{"id":134,"date":"2022-09-04T19:01:31","date_gmt":"2022-09-04T10:01:31","guid":{"rendered":"https:\/\/prodskill.com\/?p=134"},"modified":"2022-11-15T11:54:12","modified_gmt":"2022-11-15T02:54:12","slug":"job-scheduling-using-1d-bin-packing-algorithm-2","status":"publish","type":"post","link":"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-2\/","title":{"rendered":"Optimization of work distribution using one-dimensional bin packing algorithm_2.Algorithm (1)"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 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\" style=\"cursor:inherit\">&lt;&lt;Table of Contents&gt;&gt;<\/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-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-2\/#2_1%EC%B0%A8%EC%9B%90_Bin_Packing_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98\" >2. One-dimensional Bin Packing Algorithm<\/a><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:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-2\/#21_1%EC%B0%A8%EC%9B%90_Bin_Packing_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98_%EC%A2%85%EB%A5%98\" >2.1. One-dimensional Bin Packing Algorithm Type<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-2\/#22_Next_Fit_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98\" >2.2. Next Fit Algorithm<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-2\/#23_First_Fit_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98\" >2.3. First Fit Algorithm<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-2\/#24_Worst_Fit_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98\" >2.4. Worst Fit Algorithm<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-2\/#25_Best_Fit_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98\" >2.5. Best Fit Algorithm<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" id=\"2._1\ucc28\uc6d0_Bin_Packing_\uc54c\uace0\ub9ac\uc998\"><span class=\"ez-toc-section\" id=\"2_1%EC%B0%A8%EC%9B%90_Bin_Packing_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98\"><\/span>2. One-dimensional Bin Packing Algorithm<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"2.1._1\ucc28\uc6d0_Bin_Packing_\uc54c\uace0\ub9ac\uc998_\uc885\ub958\"><span class=\"ez-toc-section\" id=\"21_1%EC%B0%A8%EC%9B%90_Bin_Packing_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98_%EC%A2%85%EB%A5%98\"><\/span>2.1. One-dimensional Bin Packing Algorithm Type<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The four representative algorithms of Bin Packing are as follows.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Next Fit: Fill in last bin or new bin<\/li>\n\n\n\n<li>First Fit: always seek and fill from the first bin<\/li>\n\n\n\n<li>Worst Fit: Find and fill the bin that can fill the current item with the largest remaining size among all bins<\/li>\n\n\n\n<li>Best Fit: Find and fill the bin that can fill the current item with the smallest remaining size among all bins.&nbsp;<\/li>\n<\/ol>\n\n\n\n<p>In addition, a much more optimized result can be obtained by sorting all items in descending order of size and applying each algorithm. Considering the method of applying descending sort, it can be said that there are a total of 8 algorithms.<\/p>\n\n\n\n<p>The following inputs and constraints are used for explanation. (The name of the item in the input is omitted and only the size is described)<\/p>\n\n\n\n<p><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Input: 26 57 18 8 45 16 22 29 5 11 8 27 54 13 17 21 63 14 16 45 6 32 57 24 18 27 54 35 12 43 36 72 14 28 3 11 46 27 42 59 26 41 15 41 68<\/li>\n\n\n\n<li>Constraint: 80 (max size of one bin)<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<p>Note: This case data and constraints are <a href=\"http:\/\/www.developerfusion.com\/article\/5540\/bin-packing\/\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/www.developerfusion.com\/article\/5540\/bin-packing\/<\/a> The basic data of the Bin Packing Sample Application that can be downloaded from . The screen of this sample application is as follows.