Proceedings of Annual Paris Economics, Finance and Business Conference
7 - 8 April 2016, Espace Vocation Haussmann, Paris, France
ISBN: 978-1-925488-04-3
Innovative Heuristics Approach for Dynamic Production
Optimization
Perumalsamy Radhakrishnan*
Dynamic changes in demand patterns necessitate efficient and effective
management of production levels by the manufacturer leading to significant
enhancement of customer service as well as optimal production cost. Efficient
production management is a complex process as it has to capture the
dynamic nature of the demand level occurring from multiple sources. In
addition, the complexity of the problem increases when more number of
products, distribution centers, agents and customers are involved in the
process In this paper, an innovative heuristic methodology is proposed to
generate essential predictive analytics to optimize production levels in
alignment with the dynamic demand patterns emerging from multiple sources.
1. Introduction
Manufacturing enterprises have been under pressure to competently cope with a market that
is rapidly changing due to global competition, shorter product life cycles, dynamic changes of
demand patterns and product varieties. Competitiveness in today’s marketplace depends
heavily on the ability of a firm to handle the challenges of reducing lead-times and costs as
well as increasing customer service levels. All these factors have driven business
organizations to operate on near optimal production level .
Optimal production level depends on higher demand uncertainty in the global markets and is
very complex owing to the the stochastic nature of the demands. The task of managing
volatile demand can be a major challenge for organizations which are faced with increasing
pressures to lower production costs while improving customer service levels. Dynamic
changes in demand patterns necessitate efficient and effective management of production
levels by the manufacturer leading to significant enhancement of customer service as well as
optimal production cost
Efficient production management is a complex process as it has to capture the dynamic
nature of the demand level occurring from multiple sources. In addition, the complexity of the
problem increases when more number of products, distribution centers, agents and
customers are involved in the process In this paper, an innovative heuristic methodology is
proposed to generate essential predictive analytics to optimize production levels in alignment
with the dynamic demand patterns emerging from multiple sources
*Dr. Perumalsamy Radhakrishnan, Director of Research, Emirates College for Management and Information
Technology, Dubai, UAE.Email : radhakrishnan@ecmit.ac.ae
Proceedings of Annual Paris Economics, Finance and Business Conference
7 - 8 April 2016, Espace Vocation Haussmann, Paris, France
ISBN: 978-1-925488-04-3
2. Literature Review
Global competition, shorter product life cycles, dynamic changes of demand patterns and
product varieties and environmental standards cause remarkable changes in the market
scenario thereby thrusting the manufacturing enterprises to deliver their best in order to strive
Sarmiento(2007). Decrease in lead times and expenses, enrichment of customer service
levels and advanced product quality are the characteristics that determine the
competitiveness of a company in the contemporary market place Rajesh (2007).
The effective management of production in the supply chain has become unavoidable these
days due to the firm increase in customer service levels Mileff (2006). The supply chain cost
was immensely influenced by the overload or shortage of goods inventories. Thus production
optimization has transpired into one of the most recent topics as far as supply chain
management is considered Jinmei Liu (2000).
A genetic algorithm which has been approved by Chih-Yao Lo (2008) to deal with the
production-inventory problem with backlog in the real situations, with time-varied demand and
imperfect production due to the defects in production disruption with exponential distribution.
Besides optimizing the number of production cycles to generate a (R,Q) inventory policy, an
aggregative production plan can also be produced to minimize the total inventory cost on
basis of the reproduction interval searching in a given time horizon.
3. The Methodology and Model
For an organization, there are many sources of demand and it captures the demand arising
from all possible sources say distributor, wholesaler, retailer, agent and customer for every
period. We call demand level from these multiple sources as S1,S2,S3,S4, and S5
respectively Also we consider that the factory is manufacturing 5 products namely,
P1,P2,P3,P4 and P5
The methodology flow as illustrated in figure 1 is intended to determine the near optimal
production levels for each product based on the demand levels occurring from different
members of the supply chain by analyzing the past records very effectively and thus
facilitating efficient production management in order to minimize production deviation and
also to enhance customer service . The analysis flow is initiated by the selection of valid
records. In the valid record set selection, records having nil values are neglected and the
records having positive or negative values are selected for the analysis using clustering
algorithm
Proceedings of Annual Paris Economics, Finance and Business Conference
7 - 8 April 2016, Espace Vocation Haussmann, Paris, France
ISBN: 978-1-925488-04-3
Figure 1:Genetic Algorithm flow for the proposed inventory management analysis
Now we compute the Aggregate Demand level and the Aggregate production level as
follows:
ADij = Aggregate Demand for product i for period j
APij = Actual production level of product i for period j
Accordingly, AD11=S111+ S211 + S311+ S411 +S511
Then we compute Production Deviation as follows:
Production Deviation PDij= (ADij - APij)
We also fix limits for excess production and shortage of production level as 100and -100
respectively for all products. Each individual which is constituted by genes is generated with
random values between upper limit and lower limit for each product and for each period
The typical record for Production Deviation level will appear in the form of a chromosome
representation as shown in Table 1
Proceedings of Annual Paris Economics, Finance and Business Conference
7 - 8 April 2016, Espace Vocation Haussmann, Paris, France
ISBN: 978-1-925488-04-3
Table 1: The chromosome representation for the analysis taken from the past periods
Period
P1
P2
P3
P4
P5
1
14
-18
20
-10
8
Then the data set is subjected to Genetic Algorithm and the various steps performed in the
genetic algorithm methodology are discussed below.
