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Home > Operation Research > Dual Simplex method example
5. Dual simplex method example ( Enter your problem )
( Enter your problem )
  1. Algorithm (using `Z`-row method)
  2. Example-1 (using `Z`-row method)
  3. Example-2 (using `Z`-row method)
  4. Example-3 (using `Z`-row method)
  5. Algorithm (using `Z_j-C_j` method)
  6. Example-1 (using `Z_j-C_j` method)
  7. Example-2 (using `Z_j-C_j` method)
  8. Example-3 (using `Z_j-C_j` method)
  9. Algorithm (using `C_j-Z_j`method)
  10. Example-1 (using `C_j-Z_j`method)
  11. Example-2 (using `C_j-Z_j`method)
  12. Example-3 (using `C_j-Z_j`method)
 		Other related methods
  1. Formulate linear programming model
  2. Graphical method
  3. Simplex method (BigM method)
  4. Two-Phase method
  5. Primal to dual conversion
  6. Dual simplex method
  7. Integer simplex method
  8. Branch and Bound method
  9. 0-1 Integer programming problem
  10. Revised Simplex method
4. Example-3 (using `Z`-row method)
(Previous example)		6. Example-1 (using `Z_j-C_j` method)
(Next example)

5. Algorithm (using `Z_j-C_j` method)


Algorithm
Dual simplex method Steps (Rule)
Step-1: Formulate the Problem

a. Formulate the mathematical model of the given linear programming problem.

b. If the objective function is minimization type then change it into maximization type.

c. all `>=` constraint to `<=` constraint by multiply -1

d. Transform every `<=` constraint into an `=` constraint by adding a slack variable to every constraint and assign a 0 cost coefficient in the objective function.
Step-2: Find out the Initial basic solution

Find the initial basic feasible solution by setting zero value to the decision variables. That shown in the example-1
Step-3: Test for Optimality

a. If all the values of `X_B >= 0`, then current solution is the optimal solution, terminate the process.

b. If any `X_B < 0`, then select the Minimum negative `X_B` and this row is called key row.

c. Find `"Ratio"=(Z_j-C_j)/"KeyRow"_j` and `"KeyRow"_j < 0`.

d. Find Least negative ratio, and this column is called key column.

e. Find the new solution table.

f. Repeat step-3.



This material is intended as a summary. Use your textbook for detail explanation.
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4. Example-3 (using `Z`-row method)
(Previous example)		6. Example-1 (using `Z_j-C_j` method)
(Next example)


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