A priority rule-based constructive heuristic and an improvement method for balancing assembly lines with parallel multi-manned workstations

Assembly lines of big-size products such as buses, trucks and helicopters are very different from the lines studied in the literature. These products’ manufacturing processes have a lot of tasks most of which have long task times. Since traditional assembly line models including only one worker in each station (i.e. simple assembly lines) or at most two workers (two-sided assembly lines) may not be suitable for manufacturing these type of products, they need much larger shop floor for a number of stations and long product flow times. In this study, an assembly line balancing problem (ALBP) with parallel multi-manned stations is considered. Following the problem definition, a mixed integer programming formulation is developed. A detailed study of priority rules for simple ALBPs is also presented, and a new efficient constructive heuristic algorithm based on priority rules is proposed. In order to improve solutions found by the constructive heuristic, a genetic algorithm-based solution procedure is also presented. Benchmark instances in the literature are solved by using the proposed mathematical programming formulation. It has been seen that only some of the small-size instances can be solved optimally by this way. So the efficiency of the proposed heuristic method is verified in small-size instances whose optimal solutions are found. For medium- and big-size instances, heuristics’ results and CPU times are demonstrated. A comparative evaluation with a branch and bound algorithm that can be found in the literature is also carried out, and results are presented.     

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.     

U-OPT: An analysis of exact U-shaped line balancing procedures

The U-shaped assembly line-balancing problem can be solved using optimization procedures or algorithms, including branch-and-bound procedures. This paper considers design elements that should be included in these solution methods for solving the U-shaped assembly line-balancing problem. New solution procedures are proposed and compared experimentally with several existing procedures using a variety of problem sets from the literature. The results show that the substantial improvement in the efficacy of the new solution procedures over existing methods is due primarily to the newly developed 'Paired Tasks' lower bound. Results also show the relative importance of various design elements comprising a branch-and-bound procedure.     

Balancing printed circuit board assembly line systems

This paper considers the placement of components onto printed circuit boards (PCBs) using surface mount technology. Multiple automatic placement machines, a variety of PCB types and a large volume for each PCB type characterize the environment studied. The problem addressed is that of allocating and arranging the components on several placement machines, organized into one or several assembly lines, while considering a different assembly time if components are located at different feeder locations. The one assembly line problem is equivalent to balancing a multi-model assembly line where models are assembled in small batches without component rearrangement between model changes. The objective is tominimize the weighted sum of each assembly PCBcycle time, which is defined as the maximum time a PCB has to spend on each machine. We solve this problem with Lagrangian relaxation techniques. Industrial case study results are presented. We also compare the global performance of five placement machines if they are organized as a single assembly line or broken down into two or more assembly lines.     

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.     

Minimising utility work and utility worker transfers for a mixed-model assembly line

Mixed-model assembly lines (MMALs) are types of production lines that are able to respond to diversified costumers’ demand for a variety of models without holding large inventories. The effective utilisation of a mixed-model assembly line requires the determination of the assembly sequence for different models. In this paper, two objectives are considered in a sequential manner, namely minimising: (i) total utility work, which means work from an additional worker to assist an operator for completion of an assembly task; and (ii) utility worker transfer which states the move of a utility worker to a different segment of the assembly line. First, due to the NP-hard nature of the problem, three heuristic methods are proposed with the aim of minimising total utility work. Then, the solutions which are obtained from the heuristics are improved in terms of the total number of utility worker transfers via a local search based method. Furthermore, the solution approach was applied in a real life mixed model tractor assembly line. Results validated the effectiveness of sequencing approach in terms of solution quality.     

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.     

Mixed model assembly system with multiple secondary feeder lines: layout design and balancing procedure for ATO environment

The constant research for efficiency and flexibility has forced assembly systems to change from simple/single assembly lines to mixed model assembly lines, while the necessity to reduce inventory has led the transition from single to multi-line systems, where some components are assembled in secondary lines, called feeder lines, connected to the main one by a ‘pull philosophy’. A possible approach to configure such an assembly system is to balance the main line first and use the retrieved cycle time to balance each feeder line separately, which is a questionable solution, especially if operators can perform tasks on both the feeder and the main line. Moreover for its complexity the mixed model balancing problem is usually solved transforming it into a single model by creating a single ‘virtual average model’, representative of the whole production mix. The use of a virtual average model assumes that the processing times of some models are higher or lower than the cycle time, which creates overload/idle time at the stations. This approach, especially in complex multi line production systems, largely reduces the assembly line productivity and increases the buffers dimensions. This paper faces the mixed model assembly line balancing problem in the presence of multiple feeder lines, introducing an innovative integrated main-feeder lines balancing procedure in case of unpaced assembly systems. The proposed approach is compared with the classical one and validated through simulation and industrial applications.     

