1

MIXED MODEL

ASSEMBLY LINE

BALANCING

(SAYAN CHAKRABORTY)

2

1. Introduction:

Layout decisions in a typical factory consist of the determination of placement of various

departments, work groups within the department, workstations, and machines within a production

facility. The basic objective of optimizing facility layout is to arrange the above mentioned elements

in a manner so that the operational output can be maximised and bottlenecks can be eliminated. A

good layout has immense importance on reducing bottlenecks in moving people or material,

minimizing material handling costs and improvement of resource utilization. It is also important in

order to achieve flexibility, resource utilization and improving safety in a production plant.

There are basically three basic types of layout (process layout, product layout, and fixed-position

layout) and one hybrid type (group technology or cellular layout) layout.

1.1. Process Layout:

A process layout or job- shop layout or functional layout is a layout in which similar equipment

are grouped together, Process layouts are designed to increase economies of scale, allowing

individual processes to function more efficiently by pooling resources and is ideal for large

volume productions.

Fig: 1 Process layout

1.2. Product layout:

Product layout groups different workstations together, and have the advantage of keeping

specific production jobs relatively contained. This is advantageous for low-volume goods that

require a good deal of communication between workers at different stations. In a fixed-position

layout, the product remains at one location. Manufacturing equipment is moved to the product,

and useful for bulky product making industry like ship, aeroplane industries.

3

Fig: 2 Product layout

1.3. cellular layout:

In the hybrid type or cellular layout, dissimilar machines are grouped together to work on the

products having similar shapes or processing requirements.

Fig: 3 Cellular layout

The basic difference between a product layout and process layout is the pattern of workflow. In

product layout, equipment or departments are dedicated to a particular product line, duplicate

equipment is employed to avoid backtracking, and a straight-line flow of material movement is

achievable.

4

2. Definition of Assembly lines:

Since Henry Ford’s introduction of Assembly lines in the year 1913, the assembly line balancing

problem (ALBP) has been of significant industrial importance. In general sense, the assembly lines

are a special type of product layouts, developed specially for mass production. The term assembly

line refers to a progressive assembly linked by some kind of material handling device. Line balancing

is very useful in dividing a complex work structures into number of elemental tasks and removing

bottlenecks. The basic objective of line balancing is to arrange the individual processing and

assembly tasks at the workstations so that the total time required at each workstation is

approximately the same.

Fig: 4 Assembly Lines

3. Types of Assembly line balancing:

Assembly line balancing can be classified into three general models. These models are i) Single

model assembly lines and ii) Mixed model assembly lines and iii) Multi model assembly line.

i. Single model assembly line: If only a single model is assembled in the line, then the system is

defined as single model assembly line.

ii. Mixed model Assembly line: In mixed model assembly lines, all models which are variation of

the same base product but different in attributes are assembled.

iii. Multi model assembly line: In this system, the assembled products are not homogeneous

and more than one type of models is assembled in the line.

5

4. Application of Assembly line:

A single model assembly line is useful when many units of one product are required, and there is no

variety among the products. This is typically applicable to products with very high demand. Batch

model line and mixed model line are produced to more than one model. The difference lies between

batch model line and mixed model line is that for the batch model line, product variety is more

significant than mixed model line. Hence A batch model line produces each model in batches. After

one batch of the product is produced, change in the setup of the assembly line is incorporated in

order to facilitate the production of new model variety. Sequence of tasks is usually different

between models and tools used at a given workstation for the last model might not be the same as

those required for the next model. For these reason, newer setup is required before production of

each batches so production time lost is evident on batch assembly line.

This problem can be rectified by using mixed assembly line where product variety is relatively low as

the models are not produced in batches; instead, they are simultaneously produced on the same

line. Two different models can be worked in two subsequent workstations in mixed assembly line

problem. The major example of mixed model assembly line is seen in automobile industries. In

mixed product assembly line, each workstation is capable of producing multiple tasks required over

a range of models.

Due to this advantage, mixed assembly line problem eliminates the drawbacks of lost production

times and high inventories associated with batch line assembly. But designing the mixed assembly

line is much complex as to determine the sequencing the models to the workstations and getting the

right part to each workstations at the required time is a difficult task.

