Lot-streaming scheduling with consistent size sublots including defectives goods for makespan minimization in flow shop including sublot-attached setups

1. Lot-streaming scheduling with consistent size sublots
including defectives goods for makespan minimization
in flow shop including sublot-attached setups
1

2. Agenda
Introduction about the Scheduling and flow
shop lot-streaming.
Problem statement.
Literature Review.
Model.
Numerical Illustration.
Suggestions for further Research.
Learning Outcomes.
2

3. Introduction about the Scheduling
and flow shop lot-streaming
3

4. Manufacturing Scheduling
• Method of Establishing the timing of the use of equipment,
facilities and human activities in a Manufacturing Systems
• It deals with the allocation of resources to tasks over given
time periods and its goal is to optimize one or more
objectives.
• Manufacturing Scheduling can be broadly classified into
1. Single machine scheduling
2. Flow shop scheduling
3. Job shop scheduling
4. Open shop scheduling
4

5. Flow shop scheduling
• Flow shop exists when all the jobs shares the
processing orders in all the machines.
• Flow shop is a class of scheduling problems where the
flow control shall enable an appropriate sequencing for
each job and for processing on a set of machines.
• Major objectives of flow shop scheduling are
– Minimizing Makespan (Cmax)
– Minimizing Total Flow time (TFT)
– Minimizing Average WIP level (WIP)
5

6. Lot-streaming
The technique of splitting a lot into sublots
(also termed transfer lots), and processing
different sublots simultaneously over different
machines, albeit still maintaining their
movement over the machines in accordance
with their flow shop configuration, is called
lot –streaming [2].
6

7. Lot-streaming
M/C 1
M/C 2
M/C 1
M/C 2
Time Time
7

8. Benefits of Lot-Streaming
In general
• Reduces the Makespan.
• Reduces the Idle time of machines.
• Increases the Utilization .
• Increases the Throughput.
• Reduces the Mean Flow Time.
8

9. Problem statement
9

10. Problem statement
• Consider a Situation in which the Splitting of the a given
job (lot) in several units (Sublots) and scheduling it in a
Time frame, which in fact contrast to the general
scheduling .
• Main objective of the Project is to minimize makespan
(Cmax) entire set of Sublots.
• The project focuses on four main factors
– Flow-shop scheduling.
– Consistent Sublots.
– Sublot-Attached setups.
– Defectives Goods.
10

11. Literature Review
11

12. Literature Review
• The two-machine lot streaming problem has been
investigated extensively and it encompasses both
the single-lot and multiple-lot scenarios in the
literatures .
• For an ordinary 2 machine flow shop and under the
objective of minimizing the makespan of single lot
there are few supporting literature . Optimality of
the of the lot-streaming for single job with
multiple stages flow shop focused in the literature
[4].
12

13. Literature Review
• Lot-splitting methodology for minimizing average
flow time gives basic idea for lotstreaming and sizing
of lots to improve the efficiency of the lot-streaming
[6].
• Lot streaming for multi-product which introduces
concepts of intermingling of products and explains the
lotstreaming under no-wait time .
13

14. Solution methodology
1) Exact Method – Mixed Integer Programming model
2) Heuristic – Sub-lot Insertion Heuristic
14

15. Exact Method
15

16. Assumption
1. All lots are available at time zero.
2. The machine configuration that we consider constitutes a
flow shop.
3. The objective is to minimize the makespan.
4. All sublots of a lot are processed together, i.e.,
intermingling among the sublots belonging to different
lots is not permitted. Furthermore, preemption of a sublot
is not permitted, i.e., once the processing of a sublot is
started, it cannot be interrupted.
5. Sublot transfer times are assumed negligible .
6. A sublot is assumed to be transferred in entirety in the
case of equal and consistent sublots.
16

17. Indices and Parameters
- Numbers of machines
- Machine index
- Number of items in the i th Sublot of the lot
machine k
- Number of Sublots.
- Processing time per unit item in a sublot in
machine 1
- Processing time per unit item in a sublot in
machine 2
- Setup time Required for the lot on machine k
- Percentage defective per sublot after
processing on machines 1
m
k
in
s
1p
2p
kt
d
17

18. 1, if sublot i is placed on position j
0, Otherwise
= Start time of the Sublot placed in
position j on machine k
= Completion time of the sublot placed in position j
on machine k
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21. Constraints
• Constraint-1 : At any position , only one sublot
is assigned.
• Constraint-2: A sub-lot is placed only on one
sequence .
• Constraint-3: Gives the Starting time of the
sublot in the 1st position of sequence on the 1st
machine .
• Constraint-4: Ensures the Permutation relation
between any 2 sublots scheduled adjacent in the
sequence in terms of their starting time on
machine

