Robotic U-shaped assembly line balancing using particle swarm optimization

Automation in an assembly line can be achieved using robots. In robotic U-shaped assembly line balancing (RUALB), robots are assigned to workstations to perform the assembly tasks on a U-shaped assembly line. The robots are expected to perform multiple tasks, because of their capabilities. U-shaped assembly line problems are derived from traditional assembly line problems and are relatively new. Tasks are assigned to the workstations when either all of their predecessors or all of their successors have already been assigned to workstations. The objective function considered in this article is to maximize the cycle time of the assembly line, which in turn helps to maximize the production rate of the assembly line. RUALB aims at the optimal assignment of tasks to the workstations and selection of the best fit robot to the workstations in a manner such that the cycle time is minimized. To solve this problem, a particle swarm optimization algorithm embedded with a heuristic allocation (consecutive) procedure is proposed. The consecutive heuristic is used to allocate the tasks to the workstation and to assign a best fit robot to that workstation. The proposed algorithm is evaluated using a wide variety of data sets. The results indicate that robotic U-shaped assembly lines perform better than robotic straight assembly lines in terms of cycle time.     

Simulated annealing algorithms for the multi-manned assembly line balancing problem: minimising cycle time

Multi-manned assembly lines are often designed to produce big-sized products, such as automobiles and trucks. In this type of production lines, there are multi-manned workstations where a group of workers simultaneously performs different operations on the same individual product. One of the problems, that managers of such production lines usually encounter, is to produce the optimal number of items using a fixed number of workstations, without adding new ones. In this paper, such a class of problems, namely, the multi-manned assembly line balancing problem is addressed, with the objective of minimising the cycle time. A mixed-integer mathematical programming formulation is proposed for the considered problem. This model has the primary objective of minimising the cycle time for a given number of workstations and the secondary objective of minimising the total number of workers. Since the addressed problem is NP-hard, two meta-heuristic approaches based on the simulated annealing algorithm have been developed: ISA and DSA. ISA solves the problem indirectly while DSA solves it directly. The performance of the two algorithms are tested and compared on a set of test problems taken from the literature. The results show that DSA outperforms ISA in term of solution quality and computational time.     

Order-oriented cooperative sequencing optimisation in multi-mix-model assembly lines

Order-oriented products assembly sequence among different assembly lines becomes a critical problem for mass customisation manufacturing systems. It significantly affects system productivity, delivery time, and manufacturing cost. In this paper, we propose a new approach to extend the traditional products sequencing from mixed model assembly line (MMAL) to multi-mixed model assembly lines (MMMALs) to obtain the optimal assembly sequence with the objectives of minimising consumption waviness of each material in the lines, assembly line setup cost, and lead-time. A multi-objective optimisation algorithm based on variable neighbourhood search methods (VNS) is developed. We perform an industrial case study in order to demonstrate the practicality and effectiveness of the proposed approach.     

Meta-heuristics for the distributed two-stage assembly scheduling problem with bi-criteria of makespan and mean completion time

This paper focuses on the distributed two-stage assembly flowshop scheduling problem for minimising a weighted sum of makespan and mean completion time. This problem involves two inter-dependent decision sub-problems: (1) how to allocate jobs among factories and (2) how to schedule the assigned jobs at each factory. A mathematical model is formulated for solving the small-sized instances of the problem. Since the NP-hardness of the problem, we also proposed a variable neighbourhood search (VNS) algorithm and a hybrid genetic algorithm combined with reduced variable neighbourhood search (GA-RVNS) to solve the distributed two-stage assembly flowshop scheduling problems and approximately optimise makespan and mean completion time simultaneously. Computational experiments have been conducted to compare the performances of the model and proposed algorithms. For a set of small-sized instances, both the model and the proposed algorithms are effective. The proposed algorithms are further evaluated on a set of large-sized instances. The results statistically show that both GA-RVNS and VNS obtain much better performances than the GA without RVNS-based local search step (GA-NOV). For the instances with small numbers of jobs, VNS achieves better performances than GA-RVNS. However, for the instances with large numbers of jobs, GA-RVNS yields better performances than the VNS. It is also shown that the overall performances of VNS are very close to GA-RVNS with different numbers of factories, weights given to makespan and numbers of machines at the first stage.     