Line type Product Variety

Single None

Batch Substantial Product variety

Mixed Small Differences

6

5. Mixed model assembly line balancing:

The concept of mixed model assembly line balancing evolved when any particular item does not

have sufficient demand to initiate a separate assembly line but may be part family of separate

products can. Just-in –time manufacturing concept brings significant focus on producing variety of

items on the same assembly line. So the need of mixed model assembly line evolves. As the cost of

building an assembly line is very high, it is preferable to simultaneously produce one model with

different features or several models on a single line for cost effectiveness. The mixed assembly line

balancing problem (MALBP) can ensure smooth production and cost effectiveness when more than

one product or model is manufactured on an assembly line.

6. Background of the problem:

In order to meet the growing demand of the market, it is essential to reach the customers in a short

lead time. Also, when the product life cycles are short and the variety is high, different models of

product must be produced in a small lot size with adequate flexibility. Also, assembly systems must

achieve high productivity, uniform and good quality with low cost.(Thomopoulos,1967) Mixed model

assembly line balancing can efficiently handle variety in productions, but if the variety goes very high

than overall system performance is degraded along with the quality and productivity of the system.

(Hadi et Al, 1997)

7

7. Review of the past researches:

General mixed model assembly line balancing problem

Author (Year) Objective Solution approach Major assumptions

Thomopoulos Nick. T

(1967)

Development of a

heuristic for solving

MALP problem adopting

single assembly line

balancing technique.

Each model in the

MALP problem is

considered separately

and the line balancing

and model sequencing

of the system is

considered

individually.

Sequencing is used to

increase the efficiency

of the line.

In order to solve the

sequencing problem,

work delay and labour

skills are not taken into

account.

Hadi et Al. (1997) For a number of given

models, assigning the

tasks to an ordered

sequence of stations

such that the

precedence relations are

satisfied and

performance measures

are optimized.

An integer

programming model is

developed that can be

used to solve the

MALP problem.

WIP is not allowed and

common tasks of

different models are

assigned to the same

station. Also, parallel

stations are not

allowed and all the

tasks have the same

predecessor and

successor.

Erdal et Al. (1999) Shortest route

formulation of the

mixed-model assembly

line balancing problem

that leads to the optimal

solution.

The mixed-model

version of the problem

is transformed into a

single-model version

with a combined

precedence diagram.

Set of common tasks

across the models are

assumed to exist.

8

Computer assisted mixed model assembly line problem

Author (Year) Objective Solution approach Major Assumptions

Macaskill et

Al. (1972)

Assembly of different models of

the same general product on

one production line and

allocation of even work to

operators to increase model

sequence efficiency.

Balance efficiency

and speed of

computation is

considered. A

balance problem is

formulated and the

associated

difficulties are

noted.

List of task available for

assignment is constant

over time and work in

different stations are

independent.

DePuy et Al.

(2000)

Scheduling the individual

activities of a project to

minimize the overall completion

time of the project.

COMSOAL

(Computer Method

of Sequencing

Operations for

Assembly Lines)

Resource is constant over

time and known.

Mixed model assembly line balancing operating under JIT concept

Author (Year) Objective Solution approach Major Assumptions

Miltenburg

(1990)

Determine the optimal JIT

production schedule for a mixed

model facility.

Dynamic

Programming

approach,

heuristics.

Rate of assembly process is

always constant.

Bard (1989) Develop an algorithm to

effectively solve assembly line

balancing problem where both

stations and tasks are paralleled,

taking into account the

unproductive time at the

workshop.

Dynamic

programming

approach.

Task times are always

constant.

Miltenburg et

Al. (1989)

Make the parts usage of the

whole line constant in order to

meet JIT philosophy.

Scheduling

algorithm &

heuristics.

All products do not have

same operation time and

few tasks have relatively

long operation time.

9

Sequencing Scheduling and Mixed-model Assembly Line Balancing

Author (Year) Objective Solution approach Major Assumptions

Merengo et Al.

(1999)

Minimizing the rate of

incomplete jobs and probability

of starvation and WIP in

Balancing

methodology

heuristics and

simulation based

tests for effective

solution to the

sequencing

problem.

Every model has a single

non-cyclical precedence

diagram. Processing time

for each task is constant and

known.

David (1995) Maximize the workstation

throughput or minimize the

number of workstations.

Dynamic

programming

approach,

sequence

heuristics.

Assembly times are

assumed to be increasing as

the operation is delayed.

Raouf et Al.

(1980)

Prioritize the elements in the

assembly line to determine

minimum number of

workstations under a

predetermined cycle time.

Heuristic method

executed by

FORTRAN program.

The work element time is

considered to be invariant.

