Proceedings of
th
th
6 International & 27 All India Manufacturing Technology, Design and Research Conference
(AIMTDR-2016)
College of Engineering, Pune, Maharashtra, INDIA
December 16-18, 2016
Multi-Objective Optimization of Master Production
Scheduling Problems using Jaya Algorithm
Radhika S.1, Srinivasa Rao Ch.2, Neha Krishna D.3 and Karteeka Pavan K.4
1Dept.
of Mechanical Engineering, RVR&JC College of Engineering (A), Chowdavaram, Guntur, A.P., India
of Mechanical Engineering, Andhra University College of Engineering (A), Visakhapatnam, A.P., India
3Dept. of Computer Science and Engineering, International Institute of Information Technology, Bangalore, Karnataka, India
4Dept. of Computer Applications, RVR&JC College of Engineering (A), Chowdavaram, Guntur, A.P., India
E-mail: [email protected], [email protected], [email protected]
2Dept.
ARTICLE INFO
ABSTRACT
Keywords:
Master Production Scheduling
Multi-objective Optimization
Traditional Optimization Methods
Evolutionary Algorithms
Jaya algorithm
Manufacturing companies have to manage increasing product complexities, shorter time to market,
newer technologies, threats of global competition and rapidly changing environment. Master
Production Scheduling (MPS) is commonly considered to be one of the most important issues in the
planning and operation of manufacturing systems. Many production related problems, including low
machine utilization and excessive work-in-process inventories, can be assigned directly to inadequate
scheduling. Master Production Scheduling is a combinatorial optimization problem that arises
frequently in real life manufacturing applications. As this class of scheduling problems impose
several other restrictions that are not usually present in traditional job shop scheduling, the creation
of MPS becomes more complex, especially when conflicting objectives like maximization of service
level and resource utilization, minimization of inventory, overtime, stock outs and setup times are to
be considered. Traditional techniques for solving MPS problems yield a local optimal solution and
are limited in application. Evolutionary approach based meta-heuristic algorithms possess several
characteristics that are desirable for solving this kind of problems and make them preferable to
classical optimization methods. Jaya algorithm is one such recently proposed population based
algorithm which requires only common control parameters and does not require any algorithmspecific control parameters. Jaya algorithm is based on the concept that the solution obtained for a
given problem should move towards the best solution and should avoid the worst solution. The work
presents the development and use of Jaya algorithm to MPS problems (MPS Jaya), which was not
applied earlier by any of researchers so far, for solving MPS problems. The research shows that the
use of Jaya algorithm is a viable technique for creation of an efficient MPS. The Jaya algorithm
produced better results than the other techniques such as Genetic Algorithm (GA) and Differential
Evolution (DE) in terms of fitness value, with a high convergence rate.
1.
Introduction
Industries usually have several different and conflicting
objectives to be met, such as due dates and maintaining
minimum inventory levels. In any production planning, master
schedules include only key elements like, inventory and
production costs, forecast demand, plant capacity, lead time etc
that have proven their control affectivity. Unfortunately, the
complexity and effort demanded for the creation of a master
plan grows rapidly as the production scenario increases,
especially when resources are limited, which is the case for
most of the industries. Due to such complexity, industries
generally implement the usage of simple heuristics in
spreadsheets that provide a quick plan, but can compromise
planning efficiency and production costs. Fortunately,
researchers are often proposing new ideas to improve
production planning, such as use of artificial intelligence-based
heuristics. The development of an effective and efficient MPS
strategies remains an important and active research area.
The creation of a production plan intending to maximize
the use of production resources and customer service levels and
at the same time, trying to minimize inventory levels is a very
hard, time consuming task. The focus of the present work is to
develop an MPS optimization system with four goals namely
minimization of inventory level, minimization of requirement
(demand) that was not met, minimization of inventory below
safety stock level and minimization of the over capacity needed
and application of the developed MPS optimization system to
real world production scenarios.
