{"id":4399385,"date":"2021-11-22T18:43:09","date_gmt":"2021-11-22T18:43:09","guid":{"rendered":"https:\/\/www.mistservices.co.uk\/timetabling\/?p=4399385"},"modified":"2021-12-09T17:40:52","modified_gmt":"2021-12-09T17:40:52","slug":"combinations-in-timetabling","status":"publish","type":"post","link":"https:\/\/www.mistservices.co.uk\/timetabling\/combinations-in-timetabling\/","title":{"rendered":"Combinations in timetabling"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Blog Hero” _builder_version=”4.10.6″ background_color=”#00AEEF” use_background_color_gradient=”on” background_color_gradient_start=”rgba(0,0,0,0)” background_color_gradient_end=”rgba(0,0,0,0)” background_blend=”multiply” custom_padding=”19px|0px|18px|0px||” animation_style=”slide” animation_direction=”top” animation_intensity_slide=”2%” locked=”off” global_colors_info=”{}”][et_pb_row _builder_version=”3.25″ background_size=”initial” background_position=”top_left” background_repeat=”repeat” custom_margin=”|||” custom_padding=”27px|0px|27px|0px” custom_width_px=”1280px” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”3.25″ custom_padding=”|||” global_colors_info=”{}” custom_padding__hover=”|||”][et_pb_text _builder_version=”4.10.6″ text_font=”||||||||” header_font=”|700|||||||” header_text_color=”#FFFFFF” header_font_size=”42px” header_line_height=”1.3em” background_size=”initial” background_position=”top_left” background_repeat=”repeat” text_orientation=”center” background_layout=”dark” max_width=”530px” module_alignment=”center” custom_padding=”|||” header_font_size_tablet=”” header_font_size_phone=”” header_font_size_last_edited=”on|desktop” locked=”off” global_colors_info=”{}”]<\/p>\n

Combinations in timetabling<\/h1>\n

[\/et_pb_text][et_pb_text _builder_version=”4.10.6″ text_text_color=”#FFFFFF” text_font_size=”16px” text_line_height=”1.9em” background_size=”initial” background_position=”top_left” background_repeat=”repeat” text_orientation=”center” max_width=”540px” module_alignment=”center” locked=”off” global_colors_info=”{}”]<\/p>\n

\u00a0Any thoughts or comments are welcome \u2013 just email mist@mistservices.co.uk<\/a><\/p>\n

[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”4.10.6″ _module_preset=”default” custom_padding=”17px||14px|||” global_colors_info=”{}”][et_pb_row _builder_version=”4.10.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.10.6″ _module_preset=”default” global_colors_info=”{}”][et_pb_text _builder_version=”4.10.6″ _module_preset=”default” text_text_color=”#000000″ global_colors_info=”{}”]<\/p>\n

Forget all that geeky maths \u2013 I\u2019ve been timetabling for the last 20 years and don\u2019t need some maths formula to tell me it\u2019s difficult!<\/p>\n

In the previous articles I\u2019ve in essence said that the biggest challenge in timetabling software is generating acceptable solutions in a sensible timeframe.<\/p>\n

Let\u2019s go back to a simple example:<\/p>\n

School operates a 5-day timetable and has 6 period in a day.<\/p>\n

 <\/p>\n

[\/et_pb_text][et_pb_image src=”https:\/\/www.mistservices.co.uk\/timetabling\/wp-content\/uploads\/2021\/11\/daystructure.png” alt=”Day structure” title_text=”Day Structure” align=”center” _builder_version=”4.10.6″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.10.6″ _module_preset=”default” text_text_color=”#000000″ global_colors_info=”{}”]<\/p>\n

Let\u2019s really simplify things \u2013 class 7A go round school together and never mix with any other students and let\u2019s pretend their curriculum is:<\/p>\n

 <\/p>\n

[\/et_pb_text][et_pb_image src=”https:\/\/www.mistservices.co.uk\/timetabling\/wp-content\/uploads\/2021\/11\/7acurriculum.png” alt=”7A Curriculum” title_text=”7A Curriculum” align=”center” _builder_version=”4.10.6″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.10.6″ _module_preset=”default” text_text_color=”#000000″ global_colors_info=”{}”]<\/p>\n

Question<\/strong> \u2013 How many ways (combinations) can you place those lessons into the periods (forget about one per day rules etc)<\/p>\n

Answer<\/strong> \u2013 Factorial 30 (30!)<\/p>\n

Scheduling that should be a relatively straight forward task for us as a human and a quick task for the computer. Although there might be a vast array of solutions, how many are acceptable solutions? Let\u2019s take one solution below; wouldn\u2019t have thought this was an acceptable solution!<\/p>\n

 <\/p>\n

[\/et_pb_text][et_pb_image src=”https:\/\/www.mistservices.co.uk\/timetabling\/wp-content\/uploads\/2021\/11\/7aschedule.png” alt=”7A Timetable” title_text=”7A Timetable” align=”center” _builder_version=”4.10.6″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.10.6″ _module_preset=”default” text_text_color=”#000000″ global_colors_info=”{}”]<\/p>\n