Nevins (1972) Minimizing the number of

workstation needed in order to

meet production rate by

evaluation of relative merits of

alternative paths for the

sequencing problem.

Best bud heuristics,

branch & bound

technique.

Relative parameters are

constant and known over

time.

10

Mixed-model Assembly Line Balancing by alternative approach

Pedro Et Al.

(1994)

Minimize the number of

workstations along the line, for

a given cycle time, and to

balance the workloads

between and within

workstations.

Simulated

annealing

approach

Planning horizon is fixed and

each model has its own set of

precedence relationships.

Mirzapour et Al.

(2009)

Installation of a bypass sub-line

which processes a portion of

assembly operations of

products with relatively longer

assembly times.

Hybrid algorithm

based on Genetic

Algorithm (GA).

Stations are balanced i.e.

number of stations are known.

Kara et Al.

(2011)

Duplication of common task in

order to improve efficiency of a

mixed assembly line.

Fuzzy goal

programming

approach.

Common tasks exist and task

completion time is known.

Sekar et Al.

(2013)

Minimize work overload and

station to station work flow.

Weighted multi

objective based

Optimization

Method

There can be parallel machine

in some stations

Mixed-model Assembly Line Balancing in the context of setup cost minimization

Author (Year) Objective Solution approach Major Assumptions

Trvino Et Al.

(1993)

Minimize the setup cost

considering inventory carrying

cost, setup cost, storage cost,

setup time reduction cost and

quality cost.

A general equation

is drawn and goal

programming

approach is

adopted.

Relationships between the

parameters are known and

analyst can provide the values

directly.

Lee (1994) Setup time and lot size

reduction

Goal programming

approach.

All the models are of the same

general product, current lot

size is enough to meet market

demand. Model changeover is

possible without any WIP.

11

8. Solving a Mixed model Assembly line problem:

The manual mixed model assembly line can be discussed in the context of three technical issues. The

issues are

1) Determination of the number of workers

2) Solving of line balancing problem

3) Model launching.

8.1. Determining the number of workers:

It is useful to compute a theoretical minimum number of workers that will be required on the

assembly line to produce a product with known work content time.(total time of all work

elements that must be performed on the line to make one unit of the product( ), and

production rate ( ).

Steps to determine the theoretical minimum number of worker:

Step 1: Total workload/hour. (WL) to be calculated

∑

Step 2: Calculate the available time/ hour/worker. (AT)

Step 3: Theoretical minimum number of worker is

Where WL = workload (min/hr.); = production rate of model j (pc/hr.]: = work content

time of model j (min/pc); P = the number of models to be produced during the period: and j is

used to identify the model, j = 1, 2 …, P. repositioning efficiency is and line balance efficiency

is .

12

Example 1: The hourly production rate and work content time for two models to be produced

on a mixed model assembly line are given in the table below. Also given is that line efficiency E =

0.96 and manning level is 1. Determine the theoretical minimum number of workers required on

the assembly line.

Model Required Production unit/ hour Total work content time

A 4 27.0

B 6 25.0

Solution:

i) Calculate the Total workload/hour:

∑

Or, WL = (4*27) + (6*25) min/ hour

Or, WL = 258 min/ hour

ii) Calculate the Available time/ hour:

Line efficiency is given as .96, Manning level is given one worker each station.

So, Available time (AT) = 60 * .96 = 57.6 min/hour/worker

iii) Calculate the theoretical minimum number of workers:

0r,

Or,

So, theoretical minimum number of workers = 5

13

8.2. Mixed Model Line Balancing:

The algorithms used to solve line balancing problem for mixed assembly line balancing are

usually adaptation of methods developed for Single model lines. In single model line balancing,

work element times are utilized to balance the line, whereas in mixed model assembly line

balancing, total work element times per shift or per hour are used. The objective function can be

expressed as follows:

Or, ∑

Where W is number of work stations, AT= available time in the period of interest, WL = work

load to be achieved during same period (min), and is total service time at station i to

perform its assigned portion of the workload (min).

Steps for Mixed model Line balancing:

Step 1: Respective precedence diagrams for all the models to be drawn.

Step 2: All the precedence diagrams to be combined into one precedence diagram.

Step 3: Total time required for each element in each model to be calculated and summed.

∑

Where = total time within the workload that must be allocated to element k for all products

(min).

Step 4: Compute new required production rate (Rp) by summing required production rate of

each elements.

