Paced Assembly Line Research Articles

A branch, bound and remember algorithm for maximizing the production rate in the simple assembly line balancing problem

The simple assembly line balancing problem is a classical optimization problem. It aims at efficiently assigning elementary operations to the workstations of a paced assembly line to optimize some efficiency measure. In this paper, we deal with the type-2 version of the problem in which the efficiency measure is the maximization of throughput with a given number of workstations. This problem has been scarcely studied compared to its type-1 counterpart, in which the throughput is fixed and the objective is to minimize the number of workstations. This has led to the development of indirect methods using type-1 exact solution methods to tackle the type-2 case.In this paper, we provide lower bounds, logical tests, and dominance rules for the type-2 problem and adapt the state-of-the-art method for the type-1 problem to develop a direct approach for solving the type-2 problem with a direct approach. Computational results show the effectiveness of the direct method, which can outperform recent type-1-based indirect approaches. The proposed method is able to close all instances from the classical instance set and solves to optimality over 90% of the large (100 tasks) and 76.5% of the very large (1000 tasks) instances derived from the current reference set for its type-1 counterpart. The average gaps between the upper and lower bounds on the optimal cycle time are also tight and are less than 0.13% (0.4%) for large (very large) instances. Finally, our results show that direct and indirect methods are comparable in terms of solution quality, but the direct method outperforms its indirect counterpart in terms of running time and optimality gaps. Moreover, we identify that instances averaging two to three tasks per workstation and featuring large variability between task times pose significant challenges to solve to optimality.

Balancing-sequencing paced assembly lines: a multi-objective mixed-integer linear case study

ABSTRACT This paper considers the optimisation of Mixed-model assembly lines with continuous paced line control. The two minimisation goals have a mixed-integer linear multi-objective dispute. The paper proposes a criterion-space method to define the Pareto front for this class of problems. The method combines Pareto fronts obtained from integer solutions and gradually refines them until the instance's global front is determined. Comparing paced to unpaced line controls can be challenging, since they can produce the same cycle time given sufficiently long line lengths or buffers. Hence, determining Pareto fronts between cycle time and line length for paced lines allows meaningful comparisons between line controls. An industrial case study shows that line length acts as continuously distributable buffers for paced lines, leading to weaker diminishing returns. This result suggests that paced lines are more efficient than unpaced ones for lower cycle time ranges.

Dynamic takt time decisions for paced assembly lines balancing and sequencing considering highly mixed-model production: An improved artificial bee colony optimization approach

Balancing and sequencing are two important problems in paced assembly lines planning. Many studies use a precedence graph to solve the problems. Fixed takt time (fTT) is used as the paced value of assembly lines, which ignores the real-time status of assembly lines. By analyzing the position of each product on the assembly lines and the working time of the current assembly, this paper proposes to use the maximum value of the working time of each product in the current status as the value of the dynamic takt time (dTT). This method utilizes the assembly line capacity more effectively. An improved artificial bee colony (iABC) algorithm is developed to optimize balancing and sequencing simultaneously. Compared with multi-objective particle swarm optimization and non-dominated sorting genetic algorithms II, the effectiveness of the iABC algorithm is evaluated according to three performance evaluation indexes including the inverted generational distance, the spacing metric, and the set coverage metric. Case studies of different scales and the effects of fTT and dTT on idle time are analyzed, verifying the rationality of the proposed dTT method.

Benders’ decomposition for the balancing of assembly lines with stochastic demand

The quality of the balancing of mixed-model assembly lines is intimately related to the defined production sequence. The two problems are, however, incompatible in time, as balancing takes place when planning the line, while sequencing is an operational problem closely related to market demand fluctuations. In this paper, an exact procedure to solve the integrated balancing and sequencing problem with stochastic demand is presented. The searched balancing solution must be flexible enough to cope with different demand scenarios. A paced assembly line is considered and utility work is used as a recourse for station border violations. A Benders’ decomposition algorithm is developed along with valid inequalities and preprocessing as a solution procedure. Three datasets are proposed and used to test algorithm performance and the value of treating uncertainty in mixed-model assembly lines. The integration of the strategic balancing problem with the operational sequencing problem results in more robust assembly lines.

A branch-and-bound approach to schedule a no-wait flow shop to minimize the CVaR of the residual work content

The aerospace industry ranks among the largest manufacturing industries in the world facing a significant growing phase as well as an increased competition. This paper addresses the scheduling of a set of jobs in a paced assembly line in presence of uncertainty affecting the availability of production resources, stemming from the assembly process in the aircraft manufacturing industry. The production problem is modeled as a no-wait paced permutation flow shop and solved providing a robust scheduling solution minimizing the conditional value-at-risk (CVaR) of the residual work content, i.e., the amount of workload that cannot be completed during the cycle time in the stations, due to a lack of available resources. A branch-and-bound approach is developed and applied to randomly generated instances as well as to an industrial problem related to the production of aircrafts.

