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International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 6, June 2017, pp. 283–298, Article ID: IJMET_08_06_029

Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=6

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

INTELLIGENT PRODUCTION SCHEDULING

A CASE STUDY

N.K. Sethy

Mechanical Engineering Department

IGIT, Sarang, Odisha, India

Dr. D.K. Behera

Mechanical Engineering Department

IGIT, Sarang, Odisha, India

ABSTRACT

Scheduling is a significant decision making process widely used in manufacturing

production, management, computer science, etc. Operation research scheduling can

reduce material handling costs and time by optimising the procedure. Finding good

schedules for given sets of jobs so can help factory supervisors to control job flows

effectively and provide solutions for job sequencing. Scheduling problems are usually

modelled and solved in a mathematically feasible way. As a result the solutions

generated from these greatly simplified problems are infeasible for real-life cases. The

complexity and instability of production systems are still underestimated in many

scheduling techniques in academic literature and the flexible production concept in

mould shop has been rarely studied. It is necessary to develop an appropriate

scheduling procedure algorithm to meet the industry’s need.

The study presents an approach to solve NP-Hard Flexible Flow Shop problems of

more than two machine center to obtain optimum makespan. This approach uses First

in First out (FIFO) dispatching rule and second approach integrates Random key

method with Genetic Algorithm (RKGA) these approach has been implemented with

MATLAB R2014a the approach has been tested on a Flexible Flow Shop Problem

which was solved previously by the random keys representation can avoid the

existence of duplicated positions value in sequencing.

The result shows that Random Key Genetic Algorithm approach obtains the best

minimum optimum makespan for different set of jobs with different processing time.

Though the computation time is more comparatively to the FIFO approach. The

RKGA can be applied in different scheduling problems in future study.

Key words: Scheduling, Flexible Flow Shop, FIFO, RKGA, Makespan.

Cite this Article: N.K. Sethy and Dr. D.K. Behera. Intelligent Production Scheduling

- A Case Study. International Journal of Mechanical Engineering and Technology,

8(6), 2017, pp. 283–298.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=6

Intelligent Production Scheduling - A Case Study


1. INTRODUCTION

Scheduling is a significant process widely used in manufacturing technology, production

management, computer science, etc. In simple flow shop problems, each machine center has

more than one machine if at least one machine [1, 3, 4-7] the problem is called Flexible Flow

Shop problem. Flexible Flow Shops are thus the generalization of simple flow shops [2].

Scheduling jobs in Flexible Flow Shop is considered as NP-Hard problem. [8, 9].

The rest of the paper is organized as follows. Introduction and Problems in production

Planning are explained in section I. Previous works done on this field are given in the section

II. The techniques and problem that has been used is presented in section III. Implementation

of the approach and experimental results are presented in section IV. Concluding remarks are

given in section V.

1.1. Problems in Production Planning

1.1.1. Inadequacy of present product planning approach

The project schedule is discussed with customers before the launch of any project tooling

department is responsible for giving an estimated mould making time for reference. However,

production plan of each project is constructed on an ad hoc basis. The wide variation in

production routes complicates the planning process. The total processing time can only be

estimated roughly before the completion of detailed product design. When multiple projects

are running simultaneously, it is highly possible that the projects schedulesconflict with one

another’s. Currently, there are two solutions to deal with the overload problems: first

outsource some of the jobs; second, request for postpone of delivery date. The latter solution,

which can lead to dissatisfaction of customers, is less preferable. Outsourcing is usually

decided at the last minute which decreases the flexibility of the project schedule. [10]

1.1.2. Frequent happenings of unpredictable incidents

Unpredictable incidents often alter projects progress and induce rescheduling of the tasks.

