The Cutting-Stock Problem:
An Application of Integer Linear Programming

Description of the cutting-stock problem

Imagine that your company produces large rolls of paper. The rolls are 100 inches (100") wide, but you sell rolls of smaller widths to your customers. The customers can place orders for widths of any size, and you want to minimize the number of 100" rolls that you cut and minimize the amount of waste.

Formulation of problem

• The Verbal formulation
• The Mathematical formulation
• The AMPL code

Try solving your own problem

• Input the number of standards.
• Input the raw roll width.
• Input the data set: orders and widths.
• Execute the program and wait for the response.

Give it a try!

Comments and Suggestions

Give us your comments.

Acknowledgments

The pattern images are generated using routines from the gd 1.2 library.

The problem is solved using AMPL as the modeling language.

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