Solution Of Ventilation Network Problem By Linear Programming

This paper deals with the application of linear programming to the solution of mine ventilation network problems which involve only the controlled splitting of air. An airway whose air quantity is to be controlled to a prescribed value is called a "fixed-quantity" airway. In a network where the fixed-quantity airways are increased in number and are distributed such that the air quantities for the remaining airways are uniquely determined by Kirchhoff's first law, the problem reduces to determining the head losses and locations for air regulators and fans. This is one of the network problems encountered most often in underground coal mines. By formulating Kirchhoff's second law as a set of linear constraints and the total air horsepower supplied by fans as a linear objective function which is to be minimized, the problem is analyzed through the technique of linear programming. Some important properties of the problem are discussed and examples are presented.