Waste Minimisation in Stock Cutting

Problem: Cutting sheet or coil materials to varying lengths while minimising waste is demonstrated in this model.

Consider a product produced in rolls or sheets - fabric, sheet metal, or carpeting. A manufacturer of this product is constantly faced with a problem. His machinery produces rolls of a single standard width, but he must sell to an non-standardised marketplace. 

This model applies linear programming to the problem of cut patterns. 

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Given the sizes required, the amount of each size demanded, and the cut patterns available, the model minimises the waste cost associated with meeting demand.

You're the production manager in a sheet metal plant. You turn out rolls of sheet metal of a particular width. Your customers use your product in different ways requiring rolls of different widths. 

To accommodate their needs, you can cut a roll of sheet metal into more than one narrower roll. Your goal is to waste as little of the sheet metal as possible by choosing patterns that best utilise the width of a roll and closely matching the length requirements of various sizes. 

Each wasted edge strip and each length of metal cut to an unneeded width adds to your total waste cost. You must select cut patterns that meet customer needs and minimise total waste costs.

Your objective is to minimise the total waste cost - the sum of edge waste and end waste. How many feet of each pattern should you cut in order to meet customer demand at the lowest cost?

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