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CI-IAPTER 2

LITERiTURE IREVIEW

2.1 Introduction

This chapter discusses a detailed review of literature on "Assembly Line

Balancing".

Salveson (1955) first published Assembly Line Balancing in mathematical

forn~ by suggesting a linear programming solution. Since then, several research

papers appeared in the area of line balancing.

Assembly Line Balancing literature can be broadly classified into 4

categories (Soumen Ghosh and Roger J . Gagnon, 1989) as follows:

i . Single Model Determinisric (SMD) ALB problems.

2. Single Model Stochastic (SMS) ALB problems.

3 . Multi / Mixed hilodel Deterministic (MMD) ALB problems.

4. Multi / Mixed Model Stochastic (MMS) ALB problems.

The review of literature airailable in each of the above-mentioned

categories is presented in a detailed manner, in the forthcoming sections.

2.2 Single Plodel Deterministic (SAID) Assembly Line Balancing problems

This category of ALB has been mostly researched. As discussed earlier,

methodologies for solving any line balancing problem can be classified into two

categories namely, Optimum and Heuristic methods. Review of these methods is

discussed in the following sections.

2.2.1 Optimum Methods for Single Model Deterministic (SMD) problems

Salveson (1955) formulated SMD problem as a linear programming

problem, which will include all possible combinations of task assignments to

stations. But this led to difficulty of split tasks in the optimal solution.

Jackson ( 1954) has given a method for representing the ALB problem data

iri a con\-.enicnt diagram. He has developed a computational procedure for solving

the ALB problem and has indicated the mathematical justification also.

Bo~t'n~an (1960) has developed two different linear programming

approaches to the assembly line balancing problem. He has stated the problem as

a set of linear constraints in variables that can be evaluated in linear objective

hinction. He has developed algorithms to produce solutions to this problem as

\veil as the integer requirements for the variables in the linear program. He

removed the difficulty encountered insalveson's work by formulating ALB as an

i v ~ ~ a ,, t,c~-programn~ing -. - probienl assigning tasks to stations with 0 - 1 variables.

White ( 196 1 ) has later modified it.

Klein (1963) is concerned with the problem of assigning taslts to

workstations to minimize the total idle time for all possible cycle times. This

procedure consists of the following steps:

1 . Determine the set of all feasible ordering of the elementary

operations.

2. Determine an optimal balance for each of these orders over all

possible cycle times.

3 . Select the best solution from step (2).

Thangavelu and Shetty (1971) have presented an improved version of

Bowman's and White's zero - one integer programming formulation of ALB

problems. They have demonstrated that the steps in 0-1 programming algorithm

can be simplified or eliminated while solving the above problem. This model

permits integer-programming solutions.

Gutjahr and Nemhauser (1974) have presented an algorithm based on

finding a shortest route in a finite directed network to solve SMD problems. Arc

lengths of the network are such that it is sufficient to find any path from the origin

to destination node containing a minimum number of arcs. They have presented

thr con;pu~ational results in their work and the performance of the algorithm is

compared with prior analytical methods of line balancing.

Patters011 and Albracht (1975) and Talbot and Patterson (1984; formulated

ALB as a general integer-programming problem without binary variables. But

Patterson and Albracht (1 975) have considerably reduced the size of the problem

forn~ulatior,.

Among the above researchers, Klein (1963) and Gutjahr and Nemhauser

(1973) have proposed shortest path technique to solve ALB presenting integer

programming formulation, while Thangavelu and Shetty (1 97 I ) , and Patterson

and Albracht (1975), have obtained optimal solution using branch and bound

technique.

Jackson (1 956), Hu (1 961), Van Assche and Herroelen (1 979), Johnson

(1 98 1) and Wee and Magazine (1 98 1) have also used branch and bound technique

to solve ALB problen~s.

jaclcson (1956), Held and Karp (1962), Held et al., (1963) Kao and

Queyranne (1982) and Schrage and Baker (1978) have formulated ALB as

Dynainic prograrnrning problems.

Johnson (1981) has conducted a comparative investigation on the

algorithms available in the literature to solve the basic ALB problem. He has

tested each algorithm for a series of test problems. He has developed a new node

search branch and bound algorithm. This algorithm has the characteristics of

finding a feasible solution very quickly and from there it searches for optimality.

Johnson R.V. (1983) has also presented a branch and bound algorithm

which can be used to solve ALB problems adopting some modifications to the

originally formulated problem of minimizing the required number of assembly

stations, given a cycle time, a set of tasks with given deterministic task times and

precedence relaiionship. After defining and describing the original ALB problem,

so;l?c modifications to the original problem are introduced. They are allowing

planned imbalance in the total task durations and allowing specific tasks to

specific types of assembly stations.

LYilson ( 1 986) has demonstrated that integer programming can be used as a

formuiation and solution technique for designing efficient production lines by

allocating tasks to multiple manned workstations. He has attempted to

demonstrate firstly that Shutub's formulation can be simplified to give a more

natural formulation and secondly that a good integer programming computer

package can take advantage of the structure of the problems and find a solution in

a reasonable time.

Richard F. Decltro and Sarangan Rangachari (1990) have addressed a goal

progranlming approach to ALB. They have developed a zero one goal -

prograi~~ming model for ALB. This fornulation allows the decision-maker to

have greater flexibility in considering alternatives. This model also provides

greater flexibility in obtaining line balances by simultaneously considering

various operational requirements like sequencing, idle time, cycle time and costs.

l'hey have conducted a sensitivity analysis of an example highlighting the

usefi~lness of the approach in the planning stages of ALB.

Miltenburg and Wijngaard (1994) have considered the U-Line Balancing

problem in their work. The traditional line-balancing problem considers a

production line in which stations are arranged consecutively in a line. Balancing

is done by grouping the work elements into stations while moving forward or

backward through a precedence network. But recently many production lines are

being arranged in a U - line as a consequence of the use of Just-In-Time

production principles in many factories. These authors have introduced and

defined the U - line-balancing problem in their work. It is more complex than the

traditional ALB problem because tasks can be grouped into stations by moving

forward, backward or simultaneously in both directions, through the precedence

network. They have presented a dynamic programming procedure for computing

the optimal balance to a U - line-balancing problem. They have outlined two

heuristic procedures. They are the extensions of well - known heuristics for the

traditional ALB problems, which have given good solution to those problems.

