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Solving the integrated forest harvest scheduling model using metaheuristic algorithms

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Abstract

In forestry, the highest operational costs arise from the construction of forest roads and the transportation of harvested wood. Hence, optimization models have been used at the tactical level of planning to reduce these costs by integrating decisions on: (1) the allocation of harvest-blocks, (2) the allocation of access roads to these blocks, and (3) the transportation costs that result from the latter two decisions. The integration of these three decisions, in one optimization model, has been referred to as the integrated model. The integrated model, when binary decision variables are used to represent the cut-blocks and roads, is NP-hard and has been solved using two approaches: exact and metaheuristic algorithms. Unlike exact methods, metaheuristic algorithms have thus far not solved the integrated model, but have solved models which either exclude transportation costs from the objective function, or solve the model sequentially. This is a significant gap in prior research because exact solution methods can only be used on smaller forests and metaheuristic algorithms have therefore been used to solve the tactical forest planning problem, without the integration of transportation costs, on large forests. This failure to integrate transportation costs, on a large scale, is the major economic consequence of this gap. The objective of this paper is to present and evaluate a new solution procedure in which all three elements of the integrated tactical planning model are included in the objective function and solved using metaheuristics. The solution procedure was applied to three forests and the attributes and qualities of the solutions were compared to near-optimal solution values generated using an exact solution approach. The results indicate that this metaheuristic procedure generated good quality solutions. We conclude that this research is a useful first step in representing transportation costs in the integrated tactical planning models to be solved using metaheuristics.

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References

  • Andalaft N, Andalaft P, Guignard M, Magendzo A, Wainer A, Weintraub A (2003) A problem of forest harvesting and road building solved through model strengthening and Lagrangean relaxation. Oper Res 51:613–628

    Article  Google Scholar 

  • Anderson AE, Nelson J (2004) Projecting vector-based road networks with a shortest path algorithm. Can J For Res 34:1444–1457

    Article  Google Scholar 

  • Armstrong GW (2014) Considerations for boreal mixedwood silviculture: a view from the dismal science. For Chron 90:44–49

    Article  Google Scholar 

  • Bettinger P, Boston K, Sessions J (1999) Intensifying a heuristic forest harvest scheduling search procedure with 2-opt decision choices. Can J For Res 29:1784–1792

    Article  Google Scholar 

  • Bettinger P, Sessions J, Boston K (2009) A review of the status and use of validation procedures for heuristics used in forest planning. Math Comput For Nat Resour Sci 1:26–37

    Google Scholar 

  • Bjørndal T, Herrero I, Newman A, Romero C, Weintraub A (2012) Operations research in the natural resource industry. Int Trans Oper Res 19:39–62

    Article  Google Scholar 

  • Borges P, Eid T, Bergseng E (2014) Applying simulated annealing using different methods for the neighborhood search in forest planning problems. Eur J Oper Res 233:700–710

    Article  Google Scholar 

  • Boston K, Bettinger P (1999) An analysis of Monte Carlo integer programming, simulated annealing, and tabu search heuristics for solving spatial harvest scheduling problems. For Sci 45:292–301

    Google Scholar 

  • Chung W, Sessions J (2003) NETWORK 2000: a program for optimizing large fixed and variable cost transportation problems. In: Arthaud GJ, Barrett TM (eds) Systems analysis in forest resources. Managing Forest Ecosystems, vol 7. Springer, Dordrecht, pp 109–120

    Chapter  Google Scholar 

  • Chung W, Dykstra D, Bower F, O’Brien S, Abt RM, Sessions J (2012) User’s guide to SNAP for ArcGIS: ArcGIS interface for scheduling and network analysis program. USDA Forest Service PNW-GTR-847, 34 pp

  • Clark MM, Meller RD, McDonald TP (2000) A three-stage heuristic for harvest scheduling with access road network development. For Sci 46:204–218

    Google Scholar 

  • Crowe K, Nelson JD, Boyland M (2003) Solving the area-restricted harvest-scheduling model using the branch and bound algorithm. Can J For Res 33:1804–1814

    Article  Google Scholar 

  • Dahlin B, Sallnäs O (1993) Harvest scheduling under adjacency constraints—a case study from the Swedish sub-alpine region. Scand J For Res 8(1–4):281-290

    Article  Google Scholar 

  • Dijkstra EW (1959) A note on two problems in connection with graphs. Numer Math 1:269–271

    Article  Google Scholar 

  • Ghamlouche I, Crainic TG, Gendreau M (2003) Cycle-based neighbourhoods for fixed-charge capacitated multicommodity network design. Oper Res 51:655–667

    Article  Google Scholar 

  • Goycoolea M, Murray A, Vielma JP, Weintraub A (2009) Evaluating approaches for solving the area restriction model in harvest scheduling. For Sci 55:149–165

    Google Scholar 

  • Guignard M, Ryu C, Spielberg K (1998) Model tightening for integrated timber harvest and transportation planning. Eur J Oper Res 111:448–460

    Article  Google Scholar 

  • Jones JG, Hyde JFC, Meacham ML (1986) Four analytical approaches for integrating land management and transportation planning on forest lands. Research Paper INT-36 l, USDA Forest Service, Intermountain Research Station, 32 pp

  • Kirby MW, Wong P, Hager WA, Huddleston ME (1980) Guide to the integrated resources planning model. Technical report, Berkeley, California, USA

  • Kirby MW, Hager WA, Wong P (1986) Simultaneous planning of wildland management and transportation alternatives. TIMS Stud Manag Sci 21:371–387

    Google Scholar 

  • Kirkpatrick S (1984) Optimization by simulated annealing: quantitative studies. J Stat Phys 34:975–986

    Article  Google Scholar 

  • Lockwood C, Moore T (1993) Harvest scheduling with spatial constraints: a simulated annealing approach. Can J For Res 23:468–478

    Article  Google Scholar 

  • Magnanti TL, Wong RT (1984) Network design and transportation planning: models and algorithms. Transp Sci 18:1–55

    Article  Google Scholar 

  • Martin JA (1971) The relative importance of factors that determine log-hauling costs. USDA Forest Service Research Paper NE-197. Northeastern Forest Experimental Station, Upper Darby, PA, 18 pp

  • McDill ME, Rebain SA, Braze J (2002) Harvest scheduling with area-based adjacency constraints. For Sci 48:631–642

    Google Scholar 

  • Murray AT (1999) Spatial restrictions in harvest scheduling. For Sci 45:45–52

    Google Scholar 

  • Murray AT, Church RL (1995) Heuristic solution approaches to operational forest planning problems. OR-Spektrum 17:193–203

    Article  Google Scholar 

  • Naderializadeh N, Crowe KA (2018) The effect of the density of candidate roads on solutions in tactical forest planning. Can J For Res 48:679–688

    Article  Google Scholar 

  • Naderializadeh N, Crowe KA (2020) Formulating the integrated forest harvest-scheduling model to reduce the cost of the road-networks. Oper Res Int J 20:2283–2306

    Article  Google Scholar 

  • Nelson J, Brodie JD (1990) Comparison of a random search algorithm and mixed integer programming for solving area-based forest plans. Can J For Res 20:934–942

    Article  Google Scholar 

  • Öhman K, Eriksson LO (1998) The core area concept in forming contiguous areas for long-term forest planning. Can J For Res 28:1032–1039

    Article  Google Scholar 

  • Reeves CR (1993) Modern heuristic techniques for combinatorial problems. Wiley, Hoboken

    Google Scholar 

  • Richards EW, Gunn EA (2000) A model and tabu search method to optimize stand harvest and road construction schedules. For Sci 46:188–203

    Google Scholar 

  • Richards EW, Gunn EA (2003) Tabu search design for difficult forest management optimization problems. Can J For Res 33:1126–1133

    Article  Google Scholar 

  • Silva MG, Weintraub A, Romero C, De la Maza C (2010) Forest harvesting and environmental protection based on the goal programming approach. For Sci 56:460–472

    Google Scholar 

  • Tarp P, Helles F (1997) Spatial optimization by simulated annealing and linear programming. Scand J For Res 12:390–402

    Article  Google Scholar 

  • Van Deusen PC (1999) Multiple solution harvest scheduling. Silva Fenn 33:207–216

    Google Scholar 

  • Van Deusen PC (2001) Scheduling spatial arrangement and harvest simultaneously. Silva Fenn 35:85–92

    Google Scholar 

  • Veliz FB, Watson JP, Weintraub A, Wets RB, Woodruff DL (2015) Stochastic optimization models in forest planning: a progressive hedging solution approach. Ann Oper Res 232:259–274

    Google Scholar 

  • Weintraub A, Navon D (1976) A forest management planning model integrating silvicultural and transportation activities. Manag Sci 22:1299–1309

    Article  Google Scholar 

Download references

Acknowledgements

We thank NSERC, MITACS Canada, and aiTree Ltd. for funding this research. We also thank Waqas Ghouri, Timber Pricing Specialist and Tom Harries, Forest Industry Liaison Officer, from the Ontario Ministry of Natural Resources and Forestry (OMNRF) for sharing information about the parameters required to examine our model for this paper.

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  1. Faculty of Natural Resources Management, Lakehead University, 955 Oliver Road, Thunder Bay, ON, P7B 5E1, Canada

    Nader Naderializadeh, Kevin A. Crowe & Melika Rouhafza

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  1. Nader Naderializadeh
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  2. Kevin A. Crowe
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  3. Melika Rouhafza
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Correspondence to Nader Naderializadeh.

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Naderializadeh, N., Crowe, K.A. & Rouhafza, M. Solving the integrated forest harvest scheduling model using metaheuristic algorithms. Oper Res Int J 22, 2437–2463 (2022). https://doi.org/10.1007/s12351-020-00612-3

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