<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-2.png\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"329\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-2.png\" alt=\"Bin Packing Sample Application \ud654\uba74\" class=\"wp-image-137\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-2.png 602w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-2-300x164.png 300w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-2-18x10.png 18w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/a><figcaption class=\"wp-element-caption\">Bin Packing Sample Application screen<\/figcaption><\/figure>\n<\/div>\n\n\n<p>Let&#039;s take a detailed look at the pseudo code, processing process, and execution result of each algorithm.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"2.2._Next_Fit_\uc54c\uace0\ub9ac\uc998\"><span class=\"ez-toc-section\" id=\"22_Next_Fit_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98\"><\/span>2.2. Next Fit Algorithm<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>For each item, the last bin is filled if it can be filled, and if it cannot be filled, a new bin is created and filled. Next Fit is the simplest, but the result is not optimal.<\/p>\n\n\n\n<pre data-no-translation class=\"EnlighterJSRAW\" data-enlighter-language=\"java\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\" data-no-auto-translation=\"\">\/\/ Pseudo code\nitem(1)\uc744 \uc0c8\ub85c\uc6b4 Bin(1)\uc5d0 \ucc44\uc6b4\ub2e4.\nfor (i=2; i&lt;=item \uac1c\uc218; i++) {\n    j = \ub9c8\uc9c0\ub9c9 Bin index\n    if (item(i).Size &lt;= Bin(j).\ub0a8\uc740\uacf5\uac04Size) {\n        Bin(j)\uc5d0 item(i)\ub97c \ucc44\uc6b4\ub2e4;\n    }\n    else {\n        \uc0c8\ub85c\uc6b4 Bin(j+1)\uc744 \uc0dd\uc131\ud558\uace0 item(i)\ub97c \ucc44\uc6b4\ub2e4;\n    }\n}<\/pre>\n\n\n\n<p><\/p>\n\n\n\n<p>Let&#039;s take a look at the process up to the &lt;10&gt;th among the above input values in the figure below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-3.png\"><img loading=\"lazy\" decoding=\"async\" width=\"81\" height=\"322\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-3.png\" alt=\"\uccab\ubc88\uc9f8 \uc785\ub825 \uac12 <26&gt;\" class=\"wp-image-139\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-3.png 81w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-3-3x12.png 3w\" sizes=\"auto, (max-width: 81px) 100vw, 81px\" \/><\/a><\/figure>\n\n\n\n<p>The first input value &lt;26&gt; creates a new Bin1 and fills it.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-4.png\"><img loading=\"lazy\" decoding=\"async\" width=\"101\" height=\"322\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-4.png\" alt=\"\ub450\ubc88\uc9f8 \uc785\ub825 \uac12 <57&gt;\" class=\"wp-image-140\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-4.png 101w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-4-94x300.png 94w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-4-4x12.png 4w\" sizes=\"auto, (max-width: 101px) 100vw, 101px\" \/><\/a><\/figure>\n\n\n\n<p>The second input value &lt;57&gt; is larger than the remaining size (54) of bin (1) and cannot be filled, so a new bin (2) is created and filled.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-5.png\"><img loading=\"lazy\" decoding=\"async\" width=\"101\" height=\"322\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-5.png\" alt=\"\uc138\ubc88\uc9f8 \uc785\ub825 \uac12 <18&gt;\" class=\"wp-image-141\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-5.png 101w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-5-94x300.png 94w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-5-4x12.png 4w\" sizes=\"auto, (max-width: 101px) 100vw, 101px\" \/><\/a><\/figure>\n\n\n\n<p>Since the third input value &lt;18&gt; is smaller than the remaining size (23) of the current bin (2), it is filled in bin (2).