A planing mill uses 3 different types of planers. What planers should the company use
to minimize cost? The total job has to be finished in 3 hours.    
Characteristics of planers  
  Speed (ft/min) Cost ($/hour) Maximum wood thickness (inches)
Planer 1 5 $150 6
Planer 2 7 $190 4
Planer 3 8 $225 2
Wood to be planed (ft)          
  1" 2" 3" 5" Hours Cost
Planer 1 0 0 0 0 0.00 $0.00
Planer 2 0 0 0   0.00 $0.00
Planer 3 0 0     0.00 $0.00
Total 0 0 0 0 $0.00
Demand 500 800 600 300      
Problem              
A planing mill has three different planers. Each planer has a different speed, cost to operate and
maximum thickness of wood it can handle. What planers should the mill use to minimize cost, given
an amount of wood and no more than 3 hours to do the job?      
               
Solution              
The solution is structurally very similar to the one found on worksheet Alloc1.    
1) The variables are the amounts of wood that go through the different planers. In worksheet
Process, these are given the names Wood_through_planer1, Wood_through_planer2 and
Wood_through_planer3.            
2) The logical constraints are all defined via the Assume Non-Negative option:    
  Wood_through_planer1 >= 0        
  Wood_through_planer2 >= 0        
  Wood_through_planer3 >= 0        
The time and demand constraints give          
  Total_hours <= Hours_available        
  Total_planed >= Demand          
3) The objective is to minimize cost and this is defined on the worksheet as Total_cost.
               
Remarks              
This is only a small example of a process selection. An example where process selection is very
important is the oil industry. A process selection model is often used to decide what method to use
to create a product.