Mohammad Kamal Uddin*Tampere College of Technology, FinlandJose Luis Martinez LastraTampere University of Technology, Finland

*Address all correspondence to:

DOI: 10.5772/19953

From the Edited Volume

1. Introduction

Assembly line balancing (ALB) and sequencing is an energetic location of optimization research study in operations administration. The concept of an assembly line (AL) came to the truth once the finiburned product is inclined to the perception of product modularity. Typically interchangeable parts of the last product are assembled in sequence making use of finest maybe designed logistics in an AL. The initial phase of configuring and developing an AL was focused on expense reliable mass production of standardized products. This led to high expertise of work and the matching learning effects. However before, the recent trend acquired the understanding of the manufacturers of changing the AL configuration to low volume assembly of customized products, mass customization. The strategic shift took impact as a result of the diversified customer requirements in addition to the individualization of products. This inevitably prompted the study on AL balancing and also sequencing for customized commodities on the very same line in an intermix scenario, which is characterized as mixed-model assembly line balancing (MMALB) and also sequencing. The configuration planning of such ALs has actually gained an important worry as high initial investment is allied through making, installing and also re-making an AL.

You are watching: Assembly lines are a special case of a project layout.

The research study brought out in this manumanuscript aims to contribute to the problem domajor of MMALB and also sequencing. Balancing describes objective depended workfill balance of the assembly tasks to various workstations. Sequencing describes find an optimal routing/task dispatching queue considering the demand scenario, available time slots and also sources. Key factors linked to this difficulty domajor has different assembly plans (e.g. mixed/batch/single version production), variations in handling workstations (e.g. manual/robotic/hybrid stations), physical line layouts (e.g. straight/parallel/U-shaped lines) and also differed job-related delivering methods (e.g. conveyor/pallet-based). These components are greatly plant specific and have to be taken into consideration as the architecture pre-requisites for line balancing and sequencing.

The contribution of this occupational is twofold. Firstly, a brief testimonial of the problem doprimary of ALB and also sequencing is presented. This includes methodical style approach of an AL and also different performance and workstation associated indexes which helps the line designer to determine plant particular style determinants for line balancing, re-balancing and also sequencing. Different heuristics and meta-heuristics based ALB solution methods, classification of ALB troubles, MMALB and also sequencing are likewise addressed (section 2).

Secondly, a logic and mathematical formulation based methodology for solving ALB problem is proposed (area 3), addressed to low volume product customization in shop floor (MMALB). The presented methodology outcomes in optimizing the shift time for any combicountry of product customization, assembled in an intermix order. It also defines a repeated project dispatching queue in accordance to the balancing outcomes. The proposed strategy is encoded through MATLAB and validated through referral data to prove the optimal conditions. A little range valuable shop floor trouble is also analysed via the presented methodology (area 4) to show the optimality conditions. The conclusions are drawn in section 5.

2. Assembly line design

Systematic style of ALs is not an independent and also easy task for the manufacturers. Designers must address present physical manufacturing facility layout in the initial phase. Cost and also relicapability of the device, intricacy of the tasks, tools selection, ALs operating criteria, various constraints, scheduling, terminal alplace, inventory control, buffer alarea are the many essential location of concern. The advancement of a technique to architecture of ALs consisting of salso phases portrayed in number 1.


Figure 1.

Advancement of an approach to AL design(Rekiek &Delchambre, 2006)

Tendencies and orientation of ALs are linked to line development. Designers have to collect information in this action around the tendencies of the line to be imposed. Balancing and also sequencing problem varies through the types of ALs. For instance, single model line produces a solitary product over the line. Facility layout, tool changes, workterminal indexes continues to be fairly consistent. Batch model lines develop tiny lots of different assets on the line in batches. In mixed-design situation, numerous variations of a generic product are produced at the very same time in an interblended scenario. Factor to consider of work-related transfer mechanism is likewise a worry. Acomponent from hand-operated work transport on the line, three kinds of mechanized work transfer systems are determined as constant move, synchronous deliver (intermittent transfer) and also asynchronous transport (Papadopoulos et al., 1993). Different line orientations should be figured out by the designer as it varies widely according to the manufacturing floor layout. Straight, Parallel, U-Shaped lines (Becker & Scholl, 2006) are mostly applied.