These incidents include delays in order releases of urgent orders, cancelations of orders and

machine breakdowns. Delays in order releases happen when the precedent operations cannot

finish on time or the required resources are not available. Urgent orders are usually the

reworking operations. A work piece is reworked when it cannot pass the quality check or its

specification is amended. These urgent orders add extra workloads to the shop. Cancellations

of orders occur when project managers ask for a pause. Machine breakdowns can be caused

by operation errors or malfunctions of machines. It takes a period of time to fix the problems

so the shop capacity drops until the machines are repaired. Frequent happenings of

unpredictable incidents bring chaos to the mould shop. [10]

The objective of this project is to study a scheduling algorithm which can generate

feasible schedules quickly to production planner for decision making.

The problem studied in the paper is a Flexible Flow Shop Problem where we assume each

machine center has the same number of parallel machine. This study precisely focusses on the

minimization of the makespan of the FFSP.

The algorithms have been evolved to workout Flexible Flow Shop scheduling problem

with more than two machine centers. The first one extends FIFO Rule approach to get a

nearly optimal makespan. FIFO approach is first used to assign jobs to each flow shop and a

schedule is obtained after simulation of FIFO dispatching rule. The second one is an optimal

algorithm entirely using Random Key Genetic Algorithm technique. Experimental results

show that Random Key Genetic Algorithm generates minimum optimal makespan.

N.K. Sethy and Dr. D.K. Behera


2. LITERATURE REVIEW

Over the last decade the competition among over last decade the competition among mould

makers is highly fierce many mould makers has adopted different approach in order to remain

competitive. They are aiming at making moulds with better quality, lower cost and shorter

delivery time.

An intelligent mould shop has been developed by Korean researchers Choi, B. K., KO, K.,

& Kim, B. H. [2005] to enhance production efficiency and lower dependency on human

skills. This intelligent mould shop comprises of three main location: Technical Data

Processing Station, Loading Schedule Station, and Real-time Monitoring Station. The

research points out that while most of the required technologies are available, the

collaboration from the end-users is critical. Human factors should be considered when

developing a system to replace manual works. [11]

Production scheduling is a decision-making process to handle the allocation of machines

to operations over a specific period of time in order to achieve one or multiple objectives

[Pinedo M. L., 2008]. Study of scheduling problems has been considerably increased since

1950s. The scheduling problems. A great variety of the problems in practice causes the

difficulty to formulate a common model for scheduling problems. A workable algorithm for

one problem may not be effective on another slightly different problem. Many algorithms

have been developed to deal with the variants of the problems. [12]

2.1. Intelligent Production Planning & Scheduling for Mould Making

A studied problem of the mould shop [Liu, Liao, Yang, Wang, & Zhao, 2010] is classified as

job shop scheduling problem. Genetic algorithm (GA) is employed to find the schedule with

minimum makespan. The problem consists of seven machines and nine different production

routes with 24 operations. Operation dependent transportation times and machine setup times

are considered. The chromosomes are encoded in integers. Each gene represents a job, so the

number of occurrences of a number is equal to the number of operations it undergoes. The

operations of GA include roulette wheel method for chromosome selection, position based

crossover, and two point exchange mutation. The population size is 5000, crossover

probability is 0.8; and mutation probability is 0.1. The computation time used is 49.36

seconds. [13]

Choy in the year 2011 proposed a hybrid scheduling decision support model (SDSM) to

solve the mould making scheduling problem. The studied problem of the mould shop is

classified as job shop scheduling problem with identical parallel machines. The model is

comprised of two modules: scheduling module and optimization module. The scheduling

module generates the schedules with GA with the objective to minimize the makespan. The

optimization module finds the most economic option to handle tardiness problem. It is proved

that this model is more effective than manual scheduling. [14]



Figure 2.1 Architecture of hybrid scheduling decision support model Choy [2011pp. 1931-1941] [14]

Tang LapYing in the year 2013 proposed the paper Intelligent Production Scheduling for

Mould Making to tackle the Asah is mould shop scheduling problem with new heuristic and

meta-heuristic algorithms they are Random Keys Harmony Search (RKHS), hybrid Nawaz-

