A method for optimal design of timber hauling systems under conditions of uncertainty and risk

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University of New Brunswick


This thesis describes a method for designing optimal timber hauling systems under conditions of uncertainty and risk. This method distinguishes between, and incorporates, natural uncertainty and parameter uncertainty. Natural uncertainty encompasses the variation of the trucking activity times (loading and unloading times, loaded and empty travelling times), and is handled by using probability distributions. Parameter uncertainty is the inability to accurately estimate the parameters of these probability distributions. In this study, parameter uncertainty is addressed from a Bayesian perspective by incorporating, together with some sample data, subjective estimates from experts. In addition, the decision on the optimum combination of trucks, loaders and unloaders is based on the decision maker's attitude toward risk. Design scenarios are analysed by formulating the sequence of hauling activities (i.e., loading, travelling loaded, unloading and travelling empty) as a queueing system, and the equipment combinations are then evaluated by simulation. The inputs to the simulation model include actions (representing the number of trucks, loaders and unloaders), probability distributions (of loading time, unloading time, travel loaded speed and travel empty speed), estimated parameters of these probability distributions, and constants (such as amount of wood to be hauled, hauling distances, etc). Using a cost equation, the simulation outputs are converted into cost and payoff tables. Employing utility functions, which quantify the decision maker's attitude to risk, the optimum combination of trucks, loaders and unloaders is determined based on expected payoff and expected utility criteria. Using basic data supplied by Forest Engineering Research Institute of Canada (FERIC), a two-parameter gamma distribution is selected to represent the input variables in the simulation program. Calculations to estimate the parameters of the gamma distribution using Bayesian methodologies are contrasted with the classical statistical methods. Other possible applications to illustrate the applicability of Bayesian decision analysis in forestry are also presented. The thesis concludes that Bayesian statistics and decision analysis which combines expert prior knowledge with available sample data provides a better methodology for designing timber hauling systems than that provided by classical decision analysis methodologies, especially where woodlands decisions are made with limited sample data.




Timber hauling, Simulation, Uncertainty, Risk, Bayesian statistics