Production scheduling problems are proved to be NP-hard
types of problems and are not easily or exactly solved for large
sizes [1]. The application of meta-heuristic techniques, to solve
such NP hard problems, is a must. So a need for efficient and
effective optimization techniques exists. Review of the
literature reveals that much work has not been reported in the
application of meta-heuristic techniques for solving MPS
problems. Continuous research is being conducted in this field
and nature-inspired meta-heuristic optimization techniques
proved to be better than the traditional techniques and are
widely used. Although evolutionary computation methods offer
solutions that combine computational efficiency and good
performance, evolutionary computational research has been
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ISBN: 978-93-86256-27-0
th
th
6 International & 27 All India Manufacturing Technology, Design and Research Conference (AIMTDR–2016)
College of Engineering, Pune, Maharashtra, INDIA
criticized for the consideration of artificial test problems that are
much simpler than real-life manufacturing cases.
Master production scheduling has been extensively
investigated over the last three decades and it continues to
attract the interest of both the academic and industrial sectors.
One must ensure that the proposed MPS is valid and realistic for
implementation before it is released to real manufacturing
system [2]. In this connection, several studies have suggested an
authentication process to check the validity of tentative MPS,
few of which include the works of [3], [4] and [5]. Besides the
substitution of the verification process, to solve and enhance
MPS quality, researchers also have employed various advanced
optimization techniques viz.; Vieira et al applied simulated
annealing [6], Soares et al [7] introduced new genetic algorithm
structure, Vieira [8] has compared genetic algorithms and
simulated annealing for master production scheduling problems
and Radhika et al [9], [10] applied Differential Evolution. The
objectives considered are minimized inventory level, maximize
service level, minimize inventory level below safety stock and
minimize overtime. The experimental results from the literature
have shown that Jaya is a powerful optimization method
possessing better robustness. Many researchers have started
applying the Jaya algorithm to their research problems. Unlike
the other advanced optimization methods, like Ant Colony
Optimization, Particle Swarm Optimization, Artificial Bee
Colony algorithms etc, Jaya algorithm does not require the
selection of algorithm-specific parameters and hence makes the
algorithm’s application to real-life optimization problems easy
and effective [11-14].
2.
Methodology
Jaya algorithm, proposed by Rao et al is based on the
concept that the solution obtained for a given problem should
move towards the best solution and should avoid worst solution
[15]. Although, Jaya algorithm requires only common control
parameters like the TLBO algorithm, Jaya algorithm contains
only one phase. Fig. 1 shows the flowchart of the Jaya algorithm.
Since Jaya algorithm always tries reaching the best solution, the
algorithm gets closer to success and avoids failure [16].
2.1 Initial population criteria
In the current work, the population individuals are filled up
randomly, with values ranging from zero to the maximum Gross
Requirement (GR) for the time period. These values always
respect the standard batch (lot) size restriction (i.e., they are
always multiples of the standard lot size).
2.2 Stopping criteria
The convergence of the algorithm is based on the fitness
value of the fittest individual. The stopping criteria in the
present work is “Stop by convergence or stagnation”. Stopping
criteria is said to be reached when the difference between
fitness values of fittest individuals in any two successive
generations is less than 0.0001.
3.
MPS problem considered
MPS problem is posed as a multi-objective optimization
problem. For the optimization of the selected parameters the
following multi-objective criteria is selected as the fitness
function [7].
 1 
fitness  

1  O n 
O n  c1
EI
RNM
BSS
OC
 c2
 c3
 c4
EI max
RNM max
BSS max
OC max
where,
With this fitness function, the fittest individual is the one
with the smallest On. EImax, RNMmax, BSSmax and OCmax are the
maximum values found during warm-up from the initial
population created. The coefficients c1, c2, c3 and c4 are used to
indicate the importance of each of the performance measures of
the MPS. Although, the choice of the values for these
coefficients directly affects the solution quality, assigning
proper values for these coefficients depends on the decision
maker’s preference and the production scenario. A
manufacturing scenario is selected from Soares et al [7] to study
the applicability of Jaya algorithm for solving MPS problems.
The scenario is with a planning horizon of thirteen periods, four
production resources and twenty different products. The
scenario also considered (a) different period lengths (b)
different initial inventory quantity for each product and (c)
different safety inventory levels and different standard
production lot sizes.
4.
