This problem deals with merging two statistical database files; the Income Data File and the Population Data File. Because of the large sample sizes, the problem can be solved with an algorithmic evaluation approach that controls the size of the network, and systematically considers a subset of all columns at each iteration.
There are two methods of solving this problem:
1. Simplex method
2. Algorithmic method
The simplex method solves the problem by using matrix- vector notations for the underlying linear algebra. During the simplex iteration, basic and non-basic variables are switched until the reduced cost vectors become nonnegative. The resulting current basic variable is the optimal solution that contains the minimum distance of the family size.
The algorithmic method contains a sequence of smaller sub-models which solves the overall file merge problem. The construction of each sub-model is based on evaluating the reduced cost of all variables. The recorded distances are computed during runtime and variables are either chosen to be candidates or ignored, resulting in controlled sample sizes during iterations.
The example reflects both methods plus a combination of the two.
Network Program, Simplex Method, Column Generation, Mathematical Derivation
Download AIMMS Example
You can download an AIMMS example dealing with this problem via the link below, and run it after installing the AIMMS software. If you don't have an AIMMS license yet, you can download a free license of AIMMS.
Please make sure to save this file including the .aimmspack extension so that it can be opened by AIMMS.
This example application is a simplification of reality. Please do not hesitate to contact us to discuss how AIMMS enables you to build a complete optimization application that captures the full complexity of your problem.
Screenshot AIMMS Example