Two-stage assembly flow-shop scheduling problem with non-identical assembly machines considering setup times

In this paper, we address the two stage assembly flow-shop problem with multiple non-identical assembly machines in stage two to minimise weighted sum of makespan and mean completion time. Also, sequence dependent setup times are considered for the first stage. This problem is a generalisation of previously proposed two stage assembly flow-shop problems (TSAFSP). In many real world industrial and production systems, there is more than one assembly machine to assemble job components. After extending a mathematical mixed-integer linear programming model to solve the problem, we use GAMS software. The TSAFSP has been known as NP-hard. Therefore, our more general problem is NP-hard too and so for large sized problems the right way to proceed is with the use of heuristic algorithms. So in this paper a hybrid VNS heuristic, which is a combination of the variable neighbourhood search (VNS) algorithm and a novel heuristic is developed and its solutions compared with solutions obtained by GAMS. Computational experiments reveal that the hybrid VNS heuristic performs much better than GAMS with respect to the percentage errors and run times.     

Sustainable operator assignment in an assembly line using genetic algorithm

This paper addresses the operator assignment in predefined workstations of an assembly line to get a sustainable result of fitness function of cycle time, total idle time and output where genetic algorithm is used as a solving tool. A proper operator assignment is important to get a sustainable balanced line. To improve the efficiency and meet the desired target output within the time limit, a balanced assembly line is a must. Real world lines consist of a large number of tasks and it is very time consuming and crucial to choose the most suitable operator for a particular workstation. In addition, it is very important to assign the suitable operator at the right place as his skill of operating machines finally reflects in productivity or in the cost of production. To verify better assignments of workers, a genetic algorithm is adopted here. A heuristic is proposed to find out the sustainable assignment of operators in the predefined workstations.     

On the integrated charge planning with flexible jobs in primary steelmaking processes

The integrated charge planning (ICP) problem based on flexible jobs in an integrated steel plant is extremely difficult and valuable. The purpose of this paper is to improve the efficiency and feasibility of planning by minimising the number of charges, minimising the total production costs and maximising the total throughput, considering the hard constraints and soft constraints. A multi-objective mathematical programming model for the problem is formulated, and it is shown that the problem is NP-hard. Two new meta-heuristics are designed, one is guided variable neighbourhood search (GVNS) combined with harmony search, and the other is GVNS combined with simulated annealing. Compared with enumeration algorithm, tabu search, variable neighbourhood search (VNS), harmony search, extend next fit decreasing (ENFD) and skewed VNS (SVNS), variable neighbourhood descent (VND), the numerical results by actual production data have shown that the proposed model and GVNHS are feasible and effective for ICP.     

A heuristic approach for balancing mixed-model assembly line of type I using genetic algorithm

The mixed model assembly line is becoming more important than the traditional single model due to the increased demand for higher productivity. In this paper, a set of procedures for mixed-model assembly line balancing problems (MALBP) is proposed to make it efficiently balance. The proposed procedure based on the meta heuristics genetic algorithm can perform improved and efficient allocation of tasks to workstations for a pre-specified production rate and address some particular features, which are very common in a real world mixed model assembly lines (e.g. use of parallel workstations, zoning constraints, resource limitation). The main focus of this study is to study and modify the existing genetic algorithm framework. Here a heuristic is proposed to reassign the tasks after crossover that violates the constraints. The new method minimises the total number of workstation with higher efficiency and is suitable for both small and large scale problems. The method is then applied to solve a case of a plastic bag manufacturing company where the minimum number of workstations is found performing more efficiently.     

A hybrid electromagnetism-like algorithm for two-stage assembly flow shop scheduling problem

This paper presents a study on the two-stage assembly flow shop scheduling problem for minimising the weighed sum of maximum makespan, earliness and lateness. There are m machines at the first stage, each of which produces a component of a job. A single machine at the second stage assembles the m components together to complete the job. A novel model for solving the scheduling problem is built to optimise the maximum makespan, earliness and lateness simultaneously. Two optimal operation sequences of jobs are determined and verified. As the problem is known to be NP-hard, a hybrid variable neighbourhood search – electromagnetism-like mechanism (VNS-EM) algorithm is proposed for its handling. To search beyond local optima for a global one, VNS algorithm is embedded in each iteration of EM, whereby the fine neighbourhood search of optimum individuals can be realised and the solution is thus optimised. Simulation results show that the proposed hybrid VNS-EM algorithm outperforms the EM and VNS algorithms in both average value and standard deviation.     

