{"id":3412,"date":"2020-02-19T05:43:04","date_gmt":"2020-02-19T05:43:04","guid":{"rendered":"https:\/\/commerceiets.com\/?p=3412"},"modified":"2020-02-19T05:43:04","modified_gmt":"2020-02-19T05:43:04","slug":"assignment","status":"publish","type":"post","link":"https:\/\/commerceiets.com\/assignment\/","title":{"rendered":"ASSIGNMENT -Operations Research for B.com\/ M.com\/ BBA \/ MBA Students"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_65 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title \" >Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/commerceiets.com\/assignment\/#ASSIGNMENT\" title=\"ASSIGNMENT\">ASSIGNMENT<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/commerceiets.com\/assignment\/#APPLICATIONS_OF_ASSIGNMENT_PROBLEM\" title=\"APPLICATIONS OF ASSIGNMENT PROBLEM\">APPLICATIONS OF ASSIGNMENT PROBLEM<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/commerceiets.com\/assignment\/#HUNGARIAN_METHOD\" title=\"HUNGARIAN METHOD\">HUNGARIAN METHOD<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h1 class=\"has-text-align-center wp-block-heading\" id=\"assignment\"><span class=\"ez-toc-section\" id=\"ASSIGNMENT\"><\/span><strong>ASSIGNMENT<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n\n\n<p>Assignment Problem is a special type of linear programming problem\nwhere the objective is to minimize the cost or time of completing a number of\njobs by a number of persons.<\/p>\n\n\n\n<p>The assignment problem in the general form can be stated as follows:<\/p>\n\n\n\n<p>\u201cGiven n facilities, n jobs and the effectiveness of each\nfacility for each job, the problem is to assign each facility to one and only\none job in such a way that the measure of effectiveness is optimized (Maximized\nor Minimized).\u201dSeveral problems of management have a structure identical with\nthe assignment problem.<\/p>\n\n\n\n<p><strong>Example<\/strong><\/p>\n\n\n\n<p>A manager has four persons (i.e. facilities) available for\nfour separate jobs (i.e. jobs) and the cost of assigning (i.e. effectiveness)\neach job to each person is given. His objective is to assign each person to one\nand only one job in such a way that the total cost of assignment is minimized.<\/p>\n\n\n\n<h3 class=\"has-text-align-center wp-block-heading\" id=\"applications-of-assignment-problem\"><span class=\"ez-toc-section\" id=\"APPLICATIONS_OF_ASSIGNMENT_PROBLEM\"><\/span><strong>APPLICATIONS OF ASSIGNMENT PROBLEM<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Few applications of assignment problem are as follows:<\/p>\n\n\n\n<ul><li>Assignment of employees to machines.<\/li><li>Assignment of operators to jobs.<\/li><li>Effectiveness of teachers and subjects.<\/li><li>Allocation of machines for optimum utilization\nof space.<\/li><li>Allocation of salesmen to different sales areas.\n<\/li><li>Allocation of clerks to various counters.<\/li><\/ul>\n\n\n\n<p>In all the cases, the objective is to minimize the total\ntime and cost or otherwise maximize the sales and returns.<\/p>\n\n\n\n<h3 class=\"has-text-align-center wp-block-heading\" id=\"hungarian-method\"><span class=\"ez-toc-section\" id=\"HUNGARIAN_METHOD\"><\/span><strong>HUNGARIAN METHOD<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>Hungarian method is named after Hungarian mathematician D\nKonig who developed the assignment problem.<\/p>\n\n\n\n<p>The Hungarian method is also known as Flood\u2019s Technique or the Reduced Matrix method. This method of assignment provides an efficient means of finding the optimal solutions without having to make a direct comparison of every option. It operates on a principle of matrix reduction. <\/p>\n\n\n\n<p><strong>STEPS IN HUNGARIAN METHOD<\/strong><\/p>\n\n\n\n<p>Hungarian method of assignment problem (minimization case)\ncan be summarized in the following steps:<\/p>\n\n\n\n<p><strong>STEP 1: NOTE THE\nMATRIX<\/strong><\/p>\n\n\n\n<p>From the given problem, find out the cost table. Note that\nif the number of origins is not equal to the number of destinations then a\ndummy origin or destination must be added.<\/p>\n\n\n\n<p><strong>STEP 2: ROW REDUCTION<\/strong><\/p>\n\n\n\n<p>In each row of the table find out the smallest cost element,\nsubtract this smallest cost element from each element in that row. So, that\nthere will be at least one zero in each row of the new table. This new table is\nknown as First Reduced Cost Table.