Now let\u2019s consider class 7B, they also have 30 periods, so the 7A and 7B curriculum is:<\/p>\n

 <\/p>\n

[\/et_pb_text][et_pb_image src=”https:\/\/www.mistservices.co.uk\/timetabling\/wp-content\/uploads\/2021\/11\/7ab_curriculum.png” alt=”7A and 7B curriculum” title_text=”7A and 7B curriculum” align=”center” _builder_version=”4.10.6″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.10.6″ _module_preset=”default” text_text_color=”#000000″ global_colors_info=”{}”]<\/p>\n

Question<\/strong> \u2013 If you schedule 7A and 7B how many solutions\/combinations are there?<\/p>\n

Answer<\/strong> \u2013 (30!)^2 i.e Factorial 30 squared<\/p>\n

Extension question<\/strong> – Let\u2019s say Year 7, 8 and 9 are all 2 fe entry<\/p>\n

Answer<\/strong> – (30!)^6\u00a0\u00a0 ~= 3 x 10^194<\/p>\n

But out of this number how many form a good timetable?\u00a0 The true number will be less (reasons below) but even though it will be less it’s still a huge number!\u00a0 As mentioned previously I’m no Mathematician, so thanks to Keith Johnson for checking\/correcting my work.<\/p>\n

Conclusion<\/strong><\/h2>\n

Wow, I never realised there were so many combinations to be had! On one hand this is true but in our simple curriculum, there is no blocking, and no teachers were considered, lesson spread, doubles and singles etc weren\u2019t considered either. So, the million-dollar question is how many of those combinations are valid? I don\u2019t know is the answer. Then even out of all the valid combinations the computer can\u2019t go through them all in any sensible timeframe!<\/p>\n

For the mathematicians out there – Timetabling is ‘NP Complete’, as so far, no polynomial algorithm is known for solving the problem.<\/p>\n

So, can a computer create a timetable? Yes, it can, but as the software is dependent on its algorithms and not being able to look at every combination, given your timetable constraints finding an acceptable solution in any sensible time might not be possible.<\/p>\n

Then what happens when the parameters are changed? For example, the curriculum allocation is changed, staffing is changed, or a part-time constraint is changed. One simple answer is you might need to start again or as a minimum review whether your current solution is an acceptable one given the new parameters.<\/p>\n

Every day I say I can\u2019t do the job I do without the software solutions available to schools, but they still need me! As years go on and the algorithms get better\/reduce time (and if anyone can say P=NP then my role will change). But until then in my opinion the human is still required as we have the working knowledge of what is an acceptable solution, not just whether something clashes or doesn\u2019t!<\/p>\n

With this said future articles are going to be:<\/p>\n

    \n
  1. What makes a good timetable?<\/li>\n
  2. Is scheduling without staff a good idea?<\/li>\n
  3. Are split groups a bad thing?<\/li>\n
  4. Changing school week<\/li>\n
  5. Part-time staff<\/li>\n
  6. Rules for scheduling<\/li>\n
  7. Degree of freedom<\/li>\n
  8. Order of scheduling (strategy)<\/li>\n
  9. Grade only teachers<\/li>\n
  10. Drawing a curriculum diagram<\/li>\n
  11. Option structures \u2013 heterogeneous, homogeneous blocks and course structure<\/li>\n
  12. How many option groups should I have?<\/li>\n
  13. Calculating curriculum demand<\/li>\n
  14. Teacher teams<\/li>\n
  15. Compatibility of time<\/li>\n
  16. Conflict matrix<\/li>\n
  17. Rooming fractions<\/li>\n<\/ol>\n

    All with the idea that you take ideas away that will help you formulate a timetabling strategy (what are your boulders, stones, and sand) that allows you success and you and your software work in partnership. Don\u2019t just rely on the big \u2018Schedule\u2019 button!<\/p>\n

    Still to this day I remember running a scheduling course and the training data was designed so that it wouldn\u2019t schedule. When this gentleman\u2019s computer stopped scheduling his question was where is the bigger \u2018Schedule\u2019 button!\u00a0 He was horrified that intervention or compromise was required!<\/p>\n

     <\/p>\n

    [\/et_pb_text][et_pb_divider divider_weight=”2px” _builder_version=”4.10.6″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_divider][et_pb_text _builder_version=”4.10.6″ _module_preset=”default” global_colors_info=”{}”]<\/p>\n

    Any questions please just ask or more information about the services we offer please click your software solution below.<\/strong><\/p>\n

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    Combinations in timetabling\u00a0Any thoughts or comments are welcome \u2013 just email mist@mistservices.co.ukForget all that geeky maths \u2013 I\u2019ve been timetabling for the last 20 years and don\u2019t need some maths formula to tell me it\u2019s difficult! In the previous articles I\u2019ve in essence said that the biggest challenge in timetabling software is generating acceptable solutions […]<\/p>\n","protected":false},"author":1,"featured_media":4399399,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[44,50,49,48],"tags":[46,19,47,18,45],"yoast_head":"\r\nCombinations in timetabling - MIST Services - Everything Timetabling<\/title>\r\n<meta name=\"description\" content=\"AT MIST Services with do everything timetabling. 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