Some Solution Approaches to Reduce the
Imbalance of Workload in Parallel Machines
while Planning in Flexible Manufacturing
System
B.V.Raghavendra 1,, Dr. A.N.N.Murthy 2
1*
Assistant Professor, Dept. of Mechanical Engg,. JSS Academy of Technical Education, Bangalore-India 2
Director, DIT School of Engineering, Greater Noida, UP. India
*
For Corresopondace. Email: [email protected]
Abstract:
The loading problem in a Flexible Manufacturing System (FMS) is viewed as selecting a subset of jobs from a job pool and allocating the jobs among the machines. Balancing the workload on the parallel machines will reduce the bottleneck and improve the utilization of the machine tools. In this paper an effort is made for developing the strategies in the pre-release / planning stage which will reduce the imbalance between the parallel machines. Two different strategies are developed and the traditional sequencing shortest and longest processing time rule is applied to determine the relative performance index. An illustrative example is accompanies with the shortest processing time.
Key Words: Parallel Machines, Workload Balance, FMS
Introduction:
Flexible Manufacturing System (FMS) is a group of automated machines interconnected by automated material handling devices and controlled by a central computer system. FMS is handling a wide range of multi products from small batch as one to several thousands in a batch. FMS is capable of manufacturing different part types simultaneously for high degree of utilization. FMS need to have high investment for the resources such as sophisticated machine tools, automated material handling system, AS/RS, computers, robots, pallets, fixtures etc,. However major portion (nearly 70%) of the investment required for the sophisticated machine tools. Therefore for the manufacturing industries it is the challenge and the primary goal to utilize the machine tools effectively at the maximum extend. Hence it is essential to the managers to make the efficient plan / schedule the work which will meet the primary goal of the industry.
Literature Survey:
The decision for the FMS is categorized into pre release and post release decision problems. Pre release decision problems are planning problem in FMS and post release decision problems are scheduling problems when system is in operation. Stecke [1] described the pre-release decision problems of a FMS are.
1. Selecting the set of part types to be manufactured simultaneously. 2. Production ratio determination of various parts
3. Resource allocation
4. Partitioning machines into groups of identically tooled machines
5. The machine groups are to be loaded by assigning operations of the job and required tools.
The pre and post release decision need to be taken in the FMS considering the various objectives. There are six objective described by stecke [1].
1. Balancing the machine processing time 2. Minimizing the number of movements.
3. Balancing the workload per machine for system of groups of pooled machines of equal sizes. 4. Unbalancing the work load per machine for a system of groups of pooled machines of unequal sizes. 5. Filling the tool magazine as densely as possible
6. Maximizing the sum of operation priorities.
The first three decision problems are categorized as loading problems and next two decision problems are pertaining to grouping and batching problems.
The loading problems are addressed by various researchers to meet the above mentioned six objectives with different approaches. However in the literature it has not been found that any one approach / methods, which will address all the six objectives. In many situations some of the objectives are conflicting while the others, several objectives may be equally important to consider. A loading problem is strongly affected by the types of machine tools, size of tool magazine, and capability of machine tool to perform various operations. This introduces constraints at the loading level on the capacity of the machine.
From the literature reviewed it appears that two objectives, workload balance and throughput, have attracted maximum research attention. In the context of FMS involving high capital investment, the genuine objective of high machine utilization is related to the minimization of idle time, and is achieved by balancing the workload [2] while satisfying the various constraints such as available production time, tool magazine capacity, minimization of inter-machine part movement, work in process inventory etc,. A number of methodologies are suggested by Berrada and Stecke (1984), Shanker and Tzen (1985), Shanker and Srinivasulu (1989)[2], Sawik (1989) stecke (1989), Chen and Askin (1990),S. K. Mudhopadhyay et al. (1992), Moreno and Ding (1993) M.K.Tiwari et.al (1997), They have worked on various approaches such as MIP, branch and backtrack technique, branch and bound technique, sequencing rule etc,. S Rajakumar, V.P.Arunachalam. V. Selladurai (2004 & 2007) they have worked through the sequencing rule and GA for minimizing the workload imbalance in parallel machines. It is also been addressed by may researchers that the mathematical and multi-objective criteria failed to address the real time problems when the problem size is very large. Though the codes are available computation time is more. This will be the limitation in the real time situation. The simulation approach would be suitable but it failed to give optimum solution. Simulation approach needs more iteration to get the better solution. However it is found in many literatures that the researchers have developed different heuristic approaches and they have addressed the problem with better solution.
