When it comes to simplex method it is known to be the general and powerful method and it considered to be the available method involved in solving different linear programming problem. While getting into depth of simplex computation procedure, you will understand the following steps:
Step 1: Need to formulate given problem in relation to standard maximization LPP
Step 2: Choose initial basic feasible solution that can initiate any iterations
Step 3: Look for objective function and find out there is any non-basic variable that can help to enhance objective function, and brought the basic solution. In case such variable exists, then move to next step.
Step 4: Test any given solution for ensuring optimality
Step 5: Continue with iterations and get an optimal solution which can be an indication that there is a possibility of having unbounded solution
Linear programming simplex method
Simplex method is adopted with an idea to solve problems related to linear programming. Before getting into simplex method, it is essential convert linear program into standard form:
Max c1x1+c2x2+…+cnxnc1x1+c2x2+…+cnxn
Subject to: a11x1+a12x2+….+a1nxn=b1a11x1+a12x2+….+a1nxn=b1
a21x1+a22x2+….+a2nxn=b2a21x1+a22x2+….+a2nxn=b2
……………………………………
am1x1+am2x2+….+amnxn=bmam1x1+am2x2+….+amnxn=bm
x1x1 ≥≥ 0, x1x1 ≥≥ 0, …….., xnxn ≥≥ 0.
Reasons to study dual simplex method
- It helps to select initial basis without even adding any artificial variable
- It enables in different types of sensitivity testing
- It allows in solving any kind of integer programming problems
Steps in Dual simplex algorithm
- Formulate any mathematical model related to given linear programming problem. You need to convert inequality constraint in LPP into equality constraint and this can finally help in writing the problem in standard form.
- Calculate any of initial basic feasible solution by providing zero value to decision variables. It is a solution that can be found in initial dual simplex table.
- In case the values under X5 column ≥ 0 then make sure not to implement dual simplex method as optimal solution can be gained by simplex method. On the other hand, if the value is under X5 column <0 and the current solution becomes infeasible.
- Choose any smallest negative value that is under X5 The row might also indicate any smallest negative value.
- Choose the non-basic variables in index row (Z1 C1), and finally divide value through corresponding values of any key row.
Key column =
| Min | zj cj ——– aij |
: | aij < 0 |
Making use of dual simplex method directly
Choose the tableau and finally solve problem through dual simplex method:
Make any indicated dual simplex pivot gives:
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