22. Constraints
• Constraint-5: Ensures Sub-lot starts its processing
on a machine after the setup ,only after its
completion of processing on the previous machine in
the first position of the sequence.
• Constraint- 6&7: ensures that a sublot commence
its processing on the previous machine at a position
if and only if its processing on previous machine is
already completed along the process completion of
the sublot in the preceding position of the sequence
on the machine
• Constraint -8: Gives the Value for the completion
times of all the sublots on all machines.
22

23. Numerical Illustration
23

24. Numerical Illustration
Number of lot 1
Number of Sublot 4
Lot Size 100 units
Setup time for a sublot in machine 1 10 minutes
Setup time for a sublot in machine 2 10 minutes
Processing time of machine 1 per unit 1 minutes
Processing time of machine 2 per unit 2 minutes
Defective percentage of a sublot on machine 1 10%
Problem is Solved using IBM ILOG CLPEX Solver
24

27. Results
Makespan 245 minutes
Sequence of Sublots 1-2-3-4
Start Time in machine 1 for each sublots [10,35,65,110]
Start Time in machine 2 for each sublots [35,72,118,191]
Finish Time in machine 1 for each sublots [25,55,100,140]
Finish Time in machine 2 for each sublots [62,108,181,245]
Solution processing time 24 seconds
27

28. With Lot-Streaming
10
25 100
6535
55 140
110
25 62 108 245
35 72 118
181
191
MC 1
MC 2
Time (minutes)
- Setup
- Sublot 1
- Sublot 2
- Sublot 3
- Sublot 4

29. Without Lot-Streaming
10
110
300
120
MC 2
MC 1
Time (minutes)
- Setup
- Lot
29

30. Inference
• The results prove that the lot-streaming
scheduling with consistent size sublots
including defective goods for makespan
minimization in flow-shop including sub-lot
attached setups are more efficient than that of
the same model without the lot-streaming
30

31. Heuristic

32. Sub-lot insertion Heuristic
S be the initial sequence (any arbitrary Sequence).
[k]- represents index of a Sublots placed at position at
position k in sequence S.
for (i= 1 to n)
{
for(k=1 to n)
{
If [k]!=i
{ 32

33. Choose the best sequence among (n-1) sequence
evaluated with objective function, Makespan.
Place the sub-lots i in the position k without altering the
relative position other sublots in the sequence S.
IF( The best sequence obtained is equal to initial
Sequence S)
Retain S
Other wise
Replace initial sequence S with the obtained
best among the (n-1) sequence.
}
}
}
33

34. Illustration
• Let us Assume a initial sequence
• S= [2-3-1-4] for same input as of Exact Model
k i S Makespan
1 1 1-2-3-4 245
2 1 2-1-3-4 250
3 1 2-3-1-4 250
4 1 2-3-4-1 250
34

35. Suggestions for Further research
35

36. Suggestions for Further research
• Research can be extended for N-machine flow
shop lot streaming.
• Optimizing lot-size in order minimize
makespan objective.
• Multi-objective models with minimization of
Mean Flow Time (MFT) , and Average WIP
level (WIP).
36

37. Learning Outcomes
• Acquired good basic knowledge on flow shop
lot-streaming scheduling.
• Had hands-on experience in IBM ILOG CPLEX
solver software.
• Got a good exposure working in Heuristic
approaches.
37

38. References
1. Michael L. Pinedo, ‘Scheduling Theory , Algorithms
and Systems’, New York , New York University ,Fourth
Edition 2010, 13-26.
2. Subhash C. Sarin., &, Puneet Jaiprakash, ‘Flow Shop
Lot Streaming’, 2007, 1-153.
3. Kenneth R. Baker ‘Lot streaming in the two-machine
flow shop with setup times’,The Amos Tuck School of
Business Administration, Dartmouth College, Hanover,
1995.
38

39. References
4. Topaloglu, E., A. Sen, and O. S. Benli, “Optimal
streaming of a single job in an m stage flow shop
with two sublots,” Bilkent University, Ankara, 1994.
5. Chen, J. and G. Steiner, “Discrete lot streaming in 2
machine flow shops,” Information Systems and
Operations Research, 37(2): 160–173, 1999.
6. Bukchin, J., M. Tzur and M. Jaffe, “Lot splitting to
minimize average flow-time in a 2machine flow-
shop.” IIE Transactions, 34: 953–970, 2002.
7. Sriskandarajah, C. and E. Wagneur, “Lot streaming
and scheduling multiple products in 2-machine no-
wait flowshops,” IIE Transactions, 31: 695–707,
1999,.
39

40. RESEARCH PROJECT
BY
P. Amirtha Ganesh
40

41. •
41