<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-6.png\"><img loading=\"lazy\" decoding=\"async\" width=\"122\" height=\"322\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-6.png\" alt=\"\ub124\ubc88\uc9f8 \uc785\ub825 \uac12 <8&gt;\" class=\"wp-image-142\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-6.png 122w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-6-114x300.png 114w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-6-5x12.png 5w\" sizes=\"auto, (max-width: 122px) 100vw, 122px\" \/><\/a><\/figure>\n\n\n\n<p>The fourth input value &lt;8&gt; is larger than the remaining size (5) of the current bin (2) and cannot be filled, so a new bin (3) is created and filled. As you can see here, the Next Fit method does not use even if there is space left in the bin that has already passed. Accordingly, a lot of wasted space may occur.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-7.png\"><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"322\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-7.png\" alt=\"\ub2e4\uc12f \ubc88\uc9f8 \uc785\ub825 \uac12 <45&gt;\" class=\"wp-image-143\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-7.png 100w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-7-93x300.png 93w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-7-4x12.png 4w\" sizes=\"auto, (max-width: 100px) 100vw, 100px\" \/><\/a><\/figure>\n\n\n\n<p>Since the fifth input value &lt;45&gt; is smaller than the remaining size (72) of the current bin (3), it is filled in bin (3).<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-8.png\"><img loading=\"lazy\" decoding=\"async\" width=\"122\" height=\"322\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-8.png\" alt=\"\uc5ec\uc12f \ubc88\uc9f8 \uc785\ub825 \uac12 <16&gt;\" class=\"wp-image-144\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-8.png 122w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-8-114x300.png 114w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-8-5x12.png 5w\" sizes=\"auto, (max-width: 122px) 100vw, 122px\" \/><\/a><\/figure>\n\n\n\n<p>Since the sixth input value &lt;16&gt; is smaller than the remaining size (27) of the current bin (3), it is filled in bin (3).<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-9.png\"><img loading=\"lazy\" decoding=\"async\" width=\"143\" height=\"322\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-9.png\" alt=\"\uc77c\uacf1 \ubc88\uc9f8 \uc785\ub825 \uac12 <22&gt;\" class=\"wp-image-145\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-9.png 143w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-9-133x300.png 133w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-9-5x12.png 5w\" sizes=\"auto, (max-width: 143px) 100vw, 143px\" \/><\/a><\/figure>\n\n\n\n<p>The seventh input value &lt;22&gt; is larger than the remaining size (11) of bin (3) and cannot be filled, so a new bin (4) is created and filled.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-10.png\"><img loading=\"lazy\" decoding=\"async\" width=\"143\" height=\"322\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-10.png\" alt=\"\uc5ec\ub35f \ubc88\uc9f8 \uc785\ub825 \uac12 <29&gt;\" class=\"wp-image-146\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-10.png 143w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-10-133x300.png 133w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-10-5x12.png 5w\" sizes=\"auto, (max-width: 143px) 100vw, 143px\" \/><\/a><\/figure>\n\n\n\n<p>Since the eighth input value &lt;29&gt; is smaller than the remaining size (58) of the current bin (4), it is filled in bin (4).<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-11.png\"><img loading=\"lazy\" decoding=\"async\" width=\"143\" height=\"322\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-11.png\" alt=\"\uc544\ud649 \ubc88\uc9f8 \uc785\ub825 \uac12 <5&gt;\" class=\"wp-image-147\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-11.png 143w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-11-133x300.png 133w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-11-5x12.png 5w\" sizes=\"auto, (max-width: 143px) 100vw, 143px\" \/><\/a><\/figure>\n\n\n\n<p>Since the ninth input value &lt;5&gt; is smaller than the remaining size (29) of the current bin (4), it is filled in bin (4).