They have also shown some computational results for well - known literature

problems.

Aghezzaf and Artiba (1995) have addressed tlie problem of balancing

assembly or fabrication lines. This is done to achieve a given production rate or

to optimise the use of workstations. These authors have studied the polyhedron of

the feasible solutions of ALB problems. They have developed a lagrangian

relaxation algorithm, considering the set of cycle constraints in the objective

function, which are supposed to be complicating constraints. In this type of

problems, the linear programming relaxation is having integer solutions. Then the

subgradient algorithm is used for optimising the lagrangian dual. They have used

a heuristic to find optimal feasible solutions for the original line balancing integer

program. They have also used these two bounds to reduce the size of the branch -

and -.bound tree.

Klein Robert and Scholl Arrnin (1996) have addressed the maximisation of

production rate for Type I1 ALB problems (Maximising the production rate).

They have proposed branch and bound procedure, the objective of which is to

assign tasks to a given number of workstation of a paced assembly line;

considering the precedence constraints. Existing methods for Type I1 - ALB

problems (Maximising the production rate) are based on repeatedly solving Type 1

problems (Minimising the number of workstations). But this branch and bound

method solves the Type I1 problems by a new enumeration procedure. This is

depending on the Local Lower Bound Method, which contains many bounding

and dominance rules. They have also demonstrated this method with

computational experiments.

Sprecher (1999) has proposed a branch and bound algorithm for solving

simple ALB problems. This algorithm is based on the precedence tree guided

enumeration scheme introduced for dealing with a broad class of resource -

constrained project scheduling problems. This algorithm is powerful for solving

the above problems. The ALB problems coming under Type -1 are converted as

resource- constrained project-sched~ling problems with a single renewable

resource whose availability varies with time and the problems can be solved with

general algorithm. This algorithm allows genetalising classical dominance

concepts. The computational complexity of some bounds has been reduced and

the same for other bounds has been strengthened. Computational experiments

have also been conducted.

2.2.2 Heuristic Methods for Single Model Deterministic (SMD) problems

While reasonable progress has been made in the development of optimal

approaches far SMD problems, significant research has been done in the heuristic

methods also. 'The reasons for this development can be stated as follows:

(i) Since ALB problems are NP - hard, highly efficient optimal

approaches do not exist.

(ii) Optimal approaches are not suitable for large-scale problems.

Many heuristic approaches use the priority ranking (or) tree search

technique among the four techniques discussed earlier.

Tonge (1960) has presented a heuristic procedure for balancing assembly

lines and a computer program for carrying out that procedure. He investigated the

application of complex information processing techniques to a typical industrial

problem. ile was one among those, who have started the development of heuristic

procedures for ALB. His heuristic procedure consists of 3 phases as given below:

( i ) Repeated simplification of initial problem by grouping adjacent elemental

tasks intc compound tasks.

jii) Solution of the simpler problems thus created by assigning tasks to

workstations at, the least complex level possible, breaking up the compound

tasks into their elements only when necessary for a solution.

(iii) Smoothing the resulting balance by transferring tasks among work stations

until the distribution of assigned time is as even as possit71e.

Heuristic procedure developed by Kilbridge and Wester (1 961) has drawn

the attention of many researchers since its introduction. In this technique,the work

elements at the beginning of the precedence diagram are assigned first.

Later Thomopoulos (1965) modified this technique considering the total

schedule for a whole shift and tasks are assigned to operators on a shift basis

rather than cycle time basis.

Helgeson and Bimie (1961) have developed Ranked Positional Weight

( W W ) technique, which assigns those jobs first, which have the largest RPW.

RPW of one element is the sum of its duration with those of all following

elements. This method ranks operations in the descending order of positional

weights. It selects the task with highest positional weight and assigns it to the first

available station without violating the precedence relationship. It attempts to

assign some more tasks to the first station if the Un- Assigned- Cycle- Time

(UACT) is more than the durations of those elements. The process is repeated for

the remaining stations until all the work elements are assigned.

This method was later refined and computerized by Dar - El (1 973), that is

known as Model for Assembly Line Balancing (MALB). This method attempts to

improve the initial solution provided by the RPW technique. This procedure

permits Z~acktracking after initial assignments have been made. It takes other

combinations of tasks to determine whether an improvement is possible.

Arcus' COMSBAE (1966) generates solutions for a specified number of

iterations. In COMSOAL, a list, called list - A is created containing operation

number, maximum number of preceding tasks and durations. This list is scanned

and another list, called list - B is created by listing all the tasks that do not have

preceding tasks. From that, one more list, namely, list - C is created with all

eligible jobs from list - B. A job becomes eligible if its duration is less than the

Cycle Time (CT) or less than the time remaining of the workstation.

'I'hen tasks from list - C are assigned to station 1 until the sum of durations

of assigned tasks becomes near about or equal to Cycle Time. While doing so the

follo~ving rules are used:

( i ) Larger tasks are assigned first

(ii) Tasks with more followers are assigned first.

(iii) Operations from the list-C are chosen at random.

Then list - A is updated by deducting 1 job from number of preceding jobs

for all jobs immediately following the assigned tasks. Then the above process is

continued until all the tasks are assigned to stations.

Computerized ALB (CALB) package was developed by the advanced

assembly methods project team (Magad, 1972). CALB concerns about - task

groupings, task to station assignments along with variable labour wage rates. This

technique uses number of simple rules to determine the work elements to be

assigned to a station. It first considers the position of work element in the

precedence diagram, and second the duration of work element.