Enscore-Ham (NEH), and Random Keys Genetic Algorithm (RKGA). Where he had done

comparison between both heuristic and meta-heuristic algorithms and thus suggested that

RKGA method performs best and suggests that the method gives best makespan with the job

size bellow 20 RKHS is suggested to be implemented for large jobs. [15]

Gwoboa Horng , Tzung-Pei Hong, Pei-Ying Huang and Chan-Lon Wang in the year 2007

proposed three algorithms based on they are Sriskandarajah and Sethi’s method by combining

both the LPT and the Search-and-prune approaches to get a nearly optimal makespan. It is

suitable for a medium sized number of jobs. The second one is optimal algorithm, using the

Search-and-prune technique. It can work only when the job number is small. The third one is

similar to the first one, except that it uses petrov’s approach (PT) to deal with job sequencing

instead of Search-and-prune. The experimental result shows that the computational time for

the proposed algorithm is in the relation as follows: Algorithm 3 < Algorithm 1 < Algorithm

2, and the makespan has the following relation: Algorithm 3 >Algorithm 1 > Algorithm 2. A

trade-off can thus be achieved between accuracy and time complexity. The choice among the

three approaches to solve a Flexible Flow Shop Problem thus depends on the problem size,

the allowed execution time and the allowed error. [16]

2.2. Theory of Constraints

Fredendall & Lea in the year 1997 studied the application of TOC in master production

scheduling. [17] Graham [in the year 2000 pointed out that the PERT/CPM approach can

cause project overrun as people misuse the safety buffer time. They tend to start the activity as



late as possible. TOC applies the buffer at the end of the whole project, so no feeding buffer

in between activities. [18]

Figure 2.2 Comparison between PERT/CPM and TOC with regard to safety time.Graham [2000]

3. METHODOLOGIES

The FFSSP is proved to be NP-hard, which has not been solved optimality in a reasonable

time. The problem taken in this paper is the non-permutation FFSSP. Previously the problem

has been solved by using three algorithms they are Sriskandarajah and Sethi’s method by

combining both the LPT and the Search-and-prune approaches to get a nearly optimal

makespan. It is suitable for a medium sized number of jobs. The second one is optimal

algorithm, using the Search-and-prune technique. It can work only when the job number is

small. The third one is similar to the first one, except that it uses petrov’s approach (PT) to

deal with job sequencing instead of Search-and-prune.

An integrated approach of heuristic and random keys representation is proposed to

minimize the makespan which is the completion time of the last job. The problem has been

solved by using FIFO rule then by the application of (RKGA) Random Key Genetic

Algorithm and comparison has been done between two algorithms and result has been given.

The studied problem has been formulated as bellow:

Assume five jobs, J1 to J5, each having three tasks (t1j, t2j, t3j), are to be scheduled via

three operations. Each operation is executed by a machine at the corresponding machine

center. Each machine center includes two parallel machines. Assume the execution times of

these jobs are listed. [16]

Assumptions

• Jobs are not pre-emptive.

• Each job has m (m > 2) tasks with processing times, executed respectively on each of m

machine centers.

• All machine centers have the same number of parallel machines.



Table 3.1 Processing Time for5 Jobs

Jobj t1j t2j t3j

J1 4 7 3

J2 1 5 2

J3 5 2 4

J4 2 5 3

J5 5 5 6

Table 3.2 Processing Time for 12 jobs

Job j m1 m2 m3

j1 1.75 1.25 4.25

j2 0.75 0 5.5

j3 2.5 1.25 6

j4 2.5 0 2.25

j5 3.25 0 5

j6 1.5 2 4

j7 0.75 0.25 3.5

j8 0.25 3.25 2

j9 2.75 4 0.75

j10 2 0.25 1.75

j11 3.25 1.75 2

j12 4 0 5.5

Table 3.3 Processing Time for 20 jobs

Job j m1 m2 m3

j1 0.75 0.5 5.5

j2 3.5 0 0.5

j3 2 0.25 3

j4 0.25 0 4

j5 1 0 5.25

j6 4 0 1.25

j7 1.5 0.5 2.25

j8 2 0 3.5

j9 0.25 0 4.5

j10 1.75 3.25 0.25

j11 2.75 0.5 0.5

j12 0.25 0 5.5

j13 3.5 0 3.5

j14 3 0 3.5

j15 2.25 0 3.5

j16 2.75 0 0.75

j17 0.75 2.5 2.75

j18 1.25 0.75 2

j19 1 0 2.75

j20 0.25 0.75 2.5

FIFO is the dispatching rule that does not follow either SPT (Shortest Processing Time) or

