How to Allocate Logs Among Machines to Maximize Profit: A Simple Method

A manual method for determining which logs to allocate to which machines to maximize profits in a sawmill/plywood plant is illustrated. In a hypothetical example, logs of different sizes of one species are allocated to four machines, three of which are cutting lumber (a headrig and two chipping headrigs) and one of which is peeling veneer. Only current operating costs, not factors such as depreciation, are considered. Though the method, which develops production and market data and consolidates it into visual comparisons using graphs, has the advantage of being simple to apply and easy to update, it would not be suitable for complex operations with many rapidly changing variables. The manual method is useful in showing basic machines differences. It may complement or replace linear programming methods, though often once the basic profit tradeoffs have been illustrated by the graphic method, a more comprehensive linear programming model can be helpful. Contribution Margin (CM), equal to sales revenue less variable expenses, is a measure of the contribution to profits for each log size/species/grade through each machine center. Since the amount of wood that can be processed is limited either by supply or by production constraints, the goal is defined as making the greatest profit from the wood which is used. Using CM (expressed as $/Cunit of wood used), production, marketing, and accounting data can be converted to a common factor. Profit is equal to Contribution Margin less fixed expenses.

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