Skip to main content
SpringerLink
Log in

Using mixed integer programming models to synchronously determine production levels and market prices in an integrated market for roundwood and forest biomass

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

We study a problem of integrating the supply chain of roundwood with the supply chain of forest biomass. The developed optimization model is a multiperiod, multicommodity network planning problem with multiple sources of supply, i.e., harvest areas, and multiple types of destinations, i.e., sawmills, pulp mills, and heating plants. This paper presents an extension of previous work where the set of harvest areas was given and market prices for raw materials had linear relationship with corresponding volumes. In this paper, the assumption of predefined areas is removed, and we must make the selection of harvest areas. Instead of using a traditional sequential approach to first select areas and then determine the prices, we present a new synchronous approach that can jointly choose areas and define price levels for different assortments at those chosen supply points. We test the possible settings of discretized price and use sensitivity analysis to evaluate how the variation of fixed cost concerning log forwarding at each supply point affects the wood procurement decisions. A case study from Sweden is used to analyze the market prices in an integrated market. The computational results also highlight the advantage of the proposed synchronous approach over the sequential one in both solution quality and solution time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Beaudoin, D., LeBel, L., & Frayret, J. M. (2007). Tactical supply chain planning in the forest products industry through optimization and scenario-based analysis. Canadian Journal of Forest Research, 37(1), 128–140.

    Article  Google Scholar 

  • Bredström, D., Jönsson, P., & Rönnqvist, M. (2010). Annual planning of harvesting resources in the forest industry. International Transactions in Operational Research, 17(2), 155–177.

    Article  Google Scholar 

  • Burger, D. H., & Jamnick, M. S. (1995). Using linear programming to make wood procurement and distribution decisions. Forestry Chronicle, 71(1), 89–96.

    Article  Google Scholar 

  • Carlgren, C. G., Carlsson, D., & Rönnqvist, M. (2006). Log sorting in forest harvest areas integrated with transportation planning using backhauling. Scandinavian Journal of Forest Research, 21(3), 260–271.

    Article  Google Scholar 

  • Carlsson, D., & Rönnqvist, M. (2007). Backhauling in forest transportation: models, methods, and practical usage. Canadian Journal of Forest Research, 37(12), 2612–2623.

    Article  Google Scholar 

  • Chauhan, S. S., Frayret, J. M., & LeBel, L. (2009). Multi-commodity supply network planning in the forest supply chain. European Journal of Operational Research, 196(2), 688–696.

    Article  Google Scholar 

  • Conrad, J. L., Bolding, M. C., Smith, R. L., & Aust, W. M. (2011). Wood-energy market impact on competition, procurement practices, and profitability of landowners and forest products industry in the US South. Biomass & Bioenergy, 35(1), 280–287.

    Article  Google Scholar 

  • Flisberg, P., Forsberg, M., & Rönnqvist, M. (2007). Optimization based planning tools for routing of forwarders at harvest areas. Canadian Journal of Forest Research, 37(11), 2153–2163.

    Article  Google Scholar 

  • Flisberg, P., Frisk, M., & Rönnqvist, M. (2012a). Alternative energy powers Sweden. OR/MS Today, 39(2), 18–22.

    Google Scholar 

  • Flisberg, P., Frisk, M., & Rönnqvist, M. (2012b). FuelOpt: a decision support system for forest fuel logistics. Journal of the Operational Research Society, 63(11), 1600–1612.

    Article  Google Scholar 

  • Frisk, M., Göthe-Lundgren, M., Jörnsten, K., & Rönnqvist, M. (2010). Cost allocation in collaborative forest transportation. European Journal of Operational Research, 205(2), 448–458.

    Article  Google Scholar 

  • Galik, C. S., Abt, R., & Wu, Y. (2009). Forest biomass supply in the Southeastern United States—implications for industrial roundwood and bioenergy production. Journal of Forestry, 107(2), 69–77.

    Google Scholar 

  • Garcia, O. (1990). Linear programming and related approaches in forest planning. New Zealand Journal of Forestry Science, 20(3), 307–311.

    Google Scholar 

  • Gronalt, M., & Rauch, P. (2007). Designing a regional forest fuel supply network. Biomass & Bioenergy, 31(6), 393–402.

    Article  Google Scholar 

  • Gunnarsson, H., & Rönnqvist, M. (2008). Solving a multi-period supply chain problem for a pulp company using heuristics—an application to Sodra Cell AB. International Journal of Production Economics, 116(1), 75–94.

