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.     

Assembly line sequencing for model mix

This paper describes a model sequencing algorithm for model-mix assembly lines. A new formulation of the sequencing problem is proposed, the objective function of which is to minimize the overall assembly line-length for no operator interference. Lower bounds for the overall line-length are developed.

Two types of work station interfaces are considered; ‘closed’, where boundaries cannot be violated, and ‘open’ where defined boundaries do not exist—adjacent operators being allowed to enter each others apparent work areas without causing any interference.

A complete factorial experiment was made on five factors to determine their influence on the overall assembly line length. These are, the number of models, the model cycle time deviation, the production demand deviation for each model, the operator time deviation, and the number of stations in the assembly line. The main conclusions of this experiment are discussed and recommendations made for the selection of parameters used in the design of model-mix assembly lines.

Also discussed is an approach for accommodating small changes in production demand for existing assembly lines.     

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 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.     

A heuristic procedure for the automobile assembly-line sequencing problem considering multiple product options

Mixed-model assembly nowadays is a common practice in the automobile industry. In an automobile assembly plant, many car options often need to be considered in sequencing an assembly line, for example, the multiple sequencing objectives that consider a pattern, blocking, spacing, and smoothing of options. A general heuristic procedure is developed in this paper for sequencing automobile assembly lines considering multiple options. The procedure obtains an initial sequence by an enhanced constructive procedure, swaps orders for the most deteriorating category of objectives, and performs re-sequencing attempting to improve the swapped sequence. The heuristic procedure was shown to frequently improve the initial sequences by swapping and re-sequencing when swapping opportunities exist. A further improvement step is also proposed to perform a limited search based on the swapped solution. The limited-search improvement step was shown to be effective in further improving solutions from the heuristic procedure in the computational experimentation. Solutions from the heuristic procedure in conjunction with the limited-search improvement step were compared to those from the simulated annealing procedure for large-size problems and showed relatively positive results.     

Balancing mixed-model assembly lines with adjacent task duplication

When a mixed-model assembly line (MAL) is balanced, it is generally assumed that the variants of a task over different models should be assigned to an identical station. In this study, this restriction is relaxed and the variants of a task over different models can be duplicated on two adjacent stations (referred to as adjacent task duplication) to improve the MAL’s efficiency. The adjacent task duplication incurs few additional training and tool duplication costs as each task is duplicated on at most two stations. Moreover, for each task, the assembly part storage is not duplicated as it can be shared by the two adjacent stations. The mathematical model of this problem is formulated and some important properties are characterised. A branch, bound and remember algorithm is then developed to solve the problem. The performance of the proposed algorithm is tested on 900 representative instances, of which 889 instances are optimally solved. The experimental results show that the use of the adjacent task duplication policy effectively reduces the number of stations, especially when the WEST ratios are small.     

Sequencing procedure for balancing the workloads variations in case of mixed model assembly system with multiple secondary feeder lines

In order to increase flexibility and reduce costs, assembly systems are changing from simple mixed-model assembly lines, to multi-lines systems, where some components are assembled in secondary lines, called feeder lines, connected to the main line by a ‘pull philosophy’. The production of different models in such a complex multi-lines assembly system, where the tasks to perform could be very different from model to model, impacts the production with very high workload time variations, with the consequence of lack of productivity. If operators can perform tasks on different stations on both the feeder and the main lines these time variations can generally be absorbed. But if working across the stations is not possible (closed stations), the balancing of these workload time variations becomes critical. In such contexts the consolidated approach, that allows to configure mixed-model-multi lines assembly system with a single average model representative of the whole mix, can be very limited and is unable to bring substantial results. This paper aims to introduce an innovative sequencing model for mixed-model-multi-lines system, in the case of closed stations, in which it is possible to obtain, after a first long term configuration, a short term balancing, using an appropriate sequencing, for a given production mix and characteristics of the assembly system. The proposed procedure is applied to un-paced assembly lines and validated through simulation and industrial applications.     