<\/p>\n\n\n\n<p><strong>Step 3: COLUMN\nREDUCTION<\/strong><\/p>\n\n\n\n<p>In each column of the table find out the smallest cost\nelement, subtract this smallest cost element from each element in that column.\nAs a result of this, each row and column has at least one zero element. This new\ntable is known as Second Reduced Cost Table.<\/p>\n\n\n\n<p><strong>STEP 4: MARK\nASSIGNMENTS <\/strong><\/p>\n\n\n\n<p>Now determine an assignment as follows:<\/p>\n\n\n\n<ul><li>For each row or column with a single zero element\ncell that has not be assigned or eliminated, box that zero element as an\nassigned cell.<\/li><li>For every zero that becomes assigned, cross out\nall other zeros in the same row and for column.<\/li><li>If for a row and for a column there are two or\nmore zero and one can\u2019t be chosen by inspection, choose the assigned zero cell\narbitrarily.<\/li><li>The above procedures may be repeated until every\nzero element cell is either assigned (boxed) or crossed out.<\/li><\/ul>\n\n\n\n<p>An optimum assignment is found, if the number of assigned\ncells is equal to the number of rows (and columns). In case a zero cell had chosen\narbitrarily, there may be an alternate optimum. If no optimum solution is found\ni.e. some rows or columns without an assignment then go to Step 6.<\/p>\n\n\n\n<p><strong>STEP 5: MARKING ROWS\nAND COLUMNS<\/strong><\/p>\n\n\n\n<p>Draw a set of lines equal to the number of assignments which\nhas been made in Step 4, covering all the zeros in the following manner:<\/p>\n\n\n\n<ul><li>Mark check (\u221a) to those rows where no assignment\nhas been made.<\/li><li>Examine the checked (\u221a) rows. If any zero\nelement cell occurs in those rows, check (\u221a) the respective columns that\ncontains those zeros.<\/li><li>Examine the checked (\u221a) columns. If any assigned\nzero element occurs in those columns, check (\u221a) the respective rows that\ncontain those assigned zeros.<\/li><li>The process may be repeated until now more rows\nor column can be checked.<\/li><li>Draw lines through all unchecked rows and\nthrough all checked columns.<\/li><\/ul>\n\n\n\n<p><strong>STEP 7: REASSIGNMENT<\/strong><\/p>\n\n\n\n<p>Examine those elements that are not covered by a line.\nChoose the smallest of these elements and subtract this smallest from all the\nelements that do not have a line through them.<\/p>\n\n\n\n<p>Add this smallest element to every element that lies at the intersection of two lines. Then the resulting matrix is a new revised cost table.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"497\" height=\"686\" src=\"https:\/\/commerceiets.com\/wp-content\/uploads\/2020\/02\/hungarian-metho.jpg\" alt=\"HUNGARIAN METHOD\" class=\"wp-image-3415\" srcset=\"https:\/\/commerceiets.com\/wp-content\/uploads\/2020\/02\/hungarian-metho.jpg 497w, https:\/\/commerceiets.com\/wp-content\/uploads\/2020\/02\/hungarian-metho-217x300.jpg 217w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/figure>\n\n\n\n<p><strong>EXAMPLE OF HUNGARIAN\nMETHOD<\/strong><\/p>\n\n\n\n<p><strong>In a computer centre after studying carefully the three expert\nprogrammes, the head of computer centre, estimates the computer time in minutes\nrequired by the experts for the application programmes as follows:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"335\" height=\"112\" src=\"https:\/\/commerceiets.com\/wp-content\/uploads\/2020\/02\/problem-assignment-1.jpg\" alt=\"problem assignment 1.jpg\" class=\"wp-image-3416\" srcset=\"https:\/\/commerceiets.com\/wp-content\/uploads\/2020\/02\/problem-assignment-1.jpg 335w, https:\/\/commerceiets.com\/wp-content\/uploads\/2020\/02\/problem-assignment-1-300x100.jpg 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><\/figure>\n\n\n\n<p><strong><a href=\"http:\/\/www.engineeringenotes.com\/wp-content\/uploads\/2017\/03\/clip_image007-23.jpg\" target=\"_blank\" rel=\"noopener\"><br \/>\n<\/a><\/strong>Assign the\nprogrammers to the programmes in such a way that the total computer time is\nminimum.<\/p>\n\n\n\n<p>The Hungarian method is used to obtain an\noptimal solution.<\/p>\n\n\n\n<p><strong>Step\n(1) &amp; (2):<\/strong><\/p>\n\n\n\n<p>The minimum time element in row\n1, 2 and 3 is 80, 80 and 110. respectively. Subtract these elements from all\nelements in this respective row.