In this paper author has put an effort to reduce the imbalance in random type of parallel machines while addressing the loading problem in pre-release stage (planning stage) to process different part types simultaneously in Flexible Manufacturing System.
Problem Statement:
A loading problem in FMS is solved and its performance is being judged by determining the system imbalance and the throughput. Shanker and Tzen (1985) have shown that the ‘shortest processing time’ (SPT) sequencing rule performs best on an average for the loading problems of a FMS in balancing the workload. S Rajakumar, V.P.Arunachalam. V. Selladurai (2004 & 2007) they have worked through the sequencing rule and GA for minimizing the workload imbalance in parallel machines through the relative performance index. They have worked out for ‘m’ parallel machines (m=2,3,4,5 and 6) for ‘n’ number of batches. They have shown that more balancing is possible for higher number of batches. From the publication record of Japanese production technological investigation society “Collection of European and American FMS (1981)”, where they have analyzed the data pertaining to 79 FMSs, it has been found that the maximum number of FMSs consists of four to six machines [3].
between the machines. Each strategy is worked out with two different rules based on ‘shortest processing and longest processing time’. The relative performance (RPI) of the machines are calculated based on ((maximum workload on machine-minimum workload on machine) / maximum workload on machine). The results are compared for 2,3,4,5 and 6 parallel machines. The objective of the work is to reduce the imbalance between the parallel machines. In the research the decision for the number of set-up (Si i=1..n) is already determined based on the constraints of tool slot and the machine capabilities to process the jobs.
Assumption
a) Job Loading on ‘m’ Parallel Machines ( m=1,2,3,4,5,6) b) Simultaneously processing of selected part types.
c) Machine Capacity is sufficiently available to process all the selected part types. d) Enough Tool Slots are available on machine to process selected part type. e) All the jobs and machines are simultaneously available in the beginning. f) Transportation time required to move a job/tool on the machine is negligible. g) Time required loading the tool & set-up of the machine is not considered.
h) Constraints related to material handling system, availability of other resources such as pallets, fixtures are relaxed.
i) Required tools will be loaded on machine for machining of every part types and in each set-up.
j) The set-up (Si ) will be the precedence constraint for the next set-up (Si +1 ). Precedence constraint should be satisfied.
Strategy 1: SPT / LPT (Total) and Remaining Set-ups SPT/LPT
a) For I set-up job sequence rule is based on Shortest Processing Time (SPT) / Longest Processing Time (LPT) considering total machining time (i.e sum of machining time of all the set-up of the particular job).
b) For rest of the set-up the sequence rule is based on SPT/LPT respectively considering machining time of immediate competing set-up of the work-in-process jobs (WIP).
Procedure for SPT/LPT (Total) and Remaining Set-ups SPT/LPT
a) At the beginning all the machines are available and select the job to load on the machine which has SPT (Total) / LPT(Total).
b) If machine is free load the machine by WIP jobs. If more than one WIP jobs are waiting to process then select the job which has SPT/LPT in the rest of the competing set-ups respectively. But machine should not be idle while loading the jobs. If so then select the next WIP job so that machine is not idle.
c) If no WIP jobs are available then load the machine with the remaining jobs based on SPT(Total)/LPT(Total) rule.
d) Repeat above steps till completing all the jobs.