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

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

PACING EFFECTS ON MANNED ASSEMBLY LINES

A computer simulation of an assembly line enforcing pacing on manned sequential stations indicates that unpaced station operations are superior to paced. Using the variability and work-time distribution of operator performance on repetitive tasks, a number of studies were carried out which show that an assembly line cannot perform at maximum efficiency (in terms of operator idle time and units completed) unless queues are provided before each work station. Studies of various station speed configurations indicate that the generally preferred configuration is Fast-Medium-Slow (short-medium-long cycle time) and that there is little difference among various configurations when the inter-arrival time is larger than any of the operator mean cycle times.     

Level scheduling of mixed-model assembly lines under storage constraints

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

Definition of spacing constraints for the car sequencing problem

A car sequencing problem deals with the ordering of a list of vehicles to be produced on an assembly line so that the overall capacity of each work station is not exceeded. Some types of vehicles require several time-consuming operations to be done on a work station and will naturally overload that work station. Such vehicles are spaced out in the sequence, by means of a set of spacing constraints, in order to cope with the momentary increase of workload that they create. Two questions arise: which type of vehicles should be subject to the spacing constraints and by which distance should they be spaced out in the sequence. In practice as well as in the car sequencing literature, there does not exist a methodical way to answer the first question and the existing methods for the second one is no longer adequate due to the increased diversity of cars produced in an assembly line. In this paper, we propose two new methods to answer these questions with a special emphasis on the first one. The performance of the proposed methods is illustrated using a real case study.     

Optimal selection of the local storage sizes of an assembly system

This paper describes the design of an assembly system consisting of a set of work stations and a set of quality control stations, linked by a set of transporter stations; given that the processing rates of all the work stations and the transporter stations, the defective fraction of the workpieces at each quality control station, and the expected throughput rate of the system are specified. The minimum required local storage sizes of the work stations and the transporter stations are obtained such that the probability of finding either a work station or a transporter station blocked is sufficiently close to zero.     

Assembly Lines with Overlapping Work Stations

Traditionally assembly line balancing problems have been examined under the assumption of serial work station design. Thus no pair of work stations could be simultaneously working on the same copy of a product. This paper presents two models for which this assumption is dropped. The algorithms developed for operational design of such assembly lines are presented along with sample problems to demonstrate the computational procedures and advantages of these models.     

A method for assembly line balancing with more than one worker in each station

The typical assembly line is serial with no paralleling of work elements and work stations allowed. The series assumption restricts the least cycle time to be the maximum work element time, thus limiting the production rate.

An alternative way to increase the production rate (hence lowering the cycle time) is by assigning multiple workers to one work station. In this paper we propose the parallel assignment method (PAM) for achieving a higher production rate.

In the first phase of PAM the work elements are assigned to work stations under the multi-stage upper time limits. But as two or more workers are assigned to one station, the operation time of each worker is longer in proportion to the number of workers at the station.

Therefore, in the second phase of PAM work elements are assigned to the workers in each station so that each of the workers may perform shorter work elements where the work element is a minimum rational indivisible work item.

Practical problems which cannot he solved by serial line balancing methods are provided and.solved to explain the effectiveness of PAM.     

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.     

Sequence alteration and restoration related to sequenced parts delivery on an automobile mixed-model assembly line with multiple departments

A mixed-model assembly line is commonly used in the automobile industry. When there are multiple departments on an assembly line, there are usually different sequencing considerations from various departments. Intentional sequence alteration to accommodate a different sequencing consideration can be needed for a downstream department. Unintentional sequence alteration may also take place due to rework or equipment breakdowns. There is also an increasingly common practice in automobile assembly to have parts sequenced before delivering to the final assembly line. To achieve sequenced parts delivery, the sequence needs to be known in advance. Thus, addressing sequence alteration and restoration becomes more relevant for an automobile mixed-model assembly line. A number of sequence alteration methods to accommodate a downstream department's sequencing considerations are presented. One method easily supports sequence restoration of the sequence altered by the method. Two sequence restoration methods for restoring the sequence altered by unintentional reasons are discussed; the proper sizing of the two restoration methods are also addressed. These sequence alteration and restoration approaches mainly address the design and control aspects of the mixed-model assembly line. A case study based on an automobile assembly plant is presented to demonstrate the use of these methods.     