Arthur J. Nevins (1971) has applied a general-purpose heuristic program to

ALB problem. Each iteration of this tree search program starts with a 'bud'

representing a problem to be solved. The problem associated with the bud is

cilecked whether it can give an immediate solution, If no immediate solution is

a\.aiiabIe, the bud then sprouts a number of buds each representing a problem to

be solved, the solutior~ of which would guarantee the soliltion to the problem

associated tvith the parent bud. The difficulty of each such problem is tinen

evaluated in the fornl of a 'score' associated with the bud. The program then takes

a global look at all buds that have not yet been sprouted and chooses the bud with

the best score for the next iteration. The iterations are continued until the best

solution is arrived at.

Dar - El ( 1 975) has made a comparative study between three methods for

balancing single model assembly lines. These 3 heuristic methods are referred to

as

( i ) 10 - Single Pass (SP) methcd

(ii) ARCUS method and

(iii) MALB method

Among these methods, the 10 - SP method selects the best of 10 solutions,

which are obtained by using a different ranking system for the selection of work

elements.

Ranking Systems are obtained from the following 4 heuristic rules:

RPW - Ranked Positional Weight. The positional weight of a work

element is its own processing time added to the processing times

of all following work elements. As per this priority rulet the work

element with the highest ranked positional weight is selected.

TF - Total number of jobs Following. This is the sun1 of all work

elements that follow the work element under consideration. As

per this priority rule, the work element which has the maximum

number of work elements following the work element under

consideration is selected.

LC' - l.arsest Candidate rule. As per this priority rule, the work element

ha\.-ing ?he largest processing t ~ m e is selected.

IF - 'Total niimber of Immediate Followers. As per this priority rule,

the ~vork element which is having the largest number of '

imn~ed~ate followers 1s selected.

The 10 rank% systems are then obtained as follows:

M, = RPW

1 = R P L V - TF

\I; = RPLZ' - LC

l = RPLi' - I F

hl, = R P W + T F t L C

M6 = RPW+ TF-LC T IF

M- = TF

Mb = T F - L C

M9 = TF+ IF

M l o = TF + LC + IF

Thls 10 SP algorithm solves ALB problems uslng the above 10 ranklng

systems and then selects the best solut~on.

Arcus method develops 75 sequence generat~ons at each operating cycle

time and selects the best solution.

MALB technique is an alternative technique based on optimum - seeking

backtracking method to which several heuristics are added, allowing the

algorithm to produce a single solution rapidly.

He has used Balance Delay (BD) for comparing the solution efficiencies

and compared the computation times also. With the experiment conducted, he has

suggested that the 10 - SP method is simple but effective technique for balancing

single model assembly lines.

Talbot et al., ( 1 986) have categorized heuristic line balancing techniques

into four categories namely 'single - pass', 'composite', 'backtracking' and 'time

trapped optimizing' approaches. The first two categories are almost similar. But

the firsr category assigns the work elements upon a singie attribute of each

assembly task and in the second one the decision rules are combination of the

single pass decision rules. Also the second category selects the best of the

solutions determined by the application of severalsingle - pass methods. In the

third category an attempt is made to improve a previously obtained solution by

backtracking. The fourth category aims at optimum seeking approach with an

arbitrarily limited amount of computation time.

Some examples of single - pass methods are the procedures developed by

Kilbridge and Wester (1961) Helgeson and Birnie (1961) Moodie and Young

(1965) and Steven T.Hackman et a1.,(1989). Arcus' COMSOAL method (1966) is

an example of composite, while Hoffman's partial enumeration method (1963)

and Dar - El's method (1 979) are example of backtracking methods.

Talbot et al., (1986) have also reported on a computational experiment

designed to assess the efficacy of 26 heuristic procedures to solve ALB problems

which assign tasks to work stations along an assembly line such that the number

of workstations required is minimized. The heuristic procedures evaluated vary

form simple list processing procedures that consider a single attribute of each

work task for assignment, to procedures of optimal solutions, but the search of

which are terminated through the imposition of a limit on the amount of

computation time that can be devoted to each search. They have also included

heuristic procedures which back track in an attempt to locate an improved

solution, and procedures, which probabilistically search for improved solutions.

They have used four data sets to assess heuristic performance, which include both

literature and generated problems. They have first compared the various

approaches examined with the initial solution obtained for each problem. Then

they have compared the results obtained with the optimal solution. They have

analyzed the variation in their result from the previous ones. They have also given

guidelines for balancing industrial assembiy iines.

Steven T. Hackman et al., (1989) have developed simple, fast and effective

heuristics for Simple Assembly Line Balancing Type - I problem (SALB - I)

(minimizing the number of workstations) and for Type - I1 problems (SALB - 11)

(maximizing the production rate). They have stated that the SALB - I problem is

NP - hard. Hence it is difficult to solve these problems by optimal methods.

Hencc these researchers have concentrated on heuristic methods.

They have described a branch and bound heuristic to solve SALB - I

problem which contains two aspects as given below:

(i) It incorporates a fast heuristic for bounding.

(ii) It introduces heuristic fathoming as a technique to reduce the size of the

branch and bound tree.

They have also explained another heuristic to solve SALB - IIproblems

with an improved upper bound. They have also conducted extensive experiments

to prove the effectiveness and speed of their heuristic.

Panneerselvam and Oudaya Sankar (1993) have analyzed Single Model

Deterministic (SMD) ALB problems. They have considered twelve heuristics for

comparison in their work as given below:

(i) TF

(ii) TF + LC

(iii) TF + LC + TL

(iv) TL

(v) TL+LC

(vi) TL + IF

( i i i , T L A T F

i \ i l l ) RPW

1 RPM'T IF

( 1 RPWTLC

(xi) R P W L T F ? L C

( ~ 1 1 ) NF

The above twelve heuristics are derlved from the fo l lon~ng six basic

priority rules, which are mentioned below:

RPLV - Dar-El, 1974.

7'F - Dar-El, 1974.

LC - Dar-El, 1974.

IF - Dar-El, 1974.

TL - Total number of Levels. As per this priority rule, the candidate

work element, which is having the maximum of levels on which

its folIo\vers are positioned is selected.