Strategy 2: SPT/LPT (I and Remaining Set-ups)
a) For I set-up job sequence rule is based on SPT/LPT considering I set-up machining time only.
b) For rest of the set-up the sequence rule is based on SPT/ LPT respectively considering machining time of immediate competing set-up of the work-in-process jobs.
Procedure for SPT/LPT (I and Remaining Set-ups)
a) At the beginning all the machines are available and select the job to load on the machine which has SPT/LPT (I Set-Up).
b) If machine is free load the machine by WIP jobs. If more than one WIP jobs are waiting to process then select the job which has SPT/LPT in the rest of the competing set-ups respectively. But machine should not be idle while loading the jobs. If so then select the next WIP job so that machine is not idle.
c) If no WIP jobs are available then load the machine with the remaining jobs SPT/LPT (I Set-Up) rule. d) Repeat above steps till completing all the jobs.
Input: No. of jobs(n) and
No. of Parallel
Machines (m=1,2..6)
Select the jobs as per sequence
rule
Load the jobs on available
machines for Set-up-I
Select all work in-process jobs
Select the jobs as per stated
sequence rule
Load the job on immediate
available machine
Check M/C Idleness
for Zero or Minimum
Process the job on the machine
Next Set-up
New Job
No
Yes
No
Any In-Process
Jobs?
Yes
Consider rest
of the jobs in
the sequence
No
Yes
No
Yes
Illustration:
1. Sub part of ten part types are selected from the job pool. 2. Batch size of each part type is ten
3. Two random type parallel machines are considered
4. Complete machining of the selected part types can be done in one / two set-ups.
The details of the processing unit time per set-up and the total processing time per batch are as follows
Part Type
Unit Processing time per batch
Total Processing time per Batch
I Set-Up II Set-Up
1 620 440 1060
2 530 460 990
3 380 380 760
4 340 310 650
5 320 190 510
6 330 310 640
7 310 300 610
8 750 0 750
9 67.8 0 67.8
10 173.4 51.5 224.9
Strategy 1:
SPT (Total) and Remaining Set-Ups SPT
Part Type
Set-Up
Machine 1 Out time In time Processi
ng time
9 1 0 67.8 67.8
5 1 67.8 320 387.8
7 1 387.8 310 697.8
7 2 697.8 300 997.8
4 1 997.8 340 1337.8
4 2 1337.8 310 1647.8
3 1 1647.8 380 2027.8
2 1 2027.8 530 2557.8
1 1 2557.8 620 3177.8
M/C. 2 is idle for 136.9 units of time
Maximum workload time is……3177.8 units of time on machine -1 Minimum Workload time is……3084.9 units of time on machine -2
Relative Performance Index (RPI) = (3177.8 – 3084.9 ) / 3177.8 = 0.029234 Part Type
Set-Up
Machine 2 Out Time In time Process
ing time
10 1 0 173.4 173.4
10 2 173.4 51.5 224.9
5 2 224.9 190 414.9
6 1 414.9 330 744.9
6 2 744.9 310 1054.9
8 1 1054.9 750 1804.9
3 2 1804.9 380 2184.9
2 2 2184.9 460 2644.9
1 2 2781.8 440 3221.8
Steps:
1. Arrange the selected part types on the basis of shortest processing (Sum of all set-up of particular part type machining time) time. (Part types 9,10, 5, 7, 6, 4, 8, 3, 2, 1 )
2. Select the part no. 9, which has SPT and load on machine-1 for I set-up at in time is ‘0’ and out time is 0+67.8=67.8 units of time.
3. Select the part no. 10 and load on the machine-2 for I set-up at in time is ‘0’ and out time is 0+173.4=173.4 units of time.
4. Machine-1 is free after 67.8 units of time and part no 9 is completed all the operation. Select next part on the basis of SPT which is part no 5 and load on machine for I set-up which will take 320 units of time. The completion time 67.8+320=387.8 units of time.
5. Machine-2 is free after 173.4 units of time and load the machine by part no 10 for II set-up which will comes out at 224.9 units of time and this job is completed all the operation.
