Transcript Document

Sequencing Mixed Models &
Unpaced Lines
Active Learning
Module 4
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,
Manufacturing Systems Engineering by Stanley B.
Gershwin, Prentice – Hall,1994, Chapter 2.
Any good manufacturing systems textbook which
has detailed explanation on mixed models and
unpaced lines.
Lecture Objectives
At the end of this module, the students would be
able to



Explain the fundamentals of sequencing mixed models.
Explain the basics of unpaced lines.
Solve various problems related to these topics.
Time Management
Introduction
3
Readiness Assessment Test (RAT)
5
Sequencing Mixed Models
15
Team Exercise
10
Unpaced Lines
9
Summary
5
Assignment
3
Total Time
50 Mins
Readiness Assessment Test (RAT)
Discuss the basic features of Group Technology Layout
and Just-In-Time Layout
RAT – Solution
• Group technology (GT) layout
– Dissimilar machines are grouped into work centers or cells
– Similar to process layout in that cells are designed to perform a specific
set of processes
– Similar to product layout in that cells are dedicated to a limited range of
products
• Just-in-Time layout
– Flow line similar to an assembly line
• Equipment and workstations arranged in sequence
– Job shop or process layout
• Focus on simplifying material handling
Sequencing Mixed Models
Several different products can be assembled
simultaneously on the line.
Products are generally classified as
 Type 1 – Products with constant ratio of item task
time to average item task time.
 Type 2 – Products with independent station
requirements.
Sequencing Mixed Models
Let
qj → Proportion of product type j, j=1,…,P
tij → Time to perform task I on product type j
Sk → Set of tasks assigned to workstation k
An average feasibility is
P
 q t
iS k j 1
j ij
C
k  1,....,K
Sequencing Mixed Models
For each item ‘j’, Qj items to be produced
‘r’ be the greatest common denominator of all Qj.
Cycle repeats for r times to satisfy demand.
Repeated cycle consists of Nj = Qj / r
Bottleneck station kb is the station with maximum
total work. kb = argmaxkCk
Xjn be 1 if item j is placed in nth position & 0
otherwise
j(n) denotes the type of item placed nth
Sequencing Mixed Models
Selecting the nth item to be entered in the line is to
optimize the following problem
n
min max 
1 n  N
t
j 1 iS
N
Subject to
X
jn
n 1
nN j
N
n
i, j (n)
 nCk b
kb
 Nj
n
nN j
h 1
N
 S1   X jh 
P
  t
h 1 j 1 iS k
X jn
ij
………
1
n = 1,.., N & j = 1 ,…, P ...
2
n = 1,.., N & k = 1 ,…, K …
3
j = 1,.., p
 S1
X jh  (n  S 2 )Ck
0 or 1
Sequencing Heuristics
Step 0 : Initialization. Create a list of all products to be
assigned during the cycle. This is List A
Step 1 : Assign a Product. For n = 1,….,N from List A,
create a List B of all product types that could be
assigned without violating any constraint. From
List B select the product type ( j*) that minimizes
n
 t
j 1 iS
i, j (n)
 nCk b
kb
Add product type j* to the nth position. Remove a
product type j* from A and if n < N, go to 1.
Sequencing Example
Bottleneck station is assigned with workload of 68
seconds/cycle. Actual workload by model type for that
station is provided in the table.
Model
Sales
%
Time
Red Z
250
16.7
72
Blue Q
250
16.7
68
Black R
500
33.3
68
RWB American
500
33.3
66
Example – Solution
1 Red, 1 Blue, 2 Black, 2RWB per cycle.
Set s1 = s2 = 0.9
Stage
Red Z
Blue Q
Black R
RWB
American
Assigned
1
1/6, 4
1/6, 0
1/3, 0
1/3, 2
Black
2
1/3, 4
1/3, 0
-1/3, 0
2/3, 2
Blue
3
1/2, 4
-
0, 0
1, 2
RWB
4
2/3, 2
-
1/3, 2
1/3, 4
Red
5
-
-
2/3, 2
2/3, 0
RWB
6
-
-
1, 0
-
Black
Team Exercise
Three products are produced on the same line. One half
of the demand is for A, the other half is evenly split
between B & C. Find a repeating cycle without building
unnecessary inventories or shortages. The following
table gives the bottleneck machine times.
Model
Time
A
100
B
95
C
105
Exercise – Solution
Repeating Cycle : NA = 2, NB = 1, NC = 1, N = 4
Let Max Inventory(±) < 1
Stage
A
B
C
Cum.Time Assignment
(Excess)
1
+0.5, 0
+0.75, 5
+0.75, +5
100 (0)
A
2*
+1.0, 0
+0.5, -5
+0.5, +5
195 (-5)
B
3
+0.5, -5
-
+0.25, 0
300 (0)
C
4
0, 0
-
-
100 (0)
A
* Assume A undesirable due to inventory accumulation
Unpaced Lines
Let
K - number of stations
C - Cycle times
Sk - the sum of task times for tasks assigned to
station k.
kb - bottleneck machine
All the times are deterministic
Unpaced Lines
Let us divide the line into 2 lines as 1 to kb & kb+1 to
K
Station 1 to k-1 work faster than kb
Each item has to spend skb to avoid the inventory pile
at each machine
Throughput time for Line 2 is sum of all station times.
Combining the lines, production time in system is
kb sk b  k k
K
b 1
sk
Unpaced Line - Illustration
Let S1 = 2, S2 = 4, S3 = 3
Item Enter 1 Leave 1 Enter 2 Leave 2 Enter 3 Leave 3
Flow Time
1
0
2
2
6
6
9
9
2
5
7
7
11
11
14
9
3
10
12
12
16
16
19
9
4
15
17
17
21
21
24
9
5
20
22
22
26
26
29
9
Assignment
Find a repeating cycle for entering product onto the
mixed model line. Demand and the bottleneck process
times are shown below.
Product
Demand
Time
A
1000
45
B
500
40
C
750
45
D
500
50
E
250
55
Summary
Assembly lines have greatly enhanced production
because one objective : Producing good product
Advances in computational speed makes it possible to
find optimal solutions for many problems.
Mixed model cases are handled by unpaced lines, has
advantage of allowing variability in assembly times.
Paced lines avoid need to remove and replace the
products on the transport mechanism.
Little work has been done on modeling the full range
of practical consideration in assembly line design.