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Lindo Output

In: Computers and Technology

Submitted By josefh
Words 620
Pages 3
0 1 Integer Linear Programs: Using INT Command in LINDO restricts a variable to being either 0 or 1. These variables are often referred to as binary variables. In many applications, binary variables can be very useful in modeling all or nothing situations. Examples might include such things as taking on a fixed cost, building a new plant, or buying a minimum level of some resource to receive a quantity discount.

Example: Consider the following Knapsack Problem

Maximize 11X1 + 9X2 + 8X3 + 15X4

Subject to: 4X1 + 3X2 + 2X3 + 5X4  8, and Xi either o or 1.

Using LINDO, the problem statement is

Max 11X1 + 9X2 + 8X3 + 15X4 S.T. 4X1 + 3X2 + 2X3 + 5X4 8 END INT X1 INT X2 INT X3 INT X4

The click on SOLVE. The output shows the optimal solution and the optimal value after 8 Branch and Bound Iterations

Note that instead of repeating INT four times one can use INT 4. The first four variables appeared in the objective function.

OBJECTIVE FUNCTION VALUE

1) 24.00000

VARIABLE VALUE REDUCED COST X1 0.000000 11.000000 X2 1.000000 9.000000 X3 0.000000 8.000000 X4 1.000000 15.000000

ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.000000

NO. ITERATIONS= 8

General Integer Linear Programs: Standard LP assumes that decision variables are continuous. However, in many applications, fractional values may be of little use (e.g., 2.5 employees). On the other hand, as you know by now, the integer linear programs are more difficult to solve, you might ask why we bother. Why do we not simply use a standard linear program and round the answers to the...

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