Step 5: Cycle time (Tc) for the combined assembly line to be computed.

Minute

Step 6: Total available time ) is to be computed.

Step 7: Elements are to be allocated to workstations by any single line balancing algorithm.

14

Example 2: For the two models Y and Z, hourly production rates are: 4 units/hour and 6

units/hour for Y & Z respectively. Most of the work elements arc common to the two models,

but in some cases the elements take longer for one model than for the other. The elements,

times, and precedence requirements are given in the following Table. Also given: E = 0.96 %,

repositioning time Tr = 0.15 min. and manning level is one.

(a) Construct the precedence diagram for each model and for both models combined into one

diagram.

(b) Use the Kilbridge and Wesler method to solve the line balancing problem.

(c) Determine the balance efficiency.

Work element

(K) Time on model Y Preceded by Time on model Z Preceded by

A 3 - 3 -

B 4 1 4 1

C 2 1 3 1

D 6 1 5 1

E 3 2 - -

F 4 3 2 3

G - - 4 4

H 5 5,6 4 7

15

Solution:

Step 1: Draw the precedence diagram for model Y

Precedence diagram for model Y

Step 2: Draw the precedence diagram for model Z

Precedence diagram for model Z

A C

D

H F

E B

3

6

2

4 5

4 5

3

5

3 2 4

A C

D

H F

G

B

4

4

16

Step 3: combine the precedence diagram for Y & Z

Precedence diagram for the combined model

Step 4: Compute the total time required for each element in each model

Total time required, ∑

Element (K) ∑

A 4*3 = 12 6*3 = 18 12 + 18 = 30

B 4*4 = 16 6*4 = 24 16 + 24 = 40

C 4*2 = 8 6*3 = 18 8 + 18 = 26

D 4*6 = 24 6*5 = 30 16 + 30 = 54

E 4*2 = 8 6*0 = 0 8 + 0 = 8

F 4*4 = 16 6*2 = 12 16 + 12 = 28

G 4*0 = 0 6*4 = 24 0 + 24 = 24

H 4*5 = 20 6*4 = 24 20 + 24 = 44

A C

D

H F

E B

G

YZ

YZ

YZ

YZ

Y

YZ

Z

YZ

17

Step 5: Arrange the elements in column according to the combined precedence diagram.

Element Column TTk Preceded by

A I 30 -

B II 40 1

C II 26 1

D II 54 1

E III 8 2

F III 28 2

G III 24 2

H IV 44 2

Step 6: Compute the new required production rate, cycle time and available time.

New required production rate is (6 + 4) = 10 units/hour

Step 7: Compute the new cycle time and available time.

Cycle time is given as

Or,

= 5.76 min.

Repositioning time is given as 0.15 minute.

So,

Service time (TTS) = cycle time (TC) – repositioning time (Tr)

Or, service time = 5.76 – 0.15 = 5.61 minute

18

So

Repositioning efficiency = Service time (TTS) / Cycle time (TC) = 5.61 / 5.76 = 0.974

Hence, the total available time (AT) can be calculated as-

Or,

Step 8: Solve the problem using the Kilbridge and Wesler method

Workstation Element TTk (minute) TTsi(minute)

1

A 30

C 26 56

2 D 54 54

3

B 40

E 12 52

4

F 28

G 24 52

5 H 44 44

∑258

Step 9: Compute the balance efficiency

The balance efficiency is determined by Max {TTsi} = 56 minute.

So, balance efficiency,

{ }

19

8.3. Model launching in Mixed model lines:

Launching of base parts at the beginning of the line is relatively a simple process in a single

model line as the time interval is constant and set equal to the cycle time, . But in a mixed

model line, it is more complicated as each of the models may have a different work content

time, which translates into different station service time. Hence, the time interval between

launches and the selection of which model to launch are interdependent for mixed model line.

For the mixed model line, the solution of the model launching and line balancing problems are

closely related. The solution of the model launching problem depends on the solution of line

balancing problem. The model sequence must be same that of the line balancing problem.

Time interval between successive launches is called launching discipline in mixed model line.

There are two alternative launching disciplines available. They are;

I) variable rate launching

II) Fixed rate launching.

