burlingham textile company dmm

BURLINGHAM TEXTILE COMPANY

Presented By:

Bhavna Pruthi

Ishu Singla

Soumya Sachdeva

About Case

• Brenda Last is the personnel director at Burlingham Textile Company. She has to fill 5 supervisory positions in Carding(C), Spinning(S), Weaving(W), Inspection(I) and Shipping(SH) for which she took a written test of 10 applicants. The test score for each module of the applicants are given where the higher the score is better the candidate.

Test Module ScoreCarding Spinning Weaving InspectionShipping

Roger 68 75 72 86 78Melissa 73 82 66 78 85Angela 92 101 90 79 74Maureen 87 98 75 90 92Fred 58 62 93 81 75Bob 93 79 94 92 96Ellen 77 92 90 81 93David 79 66 90 85 86Mary 91 102 95 90 88Marilu 72 75 67 93 93

The above problem can be solved by Hungarian method. But it has 2 limitations:

1.Problem should be of minimum type. Since our problem is of maximum type, we subtract each term from the highest term i.e. 102, to make it minimum.

2. Problem should be in form of square matrix. To achieve this, we add 5 dummy columns after first step.

LIMITATIONS OF HUNGARIAN METHOD

New Problem

C S W I SH D1 D2 D3 D4 D5Roger 34 27 30 16 24 0 0 0 0 0

Melissa 29 20 36 24 17 0 0 0 0 0Angela 10 1 12 23 28 0 0 0 0 0

Maureen 15 4 27 12 10 0 0 0 0 0Fred 44 40 9 21 27 0 0 0 0 0Bob 9 23 8 10 6 0 0 0 0 0

Ellen 25 10 12 21 9 0 0 0 0 0David 23 36 12 17 16 0 0 0 0 0Mary 11 0 7 12 14 0 0 0 0 0

Marilu 30 27 35 9 9 0 0 0 0 0

Solution• Step 1 : There should be a zero in each

row and column and if it is not so then we can add it by subtracting smallest element of that row or column from each element

• Since in the above problem column 1,3,4,5 doesn’t have any zero we would subtract 9,7,9,6 respectively from each row and we would get our table as

C S W I SH D1 D2 D3 D4 D5Roger 25 27 23 7 18 0 0 0 0 0Melissa 20 20 29 15 11 0 0 0 0 0Angela 1 1 5 14 22 0 0 0 0 0Maureen 6 4 20 3 4 0 0 0 0 0Fred 35 40 2 12 21 0 0 0 0 0Bob 0 23 1 1 0 0 0 0 0 0Ellen 16 10 5 12 3 0 0 0 0 0David 14 36 5 8 10 0 0 0 0 0Mary 2 0 0 3 8 0 0 0 0 0Marilu 21 27 28 0 3 0 0 0 0 0


Melissa 20 20 29 15 11 0 0 0 0 0Angela 1 1 5 14 22 0 0 0 0 0

Maureen 6 4 20 3 4 0 0 0 0 0Fred 35 40 2 12 21 0 0 0 0 0Bob 0 23 1 1 0 0 0 0 0 0

Ellen 16 10 5 12 3 0 0 0 0 0David 14 36 5 8 10 0 0 0 0 0Mary 2 0 0 3 8 0 0 0 0 0

Marilu 21 27 28 0 3 0 0 0 0 0

Subtracting from the uncovered values, the minimum value amongst them i.e. 1 adding it to the intersectional points of lines


Melissa 19 19 28 14 10 0 0 0 0 0Angela 0 0 4 13 21 0 0 0 0 0

Maureen 5 3 19 2 3 0 0 0 0 0Fred 34 39 1 11 20 0 0 0 0 0Bob 0 23 1 1 0 1 1 1 1 1

Ellen 15 9 4 11 2 0 0 0 0 0David 13 35 4 7 9 0 0 0 0 0Mary 2 0 0 3 8 1 1 1 1 1

Marilu 21 27 28 0 3 1 1 1 1 1


Melissa 19 19 28 14 10 0 0 0 0 0Angela 0 0 4 13 21 0 0 0 0 0

Maureen 5 3 19 2 3 0 0 0 0 0Fred 34 39 1 11 20 0 0 0 0 0Bob 0 23 1 1 0 1 1 1 1 1

Ellen 15 9 4 11 2 0 0 0 0 0David 13 35 4 7 9 0 0 0 0 0Mary 2 0 0 3 8 1 1 1 1 1

Marilu 21 27 28 0 3 1 1 1 1 1

Subtracting 1 from all the uncovered values which is minimum amongst them and adding the same at intersectional points of lines

C S W I SH D1 D2 D3 D4 D5Roger 23 25 21 5 16 0 0 0 0 0Melissa 18 18 27 13 9 0 0 0 0 0Angela 0 0 4 13 21 1 1 1 1 1Maureen 4 2 19 1 2 0 0 0 0 0Fred 33 38 0 12 19 0 0 0 0 0Bob 0 23 1 1 0 2 2 2 2 2Ellen 14 8 3 10 1 0 0 0 0 0David 12 34 3 6 8 0 0 0 0 0Mary 2 0 0 3 8 2 2 2 2 2Marilu 21 27 28 0 3 2 2 2 2 2

Solution

The following appointments would be made by Brenda:

• Carding - Angela

• Spinning - Mary

• Weaving - Fred

• Inspection - Marilu

• Shipping - Bob

APPOINTMENT LETTER

APPOINTMENT LETTER

Part B

• If Applicant selected for carding job doesn’t join then to whom should Brenda offer the next job?

