Linear Programing and Sensitivity Analysis for Hardwood Dimension Production

A common problem in hardwood dimension stock production is to determine the least-cost grade mix of lumber – input required to satisfy a particular cutting order. An associated problem is to determine the target lengths to be cut from each grade. If the yield of each grade of lumber is known by cutting lengths, these problems can be solved by linear programming (L. P.). Appropriate grades of lumber are purchased and given lengths of stock are cut from each grade. The L.P. minimizes total purchase and cut-up costs subject to the condition that the total board footage cut to a given length (regardless of the grade from which it is cut) is equal to or greater than that required for the cutting order. In addition to the least-cost purchasing and cutting activities, sensitivity analysis may be used to evaluate the influence of variations in lumber price and processing costs on the optimum grade mix and total cost of the cutting order. The application of sensitivity analysis to several cutting orders are detailed. The interrelationships between length-width requirements, quantity requirements, and costs involved are difficult to calculate without the aid of a synthesizing logic such as linear programming.

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