NF - Total number of unassigned jobs Not Follo~ving. This is the

difference between the total number of unassigned work elements

and the totai number ofjobs following (TF). As per this priority

rule, the work element which is having the minimum number of

unassigned jobs that are not following the work element under

consideration is selected.

They have developed a Generalized Algorithm (GA) for ALB, In which

they have suggested to select a work element under any combination of the

above-mentioned 12 priority rules. The Generalized Algorithm (GA) developed

by them is presented in Annexure -I.

After an extensive experiment, they have recommended a set of 9

Heuristics for Assembly Line - Balancing (HAL) to solve a given problem. The

best solution using the reconmended set of heuristics is selected for

~rnplernentatlon. T h ~ s recommended set of I~eurist~cs is given below.

1 ) TF

2) T F + LC

3) T F + L C + T L

4) TL

5) TL- LC

6) TL - IF

7) TL+ TI:

8) KPW

9) NF

Fayez F. Boctor (1995) has presented a four rule heuristic method for ALB

which mlnlmlzes the number of workstations for a glven cycle tlme. T h ~ s

heurist~c belongs to the category of composite line balancing methods. The

general framework of this method is the sanie as the one used by most heuristic

methods. Thls method uses a prioritizing scheme composed of four decision rules

to assign a task to a workstation. This tries both forward and backward balaricing

and the best solution is selected. He has evaluated the performance of this method

over 15 other heuristic methods ranging in complexity from random assignment

of work elements to Hoffman's enumeration procedure (1 963).

Fatih Ugurdag et al., (1997) have considered the aspect of designing paced

assembly lines with fixed number of stations. They have addressed the issue of

allocating tasks among workstations in assembly line so that the cycle time is

minimised (Type I1 problems). They have provided a two-stage heuristic

procedure, which is based on an integer programming formulation of the problem.

This procedure is similar to simplex procedure, which minimises the cycle time

and also sn~oothens the \vorkload among the workstations. They have also

conducted computational experiments on problems from the literature.

Naryanan and Panneerselvam (1998) have applied the existing set of

heuristics, Heuristic for Assembly Line - Balancing [(HAL), Panneerselvam and

Oudaya Sankar, 19931 to a case problem in a mixie manufacturing unit, which

comes under Single Model Deterministic category. The work has been carried out

to determine the best solution for the current volume of production: the best

production volume and corresponding best solution and also the best solutions at

other volumes of production. The best solution at the existing volume of

production has been suggested for implementation and the other results can be

used as ready-made solution depending on the future volume of production.

Nagendra Parashar and Somasundar (1999) have conducted a study on

design factors for line balancing, Design of production lines is a vital job to be

conducted by an Industrial Engineer. Since production lines are used for mass

production, a small improvement yields a tremendous reduction in the total cost.

These authors have addressed a number of factors that affect the performance of

the production lines like number of rvorkstations, buffer capacity etc.

2.3 Single ,Model Stochastic (SMS) Assembly Line Balancing problems

Having reviewed the literature available in the area of Single Model

Deterministic Assembly Line Balancing problems, the researcher reviews the

same related to Single Model Stochastic Assembly Line Balancing problems in

this section.

Although stochastic task times in ALB problems were incorporated by

Arcus in a later version of COMSOAL (1966), Moodie and Young (1965) were

the first to develop the heuristic methods for both constant and variable task

times. They developed a two - phase heuristic procedure for balancing the line. In

the first phase a preliminary balance is achieved using largest candidate rule. In

the second pl~ase. tasks are shifted between stations to reduce station idle times

and to equalize the variance among stations.

Mansoor and Ben - Tuvia (1956) made an attempt to determine the best

cycle time for a given number of stations perfectly balanced with stochastic tasks

times. They have proposed two plans for improxiing the efficiency of the balanced

assembly lines by considering the variability of the task duration.

Reeve and Thomas (1973) tried three solution procedures like trade and

transfer, branch and bound and a combination of heuristic branch and bound and

trade and transfer for SMS problems.

Freeman and Jucker (1 967), Kao (1 979) and Sniedovich (1 98 1) formulated

dynamic programming for getting optima! solutions. Freeman and Jucker (1967)

suggested that a unique cycle time could be established when an average output

rate and deterministic task times are available. They suggested that this is

applicable for stochastic task times also.

Sphicas and Silverman (1976) have established that under certain

conditions SMS problems can be converted into SMD problems.

Hillier and Boling (1966) have analyzed the effect of unbalancing the line

on production rate. Later on Rao (1976), Smunt and Perkins (1985), So (1989),

Baker et al., (1993) and Pike and Martin (1994) have studied the effect of

deliberately unbalancing the line on production rate in this category. They have

concluded from their research finding that the production rate is optimized by

assigning lower average operation times to the intermediate stations than to the

stations on the two ends, which led to 'Bowl Phenomenon'. They have also

indicated that balancing the production line perfectly maximizes production rate

of a two-station system and there is no benefit by unbalancing the line for a two-

station production system. In this case the buffer between workstations is

increased.

Considering the fact that the total task times at all work stations are not

equal, Wiiiier and Boling (1 966) have used 'bowl phenomena' in which middle

stations which affect both preceding and subsequent stations are treated as critical

stations. The capacity of these stations is increased to obtain more benefits.

. Payne et aP., (1972) and Camall and Wild (1976) have also considered the

above phenomena.

Hatcher (1 969): Quarels j 19671, Sheskin (1 976) and Smith and Brumbaugh

(1977) have concluded that inventory banks are useful in improving production

r-nna~ity. --r

Wyche and Wild (19771, Magazine and Silver (19781, Muth (1973) and

Rao (1976) have suggested more efficient methods for obtaining numerical

results, in case of SMS problems.

El - Rayah (1979) has developed simulation studies using bowl phenomena

in which assigning of lower operation times to the middle stations resulted in

better output rates than those of balanced lines.

Hillier and Boling (1979) have found that benefits obtained fi-om

unbalancing will be less pronounced as the amount of inter - station buffer

storage is increased, because it increases the station independence.