Minimizing the number of workers in a paced mixed-model assembly line

We study a problem of minimizing the maximum number of identical workers over all cycles of a paced assembly line comprised of m stations and executing n parts of k types. There are lower and upper bounds on the workforce requirements and the cycle time constraints. We show that this problem is equivalent to the same problem without the cycle time constraints and with fixed workforce requirements. We prove that the problem is NP-hard in the strong sense if m=4 and the workforce requirements are station independent, and present an Integer Linear Programming model, an enumeration algorithm and a dynamic programming algorithm. Polynomial in k and polynomial in n algorithms for special cases with two part types or two stations are also given. Relations to the Bottleneck Traveling Salesman Problem and its generalizations are discussed.

Optimal workforce assignment to operations of a paced assembly line

We study a paced assembly line intended for manufacturing different products. Workers with identical skills perform non-preemptable operations whose assignment to stations is known. Operations assigned to the same station are executed sequentially, and they should follow the given precedence relations. Operations assigned to different stations can be performed in parallel. The operation’s processing time depends on the number of workers performing this operation. The problem consists in assigning workers to operations such that the maximal number of workers employed simultaneously in the assembly line is minimized, the line cycle time is not exceeded and the box constraints specifying the possible number of workers for each operation are not violated. We show that the general problem is NP-hard in the strong sense, develop conventional and randomized heuristics, propose a reduction to a series of feasibility problems, present a MILP model for the feasibility problem, show relation of the feasibility problem to multi-mode project scheduling and multiprocessor scheduling, establish computational complexity of several special cases based on this relation and provide computer experiments with real and simulated data.

Designing energy-efficient serial production lines: The unpaced synchronous line-balancing problem

One of the primary elements of a sustainable manufacturing initiative is that of energy efficiency. Line balancing can be used to design efficient manufacturing systems for paced assembly lines when the operation times are known, but may provide inefficient assignments with variable task times. Thus, we propose the use of unpaced synchronous lines as an alternative to paced lines when there is considerable variability in task times. While a great deal of research has been conducted on the line-balancing problem for paced synchronous production lines as well as for unpaced asynchronous lines, relatively little has focused on the unpaced synchronous configuration, despite its practical relevance. This research addresses this type of production line, with stochastic task completion times, by formulating an appropriate model and developing and evaluating a variety of solution methodologies utilizing extreme value theory as well as simulation. Computational results are presented to gain insight into the design and operation of unpaced synchronous systems.

Hierarchical approach for paced mixed-model assembly line balancing and sequencing with jolly operators

In order to increase flexibility and reduce costs, several companies adopt mixed-model assembly lines whose output products are variations of the same basic model with specific and distinctive attributes. Unfortunately, such attributes typically lead to variations in the task process times. In the case of un-paced buffered assembly lines, these variations are smoothed by buffers with consequences in terms of work-in-progress, costs, space utilisation and lower productivity control. To face such weaknesses, some companies adopt paced un-buffered assembly lines where the cycle time is controlled by the continuous/synchronous moving of the products from the first to the last assembly station. In such contexts, the possibility of assembling different models with different assembly times can be managed through the use of supplementary flexible workforce. This article introduces an innovative balancing and sequencing hierarchical approach for paced mixed-model assembly lines using supplementary flexible workforce called ‘jolly operators’. The goals are to minimise the number of jolly operators and to limit the occurrence of work-overloads, which typically result in out-of-the-line assembly completion. The proposed approach is preliminary validated and applied to a case study from an Italian company assembling industrial air-dryers.

Workforce minimization for a mixed-model assembly line in the automotive industry

A paced assembly line consisting of several workstations is considered. This line is intended to assemble products of different types. The sequence of products is given. The sequence of technological tasks is common for all types of products. The assignment of tasks to the stations and task sequence on each station are known and cannot be modified, and they do not depend on the product type. Tasks assigned to the same station are performed sequentially. The processing time of a task depends on the number of workers performing this task. Workers are identical and versatile. If a worker is assigned to a task, he/she works on this task from its start till completion. Workers can switch between the stations at the end of each task and the time needed by any worker to move from one station to another one can be neglected. At the line design stage, it is necessary to know how many workers are necessary for the line. To know the response to this question we will consider each possible takt and assign workers to tasks so that the total number of workers is minimized, provided that a given takt time is satisfied. The maximum of minimal numbers of workers for all takts will be considered as the necessary number of workers for the line. Thus, the problem is to assign workers to tasks for a takt. We prove that this problem is NP-hard in the strong sense, we develop an integer linear programming formulation to solve it, and propose conventional and randomized heuristics.