I. Variable rate launching:

The advantage of variable rate launching is that units can be launched in any order without

causing idle time or congestion at workstations. In this method, the time difference between

two successive launches is kept equal to the cycle time of the current unit. The cycle time and

launch intervals vary with every launches, as different models have different task times per

station. The time interval in variable rate launching can be expressed as follows:

Steps for determining variable launching rate:

i) Determine number of workers (w) on the line.

ii) Determine total work content time ( ) of a particular model.

iii) Determine repositioning efficiency & balance efficiency .

iv) variable rate launching =

Where is the time interval before the next launch in variable rate launching (min), is

the work content time of the product just launched (model j) (min), w is the number of workers

and are the repositioning efficiency and balance efficiency respectively.

20

Variable rate launching has a few logistical and technical setbacks. Deliver the required

components and subassemblies to the workstations at any given moment are difficult, also,

work units cannot be attached to the conveyor matching with the variable rate launching

interval. Due to these flaws, fixed rate launching is often preferred over variable rate launching

method.

Example 3: Determine the variable rate launching intervals for models Y and Z in previous

examples. Repositioning efficiency (E,) is 0.974 and balance efficiency (Eb) = 0.921.

Solution: Variable launching rate,

For model Y,

For model Z,

So, when a unit of model A is launched onto the front of the line, 6.020 min must elapse before

the next launch. Again, when a unit of model B is launched onto the front of the line, 5574 min

must elapse before the next launch.

II. Fixed rate launching:

In fixed rate launching, the interval between launching of two models is kept constant. The

interval is usually kept taking the speed of the conveyor and the distance between work carriers

into account. It is important that the schedule is at per with the available man power on the

assembly line else there will be either station congestion or starving on the assembly line.

Steps for fixed rate launching:

i) Determine production rate (RPj) of a model.

ii) Determine work content time (Twc) of a model.

iii) Determine production rate of all models (RP) in the schedule.

iv) Launching time interval is determined as

∑

21

Where is defined as the time interval between two launch, Is the production rate of

model j, is the work content time of model j, is the production rate for all models, p is

the number of models and denotes number of workers, reposition efficiency and

balance efficiency respectively.

Congestion and idle time can be identified in each successive launch by the following expression:

∑ )

Where id the fixed rate launching interval, m = launch sequence during the period of

interest, h = launch index number for summation purpose and is the cycle time associated

with model j in launch position h (min), calculated as follows:

If the value of the above expression is positive, then congestion is recognized, which means that

the actual sum of task times for the models thus far launched (m) exceeds the planned

cumulative task time. Otherwise, there will be idle time on the assembly line. In order to

minimize both congestion and idle time, the following model is proposed, (Groover M.P, 2002).

Example 4:

Determine the fixed rate launching intervals for models Y and Z in previous examples. Repositioning

efficiency (E,) is 0.974 and balance efficiency (Eb) is 0.921.

Solution:

The combined production rate of model Y & Z is 6+4 = 10 units/ hour.

Total work content time for two models is 27 min & 25 min respectively

Theoretical number of workers, w = 5

So, Launching time interval,

∑

Or,

{ }

= 5.752 minute.

22

8.4 An alternatives approach to solve mixed assembly line balancing problem:

(Şeker, Özgürler, & Tanyaş, 2013) considers the objective of minimizing the work overload and

station-to-station product flows. The authors have developed a multi objective mixed-integer

programming (MOMIP) model to optimize these two criteria. They made the following

assumptions while formulating the model:

i. Each assembly task must be assigned to at least one station.

ii. There are parallel machines in some stations.

iii. Total space required for the tasks assigned to each station must not exceed the station’s

finite work space available.

iv. Each product must be routed to the stations subject to precedence relations defined by

its assembly plan.

v. Revisiting of stations is not allowed.

vi. Each station can perform at most one task at any given time.

vii. Transfer times between stations are not negligible.

The following notations are used in the model;

Indices:

: assembly station ∈ 𝐼, 𝐼 = {1, . . . , }

: assembly task ∈ = {1, . . . , }

: parallel machine at station {ℎ = 1, . . . , }

𝑘: product, 𝑘 ∈ 𝐾 = {1, . . . , V}

: assembly sequence, ∈ 𝑆 = {1, . . . , }.

Input Parameters:

𝑎 : working space of station for task .

𝑏 : working space for station 𝐼.

: number of parallel machines in station 𝐼.

𝑘: process time for task of model 𝑘.

23

𝑞 : transportation time from station to station .

I : the set of stations capable of performing task .

J𝑘: the set of tasks required for product 𝑘.

R : the set of immediate predecessor-successor pairs of tasks ( , ) for assembly

sequence ∈ 𝑆 such that task must be performed immediately before task .

