Forest harvesting planning under uncertainty: a cardinality-constrained approach

Harvesting planning (HP) is a key tactical decision in lumber supply chains. Harvesting areas in the forests are divided into different blocks with different types and quantities of raw materials (logs). Predicting the availability of raw materials in each block along with log demand is impossible in this industry. Hence, incorporating uncertainty into the HP problem is essential in order to obtain robust plans that do not drastically fluctuate in the presence of future perturbations in the forest and log market. In this paper, we propose a robust harvesting planning model formulated based on cardinality-constrained method. The latter provides some insights into the adjustment of the level of robustness of the harvesting plan over the planning horizon and protection against uncertainty. An extensive set of experiments based on Monte-Carlo simulation is also conducted in order to better validate the proposed robust optimisation approach.

[1]  Jorge R. Vera,et al.  Application of Robust Optimization to the Sawmill Planning Problem , 2014, Ann. Oper. Res..

[2]  Mikael Rönnqvist,et al.  A new method for robustness in rolling horizon planning , 2013 .

[3]  Luc LeBel,et al.  Supply network planning in the forest supply chain with bucking decisions anticipation , 2011, Ann. Oper. Res..

[4]  Georgia Perakis,et al.  A Robust Optimization Approach to Dynamic Pricing and Inventory Control with no Backorders , 2006, Math. Program..

[5]  Dimitris Bertsimas,et al.  A Robust Optimization Approach to Inventory Theory , 2006, Oper. Res..

[6]  Mustapha Nourelfath,et al.  An accelerated scenario updating heuristic for stochastic production planning with set-up constraints in sawmills , 2013 .

[7]  Gajendra K. Adil,et al.  A robust optimisation model for aggregate and detailed planning of a multi-site procurement-production-distribution system , 2010 .

[8]  Mustapha Nourelfath,et al.  The value of integrated tactical planning optimization in the lumber supply chain , 2016 .

[9]  Allen L. Soyster,et al.  Technical Note - Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming , 1973, Oper. Res..

[10]  Daniel Bienstock,et al.  Computing robust basestock levels , 2008, Discret. Optim..

[11]  Arkadi Nemirovski,et al.  Robust Convex Optimization , 1998, Math. Oper. Res..

[12]  Mustapha Nourelfath,et al.  A hybrid scenario cluster decomposition algorithm for supply chain tactical planning under uncertainty , 2016, Eur. J. Oper. Res..

[13]  Laurent El Ghaoui,et al.  Robust Solutions to Uncertain Semidefinite Programs , 1998, SIAM J. Optim..

[14]  Marianthi G. Ierapetritou,et al.  Robust optimization for process scheduling under uncertainty , 2008 .

[15]  A. Ben-Tal,et al.  Adjustable robust solutions of uncertain linear programs , 2004, Math. Program..

[16]  Manoj Kumar Tiwari,et al.  Tactical production planning in a hybrid Make-to-Stock–Make-to-Order environment under supply, process and demand uncertainties: a robust optimisation model , 2015 .

[17]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[18]  Constantine Caramanis,et al.  Finite Adaptability in Multistage Linear Optimization , 2010, IEEE Transactions on Automatic Control.

[19]  Daoud Aït-Kadi,et al.  Robust production planning in a manufacturing environment with random yield: A case in sawmill production planning , 2010, Eur. J. Oper. Res..

[20]  Mikael Rönnqvist,et al.  Extraction of logs in forestry using operations research and geographical information systems , 1999, Proceedings of the 32nd Annual Hawaii International Conference on Systems Sciences. 1999. HICSS-32. Abstracts and CD-ROM of Full Papers.

[21]  Mikael Rönnqvist,et al.  Using robust optimization for distribution and inventory planning for a large pulp producer , 2014, Comput. Oper. Res..

[22]  Melvyn Sim,et al.  The Price of Robustness , 2004, Oper. Res..

[23]  Arkadi Nemirovski,et al.  Robust solutions of uncertain linear programs , 1999, Oper. Res. Lett..

[24]  D. Burger,et al.  Using linear programming to make wood procurement and distribution decisions , 1995 .

[25]  Jean‐Marc Frayret,et al.  Tactical supply chain planning in the forest products industry through optimization and scenario-based analysis , 2007 .

[26]  Mikael Rönnqvist,et al.  Annual planning of harvesting resources in the forest industry , 2010, Int. Trans. Oper. Res..

[27]  Sarah M. Ryan,et al.  Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated Benders decomposition , 2016, Eur. J. Oper. Res..

[28]  Reinaldo Morabito,et al.  Production planning in furniture settings via robust optimization , 2012, Comput. Oper. Res..

[29]  Mustapha Nourelfath,et al.  A periodic re-planning approach for demand-driven wood remanufacturing industry: a real-scale application , 2014 .

[30]  Monique Guignard-Spielberg,et al.  A Problem of Forest Harvesting and Road Building Solved Through Model Strengthening and Lagrangean Relaxation , 2003, Oper. Res..

[31]  M. Rönnqvist,et al.  An optimization model for annual harvest planning , 2004 .

[32]  Yue Wu Robust optimization applied to uncertain production loading problems with import quota limits under the global supply chain management environment , 2006 .

[33]  Laurent El Ghaoui,et al.  Robust Solutions to Least-Squares Problems with Uncertain Data , 1997, SIAM J. Matrix Anal. Appl..

[34]  Louis-Martin Rousseau,et al.  Annual timber procurement planning with bucking decisions , 2017, Eur. J. Oper. Res..