Job Shop Scheduling With Heuristic Algorithms

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1 ISSN (Online): ISSN (Print) : International Journal of Research and Innovations in Science & Technology, SAINTGITS College of Engineering, INDIA Research paper, Job Shop Scheduling With Heuristic Algorithms Lokesh Kumar sahu 1 *, Dr.SridharK 2, 1 M.Tech.Scholar, Dept.of Mechanical Engg. CSIT, Drug 2 Professor in Mansa Polytechnic College as a Mechanical Engg. Bhilai * Lokesh2949@gmail.com Copyright 2015 Lokesh Kumar sahu and SridharK.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Job shop scheduling is atypical procedure compared with the scheduling procedure of mass production system. In this paper palmer s heuristic algorithm, CDS heuristic algorithm and NEH algorithm are presented the arrive the solution for a job scheduling problem. The relevant data is collected from a medium scale manufacturing unit job order. The results obtained from the heuristic algorithm are compared with lekin software. Keywords: Job shop scheduling, Make span time, CDS heuristic algorithm, NEH heuristic algorithm, Palmer s heuristic algorithm, lekin Software. 1. Introduction Scheduling is widely defined as the manufacturing process of assigning a set of jobs to resources over a period of time. Job sequence and scheduling problem has a large application in the manufacturing system. Which minimize the total flow time by selecting the most suitable sequence and give the optimal solution.and many researchers followed the same direction: Firstly focus on Modrak and V.(2009) To compare the various heuristics algorithms based on the output value of the make span. The heuristics has palmer, CDS and NEH algorithms. Chia and Lee (2009) [7] to minimize the various completion time in a flow shop problem.hejazi and Saghfian (2005) [2] A heuristic method with the objective of minimizing the total time to complete the schedule. Kalczynski, P.J (2007) [1] It is used NEH heuristic for minimizing the make span in permutation flow shop problem. Modrak,V.(2010) [3] flow shop scheduling algorithms to minimize completion time for n-jobs in m-machine problem. Kamburowski, P.J (2008) [10] An improved NEH heuristic to minimize make span in permutation flow shops. In this paper we have used A heuristic algorithms is to be developed to minimize the maximum completion make span time. The result obtained is to be compared with lekin software. 2. Literature Review The main objective of this research paper is to minimize the total make-span time. In flow shop scheduling problem; most of the Research Work has been done in this field. Jao Vitor Moccelin;Marcelo seido Nangano(2011)[4] Heuristic for flow shop sequencing with separated and sequence independent setup time The main purpose of this paper is to minimize the total time by using flow shop scheduling problem. Pavol Semančo and Vladimír Modrák (2012)[9] The objective of this algorithms is to minimize the make span time by using heuristic algorithm, with NEH, Palmer s Slope Index, CDS and Gupta s algorithm. Md. Sanowar Hossain, Ashraful Alam Nayon, Priyanka (2014)[5] In this paper the author used, CDS heuristic, NEH algorithm,palmer s heuristic, to solve the flow shop scheduling Problem, to minimize the make span time. Amar Malik, Ashwani K. Dhingra (2013)[8] A Comparative Analysis of Heuristics for Make span minimising in Flow Shop Scheduling. This algorithm is also used to minimize the make span time by using heuristic, and tested for the problems upto 10 jobs with 3, 4 and 5Machines respectively. Shariar Farahmand Rad,Ruben Ruiz,Naser Boroojerdian(2006)[6] A heuristic method for minimizing make span time in permutation flow shop problem. 39