EDD (Earliest Due Date).

A schedule can be obtained after simulation of FIFO, below is the FIFO dispatching flow

chart:



Table 3.4 Input Parameters for FIFO

N Number of jobs

L Number of stages

Mi Number of machines at Stage i

Vi k Speed of Machine k at Stage i

Ui,j Standard processing time of Job j at Stage i

Si Setup time of a job at Stage i

L Entry point sequence of job set

A0,k Available time of Machine k at Stage 0, i.e. current machine

available time

F0,j Finish time of Job j at Stage 0, i.e. job release time

Table 3.5 Variables FIFO

Ki,j Selected machine of Job j at Stage i

Pi,j Processing time of Job j at Stage i

Ri,j Release time of Job j at Stage i

Fi,j Finish time of Job j at Stage i

Ai,k Available time of Machine k at Stage i

MS Makespan of the schedule

Figure 3.1 FIFO Algorithm Flow Chart



Random Keys Genetic Algorithm.

Figure 3.2 Flow Chart of Random Key Genetic Algorithm

4. IMPLIMENTATION

The proposed algorithm is coded in MATLAB(2014) and executed on a laptop with 2.41GHz

Intel i3 processor, 4GB RAM and windows 8 operating system.

MATLAB is chosen over the other programming languages because it has matrix

manipulation ability. Several mathematical operations that work on arrays or matrices are

built-in to the MATLAB environment. The graphical output is optimized for interaction.

Plotting is easy using the graphical interactive tools.

MATLAB’s functionality can be greatly expanded by the addition of toolboxes. Excel

link allows data to be written in a format recognized by Excel. There are numeric resources

about coding in MATLAB on internet.

Problem instances are generated for testing the effectiveness of the proposed scheduling

algorithms the static data such as machine speed, setup time, job initial release time, machine

initial release time are kept constant. The experiment has conducted 10 iteration for 3

different sets of job for FIFO dispatching approach and the computation time is taken. Then

RKGA approach is implemented with 100 iterations for 3 different sets of jobs and the

optimum makespan is obtained the data has been taken from literature. Comparison between

the makespan and computation times of both algorithms are done.

The detailed about FIFO has been caried by[Tang LapYing in the year 2013](15).



5. EXPERIMENT AND RESULT

5.1. First In First Out (FIFO)

The result analysis is shown in this part. For FIFO dispatching rule the algorithm has been

computed which obtains a Machine available time, Makespan & computation time in seconds

for 3 different sets of job and different processing time with 10 iteration given below:

Table 5.1 Machine available time for 5 jobs

JOB j M1 M2 M3

J1 14 21 28

J2 11 22 31

J3 15 26 30

J4 12 22 34

J5 14 26 34

Table 5.2 Machine available time for 12 jobs.

JOB j M1 M2 M3

J1 25.75 36.75 54.25

J2 24.75 39 52.75

J3 26.5 39.75 55.25

J4 26.5 38.5 57.75

J5 25.75 39 55.25

J6 24.75 36.75 54.25

J7 26.5 38.5 52.75

J8 26.5 39.75 57.75

J9 24.75 36.75 54.25

J10 26.5 39.75 57.75

J11 26.5 38.5 52.75

J12 25.75 39 55.25

Table 5.3 Machine available time for 20 jobs.

