Assignment Problem : Minimization Type

let's look at another example for assignment problem this assignment problem deals with minimization problems so in this problem we have five mechanics and five machines we have to assign each mechanic to each mission so this is the data given since it is a minimization problem we can directly go with the row reduction for the no reduction we have to find the smallest value in each row so in the first show the smallest value will be 15 in the second row tis 33rd load is 12 4 through ad is 14 and fifth row at this level we have to subtract all the values I mean being the first row all the values will be 15 so it will be 5 0 10 10 and 14 and in the second row we have to subtract the second row value with the minimum value that is there 13 so it will be 0 6 70 0 and 6 similarly for all the other three rows so it will be eight five two zero three and in the fourth row it is zero six six to ten to throw it is three five eight zero and lemon after the Roddick row reduction we fall over the column reduction [Music] in the corner production we have to find the smallest value in each column the first column at a zero second column it is also zero third column it will be two fourth column to 0 and in the fifth column it is three so subtract the first column value with the minimum value 0 so if you will get 5 0 8 0 3 and the second column will be 0 6 5 6 5 and third column will be 8 15 2 minus 2 will be 0 for 6 fourth column will be 1000 to 0 and the last column will be level 3 0 7 & 8 so after the column reduction we have to proceed with the allocation of zeros so for the allocation of 0 I am right in the same tableau column here it will be 5 0 8 10 11:06 15:03 eight five zero zero zero six four two seven three five six zero eight bro cell allocation will be done only if there is a single zero in each row if there are more than one zero just ignore that row so in the first row we have only one zero I'm allocating to it I am also making sure that that this allocated zero does not intersect with any other allocated zeros which is done prior me in the second row we have two zeros and so I am ignoring it the third row we have three zeros are ignoring it also fourth row we have one one zero and I can allocate this zero because in either side of it I don't have any other allocation 0 so I am allocating this and in the fourth row and checking and I have only one zero and it does not if I suppose if I allocate it it does not intersect with any other allocated zeros so I'm allocating it now I go at the column wise in the first column I already have in allocated zero so I just leave it and the second column also I have another allocated Z look so I am ignoring it and in the third column I have one zeros so I am checking on all these sites it does not have any other allocated cell so I am finally getting it and the fourth row M in the fourth column it has an allocated zero film scholar I have only one zero suppose if I allocate this one it intersects with this allocated cell which is done prior so I ignore it so after allocation of cells I can see that each mechanic is not assigned to each machine so so one mechanic is still left that is the second mechanic is still left without animation so I have to proceed further what should I do is first take all the unassigned row unassigned rows are the rows which does not have any allocation of cells second row does not have any allocation so I am picking that one so if the row this ticked then I check and then I select these zeros in it in this thick drawer I have two zeros in it these two zeros have to select the columns in it so these two zeros so I have and select these two columns after selecting of this condom I have to each column now in this column I will check whether they haven't allocated cell in this column I haven't allocated cell in this row so I disrobe in this column I'll check whether Iseman allocated cell in this column we have this allocated cell which is in this row after doing all this I have to strike out all the unpicked rows we have 200 and picked rows here so I have I will strike the unpicked rows and then I will slightly pink columns so it will be this one and this one so after this I have to find my theta value for selecting the teacher value it will be the minimum value which is not being strengthened here the minimum value is 3 which is not being striped so the theta value will be 3 after selecting the theta value after construct a new table in this new table what I will do is this theta will be added with the values which has 2 intersection a cross like symbol a number which has a crop slang symbol will be added with the deeper value and and a nun know for the construction of the new table value we have the theta is equal to 3 so if a value has multiple lines over it we have to add the theta value with it if there is only a single line on a particular value we have to just write as it is without in without involving the theta value with the all the other values but does not have any other line we have to subtract it so the first value is fine since it has two lines on top of it I am going to add 3 with it which will be 5 plus 3 8 and 0 it has only single line on perfect alight as it is eight also ten has two lines over it so it will be thirty laven as it is here we have only single line so it is 0 8 plus 3 will be labbett single line 0 single line 3 again here we have another single line it will be 0 two lines so it will be three single like two single line zero again we have another single line here so five zero we have already added and it is again slope the rest of the values we have to subtract it with 3 so 6 minus 3 will be 3 15 minus 3 will be 12 3 minus 3 0 and then 6 minus 3 3 4 minus 3 1 7 minus 3 4 5 minus 3 2 6 minus 3 3 8 minus 3 5 after getting the new travel a tabular column we have to again allocate the self as we did before in the first row we have only 1 0 so I'm allocating it and it does not intersect so there is no problem and in the second row I have 3 0 so I am ignoring it in the third also I have to 0 so I am ignoring it and in the fourth row I have only 1 0 suppose if I allocate this one it does not intersect with any other cells any other unlike allocated cells so I am allocating it and in the last flow I have 1 0 if suppose I located it does it does not have any other allocated cells so there will be no issues I am allocating it now I am going through the column wise first column already has one cell allocated to it so no issues second column also has another allocated cell in the third column I have 1 0 suppose if I allocate this one there are no other allocated cells I'm assigning it to a fourth row already has an allocated zeros and in the fifth row I have two zeros suppose if I allocate this one there are no other allocated cell cells beside it or on top of it so I'm allocating this one now I can assign each mechanic to each mission that is the first mechanic is assigned to the second mission second mechanic assigned to the fifth mission third mechanic is assigned to the third mission for mechanic is assigned to the first mission fifth mechanic is assigned to the fourth cohesion so the total value which will be obtained from the original tabular column will be since the first mechanic is assigned to the second mission which will be 52nd mechanic to the fifth mission which will be 93rd mechanic to the third mission which will be 44th mechanic to the first mission which will be 14 again and mechanic to the fourth machine which will be 11 by summing up all these values will get a value of 73 so this will be the final result thank you

Channel: Mr ARUL SUJU D

Views: 316,146

Keywords: YouTube Editor

Id: I_1qPoD67bA

Length: 9min 5sec (545 seconds)

Published: Mon Feb 20 2017