One- and two-sided assembly line balancing problems with real-world constraints

In this study, we consider balancing problems of one- and two-sided assembly lines with real-world constraints like task or machine incompatibilities. First, we study the one-sided assembly line balancing problem (ALBP) with a limited number of machine types per workstation. Using a genetic algorithm (GA), we find optimal results for real-world instances. A set of larger test cases is used to compare two well-established solution approaches, namely GA and tabu search (TS). Additionally, we apply a specific differential evolution algorithm (DE), which has recently been proposed for the considered ALBP. Our computational results show that DE is clearly dominated by GA. Furthermore, we show that GA outperforms TS in terms of computational time, if capacity constraints are tight. Given the algorithm’s computational performance as well as the fact that it can easily be adapted to additional constraints, we then use it to solve two-sided ALBP. Three types of constraints and two different objectives are considered. We outperform all previously published methods in terms of solution quality and computational time. Finally, we are the first to provide feasible test instances as well as benchmark results for fully constrained two-sided ALB.     

Bayesian multiple testing procedures for hotspot identification

Ranking a group of candidate sites and selecting from it the high-risk locations or hotspots for detailed engineering study and countermeasure evaluation is the first step in a transport safety improvement program. Past studies have however mainly focused on the task of applying appropriate methods for ranking locations, with few focusing on the issue of how to define selection methods or threshold rules for hotspot identification. The primary goal of this paper is to introduce a multiple testing-based approach to the problem of selecting hotspots. Following the recent developments in the literature, two testing procedures are studied under a Bayesian framework: Bayesian test with weights (BTW) and a Bayesian test controlling for the posterior false discovery rate (FDR) or false negative rate (FNR). The hypotheses tests are implemented on the basis of two random effect or Bayesian models, namely, the hierarchical Poisson/Gamma or Negative Binomial model and the hierarchical Poisson/Lognormal model. A dataset of highway–railway grade crossings is used as an application example to illustrate the proposed procedures incorporating both the posterior distribution of accident frequency and the posterior distribution of ranks. Results on the effects of various decision parameters used in hotspot identification procedures are discussed.     

Stochastic two-sided U-type assembly line balancing: a genetic algorithm approach

In this paper, a novel stochastic two-sided U-type assembly line balancing (STUALB) procedure, an algorithm based on the genetic algorithm and a heuristic priority rule-based procedure to solve STUALB problem are proposed. With this new proposed assembly line design, all advantages of both two-sided assembly lines and U-type assembly lines are combined. Due to the variability of the real-life conditions, stochastic task times are also considered in the study. The proposed approach aims to minimise the number of positions (i.e. the U-type assembly line length) as the primary objective and to minimise the number of stations (i.e. the number of operators) as a secondary objective for a given cycle time. An example problem is solved to illustrate the proposed approach. In order to evaluate the efficiency of the proposed algorithm, test problems taken from the literature are used. The experimental results show that the proposed approach performs well.     

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.     

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.     

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.     

The economic lot and delivery scheduling problem: common cycle, rework, and variable production rate

The economic lot and delivery scheduling problem is to simultaneously determine the production sequence of several assembly components at a supplier and the delivery interval of those components to the customer. The customer, an assembly facility, is assumed to use the components at a constant rate. The objective is to find the production sequence and delivery interval that minimize the holding, setup, and transportation cost for the supply chain. Previous solutions to the problem assume a constant production rate for each component and that all components are of acceptable quality. These assumptions ignore volume flexibility and quality cost. Volume flexibility permits a system to adjust the production rate upwards or downwards within wide limits. Also, component quality may deteriorate with larger lot sizes and decreased unit production times. In this paper, we develop an algorithm for solving the economic lot and delivery scheduling problem for a supplier using a volume flexible production system where component quality depends on both lot sizes and unit production times. We test the performance of the algorithm and illustrate the models with numerical examples.     