S𝑘: the set of assembly sequences available for product 𝑘.

T : the set of tasks in assembly sequence .

Decision Variables:

= 1, if assembly sequence ∈ 𝑆 is selected; otherwise 0;

𝑥 = 1, if task is assigned to station ∈ 𝐼 ; otherwise 𝑥 = 0;

ℎ = 1, if task is assigned to parallel machine ℎ in station ∈ 𝐼 ;

Otherwise ℎ = 0;

= 1, if product in sequence is transferred from station after the completion of

task to station to perform next task; otherwise = 0;

𝑃max is the maximum station workload (cycle time).

𝑄sum represents the weighted sum of total assembly and transportation time.

The following decision variables are introduced to model the loading and routing problem:

α: the weight factor (0 < 𝛼 < 1),

: a big number

24

The problem can be stated as

𝛼𝑃 𝛼 𝑄 (1)

Subject to,

∑ ∑ ∈ ; (2)

∑ ; ∈ Ir, ( , ) ∈ , ∈ 𝑆 (3)

∑ ∑ ∑ 𝑃 ∈ ∈ ∈ ; ∈ 𝐼, ℎ ∈ 𝐻, (4)

∑ ∈ ∑ ∑ ∑ ∈ ∈ ∈ 𝐼, j ∈ J (5)

∑ ∑ ∈ ; ∈ 𝐼, ℎ ∈ 𝐻, s ∈ S (6)

∑ ∑ ∑ ∑ 𝑞 𝑄 ∈ ∈ ∈ ∈ (7)

∑ ∈ j ∈J (8)

∑ 𝑎 𝑥 ∈ 𝑏 ; ∈ 𝐼 (9)

∑ 𝑎 𝑏 ∈ ; ∈ 𝐼, ℎ ∈ 𝐻, s ∈ S (10)

∑ ∑ ∑ ∑ ∈ ∈ ∈ ; (11)

[ ][ ][ ][ℎ] [ ]; ∈ 𝐼, j ∈ J, ℎ ∈ 𝐻, s ∈ S (12)

𝑥 ; ∈ Ij, l I, l ∈ Lr, (j,r) ∈ , s ∈ S (13)

𝑥 ; ∈ Ij, l I, l ∈ Lr, (j,r) ∈ , s ∈ S (14)

; ∈ Ij, l I, l ∈ Lr, (j,r) ∈ , s ∈ S (15)

∑ ∈ ; k ∈ K (16)

∑ ∑ ∑ ∑ ∈ ∈ ∈ (17)

∑ ∑ ∑ ∑ ∈ ∈ (18)

∑ ∑ ∈ ; s ∈ S, j ∈ J, i ∈ I, h ∈ H (19)

25

Description of the model

i. The objective function is the minimization of the weighted maximum workload 𝑃max and

sum of transportation time 𝑄sum.

ii. Equation (2) shows for each product and assembly sequence selected that all of its required

tasks are allocated among the stations.

iii. Equation (3) is the flow of tasks for each station, for selected assembly sequence, and for

successively performed tasks.

iv. Equations (4) and (7) ensure the workload of the bottleneck station with parallel machines

and the total transportation time, respectively.

v. Equations (5) and (6) define the tasks that are assigned to at least one machine and not

more than all “ ” parallel machines of such a station “ ” when the product moves from

station “ ” to station “ ” to perform task “ ”.

vi. Equation (8) ensures that each task is assigned to at least one station, and by this, it admits

alternative assembly routes for products.

vii. Equation (9) is the station capacity constraint.

viii. Equation (10) shows the total flexibility capacity of all parallel machines at related station.

ix. Equation (11) represents the capacity constraint of the number of parallel machines in

station “ ”.

x. Equation (12) shows that if the sequence “ ” is not selected, all variables of related

sequence are made zero. Equation (12) shows that if we do not select any sequence, we

make all of variables in this sequence zero.

xi. Equations (13), (14), and (15) ensure that each product successively visits stations where the

required tasks may be assembled subject to precedence relations defined by the assembly

sequence selected.

xii. Equation (16) ensures that only one assembly sequence is selected for each product.

xiii. Equation (17) eliminates upstream flow of products in a unidirectional flow system.

xiv. Equation (18) eliminates assignment of tasks and products to inappropriate stations.

xv. Equation (19) ensures that all tasks, which are in the same “ ” sequence, are assigned to the

same station and the same parallel machine and that also the tasks of the same product

models are assigned to the same station and the same parallel machine.