Balancing two-sided assembly lines with sequence-dependent setup times

Two-sided assembly lines are often designed to produce large-sized products, such as automobiles, trucks and buses. In this type of production line, both left-side and right-side of the line are used in parallel. In all studies on two-sided assembly lines, sequence-dependent setup times have not yet been considered. However, in real life applications, setups may exist between tasks. Performing a task directly before another task may influence the latter task inside the same station, because a setup for performing the latter task may be required. Furthermore, if a task is assigned to a station as the last one, then it may cause a setup for performing the first task assigned to that station since the tasks are performed cyclically. In this paper, the problem of balancing two-sided assembly lines with setups (TALBPS) is considered. A mixed integer program (MIP) is proposed to model and solve the problem. The proposed MIP minimises the number of mated-stations (i.e., the line length) as the primary objective and it minimises the number of stations (i.e., the number of operators) as a secondary objective for a given cycle time. A heuristic approach (2-COMSOAL/S) for especially solving large-size problems based on COMSOAL (computer method of sequencing operations for assembly lines) method is also presented. An illustrative example problem is solved using 2-COMSOAL/S. To assess the effectiveness of MIP and 2-COMSOAL/S, a set of test problems are solved. The computational results show that 2-COMSOAL/S is very effective for the problem.     

The effect of breakdowns on U-shaped production lines

Consider a synchronized line performing assembly or fabrication tasks. Tasks are grouped into stations and stations are positioned on a line that is U-shaped. Stations may break down and be repaired. Small buffer inventories may be placed between stations to lessen the effect of breakdowns at one station on production at other stations. This paper investigates the effect of the U-shape of the line on the line effectiveness. We find that effectiveness increases when the line is U-shaped, compared with the traditional straight line shape.     

The effects of work-in-process inventory costs on the design and scheduling of assembly lines with low throughput and high component costs

This paper considers a class of assembly systems with long cycle times (low volume of output) and highly expensive components or subassemblies. Systems such as these are typical for companies in the aerospace industry assembling missiles and airplanes. As each unit of the product moves along the assembly line, its value increases owing to additional parts or components installed and the additional work performed. We show that sequencing activities according to ascending values of the ratios of the 'value added' to activity duration minimizes inventory holding cost within a given workstation. A branch-and-bound procedure is then used to allocate activities optimally to a given number of workstations. The objective function used in this paper is to maximize the net profit of a production line, which comprises net revenues minus inventory holding costs and fixed costs of workstations. The design of the assembly line is affected by two decision variables: number of workstations and cycle time. Finally, it is shown that a 'balanced' line is not necessarily an optimal one and 'pushing' activities to the right (the end of the assembly line) may reduce total holding costs and improve the profitability of the line.     

Simultaneous versus sequential loading and scheduling of flexible assembly systems

A monolithic and a hierarchical approach is presented for loading and scheduling in a general flexible assembly system and a flexible assembly line. The system is made up of a set of assembly stations of various types each with limited working space and is capable of simultaneously producing a mix of product types. The objective is to determine an assignment of assembly tasks to stations and an assembly schedule for all products so as to complete the products in a minimum time. In the monolithic approach loading and scheduling decisions are made simultaneously. In the hierarchical approach, however, first the station workloads are balanced by solving the loading problem, and then detailed assembly schedule is determined for prefixed task assignments and assembly routes by solving a standard job-shop problem. Mixed integer programming formulations are presented for simultaneous and for sequential loading and scheduling. Loading and scheduling with alternative or with single task assignments are considered. Numerical examples are included to illustrate and compare the two approaches proposed.