FIRST CASE 



SECOND CASE 



Figure 2. — Schematic of work road configurations for optimum spaaing 



The above expressions were summed into a total cost equation = ^C^g that 

 represents the average cost in dollars to remove one thousand board feet of timber 

 from an area. The objective is to be able to select the construction and skidding 

 methods that give a minimum value of total cost (C^). The minimum value of .C^ occurs 

 at some unique value of road spacing or some unique combination of values for road and 

 landing spacing. The first step in finding the optimum combination of methods is to 

 find the layout or spacing that yields minimum cost for each possible combination. 

 Then the combination that gives minimum total cost can be identified. 



Because the objective was to find the optimum spacing of roads and landings, the 

 partial derivatives for X (road spacing) and Y (landing spacing), when each equation 

 was set to zero, were taken for the case of landings and no landings. This was done 

 first for the case with no landings. The two equations were solved simultaneously, 

 using iteration, to find the road and landing spacings that gave the minimum total cost 

 of logging. An electronic computer was used for the solution; the flow diagram (fig. 2) 

 shows how this solution is obtained. The computer program is in Fortran language 

 written for an XDS Sigma 7 computer.^ 



^The Fortran program is available from the Forestry Sciences Laboratory located on 

 tho cumpus of Montana State University at Bozcman. 



8 



