{"id":4399319,"date":"2021-10-25T09:00:11","date_gmt":"2021-10-25T09:00:11","guid":{"rendered":"https:\/\/www.mistservices.co.uk\/timetabling\/?p=4399319"},"modified":"2021-10-15T11:16:20","modified_gmt":"2021-10-15T11:16:20","slug":"can-software-generate-the-school-timetable-part-2","status":"publish","type":"post","link":"https:\/\/www.mistservices.co.uk\/timetabling\/can-software-generate-the-school-timetable-part-2\/","title":{"rendered":"Can software generate the school timetable \u2013 Part 2"},"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

Can software generate the school timetable – Part 2<\/h1>\n

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\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

In the last article there were two Sudoku puzzles where the first one was relatively straight forward but the second one was harder!<\/p>\n

What was the difference between solving them?\u00a0 For me as a non-mathematician the differences were:<\/p>\n

1 \u2013 Time, the second one took me longer!<\/p>\n

2 \u2013 I had to guess at times on the second one (and then check my work)!<\/p>\n

Just to re-iterate I\u2019m no maths genius and haven\u2019t had a maths lesson for pushing 30 years but to put it into something maths framework:<\/p>\n

Sudoku is what is known as a NP problem!<\/p>\n

Which basically means it might take time and effort to solve but once it\u2019s solved it\u2019s pretty quick to check that it\u2019s correct.<\/p>\n

For all you the mathematically minded people then think of P problems (easily solved by computers) and NP problems which aren\u2019t easily solvable, but if you present a potential solution it\u2019s easy to verify whether it\u2019s correct or not.<\/p>\n

So, all P problems are NP problems.<\/p>\n

Hold up, Chris \u2013 getting a bit technical there!\u00a0 Let’s put it back into timetabling terms; given time a timetable (schedule) can be generated and it\u2019s easy to check (verify) that it doesn\u2019t break any rules.<\/p>\n

That\u2019s great then, the computer\/software will generate a timetable for me.\u00a0 Well yes and no \u2013 timetabling is classed as NP-Hard which again for the mathematicians out there will know what that means or you can have a Google.\u00a0 To try to contextualise what a NP-Hard problem is let\u2019s take a classic NP-hard problem the Travelling Sales Man and have a bit of fun.\u00a0 The following example if taken from the book \u2018The Millennium Problems\u2019 by Keith Devlin<\/p>\n

Chris is now a Travelling sales man and is based in City A but has customers in Cities B, C and D to which he has to visit all of them.\u00a0 To save time and petrol, it makes sense to plan a route so that the total distance travelled is as short as possible.<\/p>\n

Here is a table that shows the distance between then cities<\/p>\n

[\/et_pb_text][et_pb_image src=”https:\/\/www.mistservices.co.uk\/timetabling\/wp-content\/uploads\/2021\/10\/tsp_cities.jpg” alt=”Travelling sales person – Cities” title_text=”Travelling sales person – Cities” 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” global_colors_info=”{}”]<\/p>\n

Due to one-way systems some journeys aren\u2019t the same distance it all depends on the direction of travel.<\/p>\n

Task<\/strong> \u2013 order the three cities to minimise distance travelled.<\/p>\n

Below is a table showing the different routes i.e. row one is City A to City B, leave City B to go to City C etc<\/p>\n

[\/et_pb_text][et_pb_image src=”https:\/\/www.mistservices.co.uk\/timetabling\/wp-content\/uploads\/2021\/10\/tsp_journeytable.jpg” alt=”Travelling sales person – journey table” title_text=”Travelling sales person – journey table” 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” global_colors_info=”{}”]<\/p>\n

From the table above you can see the shortest route is 249 miles<\/p>\n

[\/et_pb_text][et_pb_image src=”https:\/\/www.mistservices.co.uk\/timetabling\/wp-content\/uploads\/2021\/10\/tsp_mileage.jpg” alt=”Travelling sales person – mileage table” title_text=”Travelling sales person – mileage table” 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” global_colors_info=”{}”]<\/p>\n

The number of combinations you had to test was 3 * 2 * 1 = 6 (ignore City A as that is your start\/finish).<\/p>\n

The above task was relatively straight forward, bit like the Sudoku \u2013 given a bit of time and thought and it was completed in five minutes.\u00a0 Having spent five minutes you get a call saying that City B doesn\u2019t need a visit, but City E has become a prospect.\u00a0 City E is 45 miles away from City A (in both directions).<\/p>\n

How do you feel about this?\u00a0 Does it impact on your answer\/route?<\/p>\n

Putting this into real-life timetabling, when you are scheduling you are working on a specific set of data and parameters, if after a days\u2019 worth of work should the data and\/or parameters change it might force you to start again!<\/p>\n

10 City \u2013 salesperson<\/strong><\/p>\n

Let\u2019s up the stakes a bit; If you had a salesperson who had to visit 10 cities then the number of solutions is 10 factorial i.e. 10! Which means<\/p>\n

10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800<\/p>\n

Wow I\u2019m not drawing that out in a table and working out myself!<\/p>\n

Can you see where I\u2019m going with this?\u00a0 How about 100 cities?\u00a0 We\u2019re in the realms of the number is so great that not even a super-computer can explore and compute them all.<\/p>\n

But Chris, this seems a little complicated.\u00a0 Yes, understanding or trying to quantify the problem is quite complicated but all I can say is for people like me it just means timetabling is a tough task which no computer can look through all the combinations (and check them) in a sensible time!\u00a0 I\u2019ve been timetabling for the last 20 years and not needed to understand any of the maths so fear not everyone can timetable.\u00a0 To me it\u2019s having the understanding\/strategy correct and as the computer can\u2019t explore all combinations it\u2019s about working in partnership i.e. break the task up and let the computer look at smaller problems.<\/p>\n

People might disagree with what I\u2019m going to say but for many schools the software can\u2019t just create a valid timetable given all your constraints i.e let’s type in all our data and press the Schedule button.\u00a0 Or it can\u2019t create a valid timetable in a sensible timeframe.\u00a0 All software works in different ways, so treat my text as general thoughts.<\/p>\n

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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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Can software generate the school timetable – Part 2\u00a0Any thoughts or comments are welcome \u2013 just email mist@mistservices.co.ukIn the last article there were two Sudoku puzzles where the first one was relatively straight forward but the second one was harder! What was the difference between solving them?\u00a0 For me as a non-mathematician the differences were: […]<\/p>\n","protected":false},"author":3,"featured_media":4399317,"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":[44,48],"tags":[46,19,47,18,45],"yoast_head":"\r\nCan software generate the school timetable \u2013 Part 2 - MIST Services - Everything Timetabling<\/title>\r\n<meta name=\"description\" content=\"AT MIST Services with do everything timetabling. 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