Kottas and Lau (1973, 1981) have developed heuristic methods for SMS

problems. In their former work, they made an attempt to obtain desired output rate

with economical operation costs. But cycle time is high and only one line balance

is generated. In their later work, they removed these limitations. They have

implemented this in two stages. In the first stage, a probabilistic hearistic is

developed producing low - cost line designs and the most economical design is

selected in the second stage.

Smunt and Perkins (1985) have analyzed more realistic environment using

simulation methods.

Shtub and Dar- Ei (1990), have developed a model for SMS category of

AER, n.hich considers the information available in the assembly chart of the

product. This model incorporates an 'efscient frontier' from which a solution has

to be chcsen base:! or, trade -- off between the effort to minimize the number of

sub -assemblies handled by work stations. The authors have divided the problems

into 2 categories in order to minimize the number of sub assemblies handled by

the workstation and to minimize the idle time of the line as follows:

Category 1: Each objective function is given a suitable weight and the solutions

are subjective to these weights.

Category 2: The objectives are formulated into constraints and an efficient

frontier is constructed in order to minimize the total idle time of t l ~ e line.

Bhattacharjee and Sahu (1 990) have described a method for generating

,4LB problems randomly and measuring their complexities. An ALB problem

may be called as a complex problem, if it can not be solved with in a reasonable

CPL time. The computing time is proportional to the complexity of the problem.

This depends on the factors like size of the problem, cycle time, number of

workstations, method used for solving the problem etc.,

The optimal methods may require more processing time when compared

with heuristic methods. Depending on the precedence diagram, there are number

of possible sequences. An optimal procedure has to scan through all sequences for

optimization, whereas the heuristic method has to scan lesser number of

sequences. The size of the problems that can be solved by optimal methods is

limited. Hence various researchers have used heuristic methods but they give only

sub optimal solutions. Since ALB problems come under combinatorial

optimization category, global search methods like Simulated Annealing (SA) have

been tried.

Suresh and Sahu j 1994) have addressed the stochastic Assembly Line

Balancing problems, using Simulated Annealing in their work. SA presented by

these authors tries to reach the global optimum by not getting trapped at the

cjiffei~rli local opti~nurn points. These authors have used SA to solve ALB

problems and compared the results with those ofMoodie and Young (1965) and

the trade and transfer approach of Reeve ( 1 97 1).

The structure of Simulated Annealing is presented here.

Simulated Annealing (SA) is a random search technique. It is similar to that

of physic'al annealing of solids, where a metal is brought to its loivest eriergji state

by first bringing it to a very high tenlperature (usually melting point temperature)

and then cooling at a very slow rate, to a very low temperature. If the cooling is

not slow enough, it may result in quenching which is undesirable. SA is based oil

the analogy between the simulation of annealing of solids and the problem of

solving combinatorial optimization problems.

SA employs the above principle in combinatorial optimization problems to

minimize the objective function value. This method starts with an initial solution

at an initial value of control parameter, which is similar to the temperature in

physical annealing. The value of the objective function for the initial solution is

computed. A neighbour to this initial solution is generated either by trade, which

is nothing but interchanging the positions of two jobs or by transfer, which is

nothing but shifting a job from one station to another. Then the value of new

objective function is computed and if it is less, current value is replaced by the

new one. A neighbour with increase in the objective function value is also

accepted as long as it satisfies the acceptance criteria. This process is started with

a high value of control parameter and it is being reduced later. The procedure is

stopped when a stopping criterion is reached.

But the major disadvantages of this method are stated as follows:

( i ) This method stops the procedure to get optimal solution when the

stopping criterion is reached.

(iij SA starts with an inferior initial solution.

The above two issues have to be properiy addressed to get near optimal

solution.

Dimitradis and Georgiadis (1995) have addressed ALB with smoothed

workstation assignments. They have proposed a method for the above in their

work. Smoothed workstation assignment contains an addiiionai criterion: when

the assembly line is designed. In case of assembly lines having large number of

tasks, a small variation in duration and lesser number of precedence constraints

are common in industries. In the above lines, the method proposed by these

authors performs in an efficient manner. They have demonstrated this with a case

problem in a Jeep type vehicle in a major Greek company.

Suresh et al., (1994) have presented a Genetic Algorithm for stochastic

ALB. They have discussed that because of the computational co~nplexity involved

in the ALB problems, near optimai solutions are preferred over optimal solutions.

To obtain near optimal solution random search technique like Genetic Algorithm

is preferred. They have presented a general approach Genetic Algorithm to obtain

a good quality solution for ALB problem. They have proposed a genetic

algorithm, which works with only feasible solutions for the ALB problem. Then

they have presented a modified method in which two populations, one allowing

only feasible offspring and the other allowing a certain amount of infeasible

solution also. In this scheme, by exchanging members of the population at regular

intervals the search can be carried out more efficiently. They have forrnu1ate.d

ALB problems and conducted experiments to compare the performance of the

algorithm proposed by them using tn.0 well known formulations available in the

literature (Moodie and Young 1964 and Reeve 197 1).

Mitsuo Gen et a]., (1996) have addressed Fuzzy ALB using Genetic

Algorithm. Genetic Algorithms have powerful performance in solving

cornblnatorial optimization problems. The real world practical problems involve

data, ~vhich are imprecise, vague or uncertain. In ,4LB problems the duration of

each job cannot be certain. They are stochastic in nature. Hence they can be

represented by fuzzy numbers. These authors have solved ALB problem with

fuzzy durations of work elements using Genetic Algorithm to minimize the total

operation time ir, each workstation. The genetic operators suitable for the ALB

problems are discussed. They hate generated a numerical example and solved it

by their algorithm.

Hong and Cho (1997) have considered the generation of robotic assembly

sequences and balanced the line using Simulated Annealing (SA). An assembly

sequence is considered to be optimal where the sequence satisfies assembly

constraints and yields the minimum assembly cost. These authors have proposed a

method using Simulated Annealing in which an energy function is derived to

satlsfy the assembly constraints and minimize the idle time and assembly cost.