<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-12.png\"><img loading=\"lazy\" decoding=\"async\" width=\"143\" height=\"322\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-12.png\" alt=\"\uc5f4 \ubc88\uc9f8 \uc785\ub825 \uac12 <11&gt;\" class=\"wp-image-148\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-12.png 143w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-12-133x300.png 133w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-12-5x12.png 5w\" sizes=\"auto, (max-width: 143px) 100vw, 143px\" \/><\/a><\/figure>\n\n\n\n<p>Since the tenth input value &lt;11&gt; is smaller than the remaining size (24) of the current bin (4), it is filled in bin (4).<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>If you keep filling up to the last item in the Next Fit method, you can get the following result. (Result screen of Bin Packing Sample Application)<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-13.png\"><img loading=\"lazy\" decoding=\"async\" width=\"599\" height=\"453\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-13.png\" alt=\"Bin Packing Sample Application: Next Fit \uacb0\uacfc \uc608\uc2dc\" class=\"wp-image-149\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-13.png 599w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-13-300x227.png 300w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-13-16x12.png 16w\" sizes=\"auto, (max-width: 599px) 100vw, 599px\" \/><\/a><figcaption class=\"wp-element-caption\">Bin Packing Sample Application: Example of Next Fit Results<\/figcaption><\/figure>\n<\/div>\n\n\n<p>As can be seen in the figure above, the result of the Next Fit method is difficult to see as the optimal result because of the large waste of space. However, it has the advantage of fast execution speed due to the small number of iterations. The total space is 1,840 (size 80 per bin * number of bins 23), and the total remaining space is 488, and the space inefficiency is about 26.52% (488\/1,840).<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"2.3._First_Fit_\uc54c\uace0\ub9ac\uc998\"><span class=\"ez-toc-section\" id=\"23_First_Fit_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98\"><\/span>2.3. First Fit Algorithm<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>For each item, check whether the entire bin can be filled, fill it in the first bin that can be filled, and if not, create a new bin and fill it.<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"java\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\" data-no-auto-translation=\"\">\/\/ Pseudo code\nitem(1)\uc744 \uc0c8\ub85c\uc6b4 Bin(1)\uc5d0 \ucc44\uc6b4\ub2e4.\nfor (i=2; i&lt;=item \uac1c\uc218; i++) {\n    for (j=1; j&lt;=Bin\uac2f\uc218: j++) { \/\/ \ud56d\uc0c1 \ucc98\uc74c Bin\ubd80\ud130\n        if (item(i).Size &lt;= Bin(j).\ub0a8\uc740\uacf5\uac04Size) {\n            \/\/ item(i)\ub97c \ucc44\uc6b8 \uc218 \uc788\ub294 Bin(j) \ud0d0\uc0c9\n            Bin(j)\uc5d0 item(i)\ub97c \ucc44\uc6b4\ub2e4;\n            exit for;\n        }\n    }\n    if (\ub9c8\uc9c0\ub9c9 Bin\uae4c\uc9c0 \ud0d0\uc0c9\ud574\ub3c4 \ucc44\uc6b8 \uc218 \uc5c6\uc5c8\uc73c\uba74) {\n        \uc0c8\ub85c\uc6b4 Bin(j+1)\uc744 \uc0dd\uc131\ud558\uace0 item(i)\ub97c \ucc44\uc6b4\ub2e4;\n    }\n}<\/pre>\n\n\n\n<p>The process of filling up to the first 10 of the above input data with the First Fit method is shown in the figure below.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-14.png\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"286\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-14.png\" alt=\"First Fit \uacfc\uc815(\ucc98\uc74c 10\uac1c)\" class=\"wp-image-151\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-14.png 602w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-14-300x143.png 300w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-14-18x9.png 18w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/a><figcaption class=\"wp-element-caption\">First Fit course (first 10)<\/figcaption><\/figure>\n<\/div>\n\n\n<p>Filling the entire