Primal–dual methods for sustainable harvest scheduling problems

Timber harvest schedules form the heart of forest resource management. The operations research methodology is applied to resolving the multi-product, multi-period sustainable timber harvest scheduling problems, where area constraints, harvest flow constraints, and ending inventory constraints are imposed. By taking advantage of the model characterization of block diagonal constraints with multiple sets of network sub-problems and the set of coupling constraints, an efficient algorithm is explored. Specifically, a primal–dual method of closed-form solutions is first developed to solve the network sub-problems on the individual basis. Then, a primal–dual steepest-edge algorithm that achieves the global optimum is presented. A numerical example illustrating steps of the solution procedure is presented. The proposed algorithm is implemented, and its performance is compared with that of the AMPL-CPLEX package. The proposed primal–dual algorithm achieves, on the average, an approximately four to one reduction in iteration numbers and an about eight to one reduction in the CPU execution time.