3.1 Generation of Individuals
Each individualchromosome which is constituted by genes is generated with random values
between upper limit and lower limit for each product and for each period. Two random
individual chromosomes generated for the genetic operation is illustrated in figure 2.
Figure 2: Random individual generated for the genetic operation
P1
P2
P3
P4
P5
14
-18
20
-10
8
-15
14
18
16
-9
Each gene of the chromosome displayed in the figure 2 describes production deviation levels
for a particular product for a particular period.
3.2 Evaluation of Fitness function
A specific kind of objective function that enumerates the optimality of a solution in a genetic
algorithm in order to rank certain chromosome against all the other chromosomes is known
as a Fitness function.
Fitness functions ensure that the evolution is toward optimization by calculating the fitness
value for each individual in the population. The fitness value evaluates the performance of
each individual in the population.
Proceedings of Annual Paris Economics, Finance and Business Conference
7 - 8 April 2016, Espace Vocation Haussmann, Paris, France
ISBN: 978-1-925488-04-3
The evaluation function is determined for each randomly generated individual. The function
is given by
Ê n (i) ˆ
f(i)= log ÁÁ1 - occ ˜˜ ; i= 1,2,…,n
ntot ¯
Ë
nocc (i )
is the number of occurrences of the chromosome i in the record set
ntot
is the total number of records that have been collected from the past or total number of
data present in the record set.
n is the total number of chromosomes for which the fitness function is calculated.
The fitness function is carried out for each chromosome and the chromosomes are sorted on
the basis of the result of the fitness function. After the generation of the individuals, the
number of occurrences of the individual in the past records is determined.
In the fitness function, [1-( nocc (i ) / ntot ) ]will ensure minimum value corresponding to the
maximum occurrence of a typical chromosome in the record set..
So, the fitness function is structured to retain the minimum value corresponding to the various
chromosomes being evaluated iteration after iteration and this in turn ensures that the fitness
function evolution is towards optimization.
3.3 Genetic operations
Once fitness calculation is done, Genetic operations are performed. Selection, Crossover and
mutation comprise Genetic operations.
3.3.1. Selection:
The selection operation is the initial genetic operation which is responsible for the selection of
the fittest chromosome for further genetic operations. This is done by offering ranks based on
the calculated fitness to each of the prevailing chromosome. On the basis of this ranking,
best among the chromosomes so far considered are selected for further processing.
3.3.2. Crossover:
Among the numerous crossover operators in practice, for our complex operation, we have
chosen two point crossover. From the matting pool, two chromosomes are subjected to the
Proceedings of Annual Paris Economics, Finance and Business Conference
7 - 8 April 2016, Espace Vocation Haussmann, Paris, France
ISBN: 978-1-925488-04-3
two point crossover. The crossover operation performed in our analysis is shown in figure 3
and 4
Figure 3: Chromosomes before 2- point Crossover
C1
C2
14
-18
20
-10
8
-15
14
18
16
-9
Figure 4: Chromosomes after 2- point Crossover
C1C2
14
14
18
-10
8
-15
-18
20
16
-9
As soon as the crossover operation is completed, the genes of the two chromosomes present
within the two crossover points get interchanged. The genes before the crossover point C1
and the genes beyond the crossover point C2 remain unaltered even after the crossover
operation.