Various style components are necessary to study and combine through the AL style and also balancing. The decisive solution variations depend on the production philosophies, objective functions and constraints. A few of the design constraints pertained to ALB are precedence constraints, zoning constraints and capacity constraints (Vilarinho & Simaria, 2006). Efficient description of line design problem is connected through database enrichment. To collect AL data, knowledge around several performance indexes and also workterminal indexes are necessary for a line designer (Table 1).

Performance IndexesWorkstation Indexes
1. Variance of time among product versions1. Operator ability, motivation
2. Cycle time2. Tools required
3. No of stations3. Tools change necessary
4. Traffic problems4. Setup time
5. Station space5. Buffer allocation
6. Transportation networks6. Mean station time
7. Communication among the groups7. Variance of time among product versions (diff. models)
8. Task complexity8. Ergonomic worths (compelled grip strength)
9. Reliability9. Need of storage
10. Working place
11. Worker absenteeism throughout operation

AL design version and also solution methodology incorporate the model phase. Design devices are modelled and formulated after arsenal and confirmation of the input information. Deauthorize devices modelling include the output data, interactivity between various modules and techniques to be occurred. Wide variety of heuristic as Branch and also Bound search, Positional weight approach, Kilbridge and Wester Heuristic, Moodie-Young Method, Immediate Upday First-Fit (IUFF), Hoffguy Precedence Matrix (Ponnambalam et al., 1999) and also meta-heuristic based solution tactics as Genetic Algorithm GA (Sabuncuoglu et al., 1998), Tabu Search TS (Chiang, 1998), Ant Colony Optimization ACO (Vilarinho & Simaria, 2006), Simulated Annealing SA (Suresh & Sahu, 1994) for ALB difficulties are adopted in commercial and also research study level (figure 2). Validation of the models is an outcome of performance towards the goals of that certain line.

Line performances of AL style is a measure of multi-objective characteristics. Varied objective functions are taken into consideration for ALB (Tasan & Tunali, 2006). Designer’s goal is to architecture a line considering better efficiency, less balance delay, smooth manufacturing, optimized processing time, expense effectiveness, overall labour effectiveness and also just in time manufacturing (JIT). The aim is to propose a line by exploiting the ideal of the design approaches which will deal in actual fact via user choices.


Figure 2.

Different solution procedures for ALB

Design review describes a user friendly occurred interface wbelow all necessary AL information is available extracted from various database. Validation of different algorithms and also methods is included with various style packperiods (Rekiek & Delchambre, 2006).

2.1. Group of ALB problems

Category of ALB difficulty is mostly based on objective attributes and also problem structure. Different versions of ALB difficulties are introduced as a result of the variation of objectives(number 3).

Objective Function Dependent Problems:

Type F: Objective dependent difficulty, it is linked via the feasibility of line balance for a given combination of variety of stations and cycle time (time elapsed in between two consecutive products at the finish of the AL).

Type 1: This type of trouble encounters minimizing variety of stations, where cycle time is recognized.

Type 2: Reverse problem of kind 1.

Type E: This type of problem is considered as the many general variation of ALBP. It is connected through maximizing line efficiency by minimizing both cycle time and also number of stations.

Type 3, 4 and 5: These coincides to maximization of workload smoothness, maximization of occupational relatedness and multiple objectives with type 3 and also 4 respectively.


Figure 3.

Category of ALBP (Scholl & Boyesen, 2006)

Problem Structure Dependent Problems:

SMALB: This refers to single design ALB difficulties, wbelow just one product is developed.