2 3. Methodology In Job Shop Scheduling Problem; there are number of optimization techniques used. The techniques are: a) Mathematical programming- Integer programming, Goal programming, Dynamic programming, Liner programming, Branch and bound method, Genetic method, mixed integer liner programming, Surrogate duality, Transportation, Network. b) Enumerate procedure: Lagrangian relaxation. c) Efficient methods d) Constructive methods: priority dispatch rules, composite dispatching rules. e) Insertion algorithms: bottleneck based heuristics, shifting bottleneck procedure. f) Evolutionary programs: Genetic algorithm, particle swarm optimization. g) Local search techniques: ant colony optimization, adaptive search, tabu search, simulated annealing, problem space method. h) Iterative methods: Artificial intelligence techniques. i) Artificial neural network: Hopfield networks and back error propagation. j) Heuristics algorithms (NEH,CDS, Palmers) k) Beam search l) Hybrid techniques. In this paper, use heuristics algorithms such as NEH, CDS, and Palmers to give the optimal solution. 4. Heuristic algorithms 4.1 Palmer s algorithm Implement this method to find out a weight age sum of each jobs. Step 1:- Consider a job scheduling problem for 5 machines and 10 jobs. Step 2:- Assign weights to each machine. Weight (M1) = -4, Weight (M2) = -2, Weight (M3) = 0, Weight (M4) = +2, Weight (M5) = +4. Step 3:- Evaluate the weight of each job, by multiplying the weights with the processing times. Step 4:- Sort the jobs in decreasing order of their weights. Step 5:- Formulate a sequence based on the sorting done in Step 4. Step 6:- Calculate the Make Span time followed by the above steps. Example Consider 10 jobs, 5-machines problem Table 1 10 jobs, 5-machines problem J J J J J J J J J J Calculate the weight of each job J1= (16*4)+(4*4)+(4*0)+(14*2)+(12*4)=4 Same procedure follows and find out J2 = 6, J3 = 0, J4 = 16, J5 = 12, J6 = 14, J7 = 18, J8 = 14, J9 =4, J10 = 12. In decreasing order sequence: J7 - J4 - J6 - J8 - J5 - J10 - J2 - J1 - J9 - J3. Make-span time associated with this sequence is- 147 hours 40

3 Table 2 Calculate the make span time above sequence Job/Machine M1 M2 M3 M4 M5 J J J J J J J J J J CDS (Campbell Dudek Smith) Algorithm CDS algorithm uses the Johnson s algorithm at its each iteration so as to reach a better optimal solution. For m Machine: M1, M2, M3... M (m) & n Jobs Step 1:- We create (M-1) Sequence Table 3 (M-1) Sequence S1 M1 M(m) S2 M1+M2 M(m-1)+M(m) S3 M1+M2+M3 M(m-2)+M(m-1)+M(m) M1+M2+M3+. M1+M2+M3+. S(m-1) M1+M2+M3+ M(m-1) M2+M3+..+M(m) Step 2:- Apply Extension of Johnson Algorithm to each of the above (m-1) sequences. Step 3:- Take the best possible Make Span out of them. Step 4:- CDS evaluates (m-1) sequences. Consider 10 jobs 5 machine problem Step1: (m-1) sequence; consider 5 machine problems so create a 4 sequence S1 sequence shown in Table 5 Table 4 4 sequence S1 M1 M5 S2 M1+M2 M4+M5 S3 M1+M2+M3 M3+M4+M5 S4 M1+M2+M3+M4 M2+M3+M4+M5 Table 5 S1 sequence J J J J J J J J J J Make span time with this sequence is 138 hr. S2 sequence shown in Table 6 41

4 Table 6 S2 sequence J J J J J J J J J J Make span time is 147 hr. S3 is the given sequence Table 7 Table 7 S3 sequence J J J J J J J J J J Make span 147 hr. S4 is the given sequence Table 8 Table 8 S4 sequence J J J J J J J J J J Make span time 148 hr Among the sequence S1, S2, S3 & S4. Given the optimal solution S1 is 138 hr. 4.3 NEH (Nawaz Enscore Ham) Algorithm This algorithm is known as insertion algorithm. And this algorithm is used for make span minimization then it is called NEH Algorithm. Steps for this NEH Algorithm:- Step 1:- Calculate the sum of processing time for each job. Step 2:- Sort the jobs in the decreasing order of processing times for each job. Step 3:- Take the first to jobs in the sorted sequence and formulate different combinations. Step 4:- find the make span for each of the combination. Step 5:- choose the combination with minimum make span. Step 6:- Insert the next job from the sequence obtained in Step 2. Step 7:- Carry out all possible combination of the 3 jobs now. Step 8:- Repeat Step 4 followed by Step 5 followed by Step 6. Step 9:- Continue the process till all jobs are completed. Consider 10 jobs 5 machine problem: 42

