MENENTUKAN SOLUSI OPTIMAL PADA PEMROGRAMAN LINIER DENGAN n FUNGSI OBJEKTIF MENGGUNAKAN SOLVER METODE SIMPLEKS

Abstract

Linear programming is a Mathematical model that uses programming language technique to
model and solve optimization problems with linear objective functions and constraints.
A Mathematical model for optimization problems such as, linear programming with one objective
function can be written as:
Objective Function: Minimum or Maximum f X1,X2 ,...,Xn 
Constraints:
 
 
  



 






m n m
k n k
n
f X ,X ,...,X b
f X ,X ,...,X b
f X ,X ,...,X b
1 2
1 2
1 1 2 1


X1,X2 ,...,Xn  0
However, in fact there are sometimes more than one objective functions that should be reached,
either be maximized, minimized or both. This research aims to determine procedures in obtaining
the optimal solution of linear programming with n objective functions using Solver simplex
method in a sample case.
The method of this research is a literature study by collecting and studying references that are
relevant about linear programming models with n objective functions, Solver Parameters, and
simplex method. Then, determining procedures to obtain the optimal solution to the model in
a sample case.
The result shows that the procedures of obtaining optimal solution in a linear programming
model with n objective functions using Solver simplex method are: identifying and understanding
the problem; determining decision variables Xi, objective functions fi Xi, and constraints
gi Xi; formulating components in linear programming model into a spreadsheet MS Excel;
solving the optimal value for each objective function with Solver Parameters; determining the
optimal value for i th objective function as the i th goal value; determining deviation function for
each objective function; giving weights wi for the deviation function of each objective function;
determining the maximum value of feasible deviation function from its objective functions
(variable Q); minimizing variable Q to obtain the optimal solution; and making decision.