Just‐in‐time parts feeding policies for paced assembly lines: possible solutions for highly constrained layouts

AbstractThis paper deals with the dimensioning of a just‐in‐time (JIT) parts feeding system, for a paced assembly line. Specifically, we consider the quite frequent case of an old‐fashioned, push‐oriented warehouse arrangement, characterized by materials and subassemblies that are stocked in different and peripheral areas of the manufacturing plant. In these circumstance, layout changes are almost impossible and warehouses cannot be substituted by supermarkets. Nevertheless, this does not preclude the possibility to rationalize material flow and to reduce work in process (WIP) using a JIT parts feeding system. To this aim, we propose two alternative approaches, differentiating in terms of the order with which warehouses and workstations are visited. In order to dimension both systems and to estimate their expected performances, a mathematical model is also presented. At first, the model is presented in a basic formulation, which is very effective and easy to use. A more sophisticated formulation, based on Bayesian probability, is introduced next; this is not so much for practical purposes, but rather to demonstrate the potential of the proposed JIT system in very constrained operating settings.

OEE Evaluation of a Paced Assembly Line through Different Calculation and Simulation Methods: A Case Study in the Pharmaceutical Environment

Modern production systems must guarantee high performance. Increasingly challenging international competition, budget reductions for the health sector and constant technological evolution are just three of the many aspects that drive pharmaceutical companies to continuously improve the productivity of their lines.The scientific literature has for many years been proposing calculation models for estimating the productivity of a machine. One of the most famous, and still used, is overall equipment effectiveness (OEE). This allows the calculation the valuable output considering the six ‘big losses’. The limitations of this approach are noticeable when considering a production line instead of a single machine. Numerous researchers have proposed alternative methods or changes in OEE, to be able to cover the widest spectrum of possible cases.In this study, we wanted to evaluate how such theoretical models related to OEE are actually able to represent the world of tight production flows or whether, in these cases, a more complex type of simulation should be preferred. To do this, we carried out a case study of a production line in the pharmaceutical industry, and the results showed that the simulation approach gives better results because of the peculiarities not considered by the theoretical models.

Effective Cycle Time: A Real World Balancing Index for Paced Assembly Lines

Assembly Line Balancing (ALB) aims at optimally assigning the work elements required to assemble a product to an ordered sequence of workstations, while satisfying precedence constraints. Notwithstanding the advances and developments in ALB over the years, recent and thorough surveys on this field reveal that only a small percentage of companies employ ALB procedures to configure their assembly lines. This paradox may be attributed, to some extent, to the fact that ALB is addressed mostly under ideal conditions. Despite the time variability inherent in manufacturing tasks, there is a strong research trend towards designing and implementing algorithms that consider ALB on a deterministic basis and focus on the optimality of the proposed task assignments according to existing ALB performance measures. In this paper, the need to assess the performance of the proposed solutions of various algorithms in the literature is corroborated through simulation experiments on a benchmark ALB problem under more realistic conditions. A novel ALB index, namely the Effective Cycle Time, ECT, is proposed to assess the quality of alternative assembly line configurations in paced assembly lines operating under task times variations.

A scatter search based hyper-heuristic for sequencing a mixed-model assembly line

We address a mixed-model assembly-line sequencing problem with work overload minimization criteria. We consider time windows in work stations of the assembly line (closed stations) and different versions of a product to be assembled in the line, which require different processing time according to the work required in each work station. In a paced assembly line, products are feeded in the line at a predetermined constant rate (cycle time). Then, if many products with processing time greater than cycle time are feeded consecutively, work overload can be produced when the worker has insufficient time to finish his/her job. We propose a scatter search based hyper-heuristic for this NP-hard problem. In the low-level, the procedure makes use of priority rules through a constructive procedure. Computational experiments over a wide range of instances from the literature show the effectiveness of the proposed hyper-heuristics when compared to existing heuristics. The relevance of the priority rules was evaluated as well.

Cyclic job scheduling in paced assembly lines with cross-trained workers

Paced or synchronous assembly lines allow concurrent manufacturing of a mix of products by repetitive production of a minimal product set (MPS). We refer to the associated production schedules as cyclic. We consider a paced assembly line where every job (or order) visits all m assembly stations in the same sequence and spends the same amount of time (known as the production cycle) at each station, by using the appropriate number of workers. Hence, associated with each job is an m-tuple of workforce requirements. Our objective is to find a cyclic schedule of jobs such that the total required workforce size is minimized. Assuming that each worker is cross-trained to work at a number of stations, we show that the problem is strongly NP-complete. In light of this result, we develop lower bounds, heuristic algorithms and an optimal branch-and-bound procedure. Our computational experiments show that our algorithms are computationally efficient and exhibit near-optimal performance. We also compare the savings in workforce size among systems with various levels of cross training.