input data in this way gives the following result: (Result screen of Bin Packing Sample Application)<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-15.png\"><img loading=\"lazy\" decoding=\"async\" width=\"498\" height=\"452\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-15.png\" alt=\"Bin Packing Sample Application: First Fit \uacb0\uacfc \uc608\uc2dc\" class=\"wp-image-152\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-15.png 498w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-15-300x272.png 300w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-15-13x12.png 13w\" sizes=\"auto, (max-width: 498px) 100vw, 498px\" \/><\/a><figcaption class=\"wp-element-caption\">Bin Packing Sample Application: Example of First Fit Results<\/figcaption><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p>First Fit method has the advantage of less space wastage than Next Fit and smaller total space due to fewer bins. However, the disadvantage is that the execution time is long due to the relatively large number of iterations. The total space is 1,520 (size 80 per bin * number of bins 19), and the total remaining space is 168, and the space inefficiency is about 11.05% (168\/1,520).<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"2.4._Worst_Fit_\uc54c\uace0\ub9ac\uc998\"><span class=\"ez-toc-section\" id=\"24_Worst_Fit_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98\"><\/span>2.4. Worst Fit Algorithm<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>For each item, fill the bin that can be filled with the largest remaining size among all bins, and if there is no suitable bin, a new bin is created and filled.<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"java\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\" data-no-auto-translation=\"\">\/\/ Pseudo code\nitem(1)\uc744 \uc0c8\ub85c\uc6b4 Bin(1)\uc5d0 \ucc44\uc6b4\ub2e4;\nfor (i=2; i&lt;=item\uac2f\uc218; i++) {\n    long lMaxRemainSize = 0;\n    long lMaxRemainSizeBinIndex = 0;\n    for (j=1; j&lt;=Bin\uac2f\uc218: j++) {\n        \/\/ \ub0a8\uc740\uacf5\uac04Size\uac00 \uac00\uc7a5 \ud070 Bin \ud0d0\uc0c9\n        if (lMaxRemainSize &lt; Bin(j).\ub0a8\uc740\uacf5\uac04Size) {\n            lMaxRemainSize = Bin(j).\ub0a8\uc740\uacf5\uac04Size;\n            lMaxRemainSizeBinIndex = j;\n        }\n    }\n    if (item(i).Size &lt;= Bin(lMaxRemainSizeBinIndex) {\n        \/\/ \ub0a8\uc740\uacf5\uac04Size\uac00 \uac00\uc7a5 \ud070 Bin\uc5d0 item(i)\ub97c \ucc44\uc6b8 \uc218 \uc788\ub294 \uacbd\uc6b0\n        Bin(lMaxRemainSizeBinIndex)\uc5d0 item(i)\uc744 \ucc44\uc6b4\ub2e4;\n    }\n    else {\n        \uc0c8\ub85c\uc6b4 Bin(j+1)\uc744 \uc0dd\uc131\ud558\uace0 item(i)\uc744 \ucc44\uc6b4\ub2e4;\n    }\n}<\/pre>\n\n\n\n<p><\/p>\n\n\n\n<p>The process of filling up to the first 10 of the above input data by the Worst Fit method is shown in the figure below.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-16.png\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"286\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-16.png\" alt=\"Worst Fit \uacfc\uc815(\ucc98\uc74c 10\uac1c)\" class=\"wp-image-153\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-16.png 602w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-16-300x143.png 300w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-16-18x9.png 18w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/a><figcaption class=\"wp-element-caption\">Worst Fit course (first 10)<\/figcaption><\/figure>\n<\/div>\n\n\n<p>In the figure, the red item indicates a case where the filling method is different from the first fit method.