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. | |||||||