This energy function is iteratively minimized andoccasionally perturbed by SA.

When there is no hrther change in the energy, a solution of assembly sequence

with consideration of line balancing is finally obtained. They have presented case

studies of products like electrical relay and an automobile alternator to show the

effectiveness of the method.

Kyungchul Park et al.: (1997) have considered a new type of an ALB

problem which occurs in a company manufacturing electronic home appliances.

The problem has some special characteristics and the main hurdle in this problem

is that the precedence diagram is not enough to describe the precedence

relationship bet~veen tasks. Even though many Operations Research 1

Management Science techniques have been developed to solve decision making

probiems, they can not reflect many factors arising in the real world. Hence the

&ove xthors h a w prescntcd an experience to solve a real world problem. In real

world ALB problems the under mentioned constraints may be encountered. Some

pairs of tasks cannot be assigned to the same work station because of

incompatibility between them caused by different characteristics of the operations

needed, the ~naterials used, the limited work space, or other technological factors.

Also there may be a natural distinction of the tasks according to the process

design.

They have proposed a heuristic procedure based on some well-known

network algorithms to solve this new type of line balancing problem, which has

practical applications. This heuristic procedure is based on neighbourhood search

procedure and an improvement in the solution is obtained by solving two sub

problems. One sub problem is a generaiized bin-packing problem for which they

have proposed a heuristic, based on network theories. The other sub problem is

solved with-in polynomial time bound by a shortest path algorithm.

The problem presented by them has many practical applications in its form.

A few modifications can make it possible to apply the model to other situations.

They have developed a full system incorporating graphic user interface and

installed in the line. The system is used for getting good solutions and also to

evaluate several possible alternatives in the process design. The system installed

is useful for getting not only increased production rate but also improved quality

of the assembled product. The reason for the above is that the introduced system

strictly observes the restrictions imposed on the problem while a line design may

find a solution manually that violates some of the constraints. for the sake of

smaller cycle time and ease of finding the solution.

Jr Jung Lyu ( 1997) has proposed a Single - Run Optimization Algorithm

for stochastic ALB problems. This algorithm is based on single - run optimization

approach, nhich is applied to find the optimal parameters of a simulation model.

An empirical comparison is made with two other algorithms available in the

literature and it has been shown that this algorithm is fast, accurate and relatively

robust in solving stochastic ALB problems. The statistical analysis of the

experimental results is also discussed.

Kim Yong J u et al., ( 1995) have studied the effect of workload smoothing

in assembly line. They have presented a heuristic based on Genetic Algorithm for

the same. Workload smoothing has advantages like establishing the sense of

equity among workers and in\,olves them to contribute to increase the production

volume. Although a lot of research has been done on ALB, the objective of

workload smoothing has not been properly addressed. These authors have

considered workload smoothing as an objective and developed the heuristic based

on Genentic Algorithm. This Genetic Algorithm is putting emphasis on the

utilization of problem - specific information. They have conducted extensive

experiments based on this algorithm and demonstrated the advantages obtained

using this algorithm. They have also compared this heuristic with three other

heuristics and another heurisl-ic based on Genetic Algorithm.

Ajenblit and Wainwright (1998) have studied the U - shaped ,4LB problem

and applied Genetic Algorithm for this. In this type of problems, tasks can be

assigned to stations either after all its predecessors or all of its successors have

been assigned to stations. This research presents a global framework, which can

be used to deal with the two possible variations of the problem, minimizing total

idle time and balance of the workload among stations or a combination of both.

These authors have developed 6 different assignment algorithms for this problem.

Iicir;~onson (1993) has discussed a simulation exercise used to aid in

teaching assembly line concepts in a course on Production Methods and controls.

Xu et a]., (1995) have proposed a method for stochastic ALB problems

~lsing Genetic Aigorithms. They have used a directed graph approximate method

to sol\-e ALB problems. A con~putational energy function offering Neural

Setivork to solve the ALB problems is also explained.

Having analyzed the literature of SMS problems, the researcher moves on

ro discuss the literature available in Multi 1' Mixed Model Deterministic category

of ALB problems in the next section.

2.4 Itlulti 1 Mixed >lode! Deterministic (MPID) Assembly Line Balancing

problleans

Multi / Mixed ALB problem can be stated as follows:

Given number of products, each having its own constraints, the work

elements are assigned satisfying the following conditions:

( i ) Each work element is assigned to exactly one workstation.

(ii) The number of stations is the same for all products.

(iii) The precedence constraints are satisfied

(iv) The work content of any station for any given product does not

exceed the cycle time.

The literature in the area of MMD category is reviewed in this section.

Arcus7 COMSOAL (1966) is a promising method for solving Mixed Model

Problems.

Thomopoulos (1965, 1970) suggested significant methods for solving

MMD problems. In the former work, he modified Kilbridge and Wester (1961)

heuristic by converting SMD technique for MMD problems, which is based on

shift rather than cycle time basis.

In his later work, Thomopoulos (1970) has made an attempt to assign tasks

to stations in a serial fashion. For each station, number of feasible combinations is

tried until the best combination is reached. He has considered Mixed - Model

assembly line balancing with smoothed station assignments. Generally in Mixed

Model line balancing, work elements are assigned to operations on a day - to -

day basis or shift basis rather than cycle time basis as in the case of single models.

The purpose of this is to distribute evenly the total daily workload to stations.

rc'ormally, stations by station assignments on individual models are not considered

which may lead to uneven flow of work along the lirre for a given model. This

author describes how a modification to mixed model line balancing procedure or

algorithms can lead to smoother (or more consistent) station assignments on a

model by model basis. Smoother station assignments are desirable in any mixed

model assembly process. He has also shown that this procedure can be applied to

assembly lines operated on a batch basis. This procedure is applicable to most of

the line balancing procedures.