<\/p>\n\n\n\n<p>Filling the entire input data in this way gives the following result: (Result screen of Bin Packing Sample Application)<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-17.png\"><img loading=\"lazy\" decoding=\"async\" width=\"548\" height=\"451\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-17.png\" alt=\"Bin Packing Sample Application: Worst Fit \uacb0\uacfc \uc608\uc2dc\" class=\"wp-image-154\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-17.png 548w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-17-300x247.png 300w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-17-15x12.png 15w\" sizes=\"auto, (max-width: 548px) 100vw, 548px\" \/><\/a><figcaption class=\"wp-element-caption\">Bin Packing Sample Application: Example of Worst Fit Results<\/figcaption><\/figure>\n<\/div>\n\n\n<p>Worst Fit method wastes less space than Next Fit, but wastes more space than First Fit. The total space is 1,680 (size 80 per bin * number of bins 21), and the total remaining space is 328, and the space inefficiency is about 19.52% (328\/1,680).<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"2.5._Best_Fit_\uc54c\uace0\ub9ac\uc998\"><span class=\"ez-toc-section\" id=\"25_Best_Fit_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98\"><\/span>2.5. Best Fit Algorithm<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>For each item, it is a method of finding and filling a bin that has the smallest remaining size among all bins and can fill the corresponding item, and if there is no suitable bin, a new bin is created and filled.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"java\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\" data-no-auto-translation=\"\">\/\/ Pseudo code\nfor (i=2; i&lt;=item\uac2f\uc218; i++) {\n    long lMinRemainSize = \uc81c\uc57d\uc870\uac74\uc73c\ub85c \uc785\ub825\ud55c Bin\uc758 \ucd5c\ub300 \ud06c\uae30;\n    long lMinRemainSizeBinIndex = 0;\n    for (j=1; j&lt;=Bin\uac2f\uc218: j++) {\n        \/\/ \ub0a8\uc740\uacf5\uac04Size\uac00 \uac00\uc7a5 \uc801\uc73c\uba74\uc11c item(i).Size\ub97c \ucc44\uc6b8 \uc218 \uc788\ub294 Bin \ud0d0\uc0c9\n        if (oBin(j).\ub0a8\uc740\uacf5\uac04Size >= item(i).SIze) and\n           (lMinRemainSize > oBin(j).\ub0a8\uc740\uacf5\uac04Size)\n            lMinRemainSize = Bin(j).\ub0a8\uc740\uacf5\uac04Size;\n            lMinRemainSizeBinIndex = j;\n        }\n    }\n    if (\uc801\ud569\ud55c Bin\uc744 \ucc3e\uc558\uc73c\uba74) {\n        Bin(lMinRemainSizeBinIndex)\uc5d0 item(i)\uc744 \ucc44\uc6b4\ub2e4;\n    }\n    else {\n        \uc0c8\ub85c\uc6b4 Bin(j+1)\uc744 \uc0dd\uc131\ud558\uace0 item(i)\uc744 \ucc44\uc6b4\ub2e4;\n    }\n}<\/pre>\n\n\n\n<p>The process of filling up to the first 10 of the above input data in the Best Fit method is shown in the figure below.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-18.png\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"288\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-18.png\" alt=\"Best Fit \uacfc\uc815(\ucc98\uc74c 10\uac1c)\" class=\"wp-image-155\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-18.png 602w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-18-300x144.png 300w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-18-18x9.png 18w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/a><figcaption class=\"wp-element-caption\">Best Fit course (first 10)<\/figcaption><\/figure>\n<\/div>\n\n\n<p>In the figure, the red item indicates a case where the filling method is different from the first fit method. Comparing the process with First Fit and Worst Fit gives a clear understanding of the method.<\/p>\n\n\n\n<p>Filling the entire input data in this way gives the following result: (Result screen of Bin Packing Sample Application)<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-19.png\"><img loading=\"lazy\" decoding=\"async\" width=\"498\" height=\"451\" src=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-19.png\" alt=\"Bin Packing Sample Application: Best Fit \uacb0\uacfc \uc608\uc2dc\" class=\"wp-image-156\" srcset=\"https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-19.png 498w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-19-300x272.png 300w, https:\/\/prodskill.com\/wp-content\/uploads\/2022\/09\/image-19-13x12.png 13w\" sizes=\"auto, (max-width: 498px) 100vw, 498px\" \/><\/a><figcaption class=\"wp-element-caption\">Bin Packing Sample Application: Example of Best Fit Results<\/figcaption><\/figure>\n<\/div>\n\n\n<p>The best-fit method generally achieves the most optimal results, but has a disadvantage in that it takes a long time to execute due to the large number of iterations. The total space is 1,520 (size 80 per bin * number of bins 19), and the total remaining space is 168, and the space inefficiency is about 11.05% (168\/1,520).