6. Load machine-2 with the WIP part no 5 for II set-up. This will take 224.9+190=414.9 units of time.
7. Load the machine-1 with the new part no 7 for I set-up, because no WIP are available. This job out time is 697.8 units of time.
8. Load the machine-2 with the new part no 6 for I Set-up. Which will comes out at 744.9 units of time. Though the WIP part no 7 for II set-up is available but if it can be loaded on machine-2, the machine will be idle for 12.9 units of time. Since to avoid the idleness of the machine a new job is loaded.
9. Load the machine-I with part no 7 for II set-up since this is the WIP inventory. The part no 7 will comes out at 997.8 units of time and all the operations are completed.
10. Load the machine-2 with part no 6 for II set-up and which will comes out at 1054.9 units of time.
11. Machine-1 is free at 997.8 units of time. Select the next SPT part no 4 and load for I set-up which will comes out at 1337.8 units of time.
12. Machine-2 is free at 1054.9 units of time. Select the next SPT part no 8 and load the machine for I set-up. The part no 4 for II set-up is the WIP inventory. If it can be loaded on Machine-2 which will be idle for 3.9 units of time. Therefore though it is WIP the part no 8 is loaded for I set-up in order to avoid the Idle time of the machine-2.
13. Machine-1 will be free after 1337.8 units of time. The part no 4 for II set-up is loaded on this machines the out time of the part no 4 is 1647.8 units of time.
14. A new part on the basis of SPT part no 3 for I set-up on machine-1 is loaded which will comes out 2027.8 units of time. At the same time machine-2 will be available at 1804.9 units of time and the machine is loaded by WIP inventory part no 3 for II set-up. Part no.3 will be completing all the operation at 2184.9 units of time.
15. Machine-1 is free at 2027.8 units of time and loaded with next SPT part no 2 for set-up no 1. The set-up no 2 for part no 2 will be loaded on Machine-2 because which will be available at 2184.9 units of time. The part no 2 will comes out at 2644.9 units of time.
16. Machine-1 is free at 2557.8 units of time and the next SPT part no 1 will be loaded for I set-up which will comes out at 3177.8 units of time.
17. Machine-2 is free at 2644.9 units of time. The part no 1 for II set-up is loaded on machine-2. However to complete the operation on part no 1 for II set-up the machine-2 will be start for loading the II set-up at (2644.9-2781.8=136.9) 2781.8 units of time. Therefore machine-2 will be idle for 136.9 units of time. Because the part no 1 for II set-up is only available at 3177.8 units of time. The machine-2 will be start to machine last job of the part at 3177.8 units of time and completing at 3177.8+44=3221.8 units of time.
18. The machine-1 work load is 3177.8 and the machine-2 work load is 3221.8-136.9= 3084.9
19. The relative performance will be calculated on the basis of RPI= ( Wmax-Wmin) / Wmax= (3177.8-3084.9)/3177.8 = 0.029234
Comparison of Relative Performance Index (RPI):
Strategy Rule No of Parallel Machines
2 3 4 5 6 Strategy-1 SPT 0.029234 0.1382 0.1939 0.25 0.3641
LPT 0.018947 0.0347 0.0954 0.031 0.1224
Strategy-2 SPT 0.04156 0.2586 0.3417 0.322 0.4581
LPT 0.001309 0.0731 0.0894 0.151 0.1637
Conclusion and Future Scope:
LPT rule gives better RPI result for both the strategies. However strategy 2 suits best relative performance for 2 and 4 parallel machines and strategy 1 for 3,5 and 6 parallel machines. In this research only two sequencing i.e SPT and LPT are used. In order to get an optimum solution for ‘n’ number of part types the sequences are ‘n!’. The computational time required is more for getting the solution for ‘n!’ sequences. It is the limitation in the real time situations. Hence it is suggested for the future work to use random search technique where it can address the real time situation. It is also suggested to consider other resources such as AGV, pallets, fixtures etc, for the future work.
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