5 Table 9 10 jobs 5 machine problem Processing time J J J J J J J J J J Short in decreasing order processing time in Table 10, this sequence given a result 158 hr. but in NEH heuristic algorithms have 10 jobs, so 10 different randomly sequence. The sequences J1-J2-J10-J9-J3-J8-J4-J5-J6-J7 give the minimum make span time in above sequence. Table 10 Result 158 hr J J J J J J J J J J Make span time associated with this sequence is 154 hr 5. Lekin: In Generic job shop scheduling system, it contains a number of scheduling & heuristics algorithms, & it s allow the user to link and test his own heuristics and compare their performance with the heuristics algorithms that are embedded in the system. The Lekin system can be accommodating various machine environments: (1) Single machine (2) Parallel machine (3) Flow shop (4) Flexible flow shop (5) Job shop In the lekin software, firstly the user can select a menu in machine environment & enter the all necessary machine data and job data manually. In the main menu the user also has the option of opening an existing data file. An existing file contains the data with the machine environments and specific set of jobs. If the user wants to open an existing file & make changes in the file and work in the modified file. At last the user can save the modified file with a new name. If the user wants to enter a data set that is completely new, firstly the user must select a machine environment, the dialog box appears where he has to enter the most basic information. i.e. the number of work centers and the number of schedules. After the user has done, a second dialog box appears and where the user enters the more detailed work center information.i.e. the no. of machine at the work center with their availability and the details needed to determine the setup times on each machine.in the third dialog box the user has to enter the detailed information related with the job Figure 1 Flow Shop 43

6 Figure 2 Local Search Figure 3 Objective Chart Figure 4 Flexible Job Scheduling System 44

7 5. Result The comparison between algorithms with lekin software Table 11 and the DASH (shifting bottleneck) algorithms given the optimal solution, total make span time is 135 hr Table 11 Comparison between algorithms with lekin software Algorithms Make span time(hr) Palmer s 147 CDS (Campbell Dudek Smith) Algorithm 138 NEH (Nawaz Ensore Ham) Algorithm 154 DASH (shifting bottleneck ) 135 GERENAL SB ROUTIN 147 LOCAL SEARCH Conclusion The present work focused on job shop scheduling problem using heuristic method such as Palmer s heuristic,cds (Campbell Dudek Smith) Algorithm& NEH (Nawaz Ensore Ham) Algorithm to minimize the make span time. There is a large scope of work in the job shop scheduling problem but there is a no perfect method found till date. So: There are continuous research is going on to minimize the make span for a job shop scheduling problem. References [1] Kalczynski, P.J: On the NEH Heuristic for Minimising the Make span in Permutation Flow Shop. The International Journal of Management Science (2007) [2] Hejazi, and Saghafian :Flow shop Scheduling Problems with Make span Criterion.AReview, International Journal of Production Research, 43(14), 2005, pp [3] Modrak, V: Flow Shop Scheduling Algorithm to Minimize Completion Time for n-jobs m- Machines Problem, 2010, pp [4] Jao Vitor Moccelin;Marcelo seido Nangano: Heuristic for flow shop sequencing with separated and sequence independent setup time. Sequencing Mech. Sci. & Eng. [online]. 2011, vol.33, [5] Md. Sanowar Hossain, Md. Asadujjaman, Md. Ashraful Alam Nayon, Priyanka Bhattacharya: Minimization of Make span in Flow Shop Scheduling Using Heuristics method m machine n jobs problems. Industrial and Energy Engineering [6] Shariar Farahmand Rad,Ruben Ruiz,Naser Boroojerdian: A heuristic method for minimizing make span time in permutation flow shop problem(2006) [7] Chia, Lee, Minimizing the total completion Time in permutation flow shop, operations. Research, Vol.6, pp , (2009). [8] Malik, A. K. Dhingra, Comparative analysis of heuristics for make span minimizing in flow Shop scheduling. International Journal of Innovations in Engineering and Technology. Vol. 2, pp (2013). [9] P. Semančo, V. Modrák, A Comparison of Constructive Heuristics with the Objective of Minimizing Makespan in the Flow- Shop Scheduling Problem,Acta Polytechnica Hungarica, Vol. 9, pp , (2012). [10] kamburowski,p.j- An improved NEH heuristic to minimize make span in permutation Flow shop Problems. (2008) 45