Optimization Problems and Solutions Using LINGO Programming
Explore optimization problems solved using LINGO programming. Examples include minimizing total job assignment costs, finding optimal solutions, and solving knapsack problems. Follow along with detailed images and instructions for each scenario presented.
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LINGO LINGO LAB LAB 3/4 3/4
Example 2 Suppose that we have 3 jobs (1, 2, 3) waiting for being performed and 3 machines (A, B, C) that can be used to perform these jobs. The assignment costs of the jobs to the machines are given in the following table. Find the minimum total cost one-to-one assignment between the jobs and the machines by using lingo programming.
Min z= 9x11+6x12+3x13+4x21+5x22+6x23+3x31+7x32+11x33 Subject to x11+x12+x13=1 x21+x22+x23=1 x31+x32+x33=1 x11+x21+x31=1 x12+x22+x31=1 x13+x23+x33=1 x11, x12,x13,x21,x22,x23,x31,x32 and x33 are binary variables
Example 3 Find the optimal solution by using LINGO Max z= 3x1+x2+3x3 Subject to -x1+2x2+x3 4 4x2-3x3 2 X1-3x2+2x3 3 x1,x2 and x3 0 and integer
Example 4 Solve the following knapsack problem by using lingo software : Maximize z= 5X1+3X2+8X3+9X4+4X5 Subject to 3X1+X2+5X3+4X4+X5=25 0 X1 2 , 0 X2 1 , 0 X3 4 , 0 X4 2, 0 X5 1 X1,X2,X3,X4,and X5 and integer.
Example 1 : Find the optimal solution of the following model Min z = 200X1 + 250X2 + 320X3 s.t. 13X1 + 11X2 +9X3 12000 X1 5000 X2 4000 X3 10000 X3 100 X1, X2, X3 0 and integer
