A steel mill produces sheets of steel in 3 sizes. These sizes are 100, 80 and 55 inches. Unfortunately, demand is in 3 other sizes; 45,30 and 18 inches.How should the mill cut the sheets to minimize waste? Possible combinations 45" sheet 30" sheet 18" sheet Waste (inches) Number of sheets Total Waste 1 100" sheet 2 0 0 10 1 10 2 1 1 1 7 1 7 3 1 0 3 1 1 1 4 0 3 0 10 1 10 5 0 2 2 4 1 4 6 0 1 3 16 1 16 7 0 0 5 10 1 10 8 80" sheet 1 1 0 5 1 5 9 1 0 1 17 1 17 10 0 2 1 2 1 2 11 0 1 2 14 1 14 12 0 0 4 8 1 8 13 55" sheet 1 0 0 10 1 10 14 0 1 1 7 1 7 15 0 0 3 1 1 1 Totals 7 12 26 Total 122 Demand 150 200 175 Problem A steel mill produces sheets of steel in three different sizes. Demand, however, is in 3 other, smaller, sizes. How should the company cut the sheets of steel in order to minimize waste? Solution 1) There are only a limited number of ways to cut the sheets. The variables are the number of times we have to cut a sheet in a certain way. In worksheet Cutstock these are defined as Sheets_used. 2) The constraints are simple and straightforward. Sheets_made = Demand Sheets_used >= 0 via the Assume Non-Negative option Sheets_used = integer 3) The objective is to minimize waste. This is defined on the worksheet as Total_waste. Remarks In some situations it may seem rather difficult to write out all the possibilities for cutting stock as is done in this model. There is a technique that lets the computer do this, called column generation. It is beyond the scope of this example to fully discuss this technique.