    Article  Google Scholar 

  • Gunnarsson, H., Rönnqvist, M., & Lundgren, J. T. (2004). Supply chain modelling of forest fuel. European Journal of Operational Research, 158(1), 103–123.

    Article  Google Scholar 

  • Karlsson, J., Rönnqvist, M., & Bergström, J. (2004). An optimization model for annual harvest planning. Canadian Journal of Forest Research, 34(8), 1747–1754.

    Article  Google Scholar 

  • Kong, J., Rönnqvist, M., & Frisk, M. (2012). Modeling an integrated market for sawlogs, pulpwood, and forest bioenergy. Canadian Journal of Forest Research, 42(2), 315–332.

    Article  Google Scholar 

  • Lundmark, R. (2006). Cost structure of and competition for forest-based biomass. Scandinavian Journal of Forest Research, 21(3), 272–280.

    Article  Google Scholar 

  • Murphy, G., Lyons, J., O’Shea, M., Mullooly, G., Keane, E., & Devlin, G. (2010). Management tools for optimal allocation of wood fibre to conventional log and bio-energy markets in Ireland: a case study. European Journal of Forest Research, 129(6), 1057–1067.

    Article  Google Scholar 

  • Palander, T. (2011). Technical and economic analysis of electricity generation from forest, fossil, and wood-waste fuels in a Finnish heating plant. Energy, 36(9), 5579–5590.

    Article  Google Scholar 

  • Röser, D., Sikanen, L., Asikainen, A., Parikka, H., & Väätäinen, K. (2011). Productivity and cost of mechanized energy wood harvesting in Northern Scotland. Biomass & Bioenergy, 35(11), 4570–4580.

    Article  Google Scholar 

  • Troncoso, J. J., & Garrido, R. A. (2005). Forestry production and logistics planning: an analysis using mixed-integer programming. Forest Policy and Economics, 7(4), 625–633.

    Article  Google Scholar 

  • Van Belle, J. F., Temmerman, M., & Schenkel, Y. (2003). Three level procurement of forest residues for power plant. Biomass & Bioenergy, 24(4–5), 401–409.

    Article  Google Scholar 

  • Weintraub, A. (2007). Integer programming in forestry. Annals of Operations Research, 149(1), 209–216.

    Article  Google Scholar 

  • Weintraub, A., & Navon, D. (1976). A forest management planning model integrating silvicultural and transportation activities. Management Science, 22(12), 1299–1309.

    Article  Google Scholar 

  • Weintraub, A., Jones, G., Magendzo, A., Meacham, M., & Kirby, M. (1994). A heuristic system to solve mixed integer forest planning models. Operations Research, 42(6), 1010–1024.

    Article  Google Scholar 

  • Weintraub, A., Jones, G., Meacham, M., Magendzo, A., & Malchuk, D. (1995). Heuristic procedures for solving mixed-integer harvest scheduling—transportation planning models. Canadian Journal of Forest Research, 25(10), 1618–1626.

    Article  Google Scholar 

  • Wu, J. Z., Wang, J. X., & McNeel, J. (2011). Economic modeling of woody biomass utilization for bioenergy and its application in Central Appalachia, USA. Canadian Journal of Forest Research, 41(1), 165–179.

    Article  Google Scholar 

Download references

Acknowledgements

We would like to acknowledge the support of the Norwegian School of Economics (NHH) as well as the industrial support of the Forestry Research Institute of Sweden (Skogforsk). We are also indebted to the three referees for many valuable comments that helped to restructure this paper and make it more readable and accessible to both theoreticians and practitioners.

Author information

Authors and Affiliations

  1. Department of Finance and Management Science, NHH Norwegian School of Economics, Bergen, Norway

    Jiehong Kong

  2. Department of Mechanical Engineering, Université Laval, Québec, Canada

    Mikael Rönnqvist

  3. The Forestry Research Institute of Sweden, Uppsala, Sweden

    Mikael Frisk

Authors
  1. Jiehong Kong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mikael Rönnqvist
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mikael Frisk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiehong Kong.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kong, J., Rönnqvist, M. & Frisk, M. Using mixed integer programming models to synchronously determine production levels and market prices in an integrated market for roundwood and forest biomass. Ann Oper Res 232, 179–199 (2015). https://doi.org/10.1007/s10479-013-1450-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-013-1450-0

Keywords

Search

Navigation