On the influence of constitutive relation in projectile impact of steel plates

In this paper the influence of constitutive relation has been studied in numerical simulations of the perforation of 12-mm thick Weldox 460 E steel plates impacted by blunt-nosed projectiles in the sub-ordinance velocity regime. A modified version of the well-known and much used constitutive relation proposed by Johnson-Cook and both the bcc- and hcp-version of the Zerilli-Armstrong constitutive relation were combined with the Johnson-Cook fracture criterion. These models were implemented as user-defined material models in the non-linear finite element code LS-DYNA. Identification procedures have been proposed, and the different models were calibrated and validated for the target material using available experimental data obtained from tensile tests where the effects of strain rate, temperature and stress triaxiality were taken into account. Perforation tests carried out in a compressed gas gun on 12-mm-thick circular Weldox 460 E steel plates were then used as base in a validation study of plate perforation using LS-DYNA and the proposed constitutive relations. The numerical study indicated that the physical mechanisms during perforation can be qualitatively well predicted by all constitutive relations, but quantitatively more severe differences appear. The reasons for this are discussed in some detail. It was concluded that for practical applications, the Johnson-Cook constitutive relation and fracture criterion seems to be a good choice for this particular problem and excellent agreement with the experimental results of projectile impact on steel plates were obtained under the conditions investigated.     

A novel bi-level hierarchy towards available-to-promise in mixed-model assembly line sequencing problems

This article addresses advanced available-to-promise (AATP) in mixed-model assembly line sequencing problems. In the developed framework, customers are prioritized with respect to 11 defined criteria using the technique for order of preference by similarity to ideal solution (TOPSIS) method, and order quantities are calculated using a nonlinear mathematical program. Next, a mixed binary nonlinear mathematical program is developed to determine the optimum sequence of the optimized order quantities to minimize the total lateness. Since the proposed models are intractable, a hybrid genetic algorithm–simulated annealing method is also developed. Finally, an industrial case study is reported, the results of which validate the developed AATP framework.     

Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments

The direct linearization method (DLM) for tolerance analysis of 3-D mechanical assemblies is presented. Vector assembly models are used, based on 3-D vector loops which represent the dimensional chains that produce tolerance stackup in an assembly. Tolerance analysis procedures are formulated for both open and closed loop assembly models. The method generalizes assembly variation models to include small kinematic adjustments between mating parts. Open vector loops describe critical assembly features. Closed vector loops describe kinematic constraints for an assembly. They result in a set of algebraic equations which are implicit functions of the resultant assembly dimensions. A general linearization procedure is outlined, by which the variation of assembly parameters may be estimated explicitly by matrix algebra. Solutions to an over-determined system or a system having more equations than unknowns are included. A detailed example is presented to demonstrate the procedures of applying the DLM to a 3-D mechanical assembly.     

Proper Generalized Decomposition model reduction in the Bayesian framework for solving inverse heat transfer problems

In this paper, the proper generalized decomposition (PGD) is used for model reduction in the solution of an inverse heat conduction problem within the Bayesian framework. Two PGD reduced order models are proposed and the approximation Error model (AEM) is applied to account for the errors between the complete and the reduced models. For the first PGD model, the direct problem solution is computed considering a separate representation of each coordinate of the problem during the process of solving the inverse problem. On the other hand, the second PGD model is based on a generalized solution integrating the unknown parameter as one of the coordinates of the decomposition. For the second PGD model, the reduced solution of the direct problem is computed before the inverse problem within the parameter space provided by the prior information about the parameters, which is required to be proper. These two reduced models are evaluated in terms of accuracy and reduction of the computational time on a transient three-dimensional two region inverse heat transfer problem. In fact, both reduced models result on substantial reduction of the computational time required for the solution of the inverse problem, and provide accurate estimates for the unknown parameter due to the application of the approximation error model approach.     

Modified QFD and problem‐solving techniques integrated approach implementing corrective actions: a case study in an Italian manufacturing plant

The ISO 9001:2000 and Total Quality Management models impose that organizations adopt structured procedures to implement corrective and preventive actions. In this paper, a structured framework to solve a non‐conformity in a product or in a process, selecting the best corrective actions, is proposed. Some problem‐solving techniques are applied in a structural method (i) to find the problem (product or process non‐conform), (ii) setting the problem (using data‐collecting instruments), (iii) analyzing the problem (with techniques such as Pareto charts, histograms, stratification analysis) and (iv) searching possible alternative solutions. Then, a modified quality function deployment technique is applied to evaluate and to classify the alternative solutions with respect to three different parameters (benefit, cost and impact). The framework has been developed to select and implement corrective actions in an Italian manufacturing plant. The case study is presented in this paper. However, the proposed approach is applicable in many other contexts. Copyright © 2008 John Wiley & Sons, Ltd.