JOB j M1 M2 M3

J1 40.75 60.25 84.25

J2 43.5 61.25 86.75

J3 42 62.25 85.25

J4 40.25 63.5 84

J5 40.75 61.25 86.75

J6 43.5 63.5 84

J7 40.25 60.25 84.25

J8 42 62.25 85.25

J9 43.5 63.5 84

J10 42 62.25 85.25

J11 40.25 60.25 84.25

J12 40.75 61.25 86.75

J13 42 62.25 85.25

J14 40.25 60.25 84.25

J15 40.75 61.25 86.75

J16 43.5 63.5 84

J17 40.25 60.25 84.25

J18 40.75 61.25 86.75

J19 43.5 63.5 84

J20 42 62.25 85.25



As we know the highest value is taken as the makespan in case of FIFO approach.The

above machine available time has been demonstrated in the form of Bar Chart:

Figure 5.1 Machine available time for 5 jobs

Figure 5.2 Machine available time for 12 jobs.

Figure 5.3 Machine available time for 20 jobs.



Table 5.4 Computation time taken for 3 different sets of jobs by FIFO approach

Number of

jobs

Makespan Iterations Computation time

in (sec)Avg

5 34 10 0.00044173

12 57.75 10 0.00044170

20 86.75 10 0.00050487

5.2. Random Key Genetic Algorithm (RKGA)

Here In the genetic algorithm the population size is taken as 3. As Genetic Algorithm is a

heuristic approach we have taken Randomkey aproach as a result the method becomes

metaheuristic.

For the experiment we have taken 3 different job sets with different processing time and

performed 100 iteration.bellow the result is discused:

For 5 jobs:

Figure 5.4 Makespan obtained for 5 jobs.



For 12 jobs:


For 20 jobs:




Table 5.5 makespan number of iterations and computation time obtained by RKGA.

Number of jobs Makespan Iterations Computation

time

in (sec)

5 28 100 0.5977

12 43.25 100 0.5024

20 59.50 100 0.7274

Table 5.6 Comparing the computation time of FIFO with RKGA approach.

Number of jobs Computation time

in (sec)

for FIFO

Computation time

in (sec)

for RKGA

5 0.00044173 0.5977

12 0.00044170 0.5024

20 0.00050487 0.7274



Figure 5.7 The average CPU times for processing 5,12,20 jobs by FIFO and RKGA approach.

Figure 5.8 The average Makespan of processing 5,12,20 jobs by FIFO and RKGA approach.

6. CONCLUSIONS

Applicable inteligent scheduling can not only reduce manufacturing costs but also reduces the

material handling cost and time. Finding good schedules not only help company supervisors

but also helps in controling the job flows and provide god job sequencing. Scheduling jobs in

flexible flow shop has been known as NP-hard problem. In this study we have taken a NP-

hard problem which has been previously solved using sriskandrajah and sethi’s method by

combining both the LPT and the search- and prune approaches second one by search-and

prune technique third one by petrovs approach. Thus in this study two approach has been

presented based on First In First Out(FIFO)dispatching rule and the second one is integrated

approach of Random Search and Genetic Algorithm. From the result as the time complexity

in case of RKGA is higher at the cost of better makespan therefore it is economical from

above work that RKGA is recommended for small jobs preferably below 20 jobs and 3 stages.

34

57.75

86.75

28

43.25

59.5

0

20

40

60

80

100

0 5 10 15 20 25

Mak

esp

an

JOBj

Makespan of FIFO And RKGA

FIFO

RKGA



REFERENCES

[1] Campbell, H. G., R. A. Dudek and M. L. Smith, 1970. A heuristic algorithm for the n job,

m machine sequencing problem. Management Science. 16: B630-B637.

[2] Chung, S. C. and D. Y. Liao, 1992. Scheduling flexible flow shops with no setup effects.

The 1992 IEEE International Conference on Robotics and Automation. pp: 1179-1184.

[3] Dudek, R. A., S. S. Panwalkar and M. L. Smith, 1992. The lessons of flow shop

scheduling research. Operations Research. 40: 7-13.