MuMALBP: Multi version ALB problems, wbelow even more than one product is produced on the line in batches.

MMALBP: Mixed model ALB problems, miscellaneous models of a generic product are produced on the line in an intermixed situation.

SALBP: Simple ALB balancing troubles, simplest version of balancing problems, where the objective is to minimize the cycle time for a addressed variety of workterminal and also vice versa.

GALBP: A basic ALB problem contains those difficulties which are not contained in SALBP. Those are for circumstances, mixed model line balancing, parallel stations, U-shaped and 2 sided lines with stochastic task times.

2.2. MMALB and also sequencing

Production mechanism planning usually starts via the product style initially. The factor behind this, an excellent deal of future costs is figured out in this phase. Initial configuration and also installation of productive systems triggers the actual cost of the production planning of assembly system. Resources compelled by the production process likewise determines by the configuration planning. Different methodologies are made use of as illustrated in number 2, to support the configuration planning which are consisted of under the term ALB.

In the situation of combined version lines, different models frequently use accessible capacity in extremely different intensities. Therefore modification of balancing or line re-balance could be essential. A household of assets is a set of distinguimelted commodities (variants), whose primary functions are preferably comparable, normally produced by mixed-version lines. Mixed model lines are mostly employed in the instances (Rekiek & Delchambre, 2006), where

The cycle time is commonly higher than a minute.

The line price cannot be amortized by a single product model.

The product need to not be yielded in a short time.

Each product is fairly equivalent to others.

The same resources are forced to assemble the assets.

The put up time of the line demands to be short.

MMALBP occurs as soon as making or recreating a mixed-design assembly line. This is based on find a feasible assignment of tasks to workstations in such a manner that manufacturing demand of various product variants are met within the characterized change times. Minimization of assembly prices, satisfying the constraints are likewise a problem. Mixed version lines are classified into two different kinds, which are referred as dual troubles.

MMALBP-1: minimizes the variety of workstation for a offered cycle time.

MMALBP-2: Minimizes the cycle time for a given variety of workstation.

In type 1 problem cycle time or, the manufacturing rate, is pre-specified. That is why; it is more typically used to architecture a new AL wright here requirements are forecasted beforehand. Type 2 problem encounters maximization of manufacturing rate of an existing AL. This is used for example as soon as transforms in assembly procedure or in product range need the line to be redesigned.

Mixed version sequencing intends to minimize sequence dependent occupational overfill. Sequencing is based upon a detailed design scheduling depending on the operation times, worker movements, crucial tool changes compelled, station borders and also other features of the line. Different models are composed of various product alternatives and hence need different materials and also components, so that the model sequence impacts development of product demand also over time. As ALs are commonly coupled via coming before manufacturing levels by means of a simply in time (JIT) supply of compelled materials, the model sequence need to facilitate this. An crucial prerequiwebsite for JIT-supply is the stable demand price of products over time, as otherwise benefits of JIT are sapped by enlarged safety stocks that end up being necessary to protect against stock outs throughout the peak demand. Accordingly, JIT centric sequencing ideologies aim at distributing the material demands over the planning horizon (Boyesen et al., 2007).

3. Methodology for fixing MMALB and also sequencing

A logic and mathematical formulation based methodology is proposed for addressing MMALB and also sequencing. Throughout the development of this strategy, a consistent speed AL is taken into consideration wright here task transport, machine setup and also tool altering times are taken within the task times. Task time of each model, precedence relations of work are known whereas work in progression buffers, station parallelization, assignment constraints, zoning constraints are not permitted. MMALB difficulty form 2 is thought about. The balancing is accomplished in 2 consecutive stperiods which are called as initially stage and also second stage.