A hybrid algorithm for total tardiness minimisation in flexible job shop: genetic algorithm with parallel VNS execution

This paper addresses the flexible-job-shop scheduling problem (FJSP) with the objective of minimising total tardiness. FJSP is the generalisation of the classical job-shop scheduling problem. The difference is that in the FJSP problem, the operations associated with a job can be processed on any set of alternative machines. We developed a new algorithm by hybridising genetic algorithm and variable neighbourhood search (VNS). The genetic algorithm uses advanced crossover and mutation operators to adapt the chromosome structure and the characteristics of the problem. Parallel-executed VNS algorithm is used in the elitist selection phase of the GA. Local search in VNS uses assignment of operations to alternative machines and changing of the order of the selected operation on the assigned machine to increase the result quality while maintaining feasibility. The purpose of parallelisation in the VNS algorithm is to minimise execution time. The performance of the proposed method is validated by numerical experiments on several representative problems and compared with adapted constructive heuristic algorithms’ (earliest due date, critical ratio and slack time per remaining operation) results.     

Assembly line balancing by a new multi-objective differential evolution algorithm based on TOPSIS

In this paper, we propose a multi-objective differential evolution algorithm (MODEA) to solve the multi-objective simple assembly line balancing problem type-2 (SALBP-2). This problem arises when in an existing assembly line, changes in the production process or demand structure take place and the organisation wants to produce the optimum number of items using a fixed number of workstations, which is associated with optimally assigning the tasks to an ordered sequence of stations such that the precedence relations are not violated and some measures of performance are optimised. The two considered objectives are: minimising the cycle time and the smoothness index of the assembly line. To that purpose, we develop a MODEA which unlike the existing algorithms deals with the considered objectives separately in selecting the next population members by proposing a new acceptance scheme based on the Pareto dominance concept and a new evaluation scheme based on TOPSIS. Also, by using the Taguchi method, we tune the effective factors of the developed algorithm. Then its efficiency is tested over available assembly line balancing benchmarks and compared to a new algorithm provided recently in the bi-objective SALBP-2 literature. Computational experiments indicate that the developed algorithm outperforms the existing meta-heuristic over a large group of benchmarks.     

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.     

Integrated scheduling and self-reconfiguration for assembly job shop in knowledgeable manufacturing

The problems of integrated assembly job shop (AJS) scheduling and self-reconfiguration in knowledgeable manufacturing are studied with the objective of minimising the weighted sum of completion cost of products, the earliness penalty of operations and the training cost of workers. In AJS, each workstation consists of a certain number of teams of workers. A product is assumed to have a tree structure consisting of components and subassemblies. The assembly of components, subassemblies and final products are optimised with the capacity of workstations simultaneously. A heuristic algorithm is developed to solve the problem. Dominance relations of operations are derived and applied in the development of the heuristic. A backward insertion search strategy is designed to locally optimise the operation sequence. Once the optimal schedule is acquired, the teams are reconfigured by transferring them from workstations of lower utilisation to those of higher utilisation. Effectiveness of the proposed algorithm is tested by a number of numerical experiments. The results show that the proposed algorithm promises lower total cost and desirable simultaneous self-reconfiguration in accordance with scheduling.     

A Petri net-based heuristic for mixed-model assembly line balancing problem of Type-E

To effectively respond to the changing market demands, a manufacturer should produce variety of products with small lots. Thus, multiple products (models) are assembled simultaneously on a same line. However, it is very challenging to balance such an assembly line. This paper conducts a study on balancing a mixed-model assembly line of Type E. To solve this problem, a coloured-timed Petri net model is developed to describe the task precedence relationship. Also, the optimisation problem is formulated as a mathematical programming model. Then, with the models, a two-stage heuristic algorithm is proposed to solve the problem. At the first stage, based on the Petri net model, a P-invariant algorithm (PA) is presented to minimise the number of workstations. At the second stage, a heuristic is proposed to further minimise the cycle time by combining the PA with a binary search algorithm (BSA). Performance of the proposed method is evaluated by an illustrative example and numerical experiments. It is shown that it works well in terms of both solution accuracy and computational efficiency for large size problems.     

