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.