3.1. First stage: balancing from tantamount single model

Balancing in this stage finds locally optimized solution in the first stage iteration. Objective of this phase is to find solution(s) via specified number of stations via a minimum cycle time. Solutions are considered as locally optimized as the principle objective is to find a solution which will certainly define a smooth production by minimizing objective feature of second stage. The idea of ALBP-1, wright here the aim is to optimize the variety of workstations through a predefined solved cycle time is made use of in initially phase of this proposed method. The fixed cycle time is considered as the solution lower bound,CTminfor finding wanted station numbers,CTminis enhanced by 1 sec per iteration. Solution reduced bound is established via minimum cycle time (Gu et al., 2007) as:

Wright here, tiis the ithtask time and also Sis the wanted number of stations. The flow diagram of initially stage is portrayed in number 4.


Figure 4.

Flow diagram of first phase iteration

Tasks of various models are first thought about as an equivalent single model. Incorporated precedence diagram change various models right into one indistinguishable single design. A basic linked precedence relation example is offered in number 5, with 12 work, wbelow node containing the job number and also the values suggest jobs time.

The following algorithm characterized as step by action procedure, generates a variety of feasible services for identical single model. Optimized feasible remedies are stored as the input remedies of second phase.

Open a brand-new station S1through a cycle timeC=CTmin.

Determine the collection of jobs without predecessor, s=i,j…..n

Asauthorize randomly one task from sin stationS1.

Remove the assigned job from the precedence graph, upday station time as the cycle time C=CTmin−ti

Upday collection of tasks without predecessor as s=j,k….n

Asauthorize work randomly from sto S1until Cis positive and update Cand seach time.

When Cis negative or zero for randomly assigned any type of task froms, check for the various other work in sto be fitted inS1.

When Cis negative or zero for all the tasks in existings, open up a new station S2and C=CTminis recovered forS2.

Repeat measures 1 to 8 until the assignment of all jobs.

Generate all feasible services.

Check the solutions via preidentified terminal numbers. If the solutions are not feasible, repeat the above actions through C=CTmin+1and so on until the preferred variety of stations are met.

When a number of feasible services are achieved, save finally updated Cas the cycle time. Store and also return the workstation based services through the terminal assignment information for next stage.


3.1.1 First phase experimentation

Benchnoted ‘Buxey’ data sets of 29 jobs for SMALBP-2 (Scholl, 1993) are tested via first stage balancing technique. Precedence matrix (table 2) specifies the precedence constraints linked to the jobs. Precedence job collection 1, 2 refers job 2 precedes job 1 in a 0,1job matrix where column comes before the row. A 1 is inserted wright here tbelow is a precedence relation, otherwise 0. Equipment versatility can be identified from precedence matrix by measuringF−ratio(adaptability ratio). Higher F−ratiosuggests less precedence constraints and also greater adaptability in generating multiple feasible remedies (Rubinovitz et al., 1995).

Where, Zis the number of zeros above the diagonal and also Kis the variety of task elements. F−Ratiofor the combined precedence diagram of figure 5 is 0.78.


First stage MATLAB regimen compiled for ‘Buxey 29 tasks Problem’ (Scholl, 1993) and the job times are displayed in table 3.

Task No.Time, SecTask No.Time, SecTask No.Time, Sec

3.1.2. Experiment results

First phase generates multiple feasible options for various variety of stations. Tasks assignment is shown below, wright here S1 to S9 represents precharacterized 9 stations through assigned jobs. Minimum cycle time achieved 37 secs which fulfil the benchnoted solution outcome. Station assignments of the work are: S1 2, 7, 9, 10, 26, S2 1, 6, 12, 27, S3 3, 4, 5, 14, S4 8, 11, S5 13, 17, 25, S6 15, 16, 20, S7 18, 19, 21, 22, S8 23, 28, S9 24, 29.

‘Buxey’ 29 work problem
Benchmarked ResultsStage1 procedure
Preidentified stations, mMinimal cycle timeMinimal cycle time CCPU run time, sec

Benchmark results and the results acquired by first stage balancing are depicted in table 4. Figure 6 shows line balancing solution for ‘Buxey’ 9 station problem acquired by initially stage balancing procedure.

