Using Variable Domain Functions in Optimization Problems
Explore how variable domain functions like @GIN and @BIN are utilized in optimization problems solved using LINGO programming. Examples include solving knapsack problems, job assignment, and finding optimal solutions with binary variables.
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Presentation Transcript
Using Variable Domain Functions The variable domain functions are @GIN : It used for any positive integer value @BIN : It used for any binary value ( 0 or 1)
Example 1 Solve the following problem by LINGO MAX Z= 18X1+14X2+8X3+4X4 Subject to 15x1+12x2+7x3+4x4+x5 37 x1,x2,x3,x4,x5 =(0,1)
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.
