# Decision Mathematics 2 - Allocation Problems

Cards to help with D2 Allocation problems (EDEXCEL)

## Matrix Reduction

• Subtract the smallest value in each row from every other value in that row
• Subtract the smallest value in each column from every other value in that column
• This gives you the opportunity cost matrix
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## Hungarian Algorithm

• Reduce rows then columns
• Test for optimality by covering all zero cells with as few lines as possible.  If optimal, the number of lines covering the zero cells should be equal to n for an nxn matrix
• Revise the opportunity cost matrix
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## Matrix Revision

• Find the smallest uncovered number in the matrix and subtract this from all uncovered values in the matrix
• Add the same number to all cells that are covered by two lines
• If a cell is only covered by one line, do not add or subtract anything
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## Modifying a matrix to maximise

Subtract every value in the table from the largest value in the table (so to 'flip' the numbers so that the smallest is now the biggest and vice versa) and continue as normal by reducing rows, then columns, then checking for optimality, then modifying.

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## Linear Programming

For any matrix, each row and column must only have one value chosen.  Therefore, when forming a linear program, you must add one of each cell and total to one.  Example, for a matrix with 3 workers P, Q & R and 3 jobs A, B & C;

Pa + Pb + Pc = 1

Qa + Qb + Qc = 1

Ra + Rb + Rc = 1

Pa + Qa + Ra = 1

Pb + Qb + Rb = 1

Pc + Qc + Rc = 1

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Ooh! This looks useful for next year :3 thanks for uploading! :)

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No problemo :)

I'll be posting all my other D2 stuff, but as my exam is like 5 days away, I'll do it after.

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Thanks a lot! My exam for D2 is this week too, best of luck :)

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I wish you all the best for tomorrow.  To tell you the truth, I'm totally unprepared.  I've got M2 aswell.  GOOD LUCK!!!

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Could do with some diagrams. If you wish I could prepare one or two but I am not sure how to upload onto here. Otherwise very good for flash cards

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