<\/p>\n\n\n\n<p><strong>The\nreduced time matrix is shown in following table (1) Table 1:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"http:\/\/www.engineeringenotes.com\/wp-content\/uploads\/2017\/03\/clip_image008-39.jpg\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"229\" height=\"111\" src=\"https:\/\/commerceiets.com\/wp-content\/uploads\/2020\/02\/assignment-problem-2.jpg\" alt=\"http:\/\/www.engineeringenotes.com\/wp-content\/uploads\/2017\/03\/clip_image008_thumb-39.jpg\" class=\"wp-image-3417\"\/><\/a><\/figure>\n\n\n\n<p>In reduced Table (1) the minimum\ntime element in columns A, B, and C is 0,10 and 0 respectively; subtract these\nelements from all elements in this resp. column to get the reduced time matrix\nas shown in Table 2.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"229\" height=\"111\" src=\"https:\/\/commerceiets.com\/wp-content\/uploads\/2020\/02\/assignment-problem-3.jpg\" alt=\"http:\/\/www.engineeringenotes.com\/wp-content\/uploads\/2017\/03\/clip_image009_thumb-14.jpg\" class=\"wp-image-3418\"\/><\/figure>\n\n\n\n<p><a href=\"http:\/\/www.engineeringenotes.com\/wp-content\/uploads\/2017\/03\/clip_image009-14.jpg\" target=\"_blank\" rel=\"noopener\"><strong><\/strong><\/a><\/p>\n\n\n\n<p><strong>Step\n3 (a):<\/strong><\/p>\n\n\n\n<p>Examine all the rows starting\nfrom first one and make the assignments at zero. <\/p>\n\n\n\n<p>Assign this cell as shown in table 4.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/commerceiets.com\/wp-content\/uploads\/2020\/02\/assignment-problem-4-1.jpg\" alt=\"http:\/\/www.engineeringenotes.com\/wp-content\/uploads\/2017\/03\/clip_image012_thumb-27.jpg\" class=\"wp-image-3419\"\/><\/figure>\n\n\n\n<p>(c) Since the number of\nAssignments (= 3) equal the no of rows (= 3), the optimal solution is obtained.<\/p>\n\n\n\n<p>The pattern of assignment among\nprogrammers and programmes with their respective line (in minutes) is given\nbelow:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/commerceiets.com\/wp-content\/uploads\/2020\/02\/assignment-problem-5-1.jpg\" alt=\"http:\/\/www.engineeringenotes.com\/wp-content\/uploads\/2017\/03\/clip_image013_thumb-10.jpg\" class=\"wp-image-3420\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Also Study<\/strong><\/td><td><strong>Also Study<\/strong><\/td><td><strong>Also Study<\/strong><\/td><\/tr><tr><td><a href=\"https:\/\/commerceiets.com\/operations-research\/\">Operations Research<\/a><\/td><td><a href=\"https:\/\/commerceiets.com\/linear-programming\/\">Linear Programming<\/a><\/td><td><a href=\"https:\/\/commerceiets.com\/assignment\/\">Assignment<\/a><\/td><\/tr><tr><td><a href=\"https:\/\/commerceiets.com\/linear-programming-problem\/\">Linear programming problems<\/a><\/td><td><a href=\"https:\/\/commerceiets.com\/linear-programming-applications\/\">Linear programming applications<\/a><\/td><td><a href=\"https:\/\/commerceiets.com\/linear-programming-applications\/\">Models of Operations research<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/www.linkedin.com\/in\/kajal-mahajan-7549b2197\/\" target=\"_blank\" rel=\"noreferrer noopener\">CONNECT ON LINKEDIN<\/a><\/div>\n<\/div>\n\n\n\n<p><a href=\"http:\/\/www.engineeringenotes.com\/wp-content\/uploads\/2017\/03\/clip_image013-9.jpg\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>ASSIGNMENT Assignment Problem is a special type of linear programming problem where the objective is to minimize the cost or time of completing a number of jobs by a number of persons. The assignment problem in the general form can be stated as follows: \u201cGiven n facilities, n jobs and the effectiveness of each facility&#8230;<\/p>\n<p class=\"more-link-wrap\"><a href=\"https:\/\/commerceiets.com\/assignment\/\" class=\"more-link\">Read More<span class=\"screen-reader-text\"> &ldquo;ASSIGNMENT -Operations Research for B.com\/ M.com\/ BBA \/ MBA Students&rdquo;<\/span> &raquo;<\/a><\/p>\n","protected":false},"author":2,"featured_media":3414,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[228],"tags":[],"_links":{"self":[{"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/posts\/3412"}],"collection":[{"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/comments?post=3412"}],"version-history":[{"count":0,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/posts\/3412\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/media\/3414"}],"wp:attachment":[{"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/media?parent=3412"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/categories?post=3412"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/tags?post=3412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}