<\/p>\n\n\n\n<p>The result of the First Fit and Best Fit methods having the same number of bins and the same residual space is unique to the input data used as an example and may not always be the same.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-dots\"\/>\n\n\n\n<p>We have looked at each algorithm so far, and next we will compare the method of applying descending sort and the application result of each algorithm.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-medium-font-size\">&lt;&lt; <strong>List of related articles<\/strong> &gt;&gt;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-1\/\">Optimization of work distribution using one-dimensional bin packing algorithm_1.Overview<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-2\/\">Optimization of work distribution using one-dimensional bin packing algorithm_2.Algorithm (1)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-3\/\">Optimization of work distribution using one-dimensional bin packing algorithm_2.Algorithm(2)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-4\/\">Optimization of work distribution using one-dimensional bin packing algorithm_3.Implementation (1)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-5\/\">Optimization of work distribution using one-dimensional bin packing algorithm_3.Implementation (2)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-6\/\">Optimization of work distribution using one-dimensional bin packing algorithm_4.Attachment<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-7\/\">One-dimensional Bin Packing Tool Recent Changes (as of March 21, 2021)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-toc\/\">Work distribution optimization tool using one-dimensional bin packing algorithm Full Contents, Download<\/a><\/li>\n<\/ul>\n\n\n\n<p><\/p>","protected":false},"excerpt":{"rendered":"<p>2. 1D Bin Packing Algorithm 2.1. Types of 1D Bin Packing Algorithm The four representative algorithms of bin packing are as follows. In addition, even more optimized results can be obtained by sorting all items in descending order of size and applying each algorithm. Considering even how to apply a descending sort, the total...<\/p>","protected":false},"author":1,"featured_media":136,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25],"tags":[15,16,17,18],"class_list":["post-134","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-1d-bin-packing-tool","tag-python","tag-binpacking","tag-vba","tag-18"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>1\ucc28\uc6d0 Bin Packing \uc54c\uace0\ub9ac\uc998\uc744 \ud65c\uc6a9\ud55c \uc791\uc5c5 \ubc30\ubd84 \ucd5c\uc801\ud654_2.\uc54c\uace0\ub9ac\uc998(1)<\/title>\n<meta name=\"description\" content=\"1\ucc28\uc6d0 Bin Packing \uc54c\uace0\ub9ac\uc998 \uc911 \ub300\ud45c\uc801\uc778 \ub124\uac00\uc9c0 \uc54c\uace0\ub9ac\uc998\uc778 Next Fit, First Fit, Worst Fit, Best Fit\uc5d0 \ub300\ud574 \uc0b4\ud3b4\ubcf8\ub2e4. \uac01\uac01\uc758 pseudo code, \ucc98\ub9ac \uacfc\uc815 \uc694\uc57d, \uc7a5\uc810\uacfc \ub2e8\uc810, \ud6a8\uc728\uc5d0 \ub300\ud574 \ud655\uc778\ud560 \uc218 \uc788\ub2e4.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/prodskill.com\/en\/job-scheduling-using-1d-bin-packing-algorithm-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"1\ucc28\uc6d0 Bin Packing \uc54c\uace0\ub9ac\uc998\uc744 \ud65c\uc6a9\ud55c \uc791\uc5c5 \ubc30\ubd84 \ucd5c\uc801\ud654_2.\uc54c\uace0\ub9ac\uc998(1)\" \/>\n<meta property=\"og:description\" content=\"1\ucc28\uc6d0 Bin Packing \uc54c\uace0\ub9ac\uc998 \uc911 \ub300\ud45c\uc801\uc778 \ub124\uac00\uc9c0 \uc54c\uace0\ub9ac\uc998\uc778 Next Fit, First Fit, Worst Fit, Best Fit\uc5d0 \ub300\ud574 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