{"id":7371,"date":"2022-03-21T14:54:22","date_gmt":"2022-03-21T09:24:22","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7371"},"modified":"2025-11-27T08:42:38","modified_gmt":"2025-11-27T03:12:38","slug":"sequencing-problems","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/sequencing-problems\/","title":{"rendered":"Sequencing problems"},"content":{"rendered":"\n<p><a href=\"http:\/\/ecoursesonline.iasri.res.in\/mod\/resource\/view.php?id=90029#:~:text=Sequencing%20problems%20are%20concerned%20with,time%20or%20overall%20cost%20etc.\" target=\"_blank\" rel=\"noreferrer noopener\">Sequencing problems<\/a> deals with the selection of an optimum order for the number of jobs to perform with a finite number of facilities. The objective of sequencing is to determine the sequence of performing jobs such that we can minimize the total cost\/time.<\/p>\n\n\n\n<p>Sequencing problems arise in situations like a manufacturing plant for performing orders, in a hospital where the patients wait for different types of tests and in a bank where customers wait for different types of transactions, etc.<\/p>\n\n\n\n<p>To find the optimum sequence, we first need to calculate the total elapsed time for each of the possible sequences. <\/p>\n\n\n\n<p>As we see earlier, even if the values of <em>m <\/em>and <em>n <\/em>are very small, it is difficult to get the sequence what we desire with the total minimum elapsed time.<\/p>\n\n\n\n<p><strong>Note- <a href=\"http:\/\/ecoursesonline.iasri.res.in\/mod\/resource\/view.php?id=90029#:~:text=Sequencing%20problems%20are%20concerned%20with,time%20or%20overall%20cost%20etc.\" target=\"_blank\" rel=\"noreferrer noopener\">Sequencing problem<\/a> is the problem of finding an optimal sequence of completing a certain number of jobs so as to minimize the total elapsed time between completion of first and last job.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Terminologies<\/strong><\/h2>\n\n\n\n<p><strong>Processing Time&nbsp; <\/strong>: It is the time that a job i on each machine j requires.<\/p>\n\n\n\n<p>1.&nbsp; &nbsp; &nbsp;<strong>Total Elapsed Time T: <\/strong>It is the time interval between starting the first job and completing <strong>&nbsp;<\/strong>the last job including the idle time (if any) in a particular order by the given set of<strong> <\/strong>machines.<\/p>\n\n\n\n<p>2.&nbsp; &nbsp; <strong>Idle Time : <\/strong>It is the time for which a machine j does not have a job to process, i.e., idle time from the end of job (i-1) to the start of job i.<\/p>\n\n\n\n<p>3.&nbsp; &nbsp; <strong>Processing Order: <\/strong>It refers to the order or sequence in which machine requires for completing the job.<\/p>\n\n\n\n<p>4.&nbsp; &nbsp; <strong>Number of Machines: <\/strong>It refers to the service facilities available through which a job must pass before it is assumed to be completed.<\/p>\n\n\n\n<p>5.&nbsp; &nbsp; <strong>No Passing Rule: <\/strong>It refers to the condition to be satisfied in which the order of jobs are to be processed on given machines.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Assumptions<\/strong><\/h2>\n\n\n\n<p>1. The processing times on different machines are exactly known and are independent of the order of the jobs in which they are to be processed.<\/p>\n\n\n\n<p>2. The time taken by the jobs in moving from one machine to another is negligible.<\/p>\n\n\n\n<p>3. Once a job begins in a machine, it is to complete before another job can begin on the same machine.<\/p>\n\n\n\n<p>4. A job starts on a machine as soon as the previous job is over, and the machine is free to work.<\/p>\n\n\n\n<p>5. No machine can process more than one job simultaneously.<\/p>\n\n\n\n<p>6. Machines are of different types.<\/p>\n\n\n\n<p>7. The order of completion of jobs are independent.<\/p>\n\n\n\n<p>As discussed earlier, the objective of sequencing is to determine the sequence of jobs so that all the jobs are performed in a minimum completion time from the beginning of the first job till the completion of the last job. <a href=\"https:\/\/sis.iuea.ac.ug\/\" target=\"_blank\" rel=\"noreferrer noopener\" style=\"color:#fff;\">https:\/\/sis.iuea.ac.ug\/<\/a><\/p>\n\n\n\n<p>The advantages of sequencing are:<\/p>\n\n\n\n<p>1. We get the information like which machines are idle and period of idle time.<\/p>\n\n\n\n<p>2. Completion time for all the jobs to complete<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Types of Sequencing Problems<\/strong>&#8211; <\/h2>\n\n\n\n<p>There are four types of sequencing problems- n jobs through 2 machines, <\/p>\n\n\n\n<p>n jobs through 3 machines, n jobs through m machines, two jobs through m machines<\/p>\n<p><span style=\"color: #ffffff;\"><a style=\"color: #ffffff;\" title=\"slot88ku\" href=\"https:\/\/champrisainternational.com\/pre-starter-chick-care\/\">slot88ku<\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sequencing problems deals with the selection of an optimum order for the number of jobs to be performed with a finite number of facilities. <\/p>\n","protected":false},"author":28,"featured_media":5435,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31],"tags":[],"class_list":["post-7371","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Sequencing problems - Goseeko blog<\/title>\n<meta name=\"description\" content=\"Sequencing problems deals with the selection of an optimum order for the number of jobs to be performed with a finite number of facilities.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.goseeko.com\/blog\/sequencing-problems\/\" \/>\n<meta property=\"og:locale\" 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