Flashcards in Simplex Algorithm Deck (11)

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1

## Formulating a problem

###
Form as a table

Add a slack variable and make them equal to the maximum

2

## Tableau

### Basic Variable | Variables | Slack Variables | Value | Row Ops

3

## Setting up the initial tableau

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Rewrite the maximise P = ... as P - ... = 0

Write in the coefficients of every variable/slack variable in the columns and P in the basic variable

4

## Solving the problem

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Identify the most negative value in the profit equation and label as your pivot

Calculate value/pivot for each row and choose the smallest positive value

Divide the entire row by the pivot and write the variable of the pivot in that rows basic variable box

Add/subtract multiples of that row from others so the pivot column contains a 0

Repeat until there are no negatives in the pivot row

5

## Simplex answers

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Where a variable has one 1 and the others 0, it takes the value of the output of the row with a 1

Where a variable has more than 1 non-zero, it is 0

6

## Setting up equations

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When the sign is <= add a slack variable and set the sign to =

When the sign is >= subtract a surplus variable, add an artificial variable and set the sign to =

7

## Two-step simplex set up

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1. Change your inequalities to equations

2. Minimise a1 + a2 + ... so maximise I = -a1 - a2 - ...

3. Rearrange the inequalities in terms of -a1, -a1... and substitute in

4. Rearrange the I equation so it is equal to a number

8

## Two-step simplex tables

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1. Carry out the simplex regularly with the I row

2. If at the end I = 0, it is possible, delete the artificial columns as they are 0 and the I row and use simplex for the Profit function

3. If I is not equal to 0, then the artificial variables are non-zero and it can't be solved

9

## Surplus variable definition

### The amount by which a solution exceeds the minimum value of a quantity

10

## Big M Method

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Let M represent an arbitrarily large number

1. Set up each constraint by adding slack, surplus, artificial variables

2. Subtract M(a1+a2+…) from the objective

3. Rearrange to equal a number and group each coefficient

4. Solve as you would a regular simplex problem

Can be solved in a calculator by using M as 1000 e.g

11