An inverse shortest path approach to find forwarder productivity functions

Abstract

This paper presents an optimization model designed to find productivity functions for timber forwarding. Timber forwarding or skidding has for some 25 years been calculated using shortest path formulations on grid networks. Unfortunately, few productivity studies relate to such grids. Here, an inverse shortest path problem is presented, basically panning out costs on the grid based on point cost estimates. The formulation is tested using point cost estimates from the national forest inventories of Norway, together with a terrain model and other public spatial data (e.g. roads, water). The problem is optimized using the metaheuristic variable neighborhood search. The results of the test cases were achieved in reasonable time, and indicate that part of the solution space might be convex. The productivity function found for one of the test cases was used to create a variable forwarding cost map of the case area.