Identification of a Network Substructure and Some Algorithmic Considerations for Large-Scale Harvest Scheduling Problems

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Abstract:

Berck and Bible (1984) have suggested a solution approach for harvest scheduling problems based on the Dantzig-Wolfe (1960) decomposition algorithm. We first expose the fact that the area constraints in their problem possess a network structure, requiring the solution of a single longest path problem, and show that the elegant dosed-form solution derived by Berck and Bible is precisely a readily obtained longest path solution. Moreover, we show that when additional variable bounds are imposed, the network structure remains exploitable. Second, we compare the computational effort and storage requirements of the Dantzig-Wolfe algorithm and the revised simplex method for solving this problem. The slow tail-end convergence of the Dantzig-Wolfe approach is of particular concern. However, we provide operational guidelines showing when this procedure may be preferred. Other viable algorithms suitable for solving this problem are also discussed. For. Sci. 36(3):599-613.

Keywords: Linear programming; decomposition algorithm; revised simplex method

Document Type: Journal Article

Affiliations: Department of Industrial Engineering, Feng Chia University, 100, Wenhwa Rd., Seatwen, Taichung, Taiwan 40724, Republic of China

Publication date: September 1, 1990

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
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