26

Solution Approach

i) Multi objective integer programming problems may be thought as an extension of the

classical single objective integer programming problem.

ii) The weighted sum (WS) method is used to solve multi-objective integer programming

problem.

iii) The weighted sum (WS) method involves a linear or convex combination of the

objectives 𝑥 each objective is multiplied by a normalized weight factor

and the product added to give the scalar objective 𝑥 .

𝑥 ∑ 𝛼 𝑥

Where p is the number of objectives, 𝛼 = 1 and 𝛼 > 0, i = 1,.….p.

iv) To solve the underlying multi-objective mixed integer programming model, ILOG OPL

optimization software can be used.

The drawbacks of this method:

i. It misses solution points on the nonconvex part of the Pareto surface.

ii. Its diversity cannot be controlled; therefore even the distribution of weights does not

translate to uniform the distribution of the solution points.

iii. The distribution of solution points is highly dependent on the relative scaling of the

objective.

9. Research issues in Mixed Model Assembly line balancing:

In today’s competitive market, it is very important to implement more flexible production systems

that respond rapidly with the change of market demand in terms of producing more versatile

products in a short lead time. Hence balancing assembly line is a very important issue. Majorly, In a

MALB problem, efficiently balance the line is one of the most challenging tasks. Also, to increase the

overall performance, other strategic and operational decisions are to be taken. The MALB problem

can be solved either by minimizing the number of workstations for a given cycle time or minimizing

cycle time for a given number of workstations. Material movement is an important aspect in MALB

problem, also, transportation time often increase the total production time in MALB. So, optimal

routing of the parts and assigning of equal assembly time towards stations are the major issues in

MALB problem.

27

10. Conclusion:

The assembly line balancing problem (ALBP) has had significant industrial importance since Henry

Ford’s introduction of the assembly line. Assembly lines can be classified as “single model,” “multi

model,” and “mixed model” with respect to the number of different products assembled on an

assembly line. Mixed model assembly line has significant importance improving the production

efficiency in terms of varying market demand. Mixed model assembly line is also very important to

meet the goals of JIT production and in order to reduce inventory, setup and attain higher

production.

Historically, the focus almost always has been on full utilization of human labor; that is, to design

assembly lines minimizing human idle times. But newer views are much more practical and

intentions are to incorporate greater flexibility in the number of products manufactured on the line,

more variability in workstations (such as size, number of workers), improved reliability (through

routine preventive maintenance), and high-quality output (through improved tooling and training).

Balancing mixed-model is a difficult task and sequencing of task even makes it more difficult for

computation. But mixed model assembly line balancing has been recognized as a major enabler to

handle product variety, and can be found in most of the industrial environment today. With the

growing trend for product variability and shorter life cycle, they are slowly replacing the traditional

mass production assembly line.

28

11. References:

Al-e-Hashem, S., & Aryanezhad, M. (2009). An efficient method to solve a mixed-model assembly line sequencing problem considering a sub-line. World Applied Sciences Journal, 6(7), 168–181.

Balancing-sequencing, L., Author, M. A., Source, N. T. T., Series, A., & Url, I. S. (2015). Line balancing-sequencing for mixed-model assembly , 14(2).

Bard, J. F. (1989). Assembly line balancing with parallel workstations and dead time. International Journal of Production Research, 27(6), 1005–1018.

Ben-Arieh, D. (1995). Line balancing for non-traditional assembly lines, mixed models, and sequence-dependent assembly times. International Journal of Computer Integrated Manufacturing, 8(4), 286–297.

Gokcen.H.(1998). Binary Integer formulation for mixed model assembly line balancing problem. Computers & Industrial Engineering, 34(2), 451-461

Bukchin, J. (1998). A comparative study of performance measures for throughput of a mixed model assembly line in a JIT environment. International Journal of Production Research, 36(10), 2669–2685.

Bukchin, J., Dar-El, E. M., & Rubinovitz, J. (2002). Mixed model assembly line design in a make-to-order environment. Computers & Industrial Engineering, 41(4), 405–421.

Chang, H., & Chang, T. (2010). Simultaneous Perspective-Based Mixed-Model Assembly Line Balancing Problem, 13(3), 327–336.

Choudhary, S., & Agrawal, S. (2014). Mixed-Model Assembly Line Balancing Problem : A Focus on Model Formulation, (Aimtdr), 12–15.