Roberts and Villa (1970) formulated Integer Programming model to

minimize excess work content of each station. They have presented a multi

product ALB problem. The problem is formulated as a linear integer-

programming problem for which zero - one programming is applicable. It

provides a well - defined mathematical structure but highly restricted to small

problems. In spite of the difficulties encountered in obtaining solutions to integer

programs, this model serves several purposes. It provides a formal structure of the

problem in a rather standard mathematical format. This structure suggests some

highly specialized approaches to get the solution.

They have also developed one more model namely, network model which

does not possess the standard mathematical programming format. But this model

is more physically related to the problem than the previous one. This model

develops a finite directed network in which the arcs represent stations in the

assembly line and the nodes correspond to possible first station assignments of

elements from each product. The arc lengths are the idle times within the stations.

Determining the shortest path in the network or equivalently to find the minimum

number of arcs is the procedure of finding optimal solution. This model is

computationally better than the previous methods but storage requirements are

more demanding comparatively.

Macaskill (1972) developed computer-based heuristic to solve MMD

problems. Hz has stated that Mixed - Model assembly line balancing problems

have two main problems. The first of these is the mixed - model balance

problems, which is concerned with allocation of work to operators, and resembles

the single model balance problem. The second problem is dealing with the effect

of model sequence on assembly performance. He has considered only the first

problem and is concerned with a formulation that facilitates the achievement of

large - scale mixed model balances by computer. He has formulated the problen~

and noted some of the difficulties of achieving effective balances in practice. He

has designed balance procedures to obtain speedy computer solution of large scale

Mixed Model problem.

Dar - El and Cother (1975) have developed heuristics for balancing

sequencing assembly lines to minimize the overall line length of the Mixed Model

lines.

John Miltenburg (1989) has addressed level schedules for mixed model

assembly lines In Just -- In - Time production systems. Mixed model lines are

used to assemble variety of products without holding large inventories. The

effective utilization of these lines requires that a schedule for assembling the

different products be determined. This author deals. with the objective of

determining the sequence schedule for producing different products on the line.

This sequence will vary depending upon the goal like keeping a constant rate of

usage of every part used by the line, which is also known as leveling or balancing

the schedule. This work has developed a theoretical basis for scheduling these

systems. This author has formulated the problems as a mathematical model and

analyzed its properties. He has also presented new solution algorithms and

heuristics.

Thomas McCormick et al., (1989) have considered an assembly line with n

stations in series having finite capacity buffers. Blocking occurs when buffers are

full. There are M different types of products to be assembled, each with its own

processing requirements. There is a production target set for each type. The

problem is to operate the line to minimize throughput time. They have proposed

heuristic approaches to this problem based on an equivalent maximum flow

problem and on critical path techniques.

Gokcen Hadi and Ere1 Erdal (1997) have presented a goal programming

approach to Mixed-Model ALB problems. This is a binary goal-programming

model based on concepts developed by Patterson andAlbracht (1975). The model

developed by these authors provides a greater flexibility to the decision-maker,

since several conflicting goals can be simultaneously considered.

Zhao Xiaobo and Katsuhisa Ohno (1997) have developed algorithms for

sequencing mixed models on an assembly line in a JIT production system. In

almost all line balancing problems the conveyor should not be stopped. But in all

mixed model assembly lines in JIT production systems, workers have the power

and the responsibility to stop the conveyor whenever they fail to complete their

operations within their work zones. Moreover, in mixed model assembly lines in

JIT production systems, the operation times are varying in length. Hence it

becomes difficult to achieve the effective line balance for them. Consequently, the

conveyor stoppage is a very important criterion that has to be considered in these

mixed model lines. These authors have proposed two algorithms for finding an

optimal or sub - optimal sequence of mixed models to minimize the total

coilveyor stoppage time. Among these, the branch and bound algorithm is used

for finding optimal solution for smail size problems, whereas the Simulated

Annealing (SA) algorithm is used for determining near optimal solution for large

size problems. They have solved a numerical example and shown that SA 1s 100

times faster than the branch and bound algorithms to find near optimal solutions.

Ere1 and Gokcen (1 999) have considered the shortest - route formulation of

Mixed - Model ALB problems. These authors have assumed common tasks to

exist and they are performed in the same stations. Their formulation is based on

an algorithm, which is useful for solving Single Model problems. With the help of

combined precedence diagram, the Mixed - Models are transformed in to Single

Model systems. This procedure is capable of considering any constraint that can

be expressed as a function of task assignments.

2.5 hlulti / Mixed Model Stochastic (SIIWS) Assembly. Line Balancing

problems

Having discussed the literature avaiiable in the area of MMD problems, the

researcher extends his discussions on Multi / Mixed Model Stochastic (MMS)

ALB problems in this section.

The advancement in manufacturing methods has converted all the real

world MMS problems into MMD category because of automation and less - task

time variability. Hence only a few articles are available for MMS problems.

COMSOAL (1966) developed by Arcus was the first work under this

category, which has an added simulation model to handle task - time fluctuation.

Johnson (1983) has formulated a branch and bound algorithm to minimize

the number of stations permitting planned unbalance in the line and allowing

specific tasks to specific stations in this category of MMS problems.

Bolat (1997) has addressed the problem of how to sequence the jobs

defined by a set of operations so that a well-balanced mixed model assembly line

is utilized effectively for stochastic problems. The object of his work depends on

the management philosophy for completing the remaining work, which can not be

done within the predefined boundaries of stations. He has presented a

computational study of a general-purpose stochastic approach for scheduling a

minimum job set on a well-balanced Mixed Model Assembly Line. The objective

of his work is to minimize the total amount of work, which cannot be completed

by the operators within the predefined boundaries of their stations. He has adopted

linear programming approach to construct bound and develop efficient heuristics.

He has proposed a formula to determine prior bounds based on problem

parameters. He has developed multi pass procedures which are combinations of

Simulated Annealing with problem specific knowledge to get near optimal

solution. He has conducted extensive numerical experiments \\.1tl1 the test

problems generated randomly.

A brief presentation of the discussions of these sections of this chapter is

given in Table 2.1.

Remarks on the Summary of Literature on Assembly Line Baiancing :

1. Optimal solution methods are suitable only for srriall size problems.

When the number of tasks increases, these methods can not be used

because of the complexity involved in large-scale problems.

