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.