An improved mathematical program to solve the simple assembly line balancing problem

The simple assembly line balancing problem (SALBP) has been extensively examined in the literature. Various mathematical programs have been developed to solve SALBP type-1 (minimising the number of workstations, m, for a given cycle time, ct) and SALBP type-2 (minimising ct given m). Usually, an initial pre-process is carried out to calculate the range of workstations to which a task i may be assigned, in order to reduce the number of variables of task–workstation assignment. This paper presents a more effective mathematical program than those released to date to solve SALBP-1 and SALBP-2. The key idea is to introduce additional constraints in the mathematical program, based on the fact that the range of workstations to which a task i may be assigned depends either on the upper bound on the number of workstations or on the upper bound on the cycle time (for SALBP-1 and SALBP-2, respectively). A computational experiment was carried out and the results reveal the superiority of the mathematical program proposed.     

Coordinated scheduling of production and transportation in a two-stage assembly flowshop

To enhance the overall performance of supply chains, coordination among production and distribution stages has recently received an increasing interest. This paper considers the coordinated scheduling of production and transportation in a two-stage assembly flowshop environment. In this problem, product components are first produced and assembled in a two-stage assembly flowshop, and then completed final products are delivered to a customer in batches. Considering the NP-hard nature of this scheduling problem, two fast heuristics (SPT-based heuristic and LPT-based heuristic) and a new hybrid meta-heuristic (HGA-OVNS) are presented to minimise the weighted sum of average arrival time at the customer and total delivery cost. To guide the search process to more promising areas, the proposed HGA-OVNS integrates genetic algorithm with variable neighbourhood search (VNS) to generate the offspring individuals. Furthermore, to enhance the effectiveness of VNS, the opposition-based learning (OBL) is applied to establish some novel opposite neighbourhood structures. The proposed algorithms are validated on a set of randomly generated instances, and the computation results indicate the superiority of HGA-OVNS in quality of solutions.     

Incorporating Physical Demand Criteria into Assembly Line Balancing

Many assembly line balancing algorithms consider only task precedence and duration when minimizing cycle time. However, disregarding the physical demands of these tasks may contribute to the development of work-related musculoskeletal disorders in the assembly line workers. Three line balancing heuristics that incorporate physical demand criteria were developed to solve the problem of finding assembly line balances that consider both the time and physical demands of the assembly tasks: a ranking heuristic, a combinatorial genetic algorithm, and a problem space genetic algorithm. Each heuristic was tested using 100 assembly line balancing problems. Incorporating physical demands using these algorithms does impact the assembly line configuration. Results indicated that the problem space genetic algorithm was the most adept at finding line balances that minimized cycle time and physical workload placed upon participants. Benefits of using this approach in manufacturing environments are discussed.     

Balancing Multi-Manned Assembly Lines With Walking Workers: Problem Definition,Mathematical Formulation,and an Electromagnetic Field Optimisation Algorithm

Assembly lines are widely used in industrial environments that produce standardised products in high volumes. Multi-manned assembly line is a special version of them that allows simultaneous operation of more than one worker at the same workstation. These lines are widely used in large-sized product manufacturing since they have many advantages over the simple one. This article has dealt with multi-manned assembly line balancing problem with walking workers for minimising the number of workers and workstations as the first and second objectives, respectively. A linear mixed-integer programming formulation of the problem has been firstly addressed after the problem definition is given. Besides that, a metaheuristic based on electromagnetic field optimisation algorithm has been improved. In addition to the classical electromagnetic field optimisation algorithm, a regeneration strategy has been applied to enhance diversification. A particle swarm optimisation algorithm from assembly line balancing literature has been modified to compare with the proposed algorithm. A group of test instances from many precedence diagrams were generated for evaluating the performances of all solution methods. Deviations from lower bound values of the number of workers/workstations and the number of optimal solutions obtained by these methods are concerned as performance criteria. The results obtained by the proposed programming formulations have been also compared with the solutions obtained by the traditional mathematical model of the multi-manned assembly line. Through the experimental results, the performance of the metaheuristic has been found very satisfactory according to the number of obtained optimal solutions and deviations from lower bound values.     

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.