COMPUTER ASSISTED JOB
SEQUENCING
Dr. E. V. Ramana
Professor, Department of Mechanical Engineering,
VNR Vignana Jyothi Institute of Engineering &Technology, Hyderabad, India [email protected]
Abstract: Sequencing of jobs is to find an appropriate order of performing jobs on machines / work centers to in turn reduce makespan and effective utilization of machines/work centers. Johnson’s rule is a technique to schedule the jobs through two workstations to reduce makespan and idle time of work centers. In this work, software has been developed using Visual Basic to computerize Johnson’s rule to find the optimum sequence for processing “n jobs through two machines” and “n jobs through m machines” to shorten the sequencing time of jobs; and computation of idle times of machines, in and out times of jobs on machines. The proposed software enable to shorten the sequencing time of jobs, and time involved to compute in and out times of jobs and idle times of machines.
Keywords: Job sequencing, Johnson’s rule, makespan, idle times of machines
1. Introduction
An appropriate order is selected among the jobs to be performed on work centers (machines/equipment) to optimize the effectiveness measure in terms of time, cost etc. Sequencing of jobs requires faster techniques which make use of computer to arrive an optimal or near optimal solutions. It takes long time and error prone to manually perform job sequencing. Johnson rule has been implemented to sequence the n (number of jobs) jobs through two machines to minimize the total elapsed time for all jobs subjected to preconditions. The “n jobs through m (number of machines more than three) machines problem” is converted into “n jobs through two machines” by introducing two fictitious machines subjected to preconditions and subsequently Johnson’s rule is applied [1-5].
Software has been developed to computerize the techniques for “n jobs through two machines” and “n jobs through m machines” job sequencing cases. It helps to shorten the time required to sequence the jobs and to compute makespan (minimum elapsed time to complete the jobs). In addition, it can be employed to compute in and out times of jobs and idle times of machines. Johnson’s rule is computerized to find the optimum job sequence, minimum elapsed time to complete the jobs, idle times of machines, and time in and time out of each job on machines.
2. Job sequencing of n jobs through two machines
Software provides GUI based user interface to enable user to enter the details such as number of jobs to be sequenced and machines, processing time of jobs on machines in minutes. The user has to enter two as numbers of machines and jobs as desired from the list boxes as shown in the Fig.1. As a typical example, two machines and 5 numbers of jobs case is selected. The user can press OK button after selection of number of machines and jobs. If the user presses OK button without selecting number of machines and jobs, the user is prompted to enter machines/jobs by popping up with a message as shown in Fig.2.
Next button is enabled after pressing OK button to navigate to the data entry screen. In this screen, data entry sheet is displayed to enter processing times of jobs as selected earlier. If the user skips to enter processing time for any job or enter zero/negative values, the appropriate messages will be prompted. The message prompted when zero is entered for processing time is shown in Fig.3.
ISSN (Print) : 2278–9510
Fig.1 Screen for selection of number of machines and jobs
Fig.2 Message to prompt the user to enter processing time
Fig.3 Message to prompt the user to enter positive value processing time
Fig.4 displays the data entry sheet after entering processing times of five jobs on two machines. The CANCEL
Fig.4 Data entry sheet after entering processing times
The optimum sequence and minimum elapsed time to complete the jobs (makespan) for the selected number of machines and jobs are displayed as shown in Fig.5 by pressing Optimum Sequence& Elapsed Time tab.
Fig.5 Optimum Sequence& Elapsed Time
Time in and time out of every job on two machines will be displayed by pressing Jobs In& Out Times tab for the above case are shown in Fig.6 and Fig.7. The idle time of each machine is displayed, if the user chooses Idle Times of Machines tab as shown in Fig.8. Main button can be chosen if the user want to continue with another problem or Exit button to exit from the application.
Fig.6 Machine 1 Time In and Time Out of jobs Fig.7 Machine 2 Time In and Time Out of jobs
ISSN (Print) : 2278–9510
Fig.8 Idle times of machines
3. Job sequencing of n jobs through m machines
The user has to enter more than three machines and jobs as desired from the list boxes as shown in the Fig.9. The user can commit the selection of number of machines and jobs by pressing OK button and navigate to the data entry screen by pressing the Next button. Fig.10 shows a data entry sheet after entering processing times for a typical 6 jobs through 5 machines case. The user shall navigate further to Reports screen. The optimum sequence and minimum elapsed time for the selected case are displayed in Fig.11.
Fig.9 Screen for selection number of machines and jobs Fig.10 Data Entry sheet after entering processing times
Fig.11 Optimum Sequence& Elapsed Time
Fig.12 Machine 1 Time In and Time out of jobs Fig.13 Machine 5 Time In and Time out of jobs
Fig.14 Idle times of machines
4. Conclusion
GUI based job sequencing software has been developed to computerize the Job sequencing procedure adopted by Johnson’s rule and thereby reducing time taken for manual computation of optimum job sequence, makespan, time in and time out of each job and idle time of machines for n jobs through two machines and n jobs through m machines cases. In addition, it reduces the possibility of committing errors during manual computation of the same, and facilitate quicker decision making.
References:
[1] Sharma, Pankaj, and Ajai Jain. "A review on job shop scheduling with setup times. " Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 230.3 (2016): 517-533.
[2] Clark, Larry Glen. "Near optimal sequencing: N jobs and M machines; all jobs to be processed through the same order of machines." (1965).
[3] Smith, Richard Dowlen. A solution of one type of the n-job, m-machine sequencing problem. Diss. Texas Tech University, 1966. [4] Campbell, Herbert G., Richard A. Dudek, and Milton L. Smith. "A heuristic algorithm for the n job, m machine sequencing problem."
Management science 16.10 (1970): B-630.
[5] S.D.Sharma, Operations Research, Kedar Nath Ram Nath & Co Publishers, 11th Edition, pp. 417-439
ISSN (Print) : 2278–9510
