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Ta b l e 2 . 3 .
Modified inter
−
hit travel times (considering turret movements)
Hit
Hit
0
1
2
3
4
5
6
7
0
-
50
100
50
100
150
100
200
1
50
-
60
100
60
100
150
150
2
100
60
-
150
100
60
200
100
3
50
100
150
-
60
100
60
150
4
100
60
100
60
-
60
100
100
5
150
100
60
100
60
-
150
60
6
100
150
200
60
100
150
-
100
7
200
150
100
150
100
60
100
-
2.2.4
Dynamic Pick and Place (DPP) Model of Placement Sequence and
Magazine Assignment
Products assembled by robots are typical in present manufacturing system. To satisfy
growing large scale demand of products efficient methods of product assemble is es-
sential to reduce time frame and maximize profit. The Dynamic Pick and Place (DPP)
model of Placement Sequence and magazine Assignment (SMA) is an interesting prob-
lem that could be solved using standard optimizing techniques, such as discrete or per-
mutative DE. DPP model is a system consists of robot, assemble board and magazine
feeder which move together with different speeds and directions depends on relative
distances between assemble points and also on relative distances between magazine
components. Major difficulty to solve this problem is that the feeder assignment de-
pends on assembly sequence and vice versa. Placement sequence and magazine assign-
ment (SMA) system has three major components robot, assembly board and component
slots. Robot picks components from horizontal moving magazine and places into the
predefined positions in the horizontal moving assembly board. To optimize production
time frame assembly sequence and feeder assignment need to be determined. There are
two models for this problem: Fixed Pick and place model and Dynamic Pick and Place
model. In the FPP model, the magazine moves in
x
direction only while the board moves
in both
x-y
directions and the robot arm moves between fixed “pick” and “place” points.
In the DPP model, both magazine and board moves along x-axis while the robot arm
moves between dynamic “pick” and “place” points. See Fig 2.5. Principal objective is
to minimize total tardiness of robot movement hence minimize total assembly time.
There are few researchers who had solved the assembly sequence and feeder assign-
ment problem by the DPP model. This is because this problem is quite challenging. [12]
had proved that DPP has eliminated the robot waiting time by the FPP model. [11] used
simulated annealing algorithm and obtained solutions better than previous approaches
but the computation efficiency was quite low. Wang et al. have developed their own
heuristic approach to come up with some good solutions. [19] proposed a new heuris-
tic to improve Wang
s approach based on the fact that assembly time depends on the
relative position of picking points as well as placement points. The main objective of
DPP model is to eliminate the robot waiting time. To avoid tardiness robot arm tends to
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