Annals of Operations Research

, Volume 232, Issue 1, pp 41–64 | Cite as

Concurrent optimization of harvesting and road network layouts under steep terrain

  • Leo Gallus BontEmail author
  • Hans Rudolf Heinimann
  • Richard L. Church


Timber extraction is based on two transportation modes—off-road and on-road—that are connected by a set of landing nodes. Forest operations planning that is oriented toward harvesting consists of concurrently locating a truck road network, designating landing/loading sites along that network, and allocating stands to specific harvest technologies (e.g., cable roads). In central Europe, this problem has, until recently, been solved primarily with rules of thumb. By contrast, only a few attempts, designed for plantation systems, have been made to find the mathematical optima. Here, we present a modeling approach to identify a minimal-cost solution for this problem of laying out truck roads and cable roads when the terrain is steep. This technique is based on a Mixed Integer Linear Programming formulation. Our approach is as good as or better than state-of-the-art methods. Here, the overall costs of harvesting and roading were decreased by about 7 % compared with techniques that called for a heuristic solution only. Depending upon parameter choices, we also determined that a computing time ranging from 4 min to 8 hrs was required when assessing a logging area of 4.3 km2.


Cable-yarding Forest road network Mixed integer linear programming problem Steep terrain 


  1. Anderson, A. E., & Nelson, J. (2004). Projecting vector-based road networks with a shortest path algorithm. Canadian Journal of Forest Research, 34(7), 1444–1457. CrossRefGoogle Scholar
  2. Balakrishnan, A., Magnanti, T. L., & Wong, R. T. (1989). A dual-ascent procedure for large-scale uncapacitated network design. Operations Research, 37(5), 716–740. CrossRefGoogle Scholar
  3. Bellmann, R. (1958). On a routing problem. Quarterly of Applied Mathematics, 16, 87–90. Google Scholar
  4. Chung, W., Sessions, J., & Heinimann, H. R. (2004). An application of a heuristic network algorithm to cable logging layout design. International Journal of Forest Engineering, 15(1), 11–24. Google Scholar
  5. Chung, W., Stückelberger, J., Aruga, K., & Cundy, T. (2008). Forest road network design using a trade-off analysis between skidding and road construction costs. Canadian Journal of Forest Research, 38(3), 439–448. CrossRefGoogle Scholar
  6. Church, R. L. (2008). BEAMR: an exact and approximate model for the p-median problem. Computers & Operations Research, 35, 417–426. CrossRefGoogle Scholar
  7. Church, R. L., & Cova, T. J. (2000). Mapping evacuation risk on transportation networks using a spatial optimization model. Transportation Research. Part C, Emerging Technologies, 8(1–6), 321–336. doi: 10.1016/s0968-090x(00)00019-x. CrossRefGoogle Scholar
  8. Church, R. L., Gerrard, R., Hollander, A., & Stoms, D. (2000). Understanding the tradeoffs between site quality and species presence in reserve site selection. Forest Science, 46(2), 157–167. Google Scholar
  9. Clark, M., Meller, D., & McDonald, P. (2000). A three-stage heuristic for harvest scheduling with access road network development. Forest Science, 46(2), 204–218. Google Scholar
  10. Current, J. R., ReVelle, C. S., & Cohon, J. L. (1985). The maximum covering/shortest path problem: a multiobjective network design and routing formulation. European Journal of Operational Research, 21(2), 189–199. CrossRefGoogle Scholar
  11. Dean, D. J. (1997). Finding optimal routes for networks of harvest site access roads using GIS-based techniques. Canadian Journal of Forest Research, 27, 11–22. CrossRefGoogle Scholar
  12. Diaz, L. A., Ferland, J. A., Ribeiro, C. C., Vera, J. R., & Weintraub, A. (2007). A tabu search approach for solving a difficult forest harvesting machine location problem. European Journal of Operational Research, 179(3), 788–805. CrossRefGoogle Scholar
  13. Dykstra, D. P., & Riggs, J. L. (1977). An application of facilities location theory to the design of forest harvesting areas. IIE Transactions, 9(3), 270–277. doi: 10.1080/05695557708975155. Google Scholar
  14. Epstein, R., Morales, R., Séron, J., & Weintraub, A. (1999). Use of OR systems in the Chilean forest industries. Interfaces, 29(1), 7–29. CrossRefGoogle Scholar
  15. Epstein, R., Weintraub, A., Sapunar, P., Nieto, E., Sessions, J. B., & Sessions, J. (2006). A combinatorial heuristic approach for solving real-size machinery location and road design problems in forestry planning. Operations Research, 54(6), 1017–1027. CrossRefGoogle Scholar