3.3.3. Mutation:
The crossover operation is succeeded by the final stage of genetic operation known as
Mutation. In the mutation, a new chromosome is obtained. This chromosome is totally new
from the parent chromosome. The concept behind this is the child chromosome thus obtained
will be fitter than the parent chromosome. The performance of mutation operation is
illustrated in the figure 5
Figure 5: Chromosome before Mutation
Mp1
Mp2
14
14
18
-10
8
Proceedings of Annual Paris Economics, Finance and Business Conference
7 - 8 April 2016, Espace Vocation Haussmann, Paris, France
ISBN: 978-1-925488-04-3
-15
-18
20
16
-9
Figure 6: Chromosome after Mutation
14
-10
18
14
8
-15
16
20
-18
-9
As in figure 5 we have chosen two mutation points Mp1 and Mp2. The mutation is done on
the particular gene present at the Mutation points. This pointing of gene is done randomly.
Hence, the two mutation points may point to any of the five genes. These 2 chromosomes
will go through the fitness function and the best one be selected for further processing.
The process explained so far will be repeated along with the new chromosome obtained from
the previous process. In other words, at the end of each of the iteration, a best chromosome
will be obtained. This will be included with the chromosomes for the next iteration. Eventually,
we obtain an individual which is the optimal one among all the possible individuals.
4. The Findings
The analysis based on GA methodology has been implemented in the platform of MATLAB .
As stated, we have the detailed information about the production deviation levels of a
particular product for each period . The sample data having this information is given in the
Table 2.
Table 2: Sample data from database of different production deviationlevels
Period
1
2
3
4
5
6
7
P1
14
-15
14
11
-15
12
-10
P2
-18
14
18
-14
14
14
12
P3
20
-18
20
-15
18
-16
14
P4
-10
16
10
18
16
18
-17
P5
8
9
-8
12
9
9
12
Proceedings of Annual Paris Economics, Finance and Business Conference
7 - 8 April 2016, Espace Vocation Haussmann, Paris, France
ISBN: 978-1-925488-04-3
8
9
10
12
-9
12
14
15
17
16
-17
19
18
16
11
9
14
-14
For GA based analysis, we have to generate 2 random individuals having five genes for
initiating the algorithm. Table 3 describes two random individuals.
Table 3: Initial random individuals
14
-18
20
-10
8
-15
14
18
16
-9
and they will be subjected to genetic operations like Fitness evaluation, Selection, Crossover
and Mutation.
The simulation run on a huge database of 5000 past records showing Fitness function
improvement at different levels of iteration is as follows:
Simulation Result showing Fitness function improvement :
For iteration 20:
fitness =
5.7845
For iteration 50;
fitness =
5.6450;
Improvement: 2%
For iteration 70;
fitness =
5.3749;
Improvement: 5%
For iteration 100;
fitness = 4.8220;
Improvement: 10%
As for deciding the total number of iterations required, the criteria followed is that as long as
minimization of the fitness function is still possible, then the iteration continues till such a
time that no improvement in the fitness function value is noticeable. After a certain number of
iterations, if the fitness function value is not improving from the previous iterations, then this is
an indication that the fitness function value is stabilizing and the algorithm has converged
towards optimal solution. For greater accuracy, the number of iterations should be sufficiently
increased and run on the most frequently updated large database of past records.
The final individual obtained after satisfying the above mentioned convergence criteria is
given in Table 4.
Proceedings of Annual Paris Economics, Finance and Business Conference
7 - 8 April 2016, Espace Vocation Haussmann, Paris, France
ISBN: 978-1-925488-04-3
Table 4: database format of Final Individual
12
-14
16
-18
9
Proceedings of Annual Paris Economics, Finance and Business Conference
7 - 8 April 2016, Espace Vocation Haussmann, Paris, France
ISBN: 978-1-925488-04-3
The final individual thus obtained represents the most emerging pattern for the
production deviation levels for each product providing essential information for product
level deviation and thus contributing essential information towards optimal production
levels.By taking necessary steps to focus on the identified surplus or shortages of
production level ,the factory can move towards near optimal production levels in the
forthcoming period.
5. Summary and Conclusions
Optimal production management is an important component leading to significant
enhancement of customer service as well as optimal production cost. The dynamic
nature of the demand level occurring from multiple sources plays a vital role in deciding
the optimal production level. We have proposed an innovative and efficient approach
based on Genetic algorithm using MATLAB to generate essential predictive analytics to
optimize production levels in alignment with the dynamic demand patterns emerging
from multiple sources for each product for the forthcoming period.
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Mileff, Peter, Nehez, Karoly,2006 A new inventory control method for supply chain
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Rajesh Gangadharan,2007Supply Chain Strategies to Manage Volatile Demand.
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