Chutima, P. (2010). Mixed-Model U-Shaped Assembly Line Balancing Problems with Coincidence Memetic Algorithm. Journal of Software Engineering and Applications, 03(04), 347–363.

DePuy, G. W., & Whitehouse, G. E. (2000). Applying the COMSOAL computer heuristic to the constrained resource allocation problem. Computers and Industrial Engineering, 38(3), 413–422.

Mikell P. Groover. (2002). Automation, Production Systems, and Computer-Integrated Manufacturing, 3rd

edition, PHI publication.

Erel, E., & Gokcen, H. (1999). Shortest-route formulation of mixed-model assembly line balancing problem. European Journal of Operational Research, 116(1), 194–204.

Gökçen, H., & Aǧpak, K. (2006). A goal programming approach to simple U-line balancing problem. European Journal of Operational Research, 171(2), 577–585.

Kara, Y., Özgüven, C., Seçme, N. Y., & Chang, C. T. (2011). Multi-objective approaches to balance mixed-model assembly lines for model mixes having precedence conflicts and duplicable common tasks. International Journal of Advanced Manufacturing Technology, 52(5-8), 725–737.

Lee, S. M., Everett, A. M., & Melkonian, J. H. (1994). Optimizing lot size and setup time in a JIT environment: a multiple objective application. Production Planning & Control, 5(3), 308–319.

Merengo, C., Nava, F., & Pozzetti, a. (1999). Balancing and sequencing manual mixed-model assembly lines. International Journal of Production Research, 37(12), 2835–2860.

29

Miltenburg, J., Steiner, G., & Yeomans, S. (1990). A dynamic programming algorithm for scheduling mixed-model, just-in-time production systems. Mathematical and Computer Modelling, 13(3), 57–66.

Miltenburg, J. (2011). Level Schedules for Mixed-Model Assembly Lines in Just-in-Time Production Systems *. Management, 35(2), 192–207.

Nevins, a. J. (1972). Assembly Line Balancing using Best Bud Search. Management Science, 18(9), 529–539.

Raouf, a., Tsui, C. L., & El-Sayed, E. a. (1980). A new heuristic approach to assembly line balancing. Computers & Industrial Engineering, 4, 225–234.

Scheloribates, I., Badejo, M. A., Woas, S., & Beck, L. (2002). Assembly Systems and Line Balancing. a B, 86, 1–60.

Şeker, Ş., Özgürler, M., & Tanyaş, M. (2013). A weighted multiobjective optimization method for mixed-model assembly line problem. Journal of Applied Mathematics, 2013(i).

Lastra. J.(2015). Production-line balances for mixed-model lines , 19(4), 423–434.

Sivasankaran, P., & Shahabudeen, P. (2014). Literature review of assembly line balancing problems. The International Journal of Advanced Manufacturing Technology, 1665–1694.

Systems, A. (n.d.). Tambe, P. Y. (2006). Balancing Mixed-Model Assembly Line To Reduce Work Overload in a Multi-Level Production System, (May), 1–74.

Thomopoulos, N. T. (1970). Mixed Model Line Balancing with Smoothed Station Assignments. Management Science, 16(9), 593–603

Trevino, J., Hurley, B. J., & Friedrich, W. (1993). A mathematical model for the economic justification of setup time reduction. International Journal of Production Research, 31(1), 191–202.

Uddin, M. K., Luis, J., & Lastra, M. (n.d.). Assembly Line Balancing and Sequencing, (section 2).

Van Zante-de Fokkert, J. I., & de Kok, T. G. (1997). The mixed and multi model line balancing problem: a comparison. European Journal of Operational Research, 100(3), 399–412.

Vilarinho, P., & Simaria, A. (2002). A two-stage heuristic method for balancing mixed-model assembly lines with parallel workstations.

Xu, W., & Xiao, T. (2011). Strategic robust mixed model assembly line balancing based on scenario planning. Tsinghua Science and Technology, 16(3), 308–314.

Zhang, Y., Luh, P. B., Yoneda, K., Kano, T., & Kyoya, Y. (2000). Mixed-model assembly line scheduling using the Lagrangian relaxation technique. IIE Transactions, 32(2), 125–134.

Zhu, X., Hu, S. J., Koren, Y., & Marin, S. P. (2008). Modeling of Manufacturing Complexity in Mixed-Model Assembly Lines. Journal of Manufacturing Science and Engineering, 130(5), 051013.