3.2. Second stage: balancing for mixed-models

This phase finds optimal services for mixed-models with the outcomes completed from first phase. Feasible options generated from the first stage are decoded and scaled through second phase objective feature. The aim is to attain the best services from first phase in terms of second phase objective which ensures a minimal balance delay. The feasible remedies of initially phase are coded as the workstation based services. Workstation based solution representation plan is displayed in figure 7.

Figure 7.

Workstation based solution representation

Inputs for second phase objective function from the produced first stage options are as follows:

Number of workstationsS, stood for by the solution which is the greatest numerical number of the solution.

No of jobs Kin precedence graph as the length of the solution.

Tasks assignment in workstations according to the solution depiction scheme.

The initial difficulty meaning of MMALB-2 describes the inputs to the objective attribute are variety of models to be producedM, production demand for each modelNm, where m=1toMand also job times for each modeltkm.

3.2.1. Objective feature formulation

Objective function thought about for MMALBP-2 to facilitate a smooth workpack balance among the stations, while taking smoothed terminal assignment pack right into consideration. It additionally optimizes change time as cycle time of single design situation is reput by change time in mixed-version balancing.


MNumber of models to be produced.

NmScheduled quantity to be produced for each version wherem=1toM.

TShift time duration for the booked amount to be produced.

KNumber of complete work.

CTminMinimum cycle time.

tkmTask times wright here k=1toKand m = 1 to M.

tkmrepresents the occupational time of taskk on model m.

EkTotal time compelled to finish ∑m=1MNmdevices in the scheduled period for job k

SNumber of stations.

QsmAmount of time that the operator in station s is assigned on each unit of model m

TsStation time wheres=1toS.

PsmTotal time assigned to terminal s on modelm.

PmTypical amount of complete work content for all systems of design m assigned to each station.

All models of production demand also deserve to be summarized as the total assets to be created, where;


The full job times forced to complete the manufacturing of all models are:


In MMAL, operation time is denoted asQsm; wbelow s=1toSandm=1toM; which refers the amount of time compelled in terminal sfor each unit of modelm. Mixed-model line balancing solutions are obtained below from the single model balancing algorithm of first stage by replacing cycle time C to transition time duration T. Total time assigned to terminal sin duration Tcan be identified as


Total time assigned to station child version min period Tis


Now, Pmrepresents average or preferred amount from the total work content for all systems of model massigned to each terminal and also Pmdeserve to be presented as

Hence, minimizing the worth of (Pm–Psm)points to smooth out or equalize full occupational load for each version over all job-related stations. Therefore the objective functionY(SSAL,SmoothedStationAssignmentLoad), deserve to be abridged regarding minimize the following function

3.2.2. Mixed-design line sequencing

Tasks connected to ALs are mostly taking care of the repeated routine jobs emerging at a continual interval. A static AL’s job sequencing heuristic (Askin & Standridge, 1993) is integrated to the outcomes of MMALB-2 acquired from second phase. The objective of sequencing is to generate a dispatch system which controls the order of entry of the commodities to the first terminal.

Let, qmis the proportion of product type mto be assembled in the line wherem=1toM. The initial step is to build an AL balance for the weighted average product. Let tkmis the task time for kof model mand Ssis the set of tasks assigned to terminal swheres=1toS. In that case if the cycle time isCT, the average feasibility problem deserve to be stated as:

This condition shows the averaged across all items developed in the lengthy term, no workstation is overloaded. According to the feasibility problem, one single product ALB difficulty requirements to be fixed. Due to this, job time of task kdeserve to be summarized as:

For each modelm, Qmamount need to be created. If rbe the biggest prevalent denominator of allQma repeating cycle comprised of Nm=Qm/rsystems must suffice wbelow the models are fromm=1toM. The cycle would certainly be recurring rtimes to accomplish the duration demand also. In that instance, N=∑m=1MNmitems are produced in each cycle.

The objective of making such cycle is to define a smooth manufacturing price of each version type. This will additionally prevent the excessive idle time at the workterminal due to the mix-induced starving of workstations. A workstation is starved if on completion of all the characterized jobs, there are no jobs accessible for it to work on bereason the following job has not been completed in the prior station. This is also more crucial in the bottleneck stations. That is why, the keeping of a smooth flow of the components to those stations is necessarily necessary. The bottleneck stations are the stations through maximal full occupational or equivalently average work pack per cycle. If a partial sequence overloads this workterminal through respect to average cycle timeCT, the subsequent stations are starved. If a partial sequence under tons the bottleneck terminal, the initial output price from the line will be as well high which will result in accumulating the inventory. In situation of the loved one workfill of terminal sisCs, it workpack can be characterized as:

The bottleneck station Sbis the station through maximum workload or equivalently or average workpack per cycle. Hence,

Let, Xmnis the worth amounts to to 1 if model m is inserted in the nthposition and 0 otherwise. In that situation, m(n)will suggest the type of design put in nthposition in the assembly sequence. Now, the method is to select the nthmodel to be started to insert in the line to optimize as following:

Sequencing is done in two consecutive steps:

Tip 1: Initialization, create a list of all commodities to be assigned in the time of the cycle and also called as list A.

Aim of this sequencing heuristic is to create a list of unassigned assets initially, which is then decreased initially to a list of feasible assignable products and also to the single ideal feasible commodities. The assumption of this heuristic is that the operator in hands-on workstations deserve to intermix to a slight level to store the line relocating even if the terminal is temporarily overloaded.

4. Case study

A modified useful trouble definition of WXYZ Company (Askin and also Standridge, 1993) is taken into consideration below for the implementation of the addressed integrated technique for MMALB-2 and also sequencing. The difficulty defines assembly of internet camperiods of four different models. A continuous speed, conveyor based, right AL is thought about wright here jobs has no zoning constrains, capacity constraints or assignment constraints. Typical requirements per transition for 4 different types of cameras are 20 systems of version 1, 30 devices of design 2, 40 units of version 3 and also 10 devices of version 4. Aim is to balance the line for mixed-design assembly mechanism via optimized shift time. Assembly module has 4 resolved workstations (MMALB-2) where they have actually made a decision to place one operator in each station. Each workterminal is capable of percreating the exact same collection of operations on all 4 design types. Task times (sec) for each model are shown in table 5.

Now, adhering to theproposed methodology, the aim is to find:

Optimal cycle time bookkeeping for workterminal availcapacity considering linked task relationships for all models (initially stage).

Distributing the tasks of all 4 models to four different workstations keeping an overall workpack balance, i.e. SSAL as the objective of mixed-design balancing thought about below and also additionally to discover out optimized as a whole shift timing for assembly of all models according to demand (second stage).

Finally, building a recurring lot planning via model sequencing (mixed-design sequencing).

TasksModel M1Model M2Model M3Model M4Wt. Avg.Immediate predecessors
Op 11434151019-
Op21215111714Op 1
Op 33947405145Op2
Op 434475Op 1
Op 5111310911Op 3
Op 61929212123Op 4
Op 7111491011Op 5
Op 82138283230Op 3, Op 6
Op 91319151716Op 5, Op 8
Op 103341424340Op 7, Op 9

Ten various tasks or operations are established for completing the assembly of each model. Task times are various depending upon the models. Combined precedence diagram for four models are shown in number 8.

Figure 8.

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Precedence diagram of the case problem

Proposed first phase generates 2 feasible services considering minimum cycle time for the case trouble. Cycle times of both workstation based remedies are 59 seconds. Next off step is to decode and also scale the optimized remedies to accomplish the ideal one considering in its entirety SSAL. Feasible solutions represented in figure 9, decoded in table 6, 7.