Three mathematical models for bucking-to-order

The aim of this paper is to investigate different mathematical approaches to buck-to-order log merchandizing. A new bucking-to-order planning model using mixed integer programming was developed to determine the optimal production from a stand given different market constraints and forest inventory data. Three different approaches: market prices, target cutting patterns and adjusted price list were tested for generating cutting instructions to fulfill the plan created by the new planning model. The three approaches were evaluated in four test stands. The market prices approach simply applied the market prices to each stand. The target cutting patterns approach applied the sample cutting patterns generated from the planning model to the stand. The adjusted price list used a dynamic programming algorithm embedded in a search heuristic to adjust both the prices and small end diameters of log products to achieve the production goals of the planning models. The results showed that developing a buck-to-order plan is important in obtaining good order fulfillment. The target cutting patterns and adjusted price list approaches certainly outperformed the market prices approach. This paper shows that these two approaches are capable of achieving excellent order fulfillment. Further development and testing is needed to determine which method is the best at generating cutting instructions for buck-to-order merchandizing.