  16. Heinimann, H. R. (1998). A computer model to differentiate skidder and cable-yarder based road network concepts on steep slopes. Journal of Forest Research (Japan), 3(1), 1–9. CrossRefGoogle Scholar
  17. Heinimann, H. R., & Caminada, L. (1996). Helicopter logging in Switzerland, analysis of selective logging operations. In 9th pacific northwest skyline symposium, 40–45. FERIC special report SR-114, Vancouver, BC, Canada (p. 167). Google Scholar
  18. Kirby, M. (1973). An example of optimal planning of forest roads and projects. In J. E. O’Leary (Ed.), Planning and decisionmaking as applied to forest harvesting, Forest Research Laboratory, School of Forestry, Oregon State University, Corvallis OR, USA (pp. 75–83). Google Scholar
  19. Liu, K., & Sessions, J. (1993). Preliminary planning of road systems using digital terrain models. Journal of Forest Engineering, 4(2), 6. CrossRefGoogle Scholar
  20. Mandt, C. I. (1973). Network analyses in transportation planning. In J. E. O’Leary (Ed.), Planning and decisionmaking as applied to forest harvesting, Forest Research Laboratory, School of Forestry, Oregon State University, Corvallis OR, USA (pp. 95–101). Google Scholar
  21. Matisziw, T. C., Murray, A. T., & Kim, C. (2006). Strategic route extension in transit networks. European Journal of Operational Research, 171, 661–673. CrossRefGoogle Scholar
  22. Matthews, D., & Donald, M. (1942). Cost control in the logging industry. New York: McGraw-Hill. 374 pp. Google Scholar
  23. Miller, C. E., Tucker, A. W., & Zemlin, R. A. (1960). Integer programming formulation of traveling salesman problems. Journal of the Association for Computing Machinery, 7(4), 326–329. doi: 10.1145/321043.321046. CrossRefGoogle Scholar
  24. Murray, A. T. (1998). Route planning for harvest site access. Canadian Journal of Forest Research, 28(7), 1084–1087. doi: 10.1139/x98-122. CrossRefGoogle Scholar
  25. Murray, A. T., & Church, R. L. (1995). Heuristic solution approaches to operational forest planning problems. OR Spektrum, 17(2), 193–203. doi: 10.1007/bf01719265. CrossRefGoogle Scholar
  26. O’Sullivan, D., & Unwin, D. (2002). Geographic information analysis. New York: Wiley. 436 pp. Google Scholar
  27. Park, C. S., & Sharp-Bette, G. P. (1990). Advanced engineering economics. New York: Wiley. 470 pp. Google Scholar
  28. Pestal, E. (1961). Seilbahnen und Seilkräne für Holz- und Materialtransporte. Wien und München: Georg Fromme & Co. Google Scholar
  29. Richards, W., & Gunn, A. (2000). A model and tabu search method to optimize stand harvest and road construction schedules. Forest Science, 46(2), 188–203. Google Scholar
  30. Rosing, K. E., & ReVelle, C. S. (1997). Heuristic concentration: two stage solution construction. European Journal of Operational Research, 97, 75–86. CrossRefGoogle Scholar
  31. Stampfer, K., Limbeck-Lilienau, B., Kanzian, C., & Viertler, K. (2003). In F. K. F. P. Papier (Ed.), Baumverfahren im Seilgelände, Verfahrensbeispiele, Wanderfalke mit Prozessor Woody 50, Syncrofalke mit Prozessor Wolf 50 B. Wien: Institut für Alpine Naturgefahren und Forstliches Ingenieurwesen, Universität für Bodenkultur Wien. Google Scholar
  32. Stampfer, K., Visser, R., & Kanzian, C. (2006). Cable corridor installation times for European yarders. International Journal of Forest Engineering, 17(2), 71–77. Google Scholar
  33. Stückelberger, J. A., Heinimann, H. R., & Burlet, E. C. (2006a). Modeling spatial variability in the life-cycle costs of low-volume forest roads. European Journal of Forest Research, 125(4), 377–390. CrossRefGoogle Scholar
  34. Stückelberger, J. A., Heinimann, H. R., Chung, W., & Ulber, M. (2006b). Automatic road-network planning for multiple objectives. In W. Chung & H.-S. Han (Eds.), Council on forest engineering conference, Coeur d’Alene, ID, USA (pp. 233–248). Google Scholar
  35. Stückelberger, J. A., Heinimann, H. R., & Chung, W. (2007). Improved road network design models with the consideration of various link patterns and road design elements. Canadian Journal of Forest Research, 37(11), 2281–2298. CrossRefGoogle Scholar
  36. Twito, R. H., Reutebuch, S. E., Stephen, E., McGaughey, R. J., & Mann, C. N. (1987). Preliminary logging analysis system PLANS. Overview (General Technical Report PNW-GTR-199). U.S. Department of Agriculture Forest Service, Pacific Northwest Research Station, Portland, OR, USA (p. 24). Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Leo Gallus Bont
    • 1
    Email author
  • Hans Rudolf Heinimann
    • 2
  • Richard L. Church
    • 3
  1. 1.Institute of Terrestrial EcosystemsETH ZürichZurichSwitzerland
  2. 2.Institute of Terrestrial EcosystemsETH ZürichZurichSwitzerland
  3. 3.Department of GeographyUniversity of California, Santa BarbaraSanta BarbaraUSA

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