing works, stochastic task processing times are usually estimated by probability distributions or fuzzy numbers. However, in real-life applications, only their partial information is accessible. This paper studies a bi-objective stochastic disassembly line balancing problem to minimise the line design cost and the cycle time, with only the knowledge of the mean, standard deviation and upper bound of stochastic task processing times. For the problem, a bi-objective chance-constrained model is developed, which is further approximated into a bi-objective distribution-free one. Based on the problem analysis, two versions of the ?-constraint method are proposed to solve the transformed model. Finally, a fuzzy-logic technique is adapted to propose a preferable solution for decision makers according to their preferences. A case study is presented to illustrate the validity of the proposed models and algorithms. Experimental results on 277 benchmark-based and randomly generated instances show the efficiency of the proposed methods.     

An integrated model for assembly line re-balancing problem

In this paper, an integrated approach for assembly line rebalancing problem (IALRP) is proposed to quickly react and find an optimal rebalancing of the line when disruptive event occurs because of product demand changes. This model is motivated by real-life application of an automotive cable manufacturer which provides more realistic constraints. To solve the problem, we propose a genetic algorithm (GA) hybridised with a heuristic priority rule-based procedure. This hybridisation is used to add more rich seeds to the initial population and consequently to improve the convergence capability and performance of the GA. After the disturbance, we aim to find a rebalance with the proposed approach to maximise the line efficiency and distributing the idle time across the workstations as equally as possible. To evaluate the efficiency of the proposed algorithm, set of samples collected from the literature are used. The real case study and the experiment results show the proposed approach is very effective and competitive.     

Effective material flow at an assembly facility

Effective material flow in an assembly facility leads to reduced material handling costs and increased productivity. This research focuses on improving the flow of materials for an assembly facility that receives supplied parts through receiving docks and transfers the parts to material storage locations and then to part usage locations. The locations of the receiving docks, storage locations, and line locations are predetermined, but the assignment of parts to dock locations and storage locations and the material flow paths through the facility are decision variables. Furthermore, design decisions such as the dock strategy employed and the configuration of the storage areas lead to additional decision variables. The goal is to reduce overall material handling costs by effectively receiving, storing and transferring the material from loading docks to line locations. The contribution of this research is in applying multi-commodity network flow models that integrate many of the sub-problems that are assumed to be solved a priori in many existing models. This integrated approach was used to evaluate configuration changes for a collaborating facility. One of the scenarios analysed showed an improvement in the material handling costs of nearly 10% as compared to current practices.