Transcript Document

Assembly Lines – Reliable
Serial Systems
Active Learning
Module 1
Dr. César O. Malavé
Texas A&M University
Background Material
Modeling and Analysis of Manufacturing Systems
by Ronald G. Askin , Charles R. Standridge, John
Wiley & Sons, 1993, Chapter 2.
Manufacturing Systems Engineering by Stanley B.
Gershwin, Prentice – Hall,1994, Chapter 2.
Any good manufacturing systems textbook which
has detailed explanation on reliable serial systems.
Lecture Objectives
At the end of this module, the students should be
able to

Explain the fundamentals of assembly lines.

Explain the basics of problem formulation of
line – balancing problems.

Formulate the problem and solve them
Time Management
Introduction
5
Readiness Assessment Test (RAT)
5
Assembly Lines - Introduction
12
Spot Exercise
5
Problem Formulation
15
Team Exercise
5
Assignment
3
Total Time
50 Mins
Readiness Assessment Test (RAT)
Assume that there is a proposal for developing new
car. Enumerate the various and basic stages in the
development of this new product.
At the end, each team should turn in the solutions
and the instructor may ask a group to discuss with the
class.
RAT – Solution
Customers
Product
Features
Functions
Product
Design
Part
Design
Process
Planning
Fabricate
Assemble
Introduction
Assembly Line – Set of sequential workstations,
connected by a continuous material handling system.
Each Assembly activity divided into productive work
elements, adds value to product.
Group of such elements are assigned to each
workstation.
Assembly Lines rely on Principle of Interchangeability
and Division of Labor.
Principle of Interchangeability – Individual Components
that make up the final product must be interchangeable
Division of Labor – Work Simplification, Standardization
and Specialization.
Introduction – Cont…
Advantages of Assembly Lines



Ability to keep direct labor or machines busy doing work
Minimal setup requirements as products are repeated.
Less space required, lower inventory costs and shorter
throughput time.
Many items don’t justify assembly lines. So Mixed
lines are used.
Mixed Lines – Several products on the line in different
workstations at the same time.
Single or Multiple Assembly Lines depends on various
factors like economics, labor psychology etc.
Spot Exercise
Discuss the advantages & disadvantages of multiple
parallel lines
Advantages
Disadvantages
Easier to balance work load
between stations
Higher setup costs
Increased scheduling flexibility
Higher equipment costs
Job enrichment
Higher skill requirements
Work Independence
Slower Learning
Increased accountability
More complex supervision
Introduction – Cont…
Use of buffers increase productivity and flexibility.
Buffers provide the “Cushion Effect” in production.
Paced Lines – Each workstation given same amount
of time to operate on each unit of product.
Unpaced Lines – Each workstation removes a new
unit from the material handling system as soon as it
completes the previous unit.
Flexible Flow Lines – Product units routed thru
workstations based on task requirements & input
buffers. Also facilitates job enrichment & cycle time
balancing.
Problem Formulation
Objective is to minimize unit assembly cost.
Assembly Cost = Labor Cost + Idle Time Cost.
Assume
P  Production rate
M  Number of Parallel Lines
Cycle Time = m/p
No worker assigned with tasks exceeding the cycle
time.
Set IP shows the ordering constraints

IP = {(u, v): task u must precede v}
Problem Formulation – Cont…
Zoning Restrictions – Which tasks must be and must
not be assigned to the same workstation.


ZS  Set of tasks to be assigned
ZD  Set of tasks not to be assigned
Binary indicators used as decision variables
1, if task i is assigned to station k 
x 

ik 0, Otherwise

To minimize idle time, we try to force tasks into the
lowest numbered stations.
Unused stations will be discarded.
Problem Formulation – Cont…
The formulation becomes
N
Constraint ensures that the sum of
task times for the set of tasks
assigned to each workstation
doesn’t exceed the cycle time.
K
min  cik X ik
i 1 k 1
Subjectto
N
t X
i
i
ik
K
X
k 1
ik
C
1
h
X vh   X uj
k  1,...,K
i  1,..., N
h  1,...,K
j 1
K
X
k 1
uk
X vk  1
X uh  X vh  1
(u, v)  ZS
k  1,...,K
Constraint ensures that the task is
assigned to exactly one station
Constraint forces the adherence to
precedence restrictions
and (u, v)  IP
Zoning Constraint : Marriage Type
Zoning Constraint : Divorce Type
and (u, v) ZD
Problem Formulation – Cont…
Objective Function – Advantageous to fill up lower
numbered stations before opening new station.
Let K*  Number of station (workers) required by the
solution.
Balance Delay D, measure for comparing solutions,
proportion of idle time.
N
D
K * C   ti
i 1
K *C
Objective function fails to recognize a secondary
objective of allocating the idle time equally to all the
workstations.
Team Exercise
Develop a complete binary integer programming
formulation for the line balancing problem. Let C = 100.
Task
Time
Immediate
Predecessor
a
40
-
b
75
a
c
50
a
d
35
c
e
80
d
Team Exercise – Solution
e
Minim ise
4
 Cik X ik
Ci1 = 1; Ci2 = 20;
Ci3 = 400; Ci4 = 8000
i  a k 1
s.t.40X ak  75X bk  50X ck  35X dk  80X ek  100
k = 1,…,4
4
X
k 1
ik
1
for i  a, b, c, d , e
X b1  X a1


X b 2  X a1  X a 2


X b 3  X a1  X a 2  X a 3

X b 4  X a1  X a 2  X a 3  X a 4 
Likewise for (a, c),
(c, d) and (d, e)
All Xik
0 or 1
We Choose K = 4
as a start since
 ti / C = 2.8
Assignment
A manufacturer of communications equipment is
constructing a line to assemble several similar models
of speaker phones. An industrial engineer had divided
assembly of each model in to elemental tasks. Phones
require about 30 operations. Task times vary from 5 to
36 seconds. Determine the appropriate cycle time if
demand requires producing 750 phones per shift. Each
shift has 8 productive hours.