[4] Gupta, J. N. D., 1971. A functional heuristic algorithm for the flowshop scheduling

problem. Operations Research. 40: 7-13.

[5] Nawaz, M., J. E. E. Enscore and I. Ham, 1983. A heuristic algorithm for the m-machine,

n-job flowshop sequencing problem. Omega. 11(1): 91-95.

[6] Palmer, D. S., 1965. Sequencing jobs through a Multi-stage process in the minimum total

time- a Quick method of obtaining a near optimum. Operational Research Quarterly.

16(1): 101-107.

[7] Petrov’s, V. A., 1966. Flow Line Group Production Planning. Business Publications,

London.

[8] Sriskandarajah, C. and S. P. Sethi, 1989. Scheduling algorithms for flexible flow shops:

worst and average case performance. European Journal of Operational Research. 43: 143-

160.

[9] Morton, T. E. and D. W. Pentico, 1993. Heuristic Scheduling Systems with Applications

to Production Systems and Project Management. John Wiley & Sons Inc., New York.

[10] Tang, L. Y., Yu, K. M., &Wan, Peter (2011). Flexible Mould Shop Scheduling using

Harmony Search. Annual Journal of Institute of Industrial Engineers (Hong Kong), 31,

413-419.

[11] Choi, B. K., KO, K., & Kim, B. H. (2005). Development of Intelligent Mold Shop.

Computer-Aided Design & Applications, 2 (5), pp. 619-626.

[12] Pinedo, M. L. (2008). Scheduling: Theory, Algorithms, and Systems. New York:

Springer.

[13] Liu, Z., Liao, L., Yang, W., Wang, J., & Zhao, Y. (2010). Genetic Algorithm on Solving

Mould Enterprise’s Job-Shop Scheduling Problem. International Conference on

Computing, Control and Industrial Engineering, pp. 38-41.

[14] Choy, K. L., Leung, Y. K., Chow, H. K., Poon, T. C., Kwong, C. K., Ho, G. T., et al.

(2011). A hybrid scheduling decision support model for minimizing job tardiness in a

make-to-order based mould manufacturing environment. Expert Systems with

Applications, 38, pp. 1931-1941.

[15] TANG LAP YING The Hong Kong Polytechnic University Department of Industrial and

Systems Engineering Intelligent Production Scheduling for Mould Making Pao Yue-kong

Library, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 2013.

[16] Tzung-Pei Hong, Pei-Ying Huang, Gwoboa Horng and Chan-Lon Wang Department of

Computer Science and Information Engineering, National University of Kaohsiung,

Kaohsiung 811, Taiwan, R.O.C. Department of Computer Science and Information

Engineering National Taiwan University, Taipei 106, Taiwan, R.O.C. Department of

Computer Science National Chung-Hsing University, Taichung 402, Taiwan, R.O.C.

American Journal of Applied Sciences 4 (11): 887-895 2007 ISSN 1546-9239.

[17] Fredendall, L. D., & Lea, B. R. (1997). Improving the product mix heuristic in the theory

of constraints. International Journal of Production Research, 35 (6), 1535-1544.



[18] Graham, R., Lawler, E., Lenstra, J., & Rinnooy Kan, A. (1979). Optimization and

approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete

Mathematics, 5, 287-326. R. Vidhyasri and R. Sivagamasundari, A Review on Factors

Influencing Construction Project Scheduling. International Journal of Civil Engineering

and Technology, 8(3), 2017, pp. 146-157

[19] Amani, M Al Hadidi and Rami Maher. Engineering Proj ect Management Planning and

Scheduling. International Journal of Civil Engineering and Technology, 8(1), 2017, pp.

140–148.

[20] Ch. Chowdeswari, D. Satish Chandra and SS.Asadi, Op timal Planning and Scheduling of

High Rise Buildings. International Journal of Civil Engineering and Technology, 8(1),

2017, pp. 312–324.

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