Stability analysis of an optimal balance for an assembly line with fixed cycle time

We address the simple assembly line balancing problem: minimize the number of stations m for processing n partially ordered operations V = {1, 2, …, n} within the cycle time c. The processing time t i of operation i ∈ V and cycle time c are given. However, during the life cycle of the assembly line the values t i are definitely fixed only for the subset of automated operations V ⧹ V ∼ . Another subset V ∼ ⊆ V includes manual operations, for which it is impossible to fix the exact processing times during the whole life cycle of the assembly line. If j ∈ V ∼ , then operation time t j can be different for different cycles of production process. For the optimal line balance b of a paced assembly line with vector t = ( t 1, t 2, …, t n ) of the operation times, we investigate stability of its optimality with respect to possible variations of the processing times t j of the manual operations j ∈ V ∼ . In particular, we derive necessary and sufficient conditions when optimality of the line balance b is stable with respect to sufficiently small variations of the operation times t j , j ∈ V ∼ . We show how to calculate the maximal value of independent variations of the processing times of all the manual operations, which definitely keep the feasibility and optimality of the line balance b .

A comparative analysis of sequencing heuristics for solving the Toyota Goal Chasing problem

In this paper, the sequencing of a mixed model paced assembly line is investigated assuming the component parts usage smoothing as the goal of the sequence selection. This sequencing problem, commonly known as Toyota Goal Chasing method, is studied here taking into account not only the traditional Goal Chasing approaches, which assume zero-length assembly lines, but also models which consider the effective length of the assembly line. This means that the number of workstations and their extensions become critical parameters in the selection of the optimal sequence of models to be assembled: in fact, the epochs corresponding to the requirement of different components vary in accordance to the values of the line parameters. The sequencing of the parts is carried out here through a set of heuristic procedures, the commonly adopted Goal Chasing algorithms and a simulated annealing, whose performances are compared with respect to different line scenarios. In particular, the numbers of workstations, parts to be worked and components to be assembled are varied to statistically test their influence on the efficiency of the optimizing procedures and on the differences between zero and finite length approaches.

Assessing the impact of alternative manufacturing layouts in a service setting

This paper summarizes the results of a project designed to study and ultimately improve the overall operation of a service process, as found in one regional blood center. Driving this project was recognition that the current process, initially designed to accommodate a single customer group, was ill equipped to handle a changing customer mix now consisting of three disparate groups. The resulting mismatch between the process and users created long delays and an increase in the overall level of dissatisfaction with the existing process. To improve overall performance, this study turned to process analysis and computer simulation to stimulate a critical analysis of the process. As part of this approach, the study investigated three layouts: the existing worker paced assembly line, a modified assembly line, and service cells. The study examined the relationship between layout, customer mix and system performance. Key among the results was that a service cell approach led to higher performance and better customer satisfaction.

A mathematical model for selecting mixed models with due dates

The performance of a sequencing procedure to smooth out the fluctuating workload (and part utilization) on a paced assembly line relies heavily on the average load of the model mixes chosen from the order-bank. Meanwhile, the due-dates of orders may conflict with this production-centred goal. This study proposes a mathematical model to select a fixed number of jobs while minimizing the total cost of producing them at the next period and satisfying capacity (RHS) limits at stations. A branch-and-bound procedure, which employs some dominance criteria, is proposed to provide optimal solutions. Pairwise interchange heuristics are developed to improve the initial solution, which is optimum but not feasible. Computational results show that optimal solutions can be obtained very efficiently for 100-job and 10-station problems. A three-factor experiment indicates that the RHS limit is the only significant parameter on the performance of the procedures. For over 1000-job problems, the best heuristic finds the optimal solution most of the time and, in the worst case, yields a solution that is 7.38% from optimality.

A spreadsheet method for calculating work completion time probability distributions of paced or linked assembly lines

This study presents a spreadsheet method for computing the work completion time probability distribution of a linked assembly line with variable station service times. Once developed, this distribution can be used to analyse the probability of completing all work at all stations within a given cycle time on either a linked or mechanically paced assembly line. The method can be used to determine what cycle time to set on a paced line, given a desired workload at each station. Alternately, given a desired cycle time and probability that all work has been completed at each station within the cycle time, the method can be used to determine how much work to allocate to each station on the paced line. The method is simple, easy to use, and works with any continuous or discrete station service time distribution that can be specified in a spreadsheet. Comparisons between the output of the spreadsheet method and simulations of the same system indicate the spreadsheet method is quite accurate. Hence, the method can be useful to both researchers and practitioners working with the design and/or behaviour of linked or paced lines, and it provides an easy-to-use teaching tool for illustrating characteristics of linked or paced assembly lines.