2. Heuristic methods, which are useful for large size problems, end up in

local optimum solutions.

3. Global Search Methods, which are obtaining global optimal solutions,

have the drawback of searching for near optimai solutions only to

limited extent because of the stopping criteria involved in them. Also.

they start with an inferior initial solution.

Hence, there is a need for designing a new method, which will take care of

the above mentioned difficulties.

Table 2.1 - Sumrnary of Iiitcrature on Assernbly 1,ine Balancing

1. Single Model Deterministic

Salveson (1 955) rr- -- - -- - - - - - - - - -- -

Method used for getting Type of solutiori 1

solution obtained Comments -- - -- - - - - - - -

SMI)) Assembly Line Balancing pr-obierns

Linear Programming - - -- - -- - - - -- - i Opt~mal Solution T1i1s 1s the first matliemat~cal for~nulat~on-for;

ALB. T h ~ s ~netliod led to dlffic~llty of split ----7 1 tasks in Lhc optima1 solution. . I

Integer P ~ o ~ ~ ~ ~ I I I I ~ ~ - ~ ~ s x ~ o ~ ~ I w ~ l m p i o v e m e n i over ~ a i ~ s o n ~ i

I I - -

Klein (1 963) 1,lnear - - Progi-an11111 / U p t m ~ a l ng Solullon / 7111s nlcihod generates il~lmbcl- of l~as tb lc /

1 solutions and sclccts the bcst one. - -

! - I

Thangavelu and Zero Optimal solution Tlus mehod is an mlprovci~~en t over I

l G u t j a h r and

/ Nernhauser ( I 974)

w o n & Abi-acl~t

/ (1975) and Talbot

1 and Patterson (1 984)

programming -- -- - - - - - - -

Algoritli17n based on fin~te T h ~ s illethod suggests that arc Icngth 01'; I

directed network I 1 network shoulil he mlnimom fix gct,111~:1

I

/ optimal solution. ---- - -- - -- - - 1 Integer I'rogramm~ng I 0ptimal ~ o l u t ~ o n I'hcse approaches r e d ~ ~ c e the proh~eni ' I- - I fosmolat~on to a considerable extent.

2.4 Focus of this Research

In this research. Deterministic Assembly Line Balancing problem is

considered for further investigation.

Optimal methods, which give optimal solutions iu A i B problems, are not

preferred because the amount of computational effort required for solving

moderately large problems is very high. Since ALB problems fall in the class of

combinatorial optimization category, the general heuristic nethods end up in local

optimum. Hence Global Search Methods (GSM) are preferred over other methods

as they give consistently good solutions which are near optimal and clearly better

than those provided by other lieuristic methods. Also, a large number of heuristics

available in the literature, have different objectives and they are useful for solving

only specific problems. But when the objective function or the nature of the work

element distribution changes, these types of heuristics may not be usehl. Since

Assembly Line Balancing is predominant in a variety of manufacturing processes,

under varying conditions. a genral method which can give fast acceptable

solutions for a variety of ALB problems is inevitable. So, the usage of Global

Search Methods is the right choice for solving larger ALB problems, since the

same algorithm can give good solutions for a variety of objective functions

without any modification in the algorithm.

But the available GSMs in the literature like Simulated Annealing method

proposed by Suresh and Sahu (1994), have some disadvantages, as discussed

earlier, which are given below.

(i) These methods stop the procedure to obtain the optimal solution

when the stopping criterion is reached.

(ii) They also start with an inferior initial solution.

So, the above two issues have to be properly addressed to get better optimal

solution. Hence, a new heuristic called, "'New Global Search Heuristic" r~lhich

addresses the above two issues for the Deternlinistic Assembly Line Balancing

probiem is developed in this work.

In Simulated Annealing (SA) and other Global Search Methods, the global

search is done only to certain extent because of the stopping criterion applied in

these methods. But this New Global Search Heuristic (YGSH), developed in this

research, searches to the fullest extent possibie to get near optimal solution.

Based on the review, the researcher also feels that in Heuristics for

Assembly Line-Balancing (HAL, Panneerselvam and Oudayasankar. 1993) totally

9 heuristics are considered based on different priority rules. Each of the 9

heuristics has been generated in different combinations of the priority rules

without fixing any weight to them. All the heuristics / priority rules may not have

equal impact on the solution. Hence in this work, the heuristics 1 priority rules are

prioritized by giving suitable weights through an experiment based on trial and

error method. Based on these weights to different priority rules? a new factor

called Composite Weight Factor (CWF) is ccmputed for each work element.

Whenever there is a tie while selecting a work element from the list-A (list of

eligible work elements) for assigning it into the current workstation, the tie is

resolved based on the maximum CWF.

Since Assembly Line Balancing problems come under combinatorial

optimization category, development of efficient heuristics is the only m-ay to solve

the problem. In view of this fact, a new heuristic, combining the above two, called

New Efficient Heuristic (NEHU) is developed in this work, which is explained

in Chapter 3.

In the proposed new heuristic, the Rest Initial Seed Is selected as the best of

the solutions of Heuristics for Assembly Line Balancing (HAL) and Composite

Weight Factor (CWF) heuristic. Qsing Nea. Global Search Heuristic (NGSI-I), the

initial seed is iterated to get near optimal solution. hloieuver, the pertbmance of

this new heuristic is compared with that of HAL. In this process, 12 Test problems

have been generated, which are presented in Annesure 11. These randomly

generated test problems have been tested using software developed in Visual

Basic. It has been demonstrated that the newly proposed heuristic performs

favourably, using an experimental design.

2.7 Summary

The researcher has made an attempt to classify the ALE3 literature at the

beginning of this chapter. Then he has reviewed comprehensively the AL,B

literature under various categories namely, Single Model Deterministic, Single

Model Stochastic, Multi /Mixed Model Deterministic and Multi / Mixed Model

Stochastic. Finally, the researcher has presented the focus of his research after the

extensive literature review.