Assumption

If candidate doesn’t join the post offered to him/her then the company would not offer any other position in the organization because

1.Selections are done by optimizing scores of all candidates in all departments

2.There is no guarantee that he/she would join the new position offered to him/her

3.If one is given offer then others might bargain for departments

C S W I SH D1 D2 D3 D4Roger 23 25 21 5 16 0 0 0 0Melissa 18 18 27 13 9 0 0 0 0Maureen 4 2 19 1 2 0 0 0 0Fred 33 38 0 12 19 0 0 0 0Bob 0 23 1 1 0 2 2 2 2Ellen 14 8 3 10 1 0 0 0 0David 12 34 3 6 8 0 0 0 0Mary 2 0 0 3 8 2 2 2 2Marilu 21 27 28 0 3 2 2 2 2

Now Angela is not joining so we would delete her row from the optimal table and solve further.


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Solution

Following appointments would be made by Brenda

• Carding – Bob

• Spinning - Mary

• Weaving - Fred


• Shipping - Ellen

APPOINTMENT LETTER

APPOINTMENT LETTER

Part C

• If Applicant selected for carding and spinning job doesn’t join then to whom should Brenda offer the next jobs?

Now Angela and Mary are not joining so we would delete their row from the optimal table and solve further.

C S W I SH D1 D2 D3Roger 23 25 21 5 16 0 0 0Melissa 18 18 27 13 9 0 0 0Maureen 4 2 19 1 2 0 0 0Fred 33 38 0 12 19 0 0 0Bob 0 23 1 1 0 2 2 2Ellen 14 8 3 10 1 0 0 0David 12 34 3 6 8 0 0 0Marilu 21 27 28 0 3 2 2 2

Since column 2 doesn’t have any zero we subtract 2 from each element of column 2. Now our problem becomes

C S W I SH D1 D2 D3Roger 23 23 21 5 16 0 0 0Melissa 18 16 27 13 9 0 0 0Maureen 4 0 19 1 2 0 0 0Fred 33 36 0 12 19 0 0 0Bob 0 21 1 1 0 2 2 2Ellen 14 6 3 10 1 0 0 0David 12 32 3 6 8 0 0 0Marilu 21 25 28 0 3 2 2 2

Subtracting minimum valve of all points which were not covered by lines that is 1 from all points which are not covered by lines

and adding the same at intersectional points of lines

C S W I SH D1 D2 D3Roger 22 22 20 4 15 0 0 0

Melissa 17 15 26 11 8 0 0 0Maureen 4 0 19 1 2 1 1 1

Fred 33 36 0 12 19 1 1 1Bob 0 21 1 1 0 3 3 3

Ellen 13 5 2 9 0 0 0 0David 11 31 2 5 7 0 0 0Marilu 21 25 28 0 3 3 3 3

Solution

Following appointments would be made by Brenda

• Carding – Bob

• Spinning - Maureen

• Weaving - Fred


• Shipping - Ellen

APPOINTMENT LETTER

APPOINTMENT LETTER

Part D

• Who would be the third applicant if three of the jobs offers were declined?

Assumption

• It is assumed that three offers were declined by the persons who were offered the position of Carding, Spinning and weaving

C S W I SH D1 D2Roger 22 22 19 4 15 0 0Melissa 17 15 25 12 8 0 0Maureen 4 0 18 1 2 3 3Bob 0 21 0 1 0 3 3Ellen 13 5 1 9 0 0 0David 11 31 1 5 7 0 0Marilu 21 25 27 0 3 3 3

Subtracting 1 from the uncovered values which is the minimum amongst them and adding the same at

intersectional points of lines

C S W I SH D1 D2Roger 21 21 18 3 14 0 0Melissa 16 14 24 11 7 0 0Maureen 4 0 18 1 2 4 4Bob 0 21 0 1 0 4 4Ellen 13 5 1 9 0 1 1David 10 30 0 4 6 0 0Marilu 21 25 27 0 3 4 4

APPOINTMENT LETTER

APPOINTMENT LETTER

Solution

Following appointments would be made by BrendaCarding – BobSpinning – Maureen Weaving - DavidInspection - MariluShipping - Ellen

Part E

• Brenda wants to retain a few of the people for the supervisor positions which she believes would open up soon. She has two vacant clerical positions which she want to offer to the 2 best candidates not selected in five original supervisor positions. Then when the positions open, she can move these people into them. How should she identify these two people?

Solution

Since these jobs at present do not specify the nature of supervisory work applicants would have to do when the positions open and at present they require to do clerical work, so she should offer these jobs to the candidates with highest total marks amongst those not selected for any of the supervisory job.

Total score of candidates not selected for any of the job

• Roger 379

• Melissa 384

• Maureen 442

• Ellen 433

• David 406

Top two scorers are Maureen and Ellen she should offer them the clerical positions

APPOINTMENT LETTER

APPOINTMENT LETTER

THANK YOUTHANK YOU

burlingham textile company dmm

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