It may seem logical that an easy way to solve integer programming problems is to round off fractional solution values to integer values. However, that can result in less than optimal (i.e., suboptimal ) results. This outcome can be seen by using graphical analysis. As an example, consider the total integer model for the machine shop formulated in the previous section:
First, we will use Excel to solve this model as a regular linear programming model without the integer requirements, as shown in Exhibit 5.1 ## Exhibit 5.1. Notice that this model results in a noninteger solution of 2.22 presses and 5.56 lathes, or x
Rounding noninteger solution values up to the nearest integer value can result in an infeasible solution . In a model in which the constraints are all (and the constraint coefficients are positive), a feasible solution is always ensured by rounding down . Thus, a feasible integer solution for this problem is A feasible solution is ensured by rounding down noninteger solution values .
However, one of the difficulties of simply rounding down non-integer values is that another integer solution may result in a higher profit (i.e., in this problem, there may be an integer solution that will result in a profit higher than $950). In order to determine whether a better integer solution exists, let us analyze the graph of this model, which is shown in Figure 5.1. ## Figure 5.1. Feasible solution space with integer solution points
In Figure 5.1 the dots indicate integer solution points, and the point x A rounded-down integer solution can result in a less than optimal (suboptimal) solution . This graphical analysis explicitly demonstrates the error that can result from solving an integer programming problem by simply rounding down. In the machine shop example, the optimal integer solution is x The traditional approach for solving integer programming problems is the |

Introduction to Management Science (10th Edition)

ISBN: 0136064361

EAN: 2147483647

EAN: 2147483647

Year: 2006

Pages: 358

Pages: 358

Authors: Bernard W. Taylor

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