Results and discussion
The applicability of the proposed MPS Jaya is tested on the
manufacturing scenario considered in section 3. The fitness is
increased by nearly 26% to that when obtained with MPS GA
[7] and the average number of iterations taken for the
convergence is 4. From Fig. 2 it is evident that the average
fitness obtained from MPS Jaya, is increased by nearly 28% to
that obtained with MPS GA and 4% than that obtained through
MPS DE [9,10].
1
0.8673
0.8976
MPS DE
MPS Jaya
0.6679
0.5
0
MPS GA
Fig. 1. Flowchart of Jaya algorithm
ISBN: 978-93-86256-27-0
Fig. 2. Comparison of fitness values
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Multi-Objective Optimization of Master Production Scheduling Problems using Jaya Algorithm
Ending Inventory
(units/hr)
In general, more service levels could be attained by
minimizing the RNM. But to achieve this, EI levels need to be
kept a bit high. MPS GA have given a result of 321.4 units of
RNM with 4555 units of EI. But the proposed MPS with Jaya
could further reduce the RNM levels to 92.9 units and at the
same time with a remarkable reduction in the EI levels. This can
be seen in the Figs. 3 and 4. The best master production
schedule found with respect to the four resources, thirteen
periods for all the twenty products along with the total MPS for
each product is shown in the Table 1.
6000
5363.2
4555.1
3182.7
4000
2000
0
MPS GA
MPS DE
MPS Jaya
Requirements not
met (Units/Hour)
Fig. 3. Comparison of EI values
400
321.4
300
200.2
200
92.9
100
0
MPS GA
MPS DE
5.
In any production planning, master schedules include only
key elements like, inventory and production costs, forecast
demand, plant capacity, lead time etc that have proven their
control affectivity. The present work considered conflicting
objectives, such as maximization of service levels, efficient use
of resources and minimization of inventory levels in the
creation of MPS.
Jaya algorithm is not applied previously for optimization of
MPS problems. Hence a decent attempt is made in the present
work to apply Jaya algorithm for optimization of selected
parameters of master production scheduling problems. The
complexity of parameter optimization problems increases with
the increase in the number of parameters. Even with an increase
in number of parameters, the proposed MPS Jaya model is
proved to be more advanced and reliable for future research.
The results demonstrate that the Jaya method produce more
optimal MPS values compared to GA. From the results, one can
conclude that, the recently developed Jaya algorithm
outperforms the rest all algorithms for multi objective
optimization MPS problems, with a minimum computational
time. Defining more suitable fitness function by considering
different weights to the coefficients and their influence may be
analyzed. The proposed MPS Jaya have proved the efficiency of
Jaya algorithms in providing solutions to MPS problem.
Notations used
MPS Jaya
MPS GA
MPS DE
EI
BSS
MPS
RNM
OC
Oi
Fig. 4. Comparison of RNM values
Table 1
best MPS obtained using jaya algorithm
Periods
Resources
Periods
1
2
3
12
13
Product 1
Res1
20
0
30
1700
3200
Res2
40
20
20
1700
3000
Res3
40
30
0
1800
4000
Res4
40
20
30
1800
4000
Total MPS
140
70
80
7000
14200
Product 2
Res1
20
20
30
2100
2000
Res2
20
20
0
2100
1000
Res3
20
0
20
800
2000
Res4
10
20
10
2100
1900
Total MPS
70
60
60
7100
6900
For conciseness products 3 thru 19 and periods 4 thru 11 are not shown
Product 20
Res1
10
10
10
1700
1000
Res2
20
20
0
1700
1000
Res3
20
0
20
1800
2000
Res4
10
10
30
1800
2000
Total MPS
60
40
60
7000
6000
MPS Jaya
0.8673
3182.7
92.9
14.5
0.323
Genetic Algorithm applied to Master Production Scheduling
Multi-objective Optimization for MPS using Differential Evolution
Ending Inventory
Below Safety Stock
Master Production Scheduling
Requirements Not Met
Overtime Capacity
Chromosome/candidate solution
References
[1]
The master plan created with MPS Jaya presented low
levels of ending inventory; low levels of requirements not met,
efficiently met safety inventory levels and could effectively
reduce the over-time capacity needed when compared to the
MPS GA. Table 2 shows the improvisation of the various
parameters obtained through MPS Jaya with those of MPS GA
(Soares 2009) and MPS DE (Radhika 2013).
Table 2
comparison among the values of performance indicators
Parameter
MPS GA
MPS DE
Avrg. Fitness
0.6679
0.8672
EI (units/hour)
4555.1
5363.2
RNM (units/hour)
321.4
200.2
BSS (units/hour)
37.03
12.53
OC (units/hour)
0.6
0.615
Conclusion
Garey M., and Johnson, D. Computer, complexity and intractability: A
guide to theory of NP-Completeness. Freeman, San Franscisco, USA,
1979.
[2] Ilham Supriyanto Fuzzy Multi-Objective Linear Programming and
Simulation Approach to the Development of Valid and Realistic Master
Production Schedule; LJ_proc_supriyanto_de 201108_01, 2011.
[3] Higgins P, Browne J Master production scheduling: a concurrent planning
approach. Prod Plan Control, 1992, 3(1):2–18.
[4] Kochhar, A. K., Ma, X., Khan, M. N. Knowledge-based systems approach
to the development of accurate and realistic master production schedules,
Journal of Engineering Manufacture, 1998, Vol. 212 pp.453-60
[5] Heizer, J. H., Render, B. Operations Management, Upper Saddle River,
New York: Pearson Prentice Hall. 2006
[6] Vieira, G. E., Ribas, C. P. A new multi-objective optimization method for
master production scheduling problems using simulated annealing,
International Journal of Production Research, 2004, Vol.42.
[7] Soares, M. M., Vieira, G. E. A New multi-objective optimization method
for master production scheduling problems based on genetic algorithm,
International Journal of Advanced Manufacturing Technology; 2009,
41:549-567.
[8] Vieira, G. E., Favaretto, F., Ribas, P. C. Comparing genetic algorithms
and simulated annealing in master production scheduling problems; 2003,
Proceedings of 17th International Conference on Production Research,
Blacksburg, Virginia, USA.
[9] Radhika.S., Rao, C. S., Pavan, K. K. : “A Differential Evolution based
Optimization for Master Production Scheduling Problems”, International
Journal of Hybrid Information Technology 2013, Vol.6, No.5, pp.163-170.
[10] Radhika.S.; Rao C. S. “A New Multi-Objective Optimization of Master
Production Scheduling Problems Using Differential Evolution”,
International Journal of Applied Science and Engineering, 2014, Vol.12,
No.1, pp.75-86. ISSN 1727-2394.
1731
ISBN: 978-93-86256-27-0
th
th
6 International & 27 All India Manufacturing Technology, Design and Research Conference (AIMTDR–2016)
College of Engineering, Pune, Maharashtra, INDIA
[11] Abhishek, K., Kumar, V. R., Datta, S., and Mahapatra, S. S. Application
of JAYA algorithm for the optimization of machining performance
characteristics during the turning of CFRP (epoxy) composites:
comparison with TLBO, GA, and ICA. Engineering with Computers,
2016, 1-19.
[12] Rao, R. V., Rai, D. P and Balic, J. Surface Grinding Process Optimization
Using Jaya Algorithm. In Computational Intelligence in Data Mining—
2016, Volume 2 (pp. 487-495). Springer India.
[13] Rao, R. V., More, K. C., Taler, J., and Ocłoń, P. Dimensional optimization
of a micro-channel heat sink using Jaya algorithm. Applied Thermal
Engineering, 2016, 103, 572-582.
ISBN: 978-93-86256-27-0
1732
[14] Pandey, H. M. Jaya a novel optimization algorithm: What, how and why?
In Cloud System and Big Data Engineering (Confluence), 2016 6th
International Conference, 2016, (pp. 728-730). IEEE.
[15] Rao, R. "Jaya: A simple and new optimization algorithm for solving
constrained and unconstrained optimization problems." International
Journal of Industrial Engineering Computations 7.1 (2016): 19-34.
[16] Zhang, Yudong, et al. "Tea category identification using a novel fractional
